<%BANNER%>

Development and Characterization of a High Average Power, Single-Stage Regenerative Chirped Pulse Amplifier

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INGEST IEID E20101210_AAAAAU INGEST_TIME 2010-12-10T05:52:55Z PACKAGE UFE0017510_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
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DEVELOPMENT AND CHARACTERIZATION OF A HIGH AVERAGE POWER, SINGLESTAGE REGENERATIVE CHIRPED PULSE AMPLIFIER By VIDYA RAMANATHAN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2006

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Copyright 2006 by Vidya Ramanathan

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To my family

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iv ACKNOWLEDGMENTS Graduate school has been an extremely enrichin g experience dispelling my naivety in more ways than one. I owe a great deal to my mentor Dr. David Reitze for his guidance and encouragement that saw me through these past six years in graduate school. Not only did he acquaint me with the rudiments of ultrafast lase rs, but he also helped me gain a d eep insight and perspective into this field. I very much appreciate Dr. Reitzes treatment of his graduate students as junior colleagues. It is encouraging as well as challenging remi nding me always of my discerning decision of joining his research team. I am grateful to my committee members Prof s. Hagen, Tanner, Stanton and Kleiman for serving on my supervisory committee and for all their advice and suggestions. I would also like to thank Prof. Nicolo Omenetto for agreeing to serve on my committee at an extremely short notice and was patient enough to read through my thesis and spot typos in just two days! My sincere gratitude also goe s to my fellow graduate stude nts Jinho Lee, Shengbo Xu and Xiaoming Wang for all their help and for creati ng a pleasant environment in the laboratory. I would like to thank Dr. Yoonseok Lee and Prad eep Bhupathi for their ideas and suggestions about cryogenics and vacuum systems and also for all the stycast that they so willingly made for me! Bill Malphurs and Marc Link from the mach ine shop deserve special mention for their brilliant imagination and craftsmanship. Many thanks go to Luke Williams for letting me benefit from his expertise in thermodynamics and CAD de signing software. I am extremely grateful to the support staff in the Physics department, Ja y Horton, Don Brennan and many more for lending a helping hand whenever I needed one. I thank Darlene Latimer and Nathan Williams for all their assistance during times of distress! I would also like to thank all the folks in Tanner Lab

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v and Hebard Lab for letting me borrow sundry items and equipment from their laboratories from time to time. I wish to thank my friends Ronojoy Saha, Karthik Shankar, Aparna Baskaran, Naveen Margankunte from the physics department and many others in Gainesville for providing respite from the trials and tribulations of graduate school with countless Friday nights filled with revelry! Finally I wish to thank my parents and my siblings for their unconditional support and patience over all thes e years and the undaunted faith they have in me. Last but not least, a great deal of credit goes to Rajkeshar Singh who, alth ough my husband of just tw o years, has been my best buddy for almost a decade now. I definitely do not envision myself here today if it were not for him.

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vi TABLE OF CONTENTS page ACKNOWLEDGMENTS.............................................................................................................iv LIST OF TABLES................................................................................................................. ......viii LIST OF FIGURES................................................................................................................ .......ix ABSTRACT....................................................................................................................... ..........xiii 1 INTRODUCTION............................................................................................................... .......1 2 ULTRASHORT PULSE GENERA TION AND CHARAC TERIZATION...............................9 2.1 Relationship between Du ration and Spectral Width.........................................................9 2.2 Time Bandwidth Product................................................................................................12 2.3 Dispersion............................................................................................................... ........14 2.4 Nonlinear Effects........................................................................................................ ....16 2.4.1 Second Order Susceptibility.................................................................................16 2.4.2 Third Order Susceptibility....................................................................................18 2.4.2.1 Nonlinear index of refraction....................................................................18 2.4.2.2 Kerr lens effect..........................................................................................19 2.4.2.3 Self phase-modulation...............................................................................20 2.5 Summary.................................................................................................................. .......22 3 DESIGN AND CONSTRUCTION OF A HIGH AVERAGE POWER, SINGLE STAGE CHIRPED PULSE AMPLIFIER............................................................................................23 3.1 Introduction............................................................................................................. ........23 3.2 Why Chirped Pulse Amplification?................................................................................23 3.3 Ti: Sapphire as Gain Medium.........................................................................................26 3.4 Mode-locked Laser........................................................................................................ .28 3.5 Dispersion............................................................................................................... ........31 3.6 Pulse Stretching and Recompression..............................................................................33 3.7 Ti: Sapphire based Laser Amplifier................................................................................39 3.7.1 Process of Amplification........................................................................................41 3.7.2 Types of Amplifiers................................................................................................42 3.8 Pulse Shaping............................................................................................................ ......45 3.9 Ultrashort Pulse Measurement........................................................................................46 3.10 Chirped Pulse Amplifier system...................................................................................49 3.11 Summary................................................................................................................. ......50 4 THERMAL EFFECTS IN HI GH POWER LASER AMPLIFIER...........................................52 4.1 Introduction............................................................................................................. ........52

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vii 4.2 Theoretical Background..................................................................................................57 4.3 Methods to Reduce Thermal Effects..............................................................................61 4.4 Liquid Nitrogen Cooled Ti Al2O3 Laser Amplifier........................................................64 4.5 Construction of a Regenerative Amplifier Cavity..........................................................66 4.6 Measurement of Thermal Lens.......................................................................................68 4.7 Calculation of Thermal Lens..........................................................................................71 4.8 Direct Measurement of th e Optical Path Deformations.................................................76 4.9 Effects of Thermal Aberrations on Beam Shape............................................................78 4.10 Summary................................................................................................................. ......80 5 CHARACTERIZATION AND OPTIMIZA TION OF HIGH AVER AGE POWER CPA......82 5.1 Amplifier Performance................................................................................................82 5.1.1 Average Power, Pulse Energy..............................................................................82 5.1.2 Spatial Beam quality.............................................................................................83 5.1.3 Spectral Characteristics........................................................................................85 5.1.4 Shot-to-shot Pulse Energy Characterization.........................................................87 5.2 Design Considerations for Si ngle Stage Cryogenic CPA System..................................88 5.3 Compensation of Modal Astigmatism............................................................................92 5.4 Summary.................................................................................................................. .......94 6 CONCLUSION................................................................................................................. ........95 A FREQUENCY RESOLVED OPTICAL GATING (FROG)...................................................98 B ACOUSTO-OPTIC PROGRAMMABLE DISPERSIVE FILTER.......................................105 B.1 Bragg diffraction of light by Acoustic waves..............................................................105 B.2 Amplitude and Phase control using an AOPDF...........................................................107 LIST OF REFERENCES.............................................................................................................111 BIOGRAPHICAL SKETCH.......................................................................................................120

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viii LIST OF TABLES Table page 2-1 Time bandwidth product for di fferent pulse shapes (Figure 2-4).....................................13 4-1 Quantitative estimate of thermal effects in sapphire.........................................................56 4-2 Thermal properties of sapphire at 300 and 77 K.............................................................65 5-1 Performance of the CPA system.......................................................................................88

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ix LIST OF FIGURES Figure page 1-1 High Harmonic generation in Ar gas...................................................................................4 1-2 A sheet of invar micromachined with (a) 10 nsec pulses an d (b) 100-fs pulses..................5 1-3 Schematic of surface spectroscopy (a) and a typical Sum-frequency Generation spectra (b).................................................................................................................... .........6 2-1 Evolution of a plane monochromatic wave in time (a) and a plane wave with Gaussian amplitude modulation in time (b).......................................................................10 2-2 Fourier transform of the (a) cosine f unction in Figure 2-1(a) and (b) Gaussian function in Figure 2-1 (b)...................................................................................................10 2-3 Time evolution of a Gaussian el ectric field with a quadratic chirp 10 b on it.............12 2-4 Intensity profile for a Gaussian pulse (s olid blue curve), hyperbolic secant (dashed blue curve) and a lorentzian (red curve)............................................................................14 2-5 Schematic relationship between phase and group velocities for a transparent mediumgvv ...............................................................................................................14 2-6 Geometry of second-harmonic generation (a) and schematic energy level diagram (b). ............................................................................................................................... .............17 2-7 Geometry (a) and schematic of third order generation (b)................................................18 2-8 Schematic representation of the Kerr lensing effect..........................................................20 2-9 Schematic of Self-phase modulation.................................................................................22 3-1 A schematic representation of a Chirped Pulse Amplifier system....................................25 3-2 Absorption and emission spectra for Ti: sapphire.............................................................26 3-3 Self-mode-locked Ti: sa pphire laser oscillator..................................................................27 3-4 Generation of ultrashort pulses by the mechanism of mode locking.................................28 3-5 Oscillator spectrum as measured by a fibe r spectrometer and its Fourier transform.........30 3-6 A Gaussian pulse possessing (a) linear chirp 0 on it and (b) quadratic chirp 0 on it.....................................................................................................................33

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x 3-7 Dispersive delay lines..................................................................................................... ...34 3-8 Prism delay line........................................................................................................... .......36 3-9 Schematic of the stretcher layout. Oscillat or pulses of duration ~20 fs are stretched to ~ 200 ps without any chromatic aberrations......................................................................38 3-10 Spectrum measured from the oscillator and after propagation through the pulse stretcher...................................................................................................................... ........38 3-11 Effect of gain narrowing in amplifiers the red curve is the fundamental laser spectrum and the blue curve is after five passes through the laser medium......................42 3-12 Schematic representation of a multipass amplifier system................................................43 3-13 A schematic representation of the rege nerative amplifier in our laboratory.....................44 3-14 Amplified pulse spectrum shows a FWHM of 33-nm. Inset, blue curve is the shaped oscillator spectrum using an AOPDF, whic h yielded an amplified bandwidth of 33nm, obtained from the original oscillator spectrum (red curve)........................................46 3-15 Experimental auto-correlator set up...................................................................................48 3-16 FROG: (a) experimental spectrogram, (b) Retrieved spectrogram with a Frog error of 0.002, (c) 43 fs pulsewidth and (d) spect rum from the retrieved Frog trace.....................48 3-17 Schematic representation of CPA......................................................................................50 4-1 Simulation of the resultant temperat ure gradient in an end pumped Ti Al2O3 laser rod at room temperature when pumpe d by 70 W of 532 nm laser light..................................52 4-2 Refractive index changes to a crystal in cident with 80 W of pump beam. The thermal gradient causes optical path deform ation for a beam traveling along the z -axis..............53 4-3 Radially curved end-faces due to increase in temperature caused due to absorption of incident pump beam...........................................................................................................54 4-4 Brewster cut Ti sapphire crystal........................................................................................62 4-5 Dependence of (a) Thermal dispersion ( dn/dT ) (Feldman et al.,1978) and (b) Thermal conductivity (Holland, 1962) of Ti sa pphire with temperature........................66 4-6 CAD drawings depicting (a) Vacuum dewa r assembly and (b) copper crystal holder......68 4-7 Boundary temperature rise as pump pow er is increased when lasing action is inhibited (red points) and when the cavity is lasing (blue points). The lines are guides to the eye..................................................................................................................... .......68

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xi 4-8 Measured thermal lens and thermal power for the two transverse axes; the boundary temperature was measured to be 87 K at zero pump power and 103 K at 55 W of pump power..................................................................................................................... ..70 4-9 Cavity stability parameter as a function of measured thermal lens...................................70 4-10 Computed temperature profile in a 6 mm long, 5 mm diameter Brewster-cut Ti: sapphire crystal single endpumped by 50 W in a 0.4 mm pump spot waist radius for and absorption corresponding to absL = 2.2 and a boundary temperature of 103 K........73 4-11 Plots (a,b) are the corresponding OPD as a function of the transverse coordinates, for the computed temperature profile in figure (3-6).........................................................74 4-12 Comparison of experimentally measured thermal lens powers (squares) against numerically predicted values using finite el ement analysis (circles ) and an analytical expression for thermal lensing (triangles)..........................................................................75 4-13 Spatial interference pattern in the Mich elson interferometer recorded in a CCD camera as a function pump power.....................................................................................76 4-14 Measured OPD compared with the FE A calculated for three different boundary conditions. There is excellent agreement with a boundary temperature of 103bTK at higher pump powers....................................................................................77 4-15 Beam shape as a function of repetition rate Increasing the repetition rate of the pump beam introduces modal distortions....................................................................................78 4-16 M2 measurement for an uncompressed amplif ied beam of average power 5W at 5 kHz repetition rate in the (a) ve rtical and (b) horizontal axis............................................79 5-1 Amplified output power as a function of pump repetition ra te (square points) measured before compression; the red-line is a guide to the eye......................................82 5-2 Amplified v/s pump pulse energy with increasing repetition rate.....................................83 5-3 Measured M2 for an uncompressed amplified beam of average power of 9 W at 8 kHz repetition rate in the (a) hori zontal and (b) vertical axis............................................84 5-4 Amplified spectrum (blue-curve) for the corresponding oscill ator spectrum (red curve) as measured using a fiber spectrometer..................................................................85 5-5 Emission spectra for Ti: sapphire......................................................................................86 5-6 Free-running spectrum for the regenerative amplifier cavity at 5 kHz repetition rate......86 5-7 Shot-to-shot pulse energy measur ed for more than 600, 000 shots...................................87

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xii 5-8 Histogram of the amplified output pulse energy. The black dots are the experimentally measured data with 20 bins and the red curve is a Gaussian fit to the data........................................................................................................................... ..........88 5-9 Thermally induced optical path difference ve rsus crystal length for a fixed radius of 2.5 mm for Tboundary=103 K (left axis) and Tboundary=77 K (right axis)...........................90 5-10 Thermally induced optical path difference versus crystal radius for a fixed length of 6 mm for Tboundary=103 K (left axis) and Tboundary=77 K (right axis)..............................91 5-11 3-mirror folded astigmatically compensated cavity...........................................................93 A-1 Schematic of the experimental set up of the FROG apparatus in our laboratory............101 A-2 Raw SHG-FROG spectrograms record ed using (a) 150 g/mm and (b) 300 g/mm grating. The horizontal axis is the wavelengt h axis and the vertical axis is the delay axis........................................................................................................................... ........102 A-3 Raw SHG-FROG spectrograms indicating (a) unfiltered (b) filtered traces. The horizontal axis is the wavelength axis and the vertical axis is the delay axis..................103 B-1 Bragg vector diagram and physical configuration for (a ) retreating and (b) oncoming sound waves.................................................................................................................... .107 B-2 Schematic of the AOPDF.................................................................................................108

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xiii Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DEVELOPMENT AND CHARACTERIZATION OF A HIGH AVERAGE POWER, SINGLESTAGE REGENRATIVE CHIRPED PULSE AMPLIFIER By Vidya Ramanathan December 2006 Chair: David Reitze Major Department: Physics Ultrashort pulses have revolutionized the fi eld of optical scien ce making it possible to investigate highly nonlinear proces ses in atomic, molecular, plas ma and solid-state physics and to access previously unexplored states of matte r. Although ultrashort pulses make an extremely useful tool, the generation of these highly ener getic but short pulses is by no means trivial. Amplified ultrashort pulses are generated by the t echnique of chirped pulse amplification (CPA). Pulses with peak powers of the order of 1012 W from the CPA lasers when focused down to a surface area that correspond to a few square-micr ons generates high in tensities capable of ionizing the medium or generate spectacu lar non-linear electromagnetic phenomena. This dissertation details the design, fabrica tion and complete characterization of a high average power, high repetition rate and single-stage chirped pulse amplifier system capable of delivering 40-45 fs pulses in the milli-joule range at multikilohertz repetition rate. In order to achieve millijoule level pulses from a single amplifier stage, the CPA systems need to be pumped with high average power sources. This introduces a host of thermal issues and thermal management then becomes necessary to increase the efficiency of such systems. In this work, we have carried out a systematic investigation of th e thermal loading effects in a high average power, regenerative CPA system. We experimentally char acterize the thermal abe rrations using a variety

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xiv of different techniques (interferometry, pump-probe thermal lens power, and M2 analysis). We compute the temperature distribution, the op tical path deformati ons (OPDs) and the corresponding thermal lens focal powers using Finite Element Analysis (FEA) for different pumping conditions. The validation of the experimental results with the FEA model allowed us to use the model to design an e ffective regenerative amplifier cavity that is stable over a wide range of thermal lens focal length and hence ov er a wide range of repe tition rates. The model could also predict optimal pumping conditions for minimizing thermal aberrations for a variety of geometries and pumping schemes. The regenerative amplifier is capable of generating 40-45 fs, ~ 1mJ pulses at 5 kHz repetition rate and ~ 300 J at 12 kHz repetition rate with mi nimal fluctuations (0.9% of mean pulse energy) in the shot-to-shot pulse energy and good beam quality (average2 M of 1.42 at 5 kHz).

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1 CHAPTER 1 INTRODUCTION Light is everywhere in the world. It has always been a carrier of information: from the real world to our brains through our eyes. Our vision defines a sense of perception, which in turn governs the way we look at the world. With the he lp of modern instruments, light has enabled us to see closely and understand phenomena be yond our limited visibility. From scrutinizing astronomical objects thousands of lig ht years away from us to delv ing into the microscopic world, light has in many ways helped us achieve the impossible. Much of this achievement witn essed accelerated growth after th e invention of lasers, which have undoubtedly been one of the greatest inventions in the history of scien ce. Since their arrival in the 1960s (Maiman, 1960) they have found themse lves useful in almost all areas of science today. Barely years after the first laser wa s demonstrated DeMari a and coworkers (1966) generated ultrashort pulses which were picosec onds long from a modelocked Nd: glass laser. Atomic and molecular processes occur on time scales as short as a few picoseconds (10-12 secs) to a few femtoseconds (10-15 secs). The generation of short la ser pulses has ma de it possible to observe such effects with very high temporal resolution. The shorter the pulse duration, the greater are the prospects of inve stigating highly nonlinear processes in atomic, molecular, plasma and solid-state physics and gain access to pr eviously unexplored states of matter. Through the 1970s picosecond pulses were genera ted from flash lamp pumped solid state materials such as ruby, Nd: glass and Nd: YAG using passive modelocking schemes such as saturable absorbers in the laser cavity. But the major drawbacks of these systems were the large fluctuations in the shot-to-shot output from the laser, and the instability of the saturable dye solution whose quality degraded with exposure to li ght. As a result focus shifted from solid state gain medium to organic dye lase rs which were capable of genera ting pulses shorter than 10-ps.

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2 The field of ultrafast laser development has seen rapid progress since the generation of high quality sub-picosecond (0.1-ps) laser pulse s by Richard Fork, Benjam in Greene and Charles Shank in 1981. Pulse durations quickly dropped to the femtosecond regime (Shank et al., 1982) using colliding pulse modelocked lasers. With the i nvention of solid state laser material such as Ti3+ doped sapphire (Ti: Al2O3) by P. F. Moulton (1986) renewed in terest in solid state lasers as they offered higher stored energies and unlimited operating and shelf lifetimes as compared to organic dye liquids. The discovery of self-modelocked Ti: sa pphire lasers by Spence et al in 1991 revolutionized the field of ultraf ast laser development. It now became possible to generate pulses as short as 5 fs (Jung, et al., 1997; Morgner et al ., 1999) directly from a laser oscillator without the use of saturable absorbers. These table top la sers easily generate peak power levels of the order of a few megawatts 610W (Huang et al., 1992a; 1992 b; Asaki et al., 1993). Ultrashort pulses allow for fast temporal reso lution. One now has the capability to freeze motion of fast moving electrons and molecules, facilitating the study of molecular dissociation dynamics, complex chemical reaction dynamics etc. thus paving way for the field of femtochemistry (Zewail, 1996), which deals with the nature of transition stat es and their control. Following the development of milli-joule level picosecond pulses by Strickland and Mourou in 1985, it became possible to genera te millijoule level femtosecond pulses via the technique of Chirped Pulse Amplification. This sa w an increase in peak power by six orders of magnitude 1210Wover those generated by the Ti: sapphire laser oscillators. Current table top laser systems can generate peak powers in the petawatt range 1510W (Perry et al., 1999; Pennington et al., 2000, Kitagawa et al., 2004).These lasers have found a variety of applications over the past decade and con tinue to do so as our understanding develops.

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3 Peak powers of a megawatt are however in sufficient for many experiments. Several nonlinear optical processes like high harmonic genera tion, ultrashort surface science, generation of extreme ultraviolet radiation (EUV) (to na me a few) are limited by the availability of ultrashort pulse energies and the average flux, making it necessary to amplify pulses from a selfmode-locked Ti: sapphire osc illators. The technique of chirped pulse amplification has progressed significantly since the amplified pico second pulses from the system developed by Strickland and Mourou (1985). Amplificatio n of ultrashort pulses by a factor of 106 to generate peak powers in excess of 1012 W (1 TW) at a repetition rate of 10 Hz was easily achieved (Maine et al., 1988; Kimetec et al., 1991; Sullivan et al ., 1991; Zhou et al., 1995; Chambaret et al., 1996). S. Backus et al. (2001) extended the chirped pu lse amplification technique to generate millijoule level, femotsecond pulses at multikilohertz repe tition rate in a single stage chirped pulse amplifier system. Advantages of liquid nitrog en cooled Ti: sapphire crystal (Moulton, 1986; Schulz and Henion, 1991) were incorporated into a multipass amplifier cavity. The advent of such high intensity, ultrafast lasers has facilitated many experiments in high-field science. Matter expos ed to intense ultrashort laser light undergoes ionization as the electronic wave packet is set free to oscillate in a laser electric fi eld that is st rong enough to overcome the effective binding poten tial. Nobel gases such as neon, argon, etc. when exposed to such intense electric fields, io nize generating electromagnetic wa ves at much higher frequencies. Also free electrons in plasma can be acceler ated over 100 MeV in a space of only a few millimeters (Umstadter, 2001) using strong laser electric fields. As a specific example, millijoule level amplified pulses are essential for non-lin ear processes such as generating sub-nanometer range radiation, which are harmonics of the fund amental laser beam (LHuillier and Balcou 1993; Bartels et al., 2000; Reitze et al., 2004). When a high-energy ultrashort laser pulse is tightly

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4 focused the intensities created corresponds to an electric field that often exceeds the binding energy of a valence electron to the core of a noble gas atom. Within the first laser period the ejected electron from the parent ion is accelerated an d it may return to the parent ion with a finite probability releasing harmonics that are coherent, directional and shorter in duration as compared to the driving laser pulse (Figure 1-1). Coherent soft and hard X-rays produced due to the harmonic up-conversion are used to conduct freque ncy interferometry in the ultraviolet to probe thin solid films and dense plasmas (Salieres et al., 1999; Descamps et al., 2000) and study electron transport dynamics in semic onductors (Rettenberger et al., 1997). Figure 1-1: Harmonic generation in Ar gas. Using (a) 6-mJ, 30-fs, 800-nm pulses at 1 kHz repetition rate, Peak intensity ~ 142310Wcm (Reitze et al., 2004) and (b) 1-mJ, 25fs, 800-nm pulses at 1 kHz repetition rate, Peak intensity ~ 142210Wcm (Bartels et al., 2000). As a second example, high intensity laser pulses can ablate material non-thermally i.e without an increase in temperature. As in Figure 1-2 the quality of ablated holes and patterns in materials that undergo fabricated microstruc tures using femtosecond and picosecond pulses is much better than those produced using nanosecond pulses (Liu X et al., 1997; Von der Linde et al., 1997). Such fast cold ablation technique where the solid is changed directly to the gas

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5 phase is highly desirable as it reduces effects ca used by heat conduction and interaction of the pulse with the ablated material. In addition, amplified ultrashort pulses can further be compressed to sub-10 fs duration by self-phased modulation of these pulses in ho llow core waveguides and pulse compression (Steinmeyer et al., 1999). Harm onics generated by su ch short and intens e pulses give rise coherent x-rays with puls e duration as short as 10-18 s (100 attoseconds) (Paul et al., 2001; Hentschel et al., 2001) to study electronic state transition processes that occur faster than femtosecond timescales. Figure 1-2: A sheet of invar micromachined w ith (a) 10 nsec pulses an d (b) 100-fs pulses. (http://www.cmxr.com/Industrial/Handbook/Chapter7.htm) Femtosecond pulses with high energy and faster repetition rates are also utilized to perform surface non-linear spectroscopy (O stroverkhov et al., 2005; Liu et al., 2005). As a second order nonlinear optical effect, second harmonic gene ration and sum-frequency generation are forbidden under the electric-dipole approximation in media with inversion symmetry. But at the surface or an interf ace this symmetry is necessarily broken Thus non-linear surface spectroscopy is surface specific. As described in Figure 1-3 (a), two lase r beams at frequencies 1 and 2 when mixed at an interface generate surface-sp ecific sum frequency (or second harmonic,

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6 when12 ) output in transmission or reflection. The signal is proportional to the square of the nonlinear susceptibility 2 2 s12 of the interface. Scanning2 over the vibrational resonances of the molecules or adsorbates on th e surface, gives rise to a vibrational spectrum, which is unique to that par ticular surface/interface. When 1 and 2 are high energy pulses derived from a high brightness femtosecond chirped pulse amplifier, the peaks in the vibration spectra are well enhanced making it possible to detect surface abnor malities with ease. Figure 1-3: Schematic of surface spectroscopy (a) and a typical Sum-frequency Generation spectra (b). [Reprinted with permission from Superfine et al., (1991)]. An intense ultrashort laser pulse as available today, with peak powers 22210Wcm, are capable of generating electric fields at an excess of 1011 V/cm, can produce a wake of plasma oscillations through the action of the ponde rmotive force (Tajima and Dawson, 1979). An electron trapped in this wake is accelerated to relativistic speeds such that the work done by the electric field Eover the wavelength of the laser field, eE approaches the rest mass energy 2 0mcof the electron, where 0mis the rest mass of the electron andc is the speed of light (Umstadter, 2001). Intense laser pulse when co me in contact with plasma confined in a 3 volume, where is the wavelength of the laser radiation, is capable of generating attosecond

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7 pulses and electron bunches (Naumova et al., 2004; Ness et al., 2005). These laser-based radiation sources may someday be used for cancer radiotherapy a nd as injectors into conventional accelerators, which are critical tools for x-ray and nuclear physics research. The above examples present but a few of the ap plications of ultrafast lasers in physics, materials science, and chemistry. There is an ever-increasing need for ultrashort pulses at high pulse energies and faster repetition rates driven by these applications. The generation of these pulses is by no means trivial: the simultaneous re quirement of high pulse energies (> 1 mJ) and high repetitions rates (> 5 kHz) necessitates high average power pumping. Thermal management then becomes the key to the operation of th ese highly pumped lasers. Improved thermal properties of sapphire at 77 K (Moulton, 1986) allows for much efficient extraction of energy from the crystal in an amplifier making it possi ble to achieve millijoule pulses at kHz repetition rates in a single amplifier st age (Backus et al., 2001). Loweri ng the crystal temperature way below the ambient only reduces and does not eliminate the deleterious thermal effects. Thus in order to increase the overall efficiency of th e chirped pulse amplifier system an extensive thermal analysis and characterization of the cr ystal in the amplifier becomes inevitable as it provides a better understanding of these thermal effects. In this thesis we develop and characteri ze a high average power, single-stage, chirped pulse amplifier system that generates 40-45-fs puls es with pulse energies close to a 1mJ at 5 kHz repetition rate. We present a systematic investig ation of the thermal loading effects in such amplifier systems. We experimentally charac terize thermal aberrations in a regenerative amplifier using a variety of techniques. Using Finite Element Analysis (FEA) we compute the temperature distributions, optical path deformations OPD and corresponding thermal focal lengths for a variety of pumping conditions. Ex cellent agreement between the FEA modeling and

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8 the experimental results allow us to predict optimal pumping conditions for minimizing thermal aberrations that could further increase the effi ciency of the system. The usage of the acoustooptic programmable dispersive fi lter (AOPDF) as a pulse shaper makes this a unique and a compact system capable of delivering ultrashort pulses in the millijoule range. High brightness sources such as this is ideally suited for high harmonic generation which is essential for the generation of attosecond pulses, plasma genera tion and acceleration of free electrons in plasma. Applications such as femtosecond micromachin ing and surface characterization using nonlinear frequency conversion techniques will benefit from the amplifiers high average powers for the high signal-to-noise measurements via lock-in detection. The layout of the dissertation is as follows: in Chapter 2 we discu ss the principles of ultrashort pulse generation and characterizatio n. The design and cons truction of the various components of a high average power, single-stage chirped pulse amplifier is described in detail in Chapter 3. Chapter 4 deals with issues relating to the design, modeling and characterization of the host of thermal effects in a regenerative CPA system. The experimentally measured results are validated numerically using Finite Element Analysis (FEA). The characterization and the optimization of the pulses from the amplifier system are elaborated in Chapter 5 along with techniques that can further impr ove the efficiency of the CPA system. Finally we conclude in Chapter 6.

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9 CHAPTER 2 ULTRASHORT PULSE GENERATI ON AND CHARACTERIZATION Before we begin to delve into the details of the construction and pe rformance of a high average power chirped pulse amplification system, it is beneficial to understand more about the fundamentals of generation and characterization of femtosecond pulses. This chapter discusses the various aspects of femtosecond pulses that are extremely crucial to the work described in this thesis. Beginning with a mathematical relationshi p between pulse width and the spectral bandwidth the chapter discusses di spersion of broad bandwidth pul ses. Principles of nonlinear effects such as the second and third order effect s that are crucial for pu lse characterization and the generation of ultra board brand sources respectively are discussed in the final sections of this chapter. 2.1 Relationship between Duration and Spectral Width A plane monochromatic wave of frequency 0 (Figure 2-1 (a)) has an infinite spread in the time domain. 00ReexpEtEit (2.1) A light pulse can be generated from a sinusoidal electric field as in equation (2.1) by multiplying it with a bell shaped function for the amplitude modulation. Choosing a Gaussian function the above equation then transforms as 2 00ReexpEtEtit (2.2) The time evolution of equation (2.2) is shown in Figure 2-1(b). is the shape factor of the Gaussian envelope. The spectral content of the two kinds of light puls es can be obtained by

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10 performing a Fourier transform to the temporal domain. Figure 2-2 (a) and (b ) are the numerical Fourier transforms for the cosine and the Gaussian function in equations (2.1) and (2.2). The monochromatic plane wave oscillates with a single frequency0 whereas the Fourier transform of the Gaussian function is also a Gaussian, with the width proportional to. Figure 2-1: Evolution of a pl ane monochromatic wave in tim e (a) and a plane wave with Gaussian amplitude modulation in time (b). Figure 2-2: Fourier transform of the (a) cosine function in Figure 2-1(a) and (b) Gaussian function in Figure 2-1 (b). From the empirical relationship between the spectral width and the pulse duration of the pulse, we can now derive a more formal relation (Seigman, pp.331). For a Gaussian electric field as in equation (2.2), the instantaneous intensity can be expressed as 2 2 2 0()()exp4ln2pt ItEtE (2.3)

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11 where p is the duration of the pulse measured at half the maximum intensity and is known as the Full Width at Half Maximum (FWHM). 2ln2p (2.4) The Gaussian spectrum in frequency is the Fourier transform of equation (2.2) 2 0 0()exp 4E (2.5) The power spectrum of the Gaussian pulse can be written in the same form as the instantaneous intensity as in equation (2.3) 2 2 0 0exp4ln2pIE (2.6) The FWHM bandwidth of the Gaussian pulse is 2ln2 2p pf (2.7) If in equation(2.2) ,aib where b is known as the chirp f actor, then the pulsewidth p and p f undergo the following modification 22ln2 2ln2 1p pa b fa a (2.8) Incorporating the in the expression for electric field equation(2.2), in the time domain

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12 22 00expexp exptotEtEatitbt Etit (2.9) where, 2 0 totttbt (2.10) is the time varying phase of the Gaussian puls e. An instantaneous pha se gives rise to an instantaneous frequencyi tot idt dt (2.11) For the Gaussian pulse described above th is instantaneous frequency is given as 2 002id ttbtbt dt (2.12) Thus a Gaussian pulse with a time-varying instantaneous linear frequency is known as being chirped with the parameter b being a measure of this chirp. Figure 2-3 demonstrates a chirped Gaussian pulse. Figure 2-3: Time evolution of a Gaussian electric fiel d with a quadratic chirp 10 b on it. 2.2 Time Bandwidth Product The product of pulsewidth and spectral bandwid th is known as the time bandwidth product (TBP). Multiplying equations (2.4) and (2.7) we get

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13 2ln2 0.44ppf (2.13) According to the uncertainty relation the time bandwidth product for a Gaussian pulse cannot be less than 0.44. Chirp on a Gaussian pulse increases the TBP. 222ln2 10.441ppbb f aa (2.14) Thus for a Gaussian pulse the minimum TB P is 0.44 and such a pulse is known as transform-limit as the linear chirp-factor0 b The TBP depends on the shape of the pulse and the definitions of f and t (rms, FWHM, etc.). The table below compares the TBP for 3 fu ndamental pulse shapes suitable for laser beams, for other forms of intensity profiles such as squa re, triangular, exponential etc. the reader is urged to refer Sala et al (1980). Table 2-1: Time bandwidth produc t for different pulse shapes (Figure 2-4) Pulse Shape Intensity I t Time bandwidth product f t Gaussian 2 x e 0.4413 Hyperbolic Secant 2sec hx 0.3148 Lorentzian 21 1 x 0.2206 Note: Adapted from Sala et al. (1980).

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14 Figure 2-4: Intensity profile for a Gaussian pulse (solid blue curve), hyperbolic secant (dashed blue curve) and a lorentzian (red curve). 2.3 Dispersion Ultrashort pulses, with its br oad spectral content undergo disp ersion as they propagate in air, materials, etc. Dispersion is said to occur when the phase velocity of the wave depends on its frequency (Born and Wolf). The vac uum dispersion relation is given as:ck where is the angular frequency of the radiation, k is the wave number and c is the velocity of light in free space. For such a dispersion relation the phase velocity v and the group velocity g v are the same. In a dispersive medium, the dielect ric constant is a function of frequency with the consequence that g vv Different components of the wave travel with different speeds and tend to change phases with respect to one another. An ultrashort pulse propagating through such a media will undergo changes in its shape ultimately leading to temporal broadening. Figure 2-5: Schematic relationship between phase and group velocities for a transparent mediumgvv The electric field of an ultrashort pulse, in the frequency domai n is given by equation (2.5). After the beam propagates through a distance x its spectrum is modified accordingly as 0()()exp E Eikx (2.15)

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15 where knc is a frequency dependent propagation constant, with nbeing the refractive index of the medium. If the propagation constant k is a slowly varying function of : it can expanded in a Taylor series expa nsion about a central frequency 0 as long as 0 0 0023 23 0000 2311 ... 2!3! kkk kk (2.16) The frequency dependent propagation constant k will modify the pulse as it propagates through the medium. Substituting th e above expression in equation (2.15) 2 0001 exp... 4 Eikxikxikx (2.17) where, 0kk and 022kk The temporal evolution of such a pulse can be obtained by a Fourier transform of its spectral shape (Rulliere, pp.33). 1 exp 2 EtEitd (2.18) 2 0 00expgx xx Etitxt vv (2.19) The first term in the exponent pr oduces a time delay by an amount x v after propagation though a distance x The quantity 00vk is the phase velocity of each of the plane wave components of the pulse in the medium. 1 0gvdkd is known as the group velocity and determines the speed of the pulse in the medium. For cases where 0 gvv and the pulse is said to undergo normal dispersion. Now 12 x ikx where 1 gkddv is known as the group velocity dispersion. Figure 2-5 is a schematic of the dispersion effect in a

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16 medium with a dispersion relation ck Thus the equation (2.19) demonstrates that a short pulse propagating through a tran sparent medium undergoes delay, a broadening of its pulse duration accompanied by a frequency chirp. 2.4 Nonlinear Effects 2.4.1 Second Order Susceptibility Light intensities generated by an ultrashort pulse can change optical properties of the medium that they pass through. The intensity depe ndent changes to the optic al properties of the material constitute nonlinear optics. Many of these nonlinear optical effects tend to be useful while generating and characterizing ultrashort pulses. On expanding the polarization in a Taylor series expansion (1)(2)(3)... P (2.20) The first term in the above equation is the linear term whereas its the higher-order terms that account for the nonlinear optical effects. Second-order optical effect or second harmoni c generation (SHG) is caused due to the second order susceptibility term(2) It is characterized by th e second-order polarization 2Pt 22 *PtEE (2.21) Two photons of frequency combine in a medium to give rise to a single photon of frequency2 (Figure 2-6). But the process of second harmonic generation is dependent on the orientation of the crystal axis and the polarization of the incomi ng light. If the medium posses an inversion symmetry, (2) vanishes uniformly over the bulk of the medium. SHG in such cases can be observed either at an interface or on the surface of the medium. For an impinging intensity I of frequency with a propagation constant 1k the intensity of the second

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17 harmonic signal 2I with the propagation constant 212 kk through a nonlinear crystal of length lis given as (Boyd) 2 2 7322 2 33sin/2 2 2 /2 kl II nckl (2.22) where, 212 kkk is known as the wavevector mismatch The SHG process is most efficient for the perfect phase matched condition where0 k Figure 2-6: Geometry of second-harmonic generati on (a) and schematic energy level diagram (b). As the SHG signal for a given crystal length, orientation and polariza tion of the incoming light is directly dependent on its intensity, it is extensively used to measure the pulsewidth of an ultrashort pulse as described in detail in appendix A. The second order susceptibility is also responsible for a variety of othe r effects that involve 3 photons such as the sum-frequency gene ration (SFG) where two incoming photons of frequency 1 and 2 combine in a nonlinear crystal and generate a signal at the sum frequency312 Difference frequency generation (D FG) is a process where the two incoming photons generate a signal at the difference frequency321 where 21 The satisfaction of the phase marching condition 123kkkk determines the efficiency of all these process within a non-centrosymmetric crystal.

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18 2.4.2 Third Order Susceptibility Three photons mix to generate third order nonlinear effects due to the third order susceptibility 3 term equation(2.20). The third order polarization term can be written as (3)(3) (3)(3).. PEEE PIE (2.23) Some of the third order effects incl ude third harmonic generation (as in Figure 2-7) where three photons of frequency combine to generate a photon of frequency3 Unlike the second order effect, the third order effect can occur in any media irrespective of the symmetry and can also occur in liquids and amorphous materials such as fused silica. The number of effects increases as the order of nonlinearity increases. The primary focus of this chapter will be to discuss the effect s related to generation and characterization of ultrashort pulses. Figure 2-7: Geometry (a) and schema tic of third orde r generation (b). 2.4.2.1 Nonlinear index of refraction The intensity of the ultrashort pulse in a medi um changes its optical properties. The third order polarization in equation (2.23) when combined with th e linear polarization term becomes (1)(3) (1)(3)3..() ,3.eff effPEIEE whereI (2.24)

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19 where 2 I E is the intensity of the incident ultrashort pulse. The second order term can be made to vanish in the above equation due to symmetry conditions in the crystal. For a centrosymmetric medium (2) vanishes and for non-centrosymme tric medium the second order effects can be eliminated by orienting the crysta l in such a way so as to satisfy the phase matching condition only for 3 effects. The refractive index of the material is defined as:214effn Substituting for eff, the refractive index can be expressed as 2 13 21412 nE (2.25) The refractive index of a material, when a high inte nsity laser beam is incident on it, can also be described by the following relation 2 02nnnE (2.26) where n0 and n2 are the linear and nonlinear i ndex of refraction respectively. Comparing the relations (2.25) and(2.26), one can obtain expressions for 0n and2n 12 (1) 0 (3) 2 014 6 n nI n (2.27) For an ultrashort pulse the intensity is a function of both space and time I rt. Both the spatial and temporal dependence of intensity leads to interesting effects such as Kerr lens effect, selfphase modulation, self-focusing, filamentation etc. Effects that lead to the generation of ultrashort pulses are discussed in the following sections. 2.4.2.2 Kerr lens effect The spatial intensity profile of a Ga ussian laser beam propagating in a 3 material is

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20 2exp I rgr (2.28) The refractive index of the material al so gains a spatial gradient given as 2onrnnIr (2.29) This generates a refractive index gradient as in Figure 2-8 that follows the gradient in the intensity profile of the inci dent ultrashort pulse. For a nonlinear index of refraction20 n the refractive index is greater at th e center of the medium as compar ed to the sides. The amount of nonlinear phase accumulated by the ultrashort pul se as it passes thr ough this graded index material is 0202222 ()()() rnlnlIrnlIr (2.30) This effect similar to a static lens, increases th e focal power of the material due to the spatial variation in the phase of a traversing beam such that beam focuses into the material. This effect known as Kerr lens effect is of utmost importance in unders tanding self mode-locked Ti: sapphire laser oscillators. Figure 2-8: Schematic representation of the Kerr le nsing effect. The KLM effect leads to the selffocusing of the intense ultrashort pulses. 2.4.2.3 Self phase-modulation The temporal profile of a Gaussian pulse incident on a 3 material is 2 0 2()exp t IrI (2.31)

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21 Thus the refractive index is then transformed as 2 020 2()exp t ntnnI (2.32) The time varying intensity leads to a time varying refractive index as the pulse propagates 2 220 222 exp dndItt nnI dtdt (2.33) An instantaneous refractive index brings about a change in the total phase ( 2 nl ) accumulated by a pulse or a phase delay as it propagates through such a medium. 0202222 ()()() tnlnlItnlIt (2.34) where is the vacuum wavelength of the carrier and 0nl is the optical length traversed by the pulse. This generates a time varying shift in frequency 02 2 20 222 () 4 ()exp ddI tnl dtdt t tlnIt (2.35) A plot of t(Figure 2-9) shows that the leading edge of the pulse shifts towards the lower frequencies (red shift) and the trailing ed ge shits towards higher fr equencies (blue shift), generating an overall increase in the bandwidth of the pulse. Although the spectral content of the pulse is increas ed as it passes th rough such a crystal the temporal structure remains unaltered by the self-focusing effect. Bu t natural dispersion occurring within the crystal tends to broaden the pulse.

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22 Ti: sapphire-based laser oscillator s make use of the Kerr-lensing effect to generate pulse as short as 6-fs (Jung et al., 1997) di rectly from an oscillator which is described in detail in the following chapter. Figure 2-9: Schematic of Self-phase modulatio n. (a) A Gaussian pulse propagating through a nonlinear system undergoes self focusing eff ect (b) which gives rise to additional frequency components which when compensate d for material dispersion generates a short pulse. 2.5 Summary We briefly discussed in this chapter the essential theoretical background needed to understand the various nonlinear process such as the generation of femtosecond lasers through the Kerr lensing effect. Also processes such as the second harmonic generation which is a commonly used tool to characterize ultrashort pulse widths, were discussed in considerable detail. More on the technique of measuring ultrashort puls es are elaborated in Appendix A at the end of this dissertation.

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23 CHAPTER 3 DESIGN AND CONSTRUCTION OF A HI GH AVERAGE POWER, SINGLE STAGE CHIRPED PULSE AMPLIFIER 3.1 Introduction Strickland and Mourou (1985) developed the firs t ultrashort laser in the year 1985, capable of delivering millijoule pulses at picosecond time scales (2x10-12 secs) at a wavelength of 1.06 m, by the technique of chirped pulse amplif ication. Ultrashort pulses by definition support a large spectral bandwidthconst. Amplification of ultrashor t pulses enforces certain minimum requirements on an amplifier system. First, the amplifier bandwidth must be wide enough to accommodate the spectral bandwidth of the seed or the un-amplified pulses. As a wide range of Fourier components is required to pr oduce an ultrashort pulse, a gain medium with a narrow emission bandwidth could not possibly suppor t ultrashort pulses. The central wavelength 0 of the seed pulses must efficiently extract the stored energy in the am plifying medium, i.e the fluence of a pulse must be cl ose to the saturation fluence of the amplifying gain medium s atgJh where g is the gain cross-section of the gain medium. Finally the peak intensities generated within the amplifier mu st be well below a certain crit ical level above which nonlinear effects as discussed in chapter 2 can distort bo th the spatial and the temporal profile of the amplified beam and in some cases can damage the optical components w ithin an amplifier as well. 3.2 Why Chirped Pulse Amplification? While amplifying femtosecond pulses, the ph ase shift experienced by a propagating ultrashort pulse in an amplifying me dium can be both linear and nonlinear

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24 0222 (,)Total TotalLinearNLnlnnIrtl (3.1) The linear phase 02 nl arises due to the linear index of refraction0n The nonlinear phase shift arises from the nonlinear response (distor tion) of the electron cloud surrounding an ion subjected to an intense electric field. As can be seen from equation (3.1), the peak intensities associated with an ultrashort pulse introduce additional phase delay 20 n and therefore experience enhanced nonlinearities, which are ma nifested both in tempor al as well as spatial distortions of the laser pulse. One can calculate the nonlinear phase accumu lated by an ultrashort pulse along an optical path L as (Koechner, 1976) 2 0022 (,)LL NLn dlnIrtdl n (3.2) where2n is the nonlinear index of refrac tion of the lasing medium and I rtis the instantaneous pulse intensity within the amplifier cavity. A peak value of 5 for the nonlinear phase NL (for historical reasons also known as the B integral) corresponds to a critical in tensity (Maine et al., 1988) above which only high spatial frequencie s are preferentially am plified, reducing the spectral bandwidth of the amplified pulses that u ltimately results in longer pulses. As noted in the previous chapter a host of nonlinear effects are associated with the spatial as well as the temporal variation of the intensity of an ultras hort pulse. And if the a ccumulated nonlinear phase exceeds this critical value, the ultrashort beam becomes distorted due to these nonlinear processes (Boyd, 2003). Thus keeping the amount of nonlinear phase that an ultrashort pulse can gather, much below the threshold value is of utmost importance in amplifying these pulses to high energy levels.

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25 Given a suitable gain media like Ti3+:Al2O3 (which shall be discussed in the following section), the technique of chirped pulse amp lification circumvents the generation of excess amplified intensities capable of damaging amplifier materials or causing nonlinear effects. Figure 3-1 illustrates a schematic of a ch irped pulse amplification system. This technique relies on increasing the durati on of the pulse being amplified by introducing a controlled amount of dispersion (chirping th e beam) and then optically compressing (Treacy, 1969; Martinez, 1987; Martinez, et al.,1984) the amplified beams to its original pulse duration. Fs-Laser Stretcher Amplifier Compressor Fs-Laser Stretcher Amplifier Compressor Figure 3-1: A schematic representation of a Chir ped Pulse Amplifier system. The pulse cartoons represent the temporal structure of the pulse at each stage in the amplification process. Temporally lengthening (or s tretching) the pulses reduces the peak intensity, enabling efficient energy extraction from the amplifier ga in media by distributing the total energy content of the pulse over a broader time scale. Chirped pul se amplification become s particularly useful for amplifiers utilizing solid-state gain media with high stored energy densities (1 10 J/cm2) well above the damage threshold of several optical components, in order to efficiently extract the entire stored energy in the gain media. The following sections contain an in depth discussion of the various components of a single stage, CPA system in our laboratory.

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26 3.3 Ti: Sapphire as Gain Medium Ultrashort pulse amplification needs very br oadband gain media. Femtosecond amplifiers in the past relied heavily on broadband laser dy es and excimer gain mediums as the amplifying material (Ippen and Shank, 1986; Downer et al., 1984; Knox et al., 1984). Due to the low saturation fluences offered by these media, the amplified output powers we re severely limited by the size of the amplifying medium. But solid-state media such as Nd: glass, Cr3+ doped BeAl2O4 (Alexandrite), Cr3+ and Ti3+ doped Al2O3 (sapphire) not only posses much higher stored energies (~ 1J/cm2) but also display extremely broad emissi on bandwidths to suppor t ultrashort pulses (Moulton, 1992). Figure 3-2: Absorption and emission spectra fo r Ti: sapphire. [Adapted from Rulliere (1998)]. Of all the solid state materials available, Ti3+ doped Al2O3 (commonly referred to as Ti: sapphire) emerged to be the most promising ma terial (Moulton, 1986). The early nineties saw a boom in the use of Ti: sapphire as an activ e medium to produce femtosecond pulses due a number of its features that were desirable as a laser host material. With a damage threshold of 810 J/cm2 (comparable with metals), hi gh saturation fluence of 0.9 J/cm2, a peak gain cross-

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27 section g of 2.7 10-19 /cm2 (Backus et al., 1998) and an ex tremely broad gain bandwidth of 230 nm (Moulton, 1986), there is little doubt as to why Ti: sa pphire is a favorite among femtosecond-laser developers! Ti: sapphire exhi bits a peak absorption maximum at 500 nm. Figure 3-2 indicates the absorpti on and emission bandwidths for Ti3+ doped Al2O3. With the availability of high average power diode-pumpe d solid-state lasers, such as the frequency doubled Nd: YAG and Nd: YLF laser source (laser emission at 532 nm), Ti: sapphire quickly became the obvious choice in the development of ta ble-top terawatt sources (Backus et al., 2001). Figure 3-3: Self-mode-locked Ti: sapphire lase r oscillator. The cavity is formed by a high reflecting mirror (HR) and an output coupler (OC). The pump beam is focused on to the crystal which is placed in a s ub-resonator formed by mirrors M1 and M2. Dispersion compensation is achieved by prisms P1 and P2. There has been a tremendous amount of progr ess in the generation of femtosecond pulses since the construction of the fi rst self mode-locked Ti: sapphi re laser by Spence et al. in 1991 generating 60-fs pulses. With further im provisations to their optical design (Figure 3-3), it became possible to generate pulses as short as 6 fs (Jung et al., 1997) directly from a laser oscillator. Short pulses were achieved by the pr ocess of Kerr-Lens mode-locking (discussed in the previous chapter), wherein an inherent nonlinearit y of the Ti: sapphire crystal was creditably exploited, which is yet anothe r reason why Ti: sapphire is th e most revered material for ultrashort pulse generation!

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28 3.4 Mode-locked Laser Mode-locking is the essential mechanism to generate pulses from a laser oscillator. A laser cavity allows oscillation only for discreet resonance frequencie s that satisfy the condition 2mmcL where cis the velocity of light and L is the length of the laser cavity and m is an integer. The longitudinal modes of a la ser cavity oscillate freely and the output intensity consists of different modes with no specific phase relation with respect to each other and the laser is said to be ope rating in a continuous wa ve or cw mode. These modes which initially possess random phases, when forced to oscillate with a well defined phase constitutes a pulse and the laser is then said to be lasing in a pul sed mode with a finite bandwidth spectrum as in Figure 3-4. Mode-locking in dye lasers and in certain solid state media was achieved either by an external modulation (active mode-locking) or by placing saturable absorbi ng medium in the laser cavity (passive mode-locking). Figure 3-4: Generation of ultrashort pulses by the mechanism of mode locking. Ti: sapphire laser does not requi re either external stimulati on or saturable absorbers to generate ultrashort pulses. This is known as se lf mode-locking. As discussed in the previous

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29 chapter, an intensity dependent variation of th e refractive index of the Ti: sapphire crystal, arising from a non-uniform power density distri bution in Gaussian beams gives rise to an intensity dependent phase-shift that leads to the generation of multiple modes within the oscillator cavity. The amplitude of the short pulse is modulated in such a way that intense pulses experience less loss than weaker pulses and can therefore sustain within the cavity. Figure 3-3 is a schematic of a self-mode-loc ked Ti: sapphire laser oscillator. The laser cavity is formed by two plane mirrors, one a high reflecting mirror (HR) and an output coupler (OC) which is partly transmitting. The Ti: sapphi re crystal is placed in a sub resonating cavity formed by two identical spherical mirrors of rad ii of curvature 10-cm, which are dichroic in nature, transmitting 532-nm and reflecting 800-nm. Two fused silica prisms placed in the longer arm of this asymmetric cavity provide the phase compensation necessary to achieve mode locking. The Ti: sapphire crystal is pumped by a 5 W Coherent Verdi which is a diode pumped Nd: YVO4 laser system. The refractive index of sapphi re varies with the intens ity of the incident pulse as02() nnnIr The crystal behaves like a converging lens as20 n The Kerr lensing effect in conjunction with the self-foc using of the laser beam within the crystal gives rise to the broadening of the spectral content of the pulse. Although the spectral co ntent of the pulse is in creased as it passes th rough the Ti: sapphire crystal the temporal structure remains unalte red by the self-focusi ng effect. But natural dispersion occurring within the crystal tends to broaden the pulse. The prism pair inside the oscillator cavity generates ne gative dispersion to compensate for the positive dispersion introduced by the crystal (Martinez et al., 1984; Fork et al., 1984), enabling the generation of femtosecond pulses from the oscillator. Careful ba lancing of the self-phase modulation effects

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30 and the group velocity dispersion due to the prism pair causes all the modes in the oscillator to have the same optical path leng th through the crystal, forcing them to os cillate in phase to generate a train of mode-locked pulses with a repetition rate 1/R where R is the round trip time around the cavity. The peak intensities inside the Ti: sapphi re crystal must be high enough to induce nonlinearity but well below a critical level, which can distort the beam within the cavity. In order to favor the high intensity pulsed operation of th e laser over the continuous-wave (cw) mode, old designs of the Ti: sapphire oscillator used a hard aperture blocking out the large waist modes that correspond to low intensity levels. Figure 3-5: Oscillator spectrum as measured by a fiber spectrometer1 and its Fourier transform. Inset is the calculated temporal profile (temporal bandwidth of 14 fs) assuming a constant phase across the en tire spectral bandwidth. Instead of the hard aperture, the pump beam in the oscillator is overlapped on the crystal with the pulsed beam, such that it preferentially keeps the cw beam in the cavity at extremely low intensities, enablin g mode-locked operation. Mode locki ng is readily achieved by gently 1 The modulations in the measured spectrum are an artifact of the fiber spectrometer. The temporal profile was calculated on first filtering the measured spectrum with a Savitzky-Golay smoothing function and then performing an inverse Fourier transform on the smoothed spectrum.

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31 stroking the prism next to the high reflecting mirror. The osc illator routinely generates 300-400mW mode-locked pulses at the re petition rate of 90 MHz (defined by the cavity length), centered at 800-nm and a full width of half-maximum ba ndwidth (FWHM) of 80-90-nm, an average pulse energy of 2-5 nJ depending on the alignment. A pair of razor edges that form a slit allows tuning of the mode locked spectrum. In order to stabilize the laser in the mode locked state, the Ti: sapphire crystal is maintained at a constant temperature of 20 C by a circulating water chiller. Also for prolonged stability, the laser is isolat ed from the environment by enclosing it in a protective case. Due to the absence of an extern al compensator to generate transform limit pulses from the oscillator, the temporal FWHM is always greater than calculated as in the inset of Figure 3-5. The seed pulses from the oscillator are then in troduced into a pulse stretcher to temporally broaden the pulses before they can be injected into the amplifier. 3.5 Dispersion The phenomenon of dispersion is very import ant to the field of ultrafast optics. As ultrashort pulses, with their broad spectral conten t undergo dispersion as they propagate in air, materials, etc., dispersion management then be comes the key to developi ng really short pulses. As previously noted, dispersion is said to occur when the phase velocity of the wave depends on its frequency (Born and Wolf). Different compone nts of the wave travel with different speeds and tend to change phases with respect to one another. An ultrashort pulse propagating through such a medium will undergo changes in its shape ultimately leading to temporal broadening. The electric field of an ultrashort pulse is represented in the frequency domain as ()()exp() Ei (3.3)

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32 where ( )is the amplitude modulation for a finite beam and () is the phase of each of the frequency components present in the beam. If the spectral phase () is a slowly varying function of (this does not hold true in region s of anomalous dispersion where n() varies rapidly over narrow intervals of ) then it can expanded in a Taylor series expansion about a central frequency 0. 0 0023 23 0000 2311 ... 2!3! (3.4) where 22 and 33 are the derivatives of phase with respect to frequency and are known as group delay, second-order dispersi on or group velocity dispersion (GVD), thirdorder dispersion (TOD), fourth-order dispersion (FOD) and so on. The variation of the group delay with frequency is 2 00000()()()()()... (3.5) From the above expression, it is clear that the 0 known as frequency-sweep rate linearly chirps the pulse and 0 generates a quadratic chirp on the pulse, etc. Figure 3-6 (a) and (b) illustrate a Gaussian pulse with a second-order a nd third order phase on it that generates a linear and quadratic chirp on it respectively. For pulses that undergo normal dispersion in materials, th e phase change is given by ()()matmatLnc Thus longer wavelength components in the pulse travel faster than the shorter wavelength components i.e r ed travels faster than blue introducing a positive chirp. A pulse compressor then becomes inevitable to compensate for this positive chirp. The management of spectral phase is thus of utmost importance in the design of a chirped pulse amplifier system. The next section deals w ith the broadening or the chirping of the pulses

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33 in order to effectively amplify them in an amp lifier and their recompression back to femtosecond time scales. Figure 3-6: A Gaussian pulse possessing (a) linear chirp 0 on it and (b) quadratic chirp 0 on it. 3.6 Pulse Stretching and Recompression As an ultrashort pulse propagates through the di fferent optical components in an amplifier cavity, the material dispersion accumulated must be compensated for in order to achieve shorter pulse durations. Also in order to reduce the risk of damaging the amplifier components and to keep the amount of accumulated non-linear phase [equation(3.2)] well below the threshold level, femtosecond pulses obtained from the Ti: sapphire oscillators must be temporally broadened before they can be injected into an amplifier. Also, in order to generate ultrashort pulses in a mode-locked Ti: sapphire oscillator it becomes n ecessary to compensate for the group velocity dispersion (GVD) such that all the spectral components of the pu lse can travel with the same group velocity around the oscillator cavity. Thus dispersive compone nts become an integral part of a chirped pulse amplifier system.

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34 Pulse stretching can simply be accomplished by material dispersion. As beams traverse through material they tend to broaden tempora lly owing to normal dispersion. But for most materials significant lengths are needed to achieve stretch factors of 104 which are required to amplify nanojoule level femtosecond pulses to the millijoule level. In addition, one cannot avoid beam distortions due to th e increased B-integral. Figure 3-7: Dispersive delay lines (a): A pair of anti-parallel gratings forms a pulse compressor (Treacy, 1969) and (b) Pulse stretcher form ed by anti-parallel gratings with a unit magnification telescope between th em by Martinez et al. (1984). In 1969 E. B. Treacy showed an extremely clever way of broadening pulses in time by using an anti-parallel grating pair (Figure 3-7(a)). Significant stre tch factors could be achieved with this arrangement, although as originally conceived the Treacy configuration was designed to produce negative group delay dispersion th at could compensate for positive material dispersion. The grating pair disperses the spectrum of the pulse, such that the blue edge of the spectrum travels faster than th e red edge through the grating arrangement. The first grating serves the purpose of dispersing the spectral content of the pulse an d hence the negative GVD, and the second grating recollimates the differe nt wavelengths. Martinez (1987) designed a compressor with dispersion opposite to that of the Treacys design (Figure 3-7(b)). A telescope

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35 placed between a pair of anti-parallel gratings modified the effective length between them yielding positive group velocity besides providi ng a high magnification yielding compression factors as high as 3000. The phase shift across the spectrum of the pul se as the beam propagates though the grating pair can be calculated as (Treacy, 1969) 0 02 ()1cossin() cos()gL d (3.6) where g L is the perpendicular distance between the gratings, is the incidence angle, is the angle between the incident and the diffracted beams, 0 is the central wavelength of the spectrum of the pulse and d is the grating constant. One can deri ve the group velocity dispersion (GVD) from the above equation 2 2 2 2 34/cos() 2 1singcL c d d (3.7) The expression for GVD for the Martinez stretcher (Figure 3-7 (b)) is the same as eq.(3.7) except with an opposite sign. The above expressi on is for a single pass through the grating pair. The beams are made to pass once again throu gh the arrangement to remove the wavelength dependent spatial walk-off, by reflec ting them off a retro-reflector or a pair of mirrors used in a roof geometry. Due to the ease of their cons truction the stretcher and the compressor are designed in such a way as to exactly reproduce the input pulse temporally. Martinez et al. (1984), showed that negative GVD can also be generated from a pair of prisms arranged in parallel. While the reflective grating geometry as in Figure 3-7 (b) is not an easily adjustable design the prism arrangement in Figure 3-8 provides both low loss as well as tunability from negative to posit ive values of GVD and hence is incorporated into the mode-

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36 locked Ti: sapphire oscillator to compensate for the varying pulse GVD which is alignment dependent. It is based on the idea that wavele ngth dependent phase delay caused by angular dispersion always yields negative GVD. Figure 3-8: Prism delay line. A pair of parallel pr isms generates negative GVD that can be varied by changing the distance between the prisms (Martinez, 1984; Fork, 1984). In the Figure 3-8, the optical path be tween the points A and B is cos cnL (3.8) The GVD term is given as 232 2222 dd dcd (3.9) Substituting for from equation (3.8) in equation (3.9) and calculating the GVD along the direction of the wave vector 0 yields 2 22 22ddnd nL ddd (3.10) The above expression yields a negative GVD regardless of the sign of the term dd The first prism, as in the case for the grating pair, ca uses the angular dispersi on and the second prism serves to recollimate the different wavelengths. The net dispersion is also easily adjustable by

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37 translating one of the prisms normal to the incide nt beam without altering the optical alignment. This allows for the introduction of material dispersion without cha nging the negative GVD. For amplified pulse duration < 35-40 fs, getting rid of the residual phase over a large spectral bandwidth becomes a formidable task due to the mismatch of the compressor i.e when it is not able to compensate completely the chirp introduced in the stretching and the amplification process. The all-refractive stretc her design by Martinez et al. (1987) introdu ces strong chromatic aberrations (a wavelength com ponent that diffracts from the fi rst grating at an angle of must arrive at the second grating at the same angl e) inevitably causing a mismatch between the dispersive delay lines in a CPA. A. Offner (U S Patents, 1971) came up with an all-reflective triplet combination that reduces the effects of ch romatic aberration. When used as a stretcher, this design makes it possible to recompress amplif ied pulse to near transform-limit. The Offner triplet consists of a single grating and the re fractive unit magnification lens telescope in the traditional stretcher design by Martinez is repla ced with two concentric spherical mirrors, one concave and the other convex. The use of sphe rical mirrors reduces th e aberrations to only spherical order, which in turn are further reduced owing to the fact that the ratio of their radii of curvature is two and they are of opposite signs. A lthough any deviation of the grating from the center of curvature (Gill and Simon, 1983) of the two mirrors, causes astigmatism leading to degradation in the temporal pulse profile. Cheriaux et al. used a slightly modified version of the Offner triplet in their stretcher design for their CPA system (1996). Although they had to place the grating out of the plane of curvature for stretching purposes, the spherical abe rrations as a result of this arrangement were calculated to be very small such that the tempor al shape of the pulses remained unchanged. Their calculations also indicated that the spherical ab errations were significantly less severe than a

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38 slight misalignment of the components in Offne rs triplet design. Furt her improvisation to the stretcher design by Cheriaux et al., (1996) M. B. Mason et al. (2000) came up with an allreflective doublet geometry (Figure 3-9) that lets the diffracti on grating lie at the aberration-free position in a stretcher configuration, enabling nearly perfect recompression of the broadened pulses. It has the capability of achieving large st retch factors with over-sized optics while totally eliminating any aberrations to the pulses. Figure 3-9: Schematic of the stretcher layout. Osci llator pulses of duration ~20 fs are stretched to ~ 200 ps without any chromatic aberrations. Figure 3-10: Spectrum measured from the osci llator and after propagation through the pulse stretcher. Spectral clipping on the red side of the spectrum is due to insufficient width of the optics in stretcher. The stretcher in our CPA system uses the Ma son doublet design to achieve stretch factors as high as 104. The pulses from the oscillat or are broadened to ~200-ps. Pulses are incident into the stretcher at an angle of 8.24 (close to Littrow angle). We use an 8-inch diameter concave

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39 mirror of radius of curvature of 120-cm to set a band-pass limit of ~100 nm on the spectrum of the seed pulses. A convex mirror of radius of cu rvature 101-cm is placed about 70-cm from the concave mirror. This arrangement produces an effective length ( Lg as in eq.(3.7)) of 121-cm. A schematic of the stretcher setup is given in Figure 3-9. Some spectral clipping (Figure 3-10) is observed in spite of the use of large optics in the stretcher. For ideal compensation the incident angles a nd the effective lengths for the stretcher and compressor must be close. But the incident angle for the compressor in our setup is 18 and the effective length is about 125 cm. This is to acc ount for the material dispersion and the higher order dispersion terms added to the total phase of the pulse due to the amplification process. 3.7 Ti: Sapphire based Laser Amplifier Amplifying femtosecond pulses in the milli-j oule range was once only possible using dyeamplifiers (Knox, 1988). Ti: sapphire based regenera tive amplifier was firs t introduced in 1991 by J. Squier, et al. following th e introduction of Ti: sapphire base d laser oscillators by Spence et al. (1991). These systems demonstrated a two-fold increase in the pulse energies. Also due to their wide tunability and low background as compar ed to the dye amplifiers, it was possible to generate more than 2 W of average power from T i: sapphire amplifiers at a repetition rate of 10 kHz (Squier et al., 1993). Due to the low pulse energies of the or der of micro-joules in high repetition rate pump lasers, low repetition rate sy stems soon grew more popul ar as pulse energies as high as a joule were available at a repetition rate of 10 Hz (Sullivan et al., 1991; Zhou et al., 1995). A few millijoules of amplified pulse energy were attainable at 1 kHz repetition rate (Vailliancourt et al., 1990; B ackus et al., 1995). When hi gh average power pump sources became available, pumping water-cooled Ti: sapphire crystal in the amplifier cavity generated huge thermal loading which then limited the pulse energies to a few mi cro-joules in high

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40 repetition rate CPA systems. As the pump power is increased to achieve large amplification factors, the residual heat in the Ti: sapphire crysta l gives rise to deleterious effects that influence pulse energies and mode quality, limiting the overall efficiency of the system. Specifically, the thermal gradient generated within the crystal due to the pump beam, consequently gives rise to a gradient in the index of refracti on of sapphire that causes the crysta l to act as a positive lens (De Franzo and Pazol, 1993; Moulton, 1986). Moulton (1986) and later Schulz and Henion ( 1991) observed that the thermal properties of sapphire improved upon cooling to 93 K. They noted that calculations of the thermo-optic aberrations indicated an increase in the out put power capabilities of a Ti: sapphire laser by 200 times at 77 K than at room temperature. Several gr oups have since devel oped high brightness, high repetition rate ultrafast laser systems which mitigate or circumvent these thermal effects. Backus et al. (2001) produced a millijoule level, femtosecond single-stage multi-pass chirped pulse amplifier at 7 kHz repetiti on rate utilizing cryogenically (LN2) cooled Ti:sapphire crystal. By cooling the crystal to temperatures near 77 K, a forty-fold increase in the thermal conductivity (Touloukain et al., 197 3; Holland, 1962) and five-fold reduction in the temperature dependent refractive index term dndTat low temperatures (Feldman et al., 1978) is obtained. Zhavoronkov and Korn (2004) demonstr ated single-stage regenerati ve Ti: sapphire amplification at multi-kilohertz repetition rate to powers of 6. 5 W at 20 kHz, using thermoelectric cooling to 210 K and a cavity design that takes into account the strong astigmatic thermal loading of the Ti: sapphire rod. Zhou, et al. (2005) have used two stages to avoid large th ermal loading present in single-stage systems to generate 7 W of aver age power at a repetiti on rate of 5 kHz.

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41 3.7.1 Process of Amplification Optical amplification occurs in a medium where the equilibrium configuration of the system comprises of its atoms or molecules in a state with highe r energy content as compared to the ground state of the system. This electronic exchange between the two energy states is achieved by an external pump source. Amplification occurs when an electromagnetic wave of appropriate frequency passes through such an inverted medium, resulting in a release of photons as the atoms drop back to a lower energy state, thereby extracting energy from the system. The gain of the amplifying medium is defi ned as the ratio of the output intensity to that of the input intensity. For a ga in curve or emission line shape 0g of a laser medium of length L the gain in energy through a single pass is expressed as 0 0o g LGe gn (3.11) where n is the population density in the uppe r energy level of the system and is the gain cross section. For successive passes through the amp lifying medium, the energy content in the seed pulse grows exponentially. This exponential incr ease in the gain with increasing paths through a laser medium with limited gain bandwidth leads to narrowing of the amp lified spectrum as the central portion of the sp ectrum experiences more gain as co mpared to the spectral components on the wings. Figure 3-11 (which is a schematic) illust rates an amplified pulse that undergoes gain narrowing in the amplifier upon multiple round trips within the laser cavity. To circumvent this, the amplifying medium should have a very br oad gain bandwidth, such that in spite of the gain narrowing effect, the amplified pulse bandwidth is still quite significant. Just as the amplified bandwidth depends on th e gain narrowing effect, the gain saturation effects in the amplifier limit the maximum energy of the amplified pulse. As the energy of the input pulse increases with each pass through the amplifying medium, the number of photons

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42 extracting energy from the medium becomes comp arable to the population density in the upper level of the host material. Consequentially the am plifiers gain falls lowering the energy of the amplified pulses after it r eaches the peak attainable gain in the cavity. For a homogeneously broadened medium, th e gain saturation is expressed as 01 s atg g EE (3.12) where, 0g is the small signal gain coefficient, E is the signal fluence and s atE is the fluence of the amplifying medium. This effect is less pronounced for materials with large saturation fluence such as the Ti: sapphire ( Esat = 0.9 J/cm2). While gain narrowing determines the amplified bandwidth and hence the pulse duration, gain saturation effect determ ines the pulse energy and these effects often dictate the type of amplifiers (either regenerative or multipass) one may need. Figure 3-11: Effect of gain na rrowing in amplifiers, the red cu rve is the fundamental laser spectrum and the blue curve is after five passes through the laser medium. 3.7.2 Types of Amplifiers Amplifiers can be classified into two broad categories: Multipass and Regenerative amplifier systems.

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43 In a multipass amplifier as in Figure 3-12 (the exact geometry may vary from system to system) (LeBlanc et al., 1993; Zhou et al., 1994; Backus et al., 1995; 2001; Lenzer et al., 1995) the seed pulse is made to pass through the gain medium just a few times and each time it follows a different path through the laser medium everytime. For media w ith a high gain co-efficient and where the pump power is not an issue, the multipass system is often the best scheme of amplification. One can get around th e effects of gain narrowing with just a few roundtrips within the multipass amplifier cavity while achieving a hi gh output power. This configuration limits the amount of gain that can be extracted from th e medium and hence is suitable only when the energy of the input pulse is high enough to begin with. Figure 3-12: Schematic representation of a multipass amplifier system. The seed pulses pass the gain medium several times but through a different path each time. On the other hand a regenerative amplifier allo ws one to achieve very high gain factors on the order of 105-106 (Wynne et al., 1994; Barty et al., 1996; Zhavoronkov et al., 2004; Ramanathan et al., 2006). Hence pulse energies of the order of a millijoule can be realized with input seed pulse energy as lo w as a few nanojoules, as is obtained from a mode-locked Ti: sapphire oscillator. Figure 3-13 is a schematic representation of the regenerative amplifier in our lab. One of the main advantages of a regenerati ve amplifier is its a laser cavity configuration which determines the spatial profile and the pointing of the amplified beam. It is capable of delivering highly energetic pulses with excelle nt beam quality. Although one of its major drawbacks is that due to the high gain per pass a nd since the number of pa sses is usually large to

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44 obtain high factors of am plification, the effect of gain narr owing restricts the bandwidth of the amplified pulses. In addition, amplified spontaneous emission can deplete the gain faster than the seed pulse. Thus systems that generate ultras hort pulses in the 1-10 mJ range often use a high gain preamplifier followed by one or two power amplification stages. Figure 3-13: A schematic representa tion of the regenerative amplifie r in our laboratory. The seed pulses are injected through a Faraday Isolat or (FI) and reflected off a Thin film Polarizer (TFP). The pockel cell (PC) and the /4 waveplate confine the seed pulses for ~250 ns (15-16 roundtri ps) in a cavity formed by mirrors M1 and M2. The amplified output is obtained thr ough the other exit in the FI. But with the advent of high average power pump lasers such as the diode pumped solid state lasers, using high thermal c onductivity crystals such as the T i: sapphire, it is now possible to generate millijoule level pulses at kHz repetition rates in a single amplifier stage (Backus et al., 2001; Zhavoronkov and Korn, 2004; Ramanathan et. al., 2006). The effects of gain narrowing and gain satura tion could be curbed to a certain extent by shaping the spectral amplitude of the seed pulses before injection into the amplifier cavity or during the amplification process. For positively chirped pulses in th e amplifier, the leading edge or the red edge of the pulse spec trum can experience a higher gain as compared to the blue or the trailing edge of the spectrum. In the past etalons were placed within the amp lifier cavity to compensate for the gain narrowing effects. Barty et al (Barty et al., 1996) used 3m thick air spaced etalon in their regenerative amplifier cav ity to obtain a ~15% increase in the amplified bandwidth thereby measuring 18 fs pulses on compre ssion. Specialized filters have been used in

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45 the amplifier cavity to generate spectrally depe ndent losses such that the maximum gain around 800-nm is reduced and distributed over the wings of the gain curve. Bagnoud and Salin (2000) used a 580m thick birefringent filter to increase the spectra of the amplified pulses from 30-nm to ~50-nm. More recently Takada et al (2006) de signed a multilayer dielectric film to introduce losses near the peak of the gain curve of Ti: sapphire, generati ng 12-fs pulses directly from a 1kHz repetition rate CPA system. But the usage of filters and etalons reduce the pulse energy as they rely on gain losses to increase the bandwidth of the amplified pulses. 3.8 Pulse Shaping Pulse shaping techniques wherein an input pulse with a slight lean in its spectral content towards the wings of the gain curve could offset the gain narrowing effect and lead to broader bandwidth with low pulse energy losses. Spatial light modulators (SLM) that serve as amplitude and or phase masks when placed in a zero-dispersion standard 4f stretcher, serves as a pulse shaping devise for ultrashort pulses (Omenetto et al., 2001; Efimov and Reitze, 1998; Efimov et al., 1995). The SLM placed in the Fourier plane betw een the two lenses of the stretcher setup as in Figure 3-7(b), allows one to write complex amp litude and phase masks that when applied to an ultrashort pulse can generate arbitrary amplitude and phase profile. Verluise et al (2000) demonstrated an ac ousto-optic programmable dispersive filter (AOPDF) or commonly known as the Dazzler as a pulse shaping device. Unlike the SLM pulse shapers, the dazzler is based on the acousto-optic interaction and does not n eed to be placed in a Fourier plane of a zero disper sion stretcher setting, making it a highly compact device. When placed between the stretcher and the amplifier, the dazzler can pre-compensate for gain narrowing and saturation effects in the amplifier. Pittman et al (2002) applied spectral and phase correction to the pre-amplified pulses using the dazzl er to generate an amplified bandwidth of 51

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46 nm. Figure 3-14 indicates an optimally shaped i nput pulse spectrum with the dazzler that generates the broadest bandwidth pulses from our amplifier. For more on the principles of operation of the dazzler system, consult Appendix B. Figure 3-14: Amplified pulse spectr um shows a FWHM of 33-nm. Inse t, blue curve is the shaped oscillator spectrum using an AOPDF, which yielded an amplified bandwidth of 33nm, obtained from the original os cillator spectrum (red curve). 3.9 Ultrashort Pulse Measurement Since electronic devices have response tim es that span a few nanoseconds to few picoseconds, they cannot be used to measure the temporal characteristics of an ultrashort pulse. In order to measure an ev ent as short as few femtoseconds, we n eed a probe that is either shorter or the same duration as the event itself. The only way then to measure a femtosecond pulse, is to use the pulse to measure itself! The most comm on method to measure ultrashort pulse has been the auto-correlation method devised by Maier et al (1966). The ultrashort pulse to be measured is split into two using a 50-50-beam splitter. Th e optical set up is similar to the Michelson Interferometer where one of the beams traverses a fixed path length through one of the arms of the interferometer and is known as the reference beam, the probe beam on the other hand passes through a delay stage (Figure 3-15). The two beams are then focused and spatially overlapped

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47 on to a nonlinear crystal that generates a sec ond harmonic generation (SHG) signal. The SHG signal which is twice the frequenc y of the fundamental beams is th en measured as a function of the delay time between the two pulses. The field enve lope of the second harmonic signal is then the product of the elect ric fields of the two pulses ,SHGEtEtEt (3.13) If the two beams have an intensity distribution as ) ( t I and) ( t I, the auto-correlation of the two pulses is ()()()SHG acItItIt I ItItdt (3.14) The measured auto-correlation signal()acI then gives us an estimate of the duration of the measured ultrashort pulse. It is evident fr om the above equation th at the auto-correlation technique cannot uniquely determine the temporal phase structure of th e pulse. For a given intensity profile as measured by the auto-c orrelation technique, one can construct several different pulses with different phase structures (Chung and Weiner, 2001). To be able to determine the temporal phase of the pulse, one needs to know the frequency domain phase of the pulse along with its magnit ude. But as the auto-correlation yields only the Fourier-transform magnitude, it re presents a classic case of th e unsolvable 1-D phase retrieval problem (Akutowicz, 1956; 1957).

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48 Figure 3-15: Experimental auto-correlator set up. The pulse to be measured is split into two; the pulses that are delayed with respect to each other are focused on a SHG crystal and measured in a detector. Figure 3-16: FROG: (a) experiment al spectrogram, (b) Retrieved spectrogram with a Frog error of 0.002, (c) 43 fs pulsewidth and (d) spectrum from the retrieved Frog trace. In the early 1990s, Trebino and Kane (1993) resorted to make the phase retrieval problem a 2-dimensional one wherein it could yield accurate information about the phase of the pulse as well (Stark, 1987). This technique known as th e Frequency Resolved Optical Gating (FROG), spectrally resolved the SHG signal in an auto -correlator and the spectrogram obtained then uniquely determines the temporal pulse widt h and the corresponding phase by using a phase

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49 retrieval algorithm. The spectrogram is a 2-dimensional representation of the pulse as a function of frequency and time delay S For a more detailed explanati on of this technique refer to appendix A at the end of this dissertation. 2 00,()()exp() SEEid (3.15) Figure 3-16 (a) and (b) is the experimental and retrieved FROG traces respectively for a compressed pulse from the CPA system in our laboratory and (c) and (d) is the retrieved temporal and spectral profile with the phase structure in the resp ective domains for a 43-fs pulse. 3.10 Chirped Pulse Amplifier system The single stage chirped pulse amp lifier system in our laboratory (Figure 3-17) employs a Coherent Corona laser, capable of generating 12-mJ pulses at an average power of 80 W at a repetition rate that can be varied from 1-25 kHz to pump a 5mm 6 mm Ti: sapphire crystal. 2030 fs pulses from a home-built Ti: sapphire oscillator is st retched to ~200 ps be fore injection into the amplifier. The crystal in the regenerative am plifier is placed in a cryogenic vacuum chamber and cooled to 87 K by the use of liquid nitrogen. Two Faraday isolators placed in the beamline prevent the backtracking of the amplified pulses into the oscill ator. Two spherical mirrors of radii of curvature 1 and 2m (high damage thre shold custom coating fr om Rocky Mountain Inc.) form the regenerative amplifier cavity. The seed pulses are introduced into the amplifier via reflection off a thin film polarizer (Alpine Rese arch Optics). A sol-gel coated Pockels cell (KD*P) and a quarter waveplate combination help reta in the amplified pulses for ~240-ns (15-16 roundtrips) within the amplifier cavity. The Pockels cell helps switc h the amplified pulses out of the amplifier. The crystal is double pumped with roughly a total of 60 W of 532-nm light from both sides. An average amplifie d power of 6 W (1.2 mJ pulse energy) at 55 W of pump power

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50 and 9 W (1.8 mJ pulse energy) at 80 W of pump power at 5 kHz repetition rate is obtained. The pulses are then magnified by an 8f -telescope system before compre ssion to minimize the risk of damage to the compressor gratings. The energy of the compressed pulses drops to 0.7 mJ and 1.3 mJ at 55 W and 80 W of pump po wer respectively due to an efficiency of about 70%, of the compressor gratings. The amplifier exhibits a variety of temperatur e related effects such as thermal lensing, thermal birefringence, and stress. Thermal manageme nt within the amplifier cavity is of utmost importance in developing a high power, high repe tition rate CPA. The next chapter is hence devoted to the understanding of th ese issues and some techniques adopted to develop a state-ofthe-art CPA system. Figure 3-17: Schematic re presentation of CPA. 3.11 Summary This chapter was devoted to the discussion of the design and constr uction of the various components that make a chirped pulse amplifier sy stem in our laboratory. Since the system is a single-stage amplifier, the Ti: sapphire crys tal is pumped with a high average power pump

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51 source that gives rise to deleterious thermal issues. The following chapter characterizes these temperature related effects and its effect on the performance of the amplifier.

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52 CHAPTER 4 THERMAL EFFECTS IN HIGH POWER LASER AMPLIFIER As discussed briefly in the previous chapter, temperature related effects in the regenerative amplifier cavity causes detrimental effects to its performance. This chapter is dedicated to discussing these effects in detail and the steps unde rtaken to mitigate them to increase the overall efficiency of the system. 4.1 Introduction Temperature K r ad i u s m mlength mmTemperature K r ad i u s m mlength mm Figure 4-1: Simulation of the resultant temp erature gradient in an end pumped Ti Al2O3 laser rod at room temperature when pumped by 70 W of 532 nm laser light. Courtesy Jinho Lee. The output of a Ti sapphire (Ti: Al2O3) laser when pumped by 80 W of frequencydoubled Nd: YAG laser of wavelength 532 nm pumpgives rise to a laser output peaked at 800 nm sinlag. Ti: sapphire has a wide absorption band in the green spectral regi on with significant absorption at 532-nm (figure2-2) due to which it absorbs 85-90% of the incident pump light (the absolute absorption is depende nt on the doping levels of Ti3+ in sapphire). The quantum defect or the Stokes shift which is the energy differe nce between the pump photon and the lasing photon sinlagpump is deposited as heat in the crystal. Th e radial intensity dependence of the beam

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53 is translated into a spatial temp erature gradient along the transver se axes in the crystal. This results in a hot area at the cente r of the crystal as compared to its edges. As an example of the severity of this effect, Figure 4-1 is a numerical simulation of the temperature rise within a crystal whose boundary is maintain ed at room temperature, when a Gaussian beam of 532-nm source at an average power of 70 W is incident on it. For the sa ke of simplicity a 6-mm long and 2.5-mm radius cylindrically symmetric crystal was assumed for the simulation which was performed using a Finite Element Analysis package by Comsol Multiphysics or commonly referred to as Femlab. The spot size of the pump beam on the crystal was 500m and the absorption parameter absL was 2.2. As Figure 4-1 indicates the center of the crystal is about 150 K above room temperature. This spatial variat ion in the temperature along the two transverse radial axes alters the refractiv e index leasing to the following th ermal effects (Koechner, 1976) Figure 4-2: Refractive index change s to a crystal incident with 80 W of pump beam. The thermal gradient causes optical path deform ation for a beam traveling along the z-axis. 1. Thermo-optic effect: The temperature gradient in the crystal changes the refractive index of the laser material along the axes perpendicular to the propagation axis'' z as in Figure 4-2. A laser beam trav ersing through the crystal e xperiences a change in the optical path length (OPD) due to th e position dependent refractive index,nrz.

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54 TT lldn OPDndzTdz dT (4.1) where 00,,TTrzTrz, Tn is the temperature dependence of refractive index. 2. Thermo-elastic deformations (Thermal Expansion): The heat generated by the absorption expands and leads to radially curv ed end-faces because of the heat generated temperature gradients. The former effect does not affect the focal characteristics of the crystal, but the thermal gradients generate increased focal power (Figure 4-3). This endface curvature causes a change in the optical path length of a transmitting laser beam. e lOPDTdz (4.2) where is the thermal expansion co-efficient. Figure 4-3: Radially curved end-faces due to in crease in temperature caused due to absorption of incident pump beam. 3. Elastooptic effect: The temperature distribution Tralso causes the center of the crystal to expand more rapidly as compared to the cooler outer edges. This generates mechanical stress in laser rod as the center is constrained by the edges of the crystal. The optical path length changes induced due to this effect is given as elel lOPDndz (4.3) where eln is the photo-elastic coeffi cients of the crystal. Thus, the total optical path difference can be calculated as

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55 TeelOPDOPDOPDOPD (4.4) These various thermal effects coupled with the fact that thermal constants of sapphire ,,dndTare functions of temperature, induce modal distortions in the lasing beam, which restrict the output power from the amplifier cavity beside s distorting the shape of the beam. Table 4-1 gives a quantitative comparison of th ese thermal effects in sapphire indicating that the elasto-optic effects can be safely neglected while calculating the net thermal effects in the Ti: Al2O3 crystal (Lawrence, 2003). The comparison made in Table 4-1assumes that the heat incident on the crystal is absorbed uniformly over the entire length of the crystal whose radius R is much larger than the beam diameter Considering only radial he at flow between the points 0rtor the temperature differences where there is no appreciable change in the thermal constants of the crystal is thus calculated as 02a rrP TTT h (4.5) where, aP is the absorbed power by a crystal of length h, is the thermal conductivity. Integrating this quantity over the entire length of the crystal yields 2aP Tdz (4.6) The relative strengths of the various thermal effects can now be calculated and compared as equation (4.6) indicates that aPTdz is a constant for any material for small changes in temperature. In order to achieve beam quality close to th e diffraction limit and higher amplified pulse energies, these optical distortions in the cavity mu st be eliminated as much as possible. In the

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56 past, numerous methods have been proposed that can lower these distorti ons (Schulz and Henion, 1991), including: 1. Pumping the crystal at lower powers such th at the available heat limits the thermal distortions in the system. 2. Using a slab geometry for the crystal rather than a cylindrical rod design in the amplifier (Koechner, 1976) reduces the heat flow to a one-dimensional problem, which then simplifies the removal of heat. 3. Reducing the quantum defect (which may be defined as sinlagpump or sinlagpump by pumping the crystal with a highe r wavelength source (Moulton, 1986). Table 4-1: Quantitative estimate of thermal effects in sapphire. Thermo-optic effect 1 Thermal expansion 0.8 Elasto-optic effect 0.2 Note Adapted from Lawrence (2003) For several reasons, the above mentioned m easures cannot be easily implemented when designing high average power system s. Pumping the crystal at lower powers reduces the output power of the amplifier. Although a slab geometry produces lower optical distortions, is it found (Miyake et al., 1990) that the cylin drical rod geometry for Ti: Al2O3 produces higher powers when cooled to liquid nitrogen temp erature. Besides a slab geometry can also give rise to various parasitic modes that can lower the useful stored energy in the crystal (K oechner, 1976). Special coatings to suppress these parasitic modes and to enhance the thermal coupling to the cooling unit can add to the cost and the design complexities of slabs. In addition slab geometries are not easily implementable in regenerative amplifier systems. The heat generated in the crystal is given by the product of the amount of heat absorbed by the crystal and the quantum defectaHP Pumping Ti: Al2O3 at 600 nm instead of 500 nm

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57 reduces the quantum defect by a f actor of two (Schulz, 1991). In or der then, to achieve the same absorbed power at 600 nm, the concentration of Ti3+ ions has to be increased in the crystal as, the absorption coefficient of Ti: Al2O3 is lower for 600 nm as compared to 500 nm (figure 2-2) (Moulton, 1986). Thus high quality crystals must be used to limit losses due to the absorption of the crystal at the lasing wavele ngth. Most significantl y the availability of high-powered pump sources at 600-nm restricts operation at this regime. This prompts a more detailed study and analysis of the two most damaging thermal effects in Ti: Al2O3 to gain a better understanding of the problem so as to be able to suggest remedial measures. 4.2 Theoretical Background As explained above, refractive index changes of Ti: sapphire with incident pump beam leads to optical distortions. Th ese changes can be separated into temperatureand stressdependent changes 0()()()Tnrnnrnr (4.7) where nris the radial variati on of refractive index; 0n is the index at the center of the laser rod and Tnrand nr are the temperature and stress dependent coefficients of refractive index respectively. Ignoring the effects of the stre ss-dependent changes (Lawrence, 2003) as per explanation above, nrcan be expressed as 0()()()(,,)Tdndn nrTrTrTxyz dTdT (4.8) This results in an OPD change as given in equation (4.1).

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58 As sapphire exhibits peak absorp tion at 532-nm, there usually is some physical distortion of the flatness of the rod ends that resu lt in a change of the optical pa th length of a laser beam that traverses through it. This de viation can be calculated as 00()() LrLTr (4.9) where, 0 is the coefficient of expansion and 0L is the original length of the laser crystal. This results in an OPD change as per equation (4.2) Thus the transverse optical path difference for propagation along the z -direction can be written in general as 0(,)([(,,)]1)LOPDxynTxyzdz (4.10) Expanding n and dzin powers of T using equation (4.8) and (4.9) equation (4.10) becomes 00 0 2 0000000 000(,)(1)() (1)([])L LLLdn OPDxynTdzTdz dT dn TdznTdzTdznOT dT (4.11) Neglecting the constant term and terms in2T the integrated optical path length is then given by 0 0(,)(1)(,,)L odn OPDxynTxyzdz dT (4.12) Analytical solutions to the above equation for cylindrically symme tric crystal geometry can be obtained by solving the steady-state heat di ffusion equation with the appropriate boundary conditions. (,,)(,,)TxyzQxyz (4.13)

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59 M. E. Innocenzi et al. (1990) solved the heat diffusion equation for an axially heated cylinder with a thermally conductive boundary at the peri phery. For an incident pump beam that is Gaussian in nature, the steady state te mperature difference is calculated as 222 000 11 222exp()22 (,)ln 4absin ppPzrrr TrzEE r (4.14) where, inP is the incident pump power, abs is the absorption coefficient that results in the heating, p is 21e radius of the Gaussian pump beam, 0ris the radius and is the thermal conductivity of the laser rod. The expression for ,Trzcan be obtained by neglecting 22 102pEr as its small for most practical cases and expanding 22 12pEr (Abramawitz and Stegun, 1965) as a power series and retaining only the terms quadratic in r. Plugging it into equation (4.1) (their calculations do not include the thermal expansion of the crystal) yields the resultant phase change or the transmitting laser beam of wavelength through the crystal 2 22 () 2 1exp() 2in abs pOPDr PdndT lr (4.15) comparing the above equation to the phase changes that occur in a lens like medium with a quadratic variation in its re fractive index (Kogelnik, 1965) 22 r f (4.16) where, f is the effective focal length. Comparing equation (4.15) with equation (4.16) the effective focal length for the laser rod can be written as 21 1exp()p th inabsf PdndTl (4.17)

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60 This effect known as thermal lensing because it alters the modal properties of a beam that transmits through it, just like a static lens but unlik e a static lens, its dynamic in nature due to its implicit dependence on pump power. In an amplif ier cavity formed by two spherical end mirrors, this effect can destabilize the cavity as the modal properties of the lasing beam starts to exhibit the same dynamism as the thermal lens in the crystal for various pump power levels. A positive value of dndT for a material generates a convergi ng thermal lens and a negative value generates a diverging lens. A lthough the above equation is calcula ted for a cylindrical crystal pumped with a continuous laser source, we can nevertheless use it to obtain an estimate of the focal length for a Brewster cut Ti sapphire crys tal pumped with a pulsed laser source (Coherent, Corona). The thermal constants for sapphire at room temperature are: 20.33Wcm (Holland, 1962), 51.2810dndT K(Feldman et al., 1978). For a crys tal with its boundaries at room temperature and pumped with 60W of green light with a spot of 500m on the crystal and a constant pump absorption-length product, 2.2absL yields a thermal lens of focal length 4th f cm To increase the thermal lens focal length or conversely to decrease the thermal lens power (defined as 1th f ), the pump power can be decreased or alternatively the pump spot size on the crystal can be increased. Recalculating the focal length for a pump spot of radius 1-mm and a decreased incident pump power of 30 W, increases the focal length to ~ 30-cm. Although reducing the pump power increasesth f but this necessarily decreases the amplified output power. Since a high overlap integral between the pump spot and the lasing beam spot sizes on the crystal is required for efficient energy extr action from the Ti: sapphire in the amplifier. This integral is a maximum when the pump beam is smaller or equa l to the amplified beam. Increasing the spot

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61 size p of the pumping beam may alter the overlap integral, again br inging about a reduction in the extracted energy from the amplifier. Thus to be able to achieve high average am plified power from a re generative Ti sapphire amplifier cavity the thermal lens effect needs to be either eliminated (ideal solution) or at least minimized (practical solution). 4.3 Methods to Reduce Thermal Effects In the past, researchers have used various met hods to reduce thermal effects in their laser systems. A quick review through some of these m easures brings about a d eeper understanding of this issue. The most intuitive method of eliminating or reducing thermal effect s in a laser cavity would be to introduce a diverging lens in the beam path to comp ensate for the induced positive or converging thermal lens generated by the crysta l. Due to the variable nature and broad range of the thermal lens, a fixed focal length passive optical element cannot compensate for a range of incident pump powers. Also such an optical element will change the beam diameter on the crystal with each pass, increasing moda l distortions in the laser beam. Salin et al. (1998) introduced the concept of thermal eigenmode amplifiers. A thermallyloaded multipass amplifier is equivalent to a series of lenses separated by a distance L that corresponds to the beam round trip length inside the cavity. An unfolded resonator with two spherically curved mirrors with radii of curvature2therm f with the crystal at the center is equivalent to a series of lenses of focal length therm f separated by a distance L. An eigenmode of this resonator, calculated from the paraxial Gaussian beam propagati on relations, reproduces itself for each round trip, which for a multipass is equivalent to re-imaging the beam onto itself after each pass. If the input beam has the same si ze and characteristics of the eigenmode of the

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62 resonator then the amplified output beam characteristics are simila r to those of the input beam producing diffraction limited amplified pulses. This is suitable when the incident pump power is maintained at a constant value, as any change in this parameter causes a change in the focal length thus changing L. This is also based on the assumption that the host medium is cylindrical, such that the thermal lens is mostly spherical ove r the entire pump beam diameter and the length between the successive passes is a constant. A Brewster cut rod (Figure 4-4) instead of a cylindrical laser rod generates an aspherical thermal lens and it then becomes difficult to calculate the thermal eigenmode accurately. MacD onald et al. (2000) have reduced the thermal lensing effect in diode-pumped Nd: YAG laser wi th multiple composite rods. These rods had undoped end caps to remove the part of thermal lens formed due to the bending of the end faces of the laser rod. Zhavoronkov and Korn (2004) thermoelectrically cooled a 3-cm Ti sapphire crystal in a three-mirror astigmatic regenerative amplifier cavity to 210 K that took into account the huge positive thermal loading of the sapphire rod. Their single-stage, multi-kilohertz laser was able to generate 6.5 W of average amplified power at 20 kHz repetition rate. While high output powers were obtained, the thermal and th ermo-optical constants did not differ significantly from their room temperature values, and it is likely that higher order spatial aberrations were present in the output beam. Figure 4-4: Brewster cu t Ti sapphire crystal.

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63 Zhou X et al. (2005) used two multipass amplifi cation stages after a regenerative amplifier cavity in order to avoid large thermal loading present in single-stage systems. They were able to generate 7W of average amplified output at a re petition rate of 5 kHz. Although they were able to solve the thermal-loading problem in their CPA system, managing multiple amplifier stages can get cumbersome. An often used technique to reduce therma l lensing in high pow er continuous wave Nd:YAG laser systems (Graf et al., 2001; Wyss et al., 2002; Mueller et al., 2002) can be incorporated to compensate for thermal effects in single-stage high repetition rate systems. The idea is to use self-compensating (adaptive) me thods to thermo-optically compensate for the thermal lens effects that change with changing power. This technique essentially uses adaptive optical devices such as self-adjusting lenses within the laser cavity that can compensate for every single pass of the lasing beam through the cavity. A material with a nega tive thermal dispersion coefficient is placed in the cavity that ge nerates a power dependen t thermal lens that compensates for the positive dndT induced by the temperature gradient in the laser crystal. Th. Graf et al. (2001) were the fi rst to successfully use an adaptive negative thermal lens to compensate for the positive thermal lens in a transversely diode-pumped Nd: YAG laser rod. The compensating element must absorb a small fractio n of the incident laser power and hence should posses a strong thermal dispersion dndT to effectively compensate for the positive dndT. This technique has also been extended to correct th ermally induced optical path length changes induced by absorption of transmissive optical co mponents such as electro-optic modulators and Faraday isolators, of gravitational wave interferometer (Mueller et al., 2002). We attempted to extend the concept of thermo-optical compensation to our regenerative amplifier. Curing gels or index matching fluids such as the OCF-446 (Nye Opticals) possesses

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64 the combined advantages of solid material s (no convection) with a strong negative dndT. With a negative thermal disper sion value as high as 3.5 10-4 C-1 and a large expansion co-efficient of 8 10-4 it seems like an ideal candidate as a compensating material with the added advantage of low absorption at the lasing wavelength of 800-nm (< 2 10-4 %/ m). Although numerical simulations by Jinho Lee seem to suggest that the thermo-op tical compensation method should work for an OCF thickness of ~ 3mm for a pump power of 80 W, but preliminary experiments have revealed the high intrac avity peak powers in the regene rative amplifier cavity causes damage to the cell containing OCF 446. It is not clear from these experiments if the damage occurred to the cell holding the OCF or if the OCF itself burns due to the absorption at the lasing wavelength. Redesigning the cavity taking into c onsideration the OCF or changing the location of the OCF could potentially solv e this problem but has not yet b een experimentally verified and could possibly be one of the avenue s that could further be explored to increase the efficiency of the present amplifier system. Meanwhile the most efficient and convenient means of reducing ther mal effects in Ti sapphire laser crystal in a chir ped pulse amplifier is by cooli ng it to cryogenic temperatures (liquid nitrogen temperature (77 K) or below) (Moulton, 1986; Schulz and Henion, 1991). Sapphire exhibits excellent therma l properties on cooling to low temperatures. The next section delves on how the thermal properties of sapphire can be exploited to reduce the temperature related effects. 4.4 Liquid Nitrogen Cooled Ti Al2O3 Laser Amplifier P.F. Moulton (1986) was the first to demonstr ate the advantages of cooling the sapphire laser crystal to liquid nitrogen temperature in a qua si cw laser. He reported an increase in the output power of the laser from 45 mW to 150 mW when the crystal was cooled to 80 K. He

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65 attributed this effect to an increase in the thermal conduc tivity of sapphire with decreasing temperature. This idea was th en extended by Schulz and Henion (1991) where they investigated the effects of thermal loading on a single-transv erse-mode of Ti: sapphire laser cooled to 93 K and reported a reduction in the ther mo-optical refractive index cha nges by more than two orders of magnitude. They realized an output power from the Ti: sapphire laser that was 200 times larger at 77 K than at room temperature! Table 4-2: Thermal propertie s of sapphire at 300 and 77 K. Property At 300 K At 77 K Thermal conductivity 0.33 W cm-1 K-1 10 W cm-1 K-1 Thermal dispersion dn/dT 1.28 10-5 K-1 0.19 10-5 K-1 Thermal expansion coefficient 5.0 10-6 K-1 0.34 10-6 K-1 Note: Adapted from Schulz and Henion (1991). Table 4-2 compares the thermal properties of Ti sapphire at room temperature and liquid nitrogen temperature. Figure 4-5 (a) and (b) show the variation of thermal conductivity and dndT with temperature, the key parameters in minimizing thermal distortions. The thermal lens focal length as given by equation (4.17) is directly proportional to the ratio dndT. Figure 4-5 indicates that as the temperature is decreased, the thermal conductivity rises steeply, and the coefficient of refractive inde x with temperature decreases thereby making the ratio of thermal conductivity to dndTincrease with increasing temperature. This leads to a decreasing thermal power (or an in creasing thermal lens focal length). Backus et al. (2001) were able to generate 13 W of amplif ied output power at 7 kHz repetition rate from a cryogenically cooled single-stage multipass am plifier with good beam quality (measured M2 of 1.2 and 1.36 along the X and Y axis). We can now calculate the effective thermal lens focal length [equation (4.17)] of a Ti sapphire crystal at LN2 temperature using the constants in Table 4-2 for an input pump power of

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66 60 W and a spot size of 500m as mentioned above. On doing so, an th f of ~8m is obtained! Thus we find that there is a tremendous decrease in the thermal lens power of about two orders of magnitude on cooling the crystal to 77 K! 50100150200250300350400450 0 200 400 600 800 1000 1200 1400 1600 50100150200250300350400450500 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 (b) Conductivity W/m K oTemeperature o K dn/dT 10-6 oKTemperature oK(a) Figure 4-5: Dependence of (a) Thermal dispersion (dn/dT) (Feldman et al.,1978) and (b) Thermal conductivity (Holland, 1962) of Ti sapphire with temperature. In order to design an effective regenerative amplifier cavity we accurately need to know the positive thermal lens generated by the crysta l with changing pump po wer. We have made a very detailed study of this, which is elaborated in the remaining sec tions of this chapter. The next section deals with the construc tion of a regenerative chirped pulse amplifier since all the experiments and numerical calculation on thermal analysis were performed on this high average power CPA system. 4.5 Construction of a Rege nerative Amplifier Cavity The entire below mentioned discussion has been based on the current amplifier system in our CPA and this section delves into the details of the construction of this amplifier.

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67 A 5-mm diameter and 6-mm long Ti sapphire crystal is the host material in our regenerative amplifier cavity. The crystal is cooled to 87 K in a vacuum chamber thats placed underneath a liquid nitrogen dewar. The vacu um chamber was designed after extensive consultations with our in -house mechanical engineer Luke Williams. The LN2 dewar is separated from the crystal by a thin copper wall of thickness ~100m. The crystal is held in a copper holder, and a 127m Indium foil is sandwiched between the crystal and the thin copper wall for better thermal contact between with the LN2 in the dewar. A thermocouple placed along one of the edges of the crystal senses the temperature of the crystal at all times. The temperature sensor has an in-built relay circuit to automatically faci litate the turning off of the pump laser when the crystal temperature exceeds 185 K. Figure 4-6 is a CAD drawing of the vacuum chamberdewar assembly in our CPA system. As can be seen in the Figure 4-6 (a), the vacuum can has 2 extended arms on either side with brewster wind ows on it as entrance and exit for both the pump beam and the amplified IR beam. A view-port right in front of the crystal allows one to position the pump beams on the crystal. Figure 4-6 (b) is the copper hol der in which the Ti sapphire crystal is placed. This particular assembly generates almost 0.6 C rise in temperature per Watt rise in the pump power (Figure 4-7). At zero watts of pump power th e crystal temperature as measured by the thermocouple is 90 K. With almost 65 W of pump power at 5 kHz repetition rate, the crystal temperature rises to about 127 K when the lasing action within the regenerative amplifier cavity is inhibited and 108 K when the cavity is in the lasing mode. The higher temperature rise when the cavity is not lasing is due to the absorpti on of fluorescence by the thermocouple which is considerably decreased during th e lasing action. This allows for continuous operation of the regenerative amplifier to repetition rates as high as 12 kHz. The amplifie d pulse energy drops to

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68 0.3 mJ at 12 kHz repetition rate with consider able disintegration of the beam shape of the amplified pulses (Figure 4-15). Figure 4-6: CAD drawings depicting (a) Vacuum dewar assemb ly and (b) copper crystal holder. Drawings by Luke Williams. 010203040506070 85 90 95 100 105 110 115 120 125 130 cavity not lasing cavity lasingTemperature oKPump Power (W) Lasing Threshold Figure 4-7: Boundary temperature rise as pump power is increased when lasing action is inhibited (red points) and when the cavity is lasing (blue points). The lines are guides to the eye. 4.6 Measurement of Thermal Lens A laser beam transmitted through a material th at acts as a thermal lens undergoes modal changes in its divergence angle relative to the input beam. By measuring these changes, one can

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69 estimate the thermal lens power of the material. The design of an optimu m regenerative amplifier cavity necessitates the need to characterize accurately the thermal lens in the Ti sapphire crystal. To be able to measure the thermal lens in our laboratory we used a He-Ne laser to probe the Ti: sapphire crystal as a f unction of pump power. The He-Ne laser was mode matched to the pump beam spot on the crystal. The changes in the divergence angl e of the beam after traversing the crystal were determined for a series of pump powers by measurin g the position dependent spot sizes with a CCD camera. By comparison w ith the He-Ne beam waist position at zero pump power, the measured waist positions for the no n-zero pump powers enabled us to calculate the thermal lens focal length within the thin-lens approximation using the ABCD matrix formulation. In Figure 4-8 is plotted the measured thermal le ns power for the two tr ansverse axes as a function of power. For a pump power of about 50-55 W the measured thermal lens focal length is about 1.1 m along the vertical axis on the crys tal and 0.2-0.3 m along the horizontal axis. The asymmetry in the thermal lens is immediately evident as th e thermal lens power along the horizontal axis rises much sharply as compared to the vertical axis. An effective amplifier is one where the cavity maintains stability over a wide range of thermal lens power. The ABCD formalism was used in which the crystal was treated as a thin spherical lens. The cavity stabil ity or the g-parameter was calcu lated for various combinations and permutations of the radii of curvature of the two end mirrors and the distance between them. The most suitable cavity was one that exhibited stability (-1 g -1) for a large range of thermal lens, where g is the stability factor. This essent ially translates as minimum changes to the spot size of the amplified beam on the crystal. The re generative amplifier cavity currently being used is 2-m long, comprised of two spherical mirro rs of radii of curv ature 1-m and 2-m. Figure 4-9 is

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70 a plot of the g-parameter calculated for different values of thermal lens power using the ABCD matrix formulation. 15202530354045505560 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 X-Axis Y-AxisThermal Lens Power m-1Pump Power W Figure 4-8: Measured thermal le ns and thermal power for the tw o transverse axes; the boundary temperature was measured to be 87 K at zero pump power and 103 K at 55 W of pump power. 012345 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 Stability parameterThermal Lens focal length (m) Figure 4-9: Cavity stability parameter as a function of measured thermal lens. From the above plot, its clear that the cavity is most stable for a thermal lens focal length values from 0.6-m to 5-m. Also the calculated laser beam spot size ( 1e radius) on the crystal shows a variation of about 15% from its minimum value of 343m at about 1-m thermal lens focal length. The imaging system of the pump be am on the crystal let us vary the pump spot

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71 from a 1eradius of 200m to 800m. This ensures a good overlap of the pump beam with the varying mode sizes of the amplified beam on the crystal, for a great ra nge of pump powers. In order to validate the thin lens approximation in calculating the thermal lens of the crystal as a function of pump pow er, we invoke the simple lens ma kers formula for the effective focal length for both thin and thick lenses. 0 12 0 0 1212111 111thinlens thin lens thicklens thicklensPnn fRR nnd Pnn fRRnRR (4.18) where lensnand 0nare the refractive index of the lens medium and the medium in which the lens is placed. 1 R and 2 R are the radii of curvature of the two cu rved surfaces of the lens of thickness d. The difference in the thermal lens power resulting from the thin lens and the thick lens treatment of the sapphire crystal is given as 0 121lensnnd fRR (4.19) For a Ti: sapphire of thickness 6dmm in vacuum and with refractive index, lensn=1.76 and assuming 10.5 R m and 21 R m the change in the focal length is 3.4 10-3. Due to the insignificant difference between th e two treatments of the crystal thermal lens, it suffices to use just the thin lens approximation in all the calculations using the measured modal changes with pump power. 4.7 Calculation of Thermal Lens Although cooling to 77 K brings about a drastic reduction in the thermal lens power of the crystal, it is in practice difficult to ac hieve boundary temperatures close to the LN2 temperature when pumping with high laser powers. For a 6mm thick Brewster-cut sa pphire crystal the thin

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72 lens approximation does not accurately describe the thermal lens. Hence to validate the use of the thin lens approximation, we compared the measured thermal lens power with that obtained from a Finite Element Analysis (FEA). An accurate know ledge of the temperature gradient inside the crystal determines the thermal lens accurately. The temperature gradient is obtained by solving the heat diffusion equation (4.13) with the appropriate boundary conditions. For cylindrical ly symmetric geomet ries, pumped with continuous sources, analytical solu tions to the heat equa tion are intuitive (Que tschke et al., 2006). Analytical solutions have also been obtained for crystals pumped with pulsed sources (Lausten and Balling, 2003), however the crystal geometry was again a cylindrically symmetric one. For more complicated geometries such as Brewster cut crystals (Figure 4-4) numerical methods are needed to calculate the temperature gradient inside the crystal. A dditionally, the physical quantities in these equations ,,dndTare temperature and therefore spatially dependent, and not analytically tractable. Hence we use a finite element analysis package (Comsol Multi-Physics) to model the pump pulse-induced temperature changes and numerically integrate equation (4.12) to compute OPD Calculations by Jinho Lee show that fo r a Brewster-cut geometry the source term on the RHS of the 3-D heat equation (4.13) takes the form 222 2222 (,,)cosexp(tan)cos 2coscosabs iriabs rrPLx Qxyzyxz (4.20) where Pis the incident laser power, abs is the absorption coefficient for the pump, is the pump waist ( 1ein field), L is the crystal length, and ,ir are the incident and refracted angles in the crystal, respectivel y. Even though the pump source is pulsed the steady state equation perfectly describes the s ituation as the thermal relaxation cons tant for Ti: sapphire laser rod is

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73 measured to be ~0.5-secs (Ito et al., 2002) which is much longer than the repetition rate of the laser. Therefore, for pump repetition rates of > 1 kHz, we can safely neglect the time dependence of the thermal gradient. Figure 4-10: Computed temperat ure profile in a 6 mm long, 5 mm diameter Brewster-cut Ti: sapphire crystal single end-pumped by 50 W in a 0.4 mm pump spot waist radius for and absorption corresponding to absL = 2.2 and a boundary temperature of 103 K. The geometry (shown in Figure 4-10) consists of a 3D-tilted cylinder corresponding to our Brewster cut crystal. Temperature dependent th ermo-optical and mechanical constants were obtained from Touloukain et al. (1973) and Ho lland (1962) were fitted over 50 300 K. The absorption at the Ti: sapphire em ission wavelength was not include d as this has a negligible effect on the temperature for Ti:sapphir e crystals with high figures of merit ( 532800200nmnmFOM ; being the absorption coefficien t). The boundary conditions were specified as a temperature bTalong the barrel of cylinde r as either a fixed or variable temperature (corresponding to contact with the bath) and on the ends as dTdnconst (corresponding to the radiation). This allowed us to explore more phys ically realistic scenarios in our amplification

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74 system. Calculating the temperatur e profile within the crystal, we can now estimate the changes in the optical path length or OPD through the crystal. The simulated OPD were calculated for an ideal thin lens of the same focal length x y f in vertical and the horizontal transver se dimensions as that obtained from the simulated temperature gradient within the crystal (Figure 4-11)The experimentally meas ured thermal lens values from the previous section were then compared to the thermal lens values obtained from the computed OPDs. -2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.5 -600 -500 -400 -300 -200 -100 0 -2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.5 -500 -400 -300 -200 -100 0 (b)Vertical Axis (a) Horizontal axis calculated OPD quadratic fit OPD (nm)crystal radius (mm) fs-beam waist fs-beam waist calculated OPD quadratic fitOPD (nm)crystal radius (mm) Figure 4-11: Plots (a,b ) are the corresponding OPD as a function of the transverse coordinates, for the computed temperature profile in figure (3-6). These values were also compared with the analytical solution to thermal lens focal length [equation(4.17)] derived by Innocenzi et al. (1990), a ssociated with the phase changes that occur inside a cylindrical laser rod due to temperature dependent refractive index ,nrz .Figure 4-12, is a plot of the measured thermal lens focal le ns power as a function of pump power, compared with the values obtained from th e FEA calculations and the expression (4.17) The and dndTvalues used in equation (4.17) corresponded to the maximu m computed temperature rise

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75 at the center of the crystal at each pump pow er. While the FEA calculations agree reasonably well with the measured values along the vertical crystal axis and quite well along the horizontal axis, the focal lens power calculated from Innocenzis analytical equation significantly underestimates the lens power along both axes. 1020304050 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1020304050 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 measured finite element method analytical formula(b) Horizontal AxisPump Power (W) measured finite element method analytical formula(a) Vertical AxisThermal Lens power m-1Pump Power (W) Figure 4-12: Comparison of experi mentally measured thermal le ns powers (squares) against numerically predicted values us ing finite element analysis (circles) and an analytical expression for thermal lensing (triangles). Formula derived from Innocenzi et al (1990). The underestimation by the analytical expressi on is somewhat surpri sing, since treating and dndTas a constant over the entire crystal vol ume underestimates the effective thermal conductivity and over estimates dndTsince ( dndT) increases (decreases) as the temperature decreases away from the b eam propagation axis. However, equation (4.17) neglects the physical expansion of the crystal, which can increase the thermal lens power by a factor of 1.8 over a pure thermo-optic lens (Lawrence, 20 03). Nonetheless, the FEA lens power estimates

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76 agree with experimental data when using boundary temperatures consistent with the experimentally measured boundary temperature values. This present regenerative amplifier cavity desi gned with the above measured thermal lens measurement and the FEA analysis has been performing exceptionally well producing average powers as high as 9 W (before co mpression) when pumped with 80 W of green light at 5 kHz repetition rate. 4.8 Direct Measurement of the Optical Path Deformations To directly measure the pump induced path length changes and further corroborate our simulations, the LN2 cooled Ti: sapphire crystal was placed in one of the arms of a Michelson interferometer. A single frequency 1064-nm Nd: YAG laser (Lightwave Co rporation NPRO) was split into two arms with the crys tal in one arm and free space thr ough the other. Th e interference pattern was recorded as a function of power on the WinCam CCD beam analyzer. Figure 4-13 is the recorded spatial interference pa ttern as a function of pump power. Figure 4-13: Spatial interference pattern in the Michelson interferometer recorded in a CCD camera as a function pump power. The zero intensity frame corresponds to zero pa th difference at 0 W of pump power. As the pump power was gradually increased, the change in the intensity of the interference pattern

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77 indicated the increase in th e OPD through the crystal. Figure 4-14 is the measured optical path difference obtained from the recorded interference pattern, in the crystal as a function of pump power. Figure 4-14: Measured OPD compared with th e FEA calculated for three different boundary conditions. There is excellent agreement with a boundary temperature of 103bTKat higher pump powers. At the highest pump power (56 W), a OPD of 350 nm +/80 nm was measured (or approximately 0.45 at 800 nm), decreasing as the pump power was lowered. The intensity fluctuation of the NPRO laser 231010 as well as path fluctuat ions caused by acoustic perturbation of the interferometer optics most li kely caused the large er ror bars at lower pump powers. Experimentally, a boundary temperature of 93K was recorded at the boundary for zero pump power. As the pump power was increased to 55 W, a bounda ry temperature rise of 20K was recorded, but a fraction of th is rise was experimentally attributed to the absorption of scattered Ti: sapphire fluorescence by the thermoc ouple; only a portion of the experimentally recorded temperature rise was due to physical heating at the boundary. Thus, we simulated the OPD for a range of constant boundary temperaturesbT, displayed in Figure 4-14. At the highest pump powers, we see good agreement between the predicted and measured optical path

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78 length for 103bTK(corresponding to 10 K rise on the boundary), although the data and simulations deviate somewhat at lo wer temperatures and most severe ly at the lowest temperature. As expected, theOPD is less severe as the boundary temperature is reduced due primarily to the strong temperature dependence of Figure 4-10 and Figure 4-11displays the computed temperature rise and OPD for a particular boundary temperature 103bTKrespectively. 4.9 Effects of Thermal Aberrations on Beam Shape Figure 4-15: Beam shape as a function of repet ition rate. Increasing the repetition rate of the pump beam introduces modal distortions. The spatial quality of the amplified beam is hi ghly sensitive to temperature changes within the crystal. The amplified beam shapes we re measured using a WinCamD-UCM CCD beam analyzer after ample attenuation Figure 4-15 is a far field measurem ent of the spatial profile of the beam with increasing repetition rates. As the pump power is increased the temperat ure within the crystal increases leading to increased spatial distortions to the beam profile. The boundary temperature as measured by a thermocouple on the crystal rose from 103 K at 5 kHz repetition rate to 123 K at 12 kHz repetition rate. Astigmatism due to the geometry of th e crystal is evident in the elliptical shape of

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79 the amplified beam even at a re petition rate of 5 kH z. The mode quality of the amplified beam was measured (5W output power) using the b eam analyzer by attenuating it suitably and focusing with a 1 m focal length lens. -120-80-4004080120 200 400 600 800 1000 1200 1400 -120-80-4004080120 200 400 600 800 1000 1200 (b) Horizontal AxisM2=1.0 M2=1.14Beam radius (um)Distance (cm)(a) Vertical AxisM2=1.0 M2=1.62Beam radius (um)Distance (cm) Figure 4-16: M2 measurement for an uncompressed amplif ied beam of average power 5W at 5 kHz repetition rate in the (a) ve rtical and (b) horizontal axis A common measure for the beam quality is known as2 M It is defined as the ratio of divergence of the amplified beam to the diverg ence of an ideal Gaussian beam of equal beam waist. 2 0 0Rmeasured GaussianM (4.21) where 0R and measured are the waist and the divergence respectively of the laser beam of unknown quality and 0 and Gaussian are the waist and the divergen ce of a fundamental laser

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80 mode (TEM00 mode). The transverse profile of the beam (0R ) was measured as a function of the propagation distance using a CCD camera. If 00R then 2measured GaussianM (4.22) These results are shown in Figure 4-16. We observed that at lower repetition rates (5 kHz) corresponding to 5 W average po wer, the amplified beam M2 values deviated from the ideal TEM00 mode by a factor of only 1.62 and 1.14 in the vertical and the horizont al axes respectively. The thermal astigmatism of the crystal ge ometry is evident in the measured M2 value (a ratio of 1.42 in the divergence angle along the two axes). For higher repetition rates (8 kHz, average amplified power output of 9W and a boundary temperature108bTK) this ratio increased further to 1.73 (measured M2 values of 2.12 and 1. 22 in the vertical and the horizontal axes respectively). The rise in the asti gmatism of the beam shape can be attributed to the changes in the temperature related thermal constants fo r sapphire crystal as the boundary temperature increases at higher repetition rates. 4.10 Summary Summarizing the contents of this chapter, we detailed the various temperature related effects in a high average power laser system and more specifically to liquid nitrogen cooled Ti: sapphire crystal in a regenerati ve chirped pulse amplifier. We thoroughly characterized these thermal effects using both experimental techniques (such as interferometry, 2 M analysis and measurement of focal power) as well as Finite El ement Analysis. These measurements helped us in designing a suitable cavity for the regenerative amplifier that generates 5 W of 40fs, amplified output. The good agreement between the measurements and the numerical methods allowed us to extend the numerical methods to predict an optimal cavity configuration to further minimize

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81 these thermal aberrations which are detailed along with the present status of the amplifier in the next chapter.

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82 CHAPTER 5 CHARACTERIZATION AND OPTIMIZATI ON OF HIGH AVERAGE POWER CPA Having fully investigated the fundamental as pects of designing and constructing a chirped pulse amplifier and the thermal issues inherent w ith high powered systems in prior chapters, this chapter concentrates on the characterization an d performance of the amplifier and discusses methods to further enhance its efficiency. 5.1 Amplifier Performance 5.1.1 Average Power, Pulse Energy The cryogenic amplifier cavity based on the ex tensive thermal analysis is capable of delivering 9 W of amplified power at 5 kH z repetition rate and 80 W of pump power. Figure 51is a plot of the measured average output power as a function of the pump lasers repetition rate. 45678910111213 4 5 6 7 8 9 Average power WRepetition Rate kHz Figure 5-1: Amplified output power as a functi on of pump repetition rate (square points) measured before compression; the re d-line is a guide to the eye. As the repetition rate is increased the out put power of the syst em drops. This drop coincides with the drop in the pulse energy of the pump laser (from 14.7 to 6 mJ). The boundary temperature around the crys tal increases from 110 K at 5 kHz to 123 K at 12 kHz. Figure 5-2 indicates the amplified and the pump pulse energy with increasing repetition rate. The efficiency

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83 of the regenerative amplifier (defined as amplifiedpumpEE) is approximately 14% at 5 kHz and drops to 5% at 12 kHz. The amplifier remain s operational until 12 kHz repetition rate above which no lasing action is observed as the cavity ceases to be st able. By altering the cavity gparameter, the amplifier can be made operational for repetition rates above 12 kHz. An average amplified output power of 4.5 W is generated at 12 kHz. About 60% of the amplified power was recovered from the compressor. This could easily go up by the usage of gratings with improved efficiency in the compressor setup. 4567891011121314 0 2 4 6 8 10 12 14 16 Amplified pulse energy Pump pulse energy Pulse Energy (mJ)Repetition Rate (kHz) Figure 5-2: Amplified v/s pump pulse energy with increasing repetition rate. Amplified pulse energy is indicated by the red points and the pump pulse energy by the blue points. The solid lines are guides to the eye 5.1.2 Spatial Beam quality The increasing thermal loading effects as a re sult of the increasing repetition rate also bring about degradation of the sp atial profile of the amplified b eam as in Figure 4-15. This is evident in the measured 2 M of the beam at 8 kHz repetition ra te. As defined in the previous chapter, 2 M is a measurement of deviation of a laser mode from the fundamental TEM00 mode. A boundary temperature of 115 K was recorded for an input pu mp power of 75 W at 8 kHz

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84 repetition rate. A measured M2 value of 1.22 and 2.12 was reco rded in the vertical and the horizontal axes respectively. An average output power of 9 W (uncompressed) was obtained. -120-100-80-60-40-20020406080100120 200 400 600 800 1000 1200 1400 1600 1800 -120-100-80-60-40-20020406080100120 200 400 600 800 1000 1200 1400 measured gaussian fitBeam radius (microns)distance (cm) (a) (b) measured gaussian fitbeam radius (microns)distance (cm) Figure 5-3: Measured M2 for an uncompressed amplified beam of average power of 9 W at 8 kHz repetition rate in the (a) ho rizontal and (b) vertical axis. The ratio of the divergence angle along the 2 axes is thus 1.73, which is a nearly 22% increase from its value at 5 kHz (1.42, Figure 4-16). If the only source of astigmatism in the cavity is due to the Brewster crystal geometry, then increasing the repetition rate should have little or no effect to beam astigmatism. But the rise in the astigmatism of the beam shape with increasi ng pump power can be attributed to the changes in the temperature related thermal constants for sapphire crystal as the boundary temperature increases at higher repetition rates. Figure 5-3 is a plot of the measured M2 along the two transverses axes plotted along with the respective divergence for a Gaussian beam of same waist.

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85 5.1.3 Spectral Characteristics The bandwidth of the amplified pulse is 25-30 nm (without any amplitude shaping) depending on the bandwidth of the seed pulses. Th e amplified spectrum is shifted to the blue end of the spectrum as compared to the oscillator spectrum (Figure 5-4). 700720740760780800820840860880900 0.0 0.2 0.4 0.6 0.8 1.0 Oscillator amplifierWavelength (nm)Intensity (arb. units)0.0 0.2 0.4 0.6 0.8 1.0 Intensity (arb. units) Figure 5-4: Amplified spectrum (blue-curve) for the corresponding os cillator spectrum (red curve) as measured using a fiber spectrometer. Figure 5-5 is the emission spectra for Ti: sa pphire at two different boundary temperatures: 87 K and 300 K. We observe that the emission spectrum is narrower at a crystal temperature of 87 K than at room temperature. As the oscillator spectrum (Figure 5-4) is red-shifted with respect to the emission spectrum the gain of the amplifier (Figure 5-5) is pulled to the bluer edge of the spectrum due to which the amplified sp ectrum peaks at 780-nm as compared to 820-nm for the oscillator spectrum. The sp ectrum for the free-running laser for the regenerative amplifier cavity confirms the reason for this sp ectral shift towards the blue end (Figure 5-6). By reshaping the oscillator spectrum as in figure 3-14 using the dazzler towards the blue end not only increases the amplified output power from the regenerative amplifier but also reduces the amount of time the seed pulse needs to stay within the cavity to be able to extract gain from the crystal. This is since the gain of the sapphire crystal peaks at 775-nm (Figure 5-5), sculpting the spectrum of the

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86 seed pulse towards the bluer edge of the spectru m leads to efficient extraction of the energy by the seed pulse from the crystal that in turn l eads to a reduction in the number of roundtrips the seed pulse needs to make to be able to gain the same amount of ener gy as a pulse with its spectrum shifted towards the red-edge. The amplified spectrum in Figure 5-4 generates 40-45 fs co mpressed pulses in a grating based compressor with an efficiency of about 60%. 60070080090010001100 0.01 0.1 1 87 K 300 KNormalized Intensity (log-scale)Wavelength (nm) Figure 5-5: Emission spect ra for Ti: sapphire. 720740760780800820840 0.2 0.4 0.6 0.8 1.0 Normalized intensityWavelength (nm) Figure 5-6: Free-running spectrum fo r the regenerative amplifier ca vity at 5 kHz repetition rate.

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87 5.1.4 Shot-to-shot Pulse Energy Characterization Measuring the fluctuation of the amplified pu lse energy for each amp lified pulse gives one an indication of its stability. The shot-to-shot pulse fluctuat ions in the pulse energy were measured using a photo-diode (Thorlabs Det110) th at was triggered by the repetition rate of the amplifier. A Labview based data acquisition syst em continuously tracked each and every pulse from the amplifier. The photodiode was calibrated by measuri ng the average amplified power by using a power meter. The pulses were monitore d for a time duration th at was approximately 2 minutes collecting 614,987 shots at 5 kHz repetition rate (Figure 5-7). Figure 5-7: Shot-to-shot pul se energy measured for more than 600, 000 shots. The mean pulse energy measured was 1.15 mJ. Th e standard deviation of the fluctuations was measured to be 0.9% of the mean pulse ener gy, making this CPA a very stable system with respect to pulse energy. Figure 5-8 is a histogram of the data in Figure 5-7. The excellent agreement with a Gaussian fit indicates that th e fluctuations were Gaussian and hence totally random in nature.

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88 1.101.121.141.161.181.20 0 20000 40000 60000 80000 100000 120000 CountsAmplified pulse energy (mJ) Figure 5-8: Histogram of the amplified output pulse ener gy. The black dots are the experimentally measured data with 20 bins and the red curve is a Gaussian fit to the data. The following table summarizes the performance of the CPA system. Table 5-1: Performance of the CPA system Average compressed Power 4.68 W Repetition rate 5 kHz Pulse Energy 940 J Bandwidth 30-35 nm Pulse width 40-45 fs 5.2 Design Considerations for Single Stage Cryogenic CPA System We now focus on methods to improve the effici ency of the amplifier system based on the FEA calculations described in chapter 4 and corr ecting for the thermally induced astigmatism in the spatial profile of the beam. Using the Finite Element Analysis described in detail in the previous chapter, one can obtain parameters of the amplifier rod geometry such as the length, radius, and boundary temperature that affect the thermal performance of the amplifier. By varying the length and the radius of the crystal while the other pa rameter was fixed gave useful insights into the optimum crystal geometry with least thermal loading effects.

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89 Figure 5-9 displays the computed OPD as a function of crystal le ngth for a fixed crystal radius of 2.5-mm along both the ve rtical as well as the horizontal axis for two representative boundary temperatures, 103boundaryTK and 77 K. The incident pump power was 80 W (double pumping) with a pump waist size of 0.4mm and a constant absorption length product, 2.2absL Three features are evident from the above figure. First and foremost is that OPD decreases by a factor of two as the length of the crystal is increased. This is particularly important for the case of 103boundaryTK Relative to the center wavelength of the amplifier (780-nm as in Figure 5-4) the aberrations are reduced from ~ 10 to 18 for the horizontal axis which displays maximum thermal loading. A OPD of this magnitude only leads to changes in the focal power of the crystal as opposed to th e introduction of higher order modes that are difficult to compensate. The focal power of the crystal can be easily compensated for by tuning the g-parameter of the cavity. The decrease in OPD with increasing lengt h is understandable for two reasons, the first being that fo r a constant absorption length product 2.2absL the increase in the length results in a reduced pow er density (since the power is distributed over a larger volume) and a consequent reduction in te mperature throughout the crystal. Additionally, increasing the length of the crystal increase s the conductive surface area thereby providing a greater path for the heat to leave the crystal. Note that the OPD scales sublinearly with increasing length, thus extending the crystal bey ond ~ 15 mm yield little improvement in thermal performance but a considerable in crease in the group velocity disper sion (which is not desirable for ultrashort pulses).

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90 For a boundary temperature of77 K, thermal induced aberrations are diminished as compared to the hot case of 103 Kby a factor of ~15. This comes about due to the severe temperature dependence of the thermal pr operties of sapphire. Thermal conductivity increases by a factor of 3 over this temp erature range. In addition, dndTis also diminishing as temperature is reduced further reducingOPD Finally there is a strong evidence of thermal astigmatism in the crystal besides the natural astigmatism due to the Brewster geometry of th e crystal. For higher bo undary temperature, the focal length along horizontal axis in the crystal is 1.4 times the vertical axis focal length over the entire range of crystal lengt hs. Although the crystal attain s a slight focal power at77 K, the magnitude of the thermal OPD is negligible (a few nanometers). 6810121416 25 30 35 40 45 50 55 60 65 70 75 80 85 OPD (nm), Tboundary = 103 KCrystal length (mm)1 2 3 4 5 6 7 OPD (nm), Tboundary = 77 K Figure 5-9: Thermally induced opti cal path difference versus crystal length for a fixed radius of 2.5 mm for Tboundary=103 K (left axis) and Tboundary=77 K (right axis). The computed OPD along the horizontal axis is shown in solid points and along the vertical axis are hollow points. The lines are guides to the eye. Figure 5-10 displays the variance of OPD with crystal radius. The calculations were again based on a total pump power of 80 W, a pump waist of 0. 4 mm, a crystal length of 6mm and 2.2absL Again the thermal astigmatism for both boundary temperatures is immediately

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91 evident with a much larger OPD for 103 K. But the most striking features of this data are, first, that the OPD increases as the radius is increased and second, the magnitude of the increase is approximately 30% less than that seen in changing the crystal length. 12345678 25 30 35 40 45 50 55 60 OPD (nm), Tboundary = 103 KCrystal radius (mm)1 2 3 4 5 OPD (nm), Tboundary = 77 K Figure 5-10: Thermally induced optical path differ ence versus crystal radius for a fixed length of 6 mm for Tboundary=103 K (left axis) and Tboundary=77 K (right axis). The computed OPD along the horizontal axis is shown in solid points and along the vertical axis are hollow points. The lines are guides to the eye. Increasing the crystal radius also increases the surface area that should lead to better conduction of heat, reducing thermal lens effect s. But by moving the boundary further from the pump area as the radius is incr eased, the thermal conductivity is reduced, resulting in a greater temperature rise and OPD Thus the above simulations show that reducing the boundary temperature as much as possible result in dramatically reduced thermo-optic deformations in Brewst er crystals due to the favorable thermal properties of sapphire at low te mperatures. In addition, the use of longer but small radii crystal results in improved therma l performance at a given boundary temperature. While longer length and shorter radii crystals offe r the best thermal performance the size of the crystal is limited by the critical heat flux (CHF) [equation(5.1)] (Kutateladze, 1948; Zuber, 1958)

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92 of LN2 which is defined as the maximum power that can be dissipated by th e boiling liquid for a given surface area. For surface area smaller than the required minimum, vapour from the cryogenic liquid completely envelopes the surface insulating it and causing a dramatic spike in the boundary temperature. 1/41/2 2() (/24)[]()lvlv fgv vlg CHFh (5.1) where, f gh is the latent heat of vapor ization and is 199 J/g for LN2, v is the vapour density and is 4.66 kg/m3, 3806lkgmis the liquid density, 0.00893Nm is the surface tension for LN2 and 29.81 gmsis the acceleration due to gravity. Using these parameters the CHF for LN2 is 20.163 Wmm Assuming boiling at the crystal surface, a 5mm diameter crystal would need to be at least 31.2mm long to dissipate 80 W. The cr ystal can also be made shorter and placed in a conductive holder with a greater surface area, but this will increase the conductive path and consequently the crystal boundary temperature. 5.3 Compensation of Modal Astigmatism The presence of large thermal astigmatism suggests that the output mode quality is compromised, and our measurements have shown this. Measured M2 values suggest that the ratio of the divergence angles for the vertical and the hor izontal axes to be 1.42 (Figure 4-16) at 5 kHz and increasing to 1.73 at 8 kHz (Figure 5-3) repetition rate. Although the magnitude of the astigmatism is large, it does not lead to the in troduction of higher order modes in the cavity. Mansell et.al. (2001) calculated the fraction of light power coupled into the higher order modes from an ideal TEM00 mode in thermally ab errated optical component s based on modal coupling coefficients (Kogelnik, 1964). Their calculations were based on cylindrically symmetric optics that treated the two dimensional power c oupling symmetrically. They found that for

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93 4OPDs all the distortions are to the sphericity of the beam wavefront which is a pure lensing effect and can be compensated by altering the cavity g factor. By treating the thermal aberrations and the asso ciated coupling into th e higher order modes inde pendently for both the vertical and the horizontal axes (fig ure 4-11) obviates the fact that the OPDs can be calculated by a parabolic fit over the waist of the seed pulse on the crystal. Thus by designing an astigmatically compensated cavity, it should be possible to produce an almost pure TEM00 mode for a limited range of pump powers. This work is ongoing in our lab. Figure 5-11: 3-mirror folded astigmatically compensated cavity. A three mirror folded resonator cavity (Kogelnik, 1972) where the center mirror has an oblique angle of incidence (Figure 5-11) introduces astigmatism that could compensate for the thermally induced modal astigmatism. The angl e of incidence is chosen to produce mode characteristics that are equal along the two tran sverse axes. The center mirror used at oblique incidence has two focal points, as it focuses the sagittal x zand the tangential y zat two different locations which are given as: cos cosy xf f ff (5.2) where f is the focal length of the mirror 1 R and is the angle of incidence. By solving the ABCD matrix independently for the two axes and carefully selecting the a ngle theta and the radii

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94 of curvature1 R and 2 R the spot sizes and hence the focal lengths x f and y f can be made equal and thus compensate for the thermally induced astigmatism. 5.4 Summary Thus the amplifier generates 9 W of uncompr essed amplified power at 5 KHz repetition rate and is operational for repetition rates as hi gh as 12 kHz. The shot-to-shot energy variation of the amplifier is Gaussian in nature with the st andard deviation of the fluctuations measuring 0.9% of its mean pulse energy at 5 kHz. Nume rical analyses indicate that reducing the boundary temperature as low as possible results in lower thermo-optics aberrations through the crystal. Furthermore the efficiency of the amplifier could be further increased by using a sapphire crystal that is longer in length and shorter in diameter as compared to the crystal presently being used in the amplifier. Also compensating for the astigm atism in the amplified beam could lead to improved mode quality as well as an increase in output power from the amplifier.

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95 CHAPTER 6 CONCLUSION The need for ultrafast high brightness source s in various high laser field sciences has motivated the development of high average powe r, ultrashort chirped pulse amplifiers. This dissertation details the design and characterization of such a system that is capable of delivering millijoule range femtosecond pulses at re petition rates as high as 12 kHz. In order to achieve high amplification factors 6~10 in single stage systems, the crystal in the amplifier needs to be pumped with high power lasers which give rise to a host of thermal issues that prove detrimental to the systems performance. A high intensity pump laser when incident on Ti: sapphire crystal in the amplifier generates a refrac tive index gradie nt within the crystal such that the crystal gains focal power altering the cavity parameters leading to deterioration in its performance. It is common knowledge now that cryogen ic cooling of the Ti: sapphire crystal in the amplifier (Moulton, 1986; Schulz and Henion, 1991) changes its thermal properties that lead to the reduc tion of these thermal issues howev er these ideas had rarely been tried in femtosecond amplifiers and never in a single stage regenerative amplifier. Through investigations of several different cooling met hods, we were able come up with an effective cooling unit housing the crystal, using liquid n itrogen that lowered the ambient temperature of the crystal to 87 K with a mere 20 K rise in the crystals boundary temperature as the pump power was increased to 56 W. While cooling the crystal reduced the variou s thermal effects but some remnant thermal loading effects still limited the performance of th e CPA. A series of experiments were performed to fully characterize the effects of temperature on the performan ce of a regenerative amplifier. The experimental results were validated with a thermal model that was solved numerically for various boundary conditions using Finite Elemen t Analysis (FEA). Measurement of the focal

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96 powers of the crystal and the good agreement of the experimental data with the numerical model allowed us to design an effectiv e regenerative amplifier cavity th at was stable for a broad range of pump powers. The thermo-optical path deformations OPD as a function of pump power and its effects on the mode qual ity of the beam was quantified using Michelson interferometry and by measuring the 2 M values for the amplified beam. In the interferometry experiment the liquid nitrogen cooled Ti: sapphire crystal was pl aced in one arm of a Michelson interferometer and the interference pattern as a function of pump power was recorded on a CCD camera. At the highest pump power a OPD of 350-nm 80-nm was measured. The experimental data was compared to the computed OPD values for three different bounda ry conditions and found that there was excellent agreement with the measur ed values for high pump powers for a boundary temperature of 103K. Although the thermocouple measured a rise in the boundary temperature of 20 K a fraction of this rise was attributed to the absorption of scattered Ti: sapphire fluorescence when the pump power was increased to 56 W. The ag reement of the interferometry data with the calculated OPD seemed to suggest a small 10 K rise in the boundary temperature We measured the mode quality of the amplified beam using a CCD camera at 5 kHz and 8 KHz repetition rates. The divergence of the amp lified beam was compared to the divergence of an ideal Gaussian beam of equal waist. At 5 kHz repetition rate corresponding to 5.5 W of average power, a ratio of 1.42 in the diverg ence angle along the two transverse axes was measured. For an amplified power of 9 W at 8 KHz repetition rate, this ratio increased to 1.73 indicating the existence and the rise of temperat ure related astigmatism with increasing repetition rate besides the natural astigmatism due to the Brewster crystal geometry. Using the FEA analysis, we explored how ch anging key parameters of the amplifier rod geometry (length, radius, and boundary temperatur e) affects the thermal performance. We found

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97 that smaller radii and longer length crystals offer the be st performance at any boundary temperature. The decreasing OPD with increasing crystal length comes about from an increase in the total surface area that provides for a greater overa ll conductive path for the heat to leave the crystal. The increasing OPD with increasing crystal radius, although less intuitive, arises from moving the boundary further from the pump area as the radius is increased, which reduces the thermal conductivity resulti ng in greater temperature ri se and hence the increased OPD Taken together the simulations show that reduc ing the boundary temperature as much as possible result in dramatically reduced thermo-optical deformations in Brewster-cut crystals. This is not surprising as both and dndThave favorable thermal properties at lower temperatures. Also, the use of longer length and sma ller radii crystals re sult in improved thermal performance at a given boundary temperature. But the size of the crystal is limited by the maximum power that can be dissipated for a given surface ar ea known as the critical heat flux. The large thermal astigmatism distorts the mode of the amplified beam. However the distortions are manifested as a pure lensing eff ect and can be easily compensated by altering the cavity g-factor. In conclusion, we have presented in this wo rk a state-of-the-art, high average power, single stage, state-of-the-art CPA system. The peak puls e power obtainable from this system is as high as 0.025 TW and peak intensities of the order of 15210 Wcm making it possible to use this system to observe a multitude of interesting nonlinear phenomena.

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98 APPENDIX A FREQUENCY RESOLVED OPTICAL GATING (FROG) Ultrashort pulses have now reached the a ttosecond regime (Baltuska, 2003; Drescher, 2001). With such short pulses it is now possible to st udy dynamics of electronic motion within atoms. Intense femtosecond pulses are used to gene rate higher frequency harmonics that give rise to attosecond pulses. Precise information about the driving pulse is extremely important in generating pulses in the attosecond regime Chirped pulses can cause much greater photodissociation than unchirped pulses (Kohler, 1995) and hence these experiments rely heavily on characterizing the chirp in the pulse accurately. Thus complete character ization of ultrashort pulses is of utmost importance in most ultrafast experiments. A commonly used method for pulse measurem ents in laboratories is the Frequency Resolved Optical Gating (FROG) technique. It involves spectrally resolving an autocorrelation signal (Trebino, 1998). The experimental apparatus is hence similar to an autocorrelator, which is easily available in any ultrafast laboratory. SPIDER or spectral phase interferometry for direct electric-field reconstruction (Iaconis and Walm sley, 1998) is also an often-used pulse characterization technique. It is based on measur ing the interference betw een two pulses that are almost identical expects that one pulse is slightly shifted in frequency with respect to the other by an amount. This generates a spectrogram, which is essentially a spectrally resolved autocorrelation of the pulse. From the spectrogr am one can obtain the spectral phase for a set of discreet frequencies separated by and the amplitude is obtai ned from an independently measured power spectrum of the pulse. The SHG-FROG technique overlaps a pulse with a replica of itself delayed in time. An ultrashort pulse is defined by its electric field Et and I tand t are its time-dependent intensity and phase respectively.

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99 0ReexpEtItitit (A.1) A time-dependent phase gives rise to an instantaneous frequency t: 0d t dt (A.2) The pulse in the frequency domain can be written as: 00exp EIi (A.3) Using FROG once can measure Et[or E ] by measuring I t[or0I ] and t [or ]. The autocorrelator splits the beam into tw o and combines them on a nonlinear crystal to generate a SHG signal,SHG I t : ,SHGItItIt (A.4) As the ,SHG I t is a function of the delay time between the two pulses, it yields some measure of the pulsewidth as no second harmonic will be observed if th ere was no overlap between the two beams. FROG measurements involve measurements in the time-frequency domain (spectrogram) that provide both temporal as well as spectral resolution simultaneously. A mathematical representation of the spectrogram is as follows: 2,exp SEtgtitdt (A.5) In the above equation, gt is the gate function. The femtos econd pulse itself is used as the gate function.

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100 If the signal measured is a SHG-based autocorr elator then the spectrogram takes the form: 2,expSHG FROG I EtEtitdt (A.6) Knowing the gate function allo ws one to accurately estimate E t hence the above expression needs to be re-written to convert it to a twodimensional phase-retrieval problem as the gate function is unknown. EtEt for an SHG autocorrelator is ,sigEt Let ,sigEt be the Fourier transform of,sigEt with respect to such that ,0sigEtEt Re-writing equation (A.6) with ,sig E t : 2,,expSHG FROGsigIEtitidtd (A.7) Equation (A.7) presents a classical phase retrieval problem in which the 2D spectrogram ,SHG FROGI is known (measured) and the complex quantity ,sigEt is unknown. This 2Dphase retrieval problem is a common occurrence in imaging techniques and is solvable (Fienup, 1982). From the spectrogram one obtains the intens ity both in the time and the frequency domain. In the 2D imaging problem, one estimates the sp ectral and hence the temporal phase by using an iterative algorithm such as the Gerchberg-Saxto n algorithm (Gerchberg and Saxton, 1972) that performs Fourier transforms back and forth be tween the time and the frequency domain with known constraints in each domain. In the SHGFROG technique the constraints on the Fouriertransform magnitudes are that they are zero outside a fi nite range of values of t and This additional information along with the measured ,SHG FROGI is sufficient to fully characterize the ultrashort pulse.

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101 The experimental FROG traces are fed into an iterative Fourier transform algorithm similar to the one described above (DeLong, 1994). The algor ithm continues with the iterations until the computed or the retrieved image satisfies the object image. The convergence of the algorithm is determined by the squared error defined as Z : 2 1 ,1,,N kk sigiisigii ijZEtEt (A.8) where ,k s igiiEt is the computed electric field in the thk iteration. Figure A-1: Schematic of the experimental set up of the FROG apparatus in our laboratory. (Trebino, 1997) The SHG-FROG trace is highly sensitive but it has an inherent temporal ambiguity. The pulse Etand Et yield the same FROG traces as the SH G signal is symmetric with respect to delay. Thus it is possible th at the actual phase is a time-revers ed version of the retrieved phase. This ambiguity is easily inferred by inserting a piece of glass in the beam line that should increase the amount of positive dispersion. The FROG apparatus in our la boratory is described in Figure A-1. The ultrashort pulse is split in two where one beam travels through a delay stage and the other through a fixed path

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102 length. They are then focused and cro ssed using a cylindrical lens, on to a 100m KDP crystal. The SHG signal due to the mixing of the two b eams is then imaged on to the slit of a spectrometer (Princeton Instruments) using a sphe rical lens after the crystal. The spectrometer contains its own imaging optics wher e the slit is further imaged on to 2D CCD chip that contains 1340 pixels along the delay axis a nd 100 pixels along the spectral ax is. Liquid nitrogen is used to cool the CCD chip to reduce the effects of thermal noise in our measurements. Figure A-2: Raw SHG-FROG spectrograms reco rded using (a) 150 g/mm and (b) 300 g/mm grating. The horizontal axis is the wavelengt h axis and the vertical axis is the delay axis. The CCD array needs to be calib rated before it can be used to obtain spectrograms. The wavelength axis was calibrated us ing a mercury lamp that genera ted spectral lines at 390-nm and 410-nm across the 100 pixels along the wavele ngth axis by using 300-g/mm grating in the spectrometer. By recording the pixel numbers wh ere the spectral lines from the Hg-source were observed, one can obtain the pixel spacing in terms of nanometers and the wavelength of the first pixel. It is possible to calibrate the wavele ngth axis with more accuracy by using a lower resolution grating that yields many more spect ral lines across the CCD chip, but the obtained

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103 FROG traces almost always recover with huge erro rs than with traces that were obtained by using a higher resolution grating (Figure A-2). The temporal axis is calibrated by introducing a known amount of delay between the two beams a nd measuring the number of pixels the FROG image moved across the CCD chip. For a delay of 10m on the stepper stage, the center of the spectrogram moved by 16-17 pixels on the CCD chip. By averaging this over several 10m motions yielded the time (in fs) per pixel, whic h was usually calculated to be 1.9-2.3-fs/pixel. Figure A-3: Raw SHG-FROG spectrograms indicat ing (a) unfiltered (b) filtered traces. The horizontal axis is the wavelength axis and the vertical axis is the delay axis. Spurious noise on the measured FROG traces th at were caused due to either dust on the CCD chip or thermal noise caused due to overheati ng the chip, were filtered (Figure A-3) using a filtering/smoothing program available with the Princeton Instruments spectrometer driver software before introducing it through the iterative FROG softwa re, to reduce FROG errors. The amplified pulses almost always recovered with FROG errors in the range 0.005-0.002. FROG errors higher than 0.005 were observed on th e days when the amplified beam shape had

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104 observable structures in it. The FROG traces we re recovered using the software Femtosoft obtained from Swamp optics.

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105 APPENDIX B ACOUSTO-OPTIC PROGRAMMABLE DISPERSIVE FILTER Pulse shaping is an important tool for generating; transform limited ultrashort pulses in a chirped pulse amplifier system. All the pulse-shapi ng work in this dissertation used an AcoustoOptic Programmable Dispersive filter (AOPDF) or commonly referred to as the Dazzler (manufactured by Fastlite). This section describe s in detail the operation pr inciples of an AOPDF and its several uses. B.1 Bragg diffraction of light by Acoustic waves An optical beam incident on a medium w ith a propagating acoustic wave experiences Bragg diffraction and the diffracted beam is shif ted in frequency corresponding to the frequency of the acoustic wave (Yariv; Brillouin, 1922; Adler, 1967). For an incident field of frequency i and an acoustic field of frequency s the frequency shift to the diffracting optical field isd is Tournois (1997) was the first to demonstr ated shaping of optical pulses through acousto-optic interaction in a birefringent crystal. An acoustic wave can lead to a change in th e optical properties of a birefringent medium that can cause a change in the polarization. The wave equation for an optical field through such a medium can then be written as: 22 2 22E EP tt (B.1) where and are the permeability consta nt and dielectric constant of the medium respectively and P is change in the polarizat ion of the medium due to the presence of sound wave. The change in polarization is characte rized by the photo-elastic tensor idkl p (a tensor of rank four)

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106 0,,,1,2,3id iidklkldPpSE ijkl (B.2) where, klS is the strain tensor and Ed is the electric field along the direction d. 1 (,)exp. 2klklssSrtSitkrcc (B.3) If the input optical fiel d consists of two plane waves polarized along the i and the d direction with wave numbers ik and dk respectively: 1 (,)()exp. 2 1 (,)()exp. 2iiiii dddddErtEritkrcc ErtEritkrcc (B.4) The RHS of equation (B.2) then takes the form: 011 exp()exp 22id iidklklssddddPpSitkrEritkr (B.5) Applying the slowly varying envelope approxi mation to the left-hand side of equation (B.1), such that 2iiiiEkdEdr : 221 (,)2. 2iiitkr i iiii idE ErtkEikecc dr (B.6) With all the above substitutions the equality in equation (B.5) is satisfied only for the following condition: ids idskkk (B.7) The above condition is known as the phase matchi ng condition and is statement of conservation of total energy and momentum.

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107 Figure B-1: Bragg vector diagra m and physical configuration for (a) retreating and (b) oncoming sound waves. [Adapted from Yariv, 1989]. Figure B-1 depicts the vector diagram for two different phase matching conditions and their corresponding physical Bragg diffraction. The diffraction conditi on is identical to the firstorder Bragg condition for the scat tering of X-rays in crystals: 2ssin n (B.8) where, 2idkkk B.2 Amplitude and Phase control using an AOPDF The AOPDF uses a birefringent uniaxial crystal that couples an ordinary (extraordinary) optical wave using an acoustic wave into the ex traordinary (ordinary) optical wave. The acoustic signal is a programmable variable function of time and is used to control the group delay and the intensity of the acoustic signal controls the amplitude of the diffracted optical pulse thus

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108 providing both phase and amplitude shaping in CPA laser systems (Tournois 1997; Verluise, 1999; Verluise, 2000). Figure B-2: Schematic of the AOPDF. [Reprint ed with permission from Pittman (2002)]. As depicted in Figure B-2 an input optical pulse along th e ordinary axis interacts with an acoustic wave launched along the same axis that then diffracts the optical pulse along the extraordinary axis of the crystal. For every fr equency component in the input optical field to satisfy the phase-matching relation in equation (B.7), it needs to travel a minimum distance before it encounters a phase-matched spatial fr equency in the acoustic grating. At this positionz part of the energy is coupled (diffracted) into the extraordinary axis. Thus the pulse leaving the second axis consists of all th e spectral components that have been diffracted at various positions. The amplitude of the diffracted optical field is controlled by intensity of the acoustic wave at z Due to the difference in velocity between th e ordinary and the extraordinary axes, each diffracted frequency will e xperience a different time delay. Then with a proper choice for a filter function in the temporal and the spectral do main one can create an arbitrary group delay distribution as a function of fr equency. The optical output out E tfrom the AOPDF is function

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109 of the optical input inEtand the acoustic signal St. From the previous section we can represent the output as a convolution of the input and the acoustic signal. outint EtEtS (B.9) The scaling factor is given as: v n c (B.10) It is the ratio of the speed of sound to the speed of light times the difference in the refractive index between the ordinary and the extraordinary axes in the crystal. For TeO2 0.118n is calculated as 60.1310 reflecting the much slower velocity for sound waves. The small value for enables the control of op tical signals in the hundre ds of terahertz range with tens of megahertz range acoustic signals. The acoustic wave is genera ted in a 2.5-cm long TeO2 crystal, by a piezoelectric transducer. The maximum achievable group delay which is depe ndent on the crystal length is ~3-ps for 25mm long TeO2 crystal. The acoustic signal of the RF-gen erator that drives the crystal module is interfaced with a computer and is programmed us ing Labview based software (Figure B-3). The Labview based software allows one to use the dazzler in both open loop and closed loop control experiments. The RF-generator is triggered th rough a digital delay gene rator which itself is externally triggered by the mode-locked oscillator. For an amplifier repetiti on rate of 5 kHz, the dazzler is programmed to trigger after every 200s. The acoustic signal travels through the crystal area in a finite amount of time ct which is 25s for a 2.5-cm crystal. Thus the maximum repetition rate at which the dazzl er can be triggered is 40 kHz. The three major application of this device in CP A laser chains is (a): amplitude shaping for the pre-compensation of the gain narrowing effect in the amplifier, (b): phase compensation to

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110 correct for the mismatch in the stretcher and th e compressor delay lines, a nd (c): arbitrary pulse shaping in both the spectral and the temporal domains.

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120 BIOGRAPHICAL SKETCH Vidya Ramanathan was born in Chennai (then Ma dras) a southern city in India on October 31st 1976. But soon thereafter her parents moved to Mumbai (then Bombay) along the west coast of the country where she was brought up with tw o younger twin siblings. After graduating from high school in May she entered the Physics department at the Ramnarain Ruia College in Bombay to obtain a B.Sc degree in physics in the fall of Sh e then received her masters degree in physics at the University of Bombay during the summer of She began her graduate studies at the Indian Institute of Technol ogy at Bombay from August Disillusioned with her progress at gr ad school, she decided to head west and landed at the University of Florida, in fall 2000. Jo ining Dr. David Reitzes optics group at UF, she nurtured her interests in the field of femtosec ond lasers and has since been involved in the development of a high average power chirped pulse amplifier system.


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DEVELOPMENT AND CHARACTERIZATION OF A HIGH AVERAGE POWER, SINGLE-
STAGE REGENERATIVE CHIRPED PULSE AMPLIFIER




















By

VIDYA RAMANATHAN


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2006
































Copyright 2006

by

Vidya Ramanathan

































To my family










ACKNOWLEDGMENTS

Graduate school has been an extremely enriching experience dispelling my naivety in more

ways than one.

I owe a great deal to my mentor Dr. David Reitze for his guidance and encouragement that

saw me through these past six years in graduate school. Not only did he acquaint me with the

rudiments of ultrafast lasers, but he also helped me gain a deep insight and perspective into this

field. I very much appreciate Dr. Reitze's treatment of his graduate students as junior colleagues.

It is encouraging as well as challenging reminding me always of my discerning decision of

joining his research team.

I am grateful to my committee members Profs. Hagen, Tanner, Stanton and Kleiman for

serving on my supervisory committee and for all their advice and suggestions. I would also like

to thank Prof. Nicolo Omenetto for agreeing to serve on my committee at an extremely short

notice and was patient enough to read through my thesis and spot typos in just two days!

My sincere gratitude also goes to my fellow graduate students Jinho Lee, Shengbo Xu and

Xiaoming Wang for all their help and for creating a pleasant environment in the laboratory. I

would like to thank Dr. Yoonseok Lee and Pradeep Bhupathi for their ideas and suggestions

about cryogenics and vacuum systems and also for all the stycast that they so willingly made for

me! Bill Malphurs and Marc Link from the machine shop deserve special mention for their

brilliant imagination and craftsmanship. Many thanks go to Luke Williams for letting me benefit

from his expertise in thermodynamics and CAD designing software. I am extremely grateful to

the support staff in the Physics department, Jay Horton, Don Brennan and many more for lending

a helping hand whenever I needed one. I thank Darlene Latimer and Nathan Williams for all

their assistance during times of distress! I would also like to thank all the folks in Tanner Lab










and Hebard Lab for letting me borrow sundry items and equipment from their laboratories from

time to time.

I wish to thank my friends Ronojoy Saha, Karthik Shankar, Aparna Baskaran, Naveen

Margankunte from the physics department and many others in Gainesville for providing respite

from the trials and tribulations of graduate school with countless Friday nights filled with revelry!i

Finally I wish to thank my parents and my siblings for their unconditional support and

patience over all these years and the undaunted faith they have in me. Last but not least, a great

deal of credit goes to Rajkeshar Singh who, although my husband of just two years, has been my

best buddy for almost a decade now. I definitely do not envision myself here today if it were not

for him.












TABLE OF CONTENTS


page

ACKNOWLEDGMENT S .............. .................... iv


LI ST OF T ABLE S ............ ...... ._ .............. viii..


LI ST OF FIGURE S .............. .................... ix


AB S TRAC T ......_ ................. ..........._..._ xiii..


1 INTRODUCTION .............. ...............1.....



2 ULTRASHORT PULSE GENERATION AND CHARACTERIZATION ............... .... ...........9


2.1 Relationship between Duration and Spectral Width ................. ............................9
2.2 Time Bandwidth Product ................. ...............12................
2.3 Dispersion ................. ...............14.................
2.4 Nonlinear Effects ................. ............... ...............16......
2.4.1 Second Order Susceptibility ................. ......... ...............16. ....
2.4.2 Third Order Susceptibility ................. ......... ...............18. ....
2.4.2.1 Nonlinear index of refraction ................. ........._. ....... 18..... ...
2.4.2.2 Kerr lens effect ............ ..... ._ ...............19..
2.4.2.3 Self phase-modulation .....__.....___ ..........._ .............2
2.5 Summary ............ ..... ._ ...............22....


3 DESIGN AND CONSTRUCTION OF A HIGH AVERAGE POWER, SINGLE STAGE
CHIRPED PULSE AMPLIFIER ............ ..... ._ ...............23...


3.1 Introducti on ............... .... .....__ .. ...............23..
3.2 Why Chirped Pulse Amplifieation? ............ .....__ ....._ ...........2
3.3 Ti: Sapphire as Gain Medium ............ ..... ._ ...............26..
3.4 M ode-locked Laser ............ ..... ._ ...............28...
3.5 Dispersion .............. .... .._ ...............31...
3.6 Pulse Stretching and Recompression............... .............3
3.7 Ti: Sapphire based Laser Amplifier............... ...............3
3.7. 1 Process of Amplifieation ............ ..... ._ ...............41.
3.7.2 Types of Amplifiers ............ ..... ._ ...............42..
3.8 Pulse Shaping............... .. ..............4
3.9 Ultrashort Pulse Measurement............... ..............4
3.10 Chirped Pulse Amplifier system ............ ......__ ...............49.
3.11 Summary ............ ..... ._ ...............50....

4 THERMAL EFFECTS IN HIGH POWER LASER AMPLIFIER ................. ............... ....52


4.1 Introducti on ................. ...............52........... ....











4.2 Theoretical Background.................. .............5
4.3 Methods to Reduce Thermal Effects .................. ...............61..
4.4 Liquid Nitrogen Cooled Ti Al203 Laser Amplifier ................. ................. ........ 64
4.5 Construction of a Regenerative Amplifier Cavity ........._._........__. ........._......66
4.6 Measurement of Thermal Lens ........._.___..... .___ ...............68...
4.7 Calculation of Thermal Lens ................. ....... ... .............7
4.8 Direct Measurement of the Optical Path Deformations ........._._. ..... ._.__............76
4.9 Effects of Thermal Aberrations on Beam Shape .............. ...............78....
4.10 Summary ............ ..... .._ ...............80...

5 CHARACTERIZATION AND OPTIMIZATION OF HIGH AVERAGE POWER CPA......82


5.1 Amplifier Performance .............. ...............82....
5.1.1 Average Power, Pulse Energy .............. ...............82....
5.1.2 Spatial Beam quality............... ...............83
5.1.3 Spectral Characteristics .............. .. ...............85
5.1.4 Shot-to-shot Pulse Energy Characterization.................. ..........8
5.2 Design Considerations for Single Stage Cryogenic CPA System ........._..... ..............88
5.3 Compensation of Modal Astigmatism ............__......__ ...._ ...........9
5.4 Summary ............ ..... ._ ...............94....

6 CONCLUSION ............ ..... ._ ...............95....



A FREQUENCY RESOLVED OPTICAL GATING (FROG) .................. ................9



B ACOUSTO-OPTIC PROGRAMMABLE DISPERSIVE FILTER ................. ................. 105


B.1 Bragg diffraction of light by Acoustic waves ................. ...............105.............
B.2 Amplitude and Phase control using an AOPDF............... ...............107.

LI ST OF REFERENCE S ................. ...............111................



BIOGRAPHICAL SKETCH ................. ...............120......... ......










LIST OF TABLES

Table page

2-1 Time bandwidth product for different pulse shapes (Figure 2-4)..........._ ... ...............1 3

4-1 Quantitative estimate of thermal effects in sapphire............... ...............56

4-2 Thermal properties of sapphire at 300 and 77 oK. .............. ...............65....

5-1 Performance of the CPA system ................. ...............88.............










LIST OF FIGURES


Figure page

1-1 High Harmonic generation in Ar gas. .............. ...............4.....

1-2 A sheet of invar micromachined with (a) 10 nsec pulses and (b) 100-fs pulses ..................5

1-3 Schematic of surface spectroscopy (a) and a typical Sum-frequency Generation
spectra (b)............... ...............6...

2-1 Evolution of a plane monochromatic wave in time (a) and a plane wave with
Gaussian amplitude modulation in time (b) ................. ...............10...............

2-2 Fourier transform of the (a) cosine function in Figure 2-1(a) and (b) Gaussian
function in Figure 2-1 (b)............... ...............10..

2-3 Time evolution of a Gaussian electric Hield with a quadratic chirp (b = 10) on it.............12

2-4 Intensity profie for a Gaussian pulse (solid blue curve), hyperbolic secant (dashed
blue curve) and a lorentzian (red curve). ............. ...............14.....

2-5 Schematic relationship between phase and group velocities for a transparent
medium (v<
2-6 Geometry of second-harmonic generation (a) and schematic energy level diagram (b).
.............................17.

2-7 Geometry (a) and schematic of third order generation (b). ................ ............ .........18

2-8 Schematic representation of the Kerr lensing effect ........__............_. ........._.._. ...20

2-9 Schematic of Self-phase modulation. ............. ...............22.....

3-1 A schematic representation of a Chirped Pulse Amplifier system. ............. ..................25

3-2 Absorption and emission spectra for Ti: sapphire. ............. ...............26.....

3-3 Self-mode-locked Ti: sapphire laser oscillator. ............. ...............27.....

3-4 Generation of ultrashort pulses by the mechanism of mode locking. ........._.._... ..............28

3-5 Oscillator spectrum as measured by a fiber spectrometer and its Fourier transform.........30O

3-6 A Gaussian pulse possessing (a) linear chirp (#"(mi,)) on it and (b) qluadratic chirp

(#"'(mi,)) on it. ......____ ...._ ....._ ...._ .... ......._ ..................33










3-7 Dispersive delay lines .............. ...............34....

3-8 Prism delay line............... ...............36..

3-9 Schematic of the stretcher layout. Oscillator pulses of duration ~20 fs are stretched to
~ 200 ps without any chromatic aberrations. ............. ...............38.....

3-10 Spectrum measured from the oscillator and after propagation through the pulse
stretcher ................. ...............38.................

3-11 Effect of gain narrowing in amplifiers, the red curve is the fundamental laser
spectrum and the blue curve is after five passes through the laser medium. .....................42

3-12 Schematic representation of a multipass amplifier system. ............... ...................4

3-13 A schematic representation of the regenerative amplifier in our laboratory. ................... .44

3-14 Amplified pulse spectrum shows a FWHM of 33-nm. Inset, blue curve is the shaped
oscillator spectrum using an AOPDF, which yielded an amplified bandwidth of 33-
nm, obtained from the original oscillator spectrum (red curve). ............. ....................46

3-15 Experimental auto-correlator set up. ........... .....__ ...............48..

3-16 FROG: (a) experimental spectrogram, (b) Retrieved spectrogram with a Frog error of
0.002, (c) 43 fs pulsewidth and (d) spectrum from the retrieved Frog trace. ....................48

3-17 Schematic representation of CPA. ............. ...............50.....

4-1 Simulation of the resultant temperature gradient in an end pumped Ti Al203 laSer rod
at room temperature when pumped by 70 W of 532 nm laser light. ............. .................52

4-2 Refractive index changes to a crystal incident with 80 W of pump beam. The thermal
gradient causes optical path deformation for a beam traveling along the : -axis.............. 53

4-3 Radially curved end-faces due to increase in temperature caused due to absorption of
incident pump beam. .............. ...............54....

4-4 Brewster cut Ti sapphire crystal. ............. ...............62.....

4-5 Dependence of (a) Thermal dispersion (dn dT) (Feldman et al., 1978) and (b)
Thermal conductivity ic (Holland, 1962) of Ti sapphire with temperature. ....................66

4-6 CAD drawings depicting (a) Vacuum dewar assembly and (b) copper crystal holder......68

4-7 Boundary temperature rise as pump power is increased when lasing action is
inhibited (red points) and when the cavity is lasing (blue points). The lines are guides
to the eye. .............. ...............68....










4-8 Measured thermal lens and thermal power for the two transverse axes; the boundary
temperature was measured to be 87 K at zero pump power and 103 K at 55 W of
pump power. ............. ...............70.....

4-9 Cavity stability parameter as a function of measured thermal lens. ............. ..................70

4-10 Computed temperature profile in a 6 mm long, 5 mm diameter Brewster-cut Ti:
sapphire crystal single end-pumped by 50 W in a 0.4 mm pump spot waist radius for
and absorption corresponding tO GabsL = 2.2 and a boundary temperature of 103 K........73

4-11 Plots (a,b) are the corresponding AOPD as a function of the transverse coordinates,
for the computed temperature profile in figure (3-6) ................. ................. ........ 74

4-12 Comparison of experimentally measured thermal lens powers (squares) against
numerically predicted values using finite element analysis (circles) and an analytical
expression for thermal lensing (triangles)............... ..............7

4-13 Spatial interference pattern in the Michelson interferometer recorded in a CCD
camera as a function pump power. ............. ...............76.....

4-14 Measured OPD compared with the FEA calculated for three different boundary
conditions. There is excellent agreement with a boundary temperature of
Tb = 103"K at higher pump powers. ............. ...............77.....

4-15 Beam shape as a function of repetition rate. Increasing the repetition rate of the pump
beam introduces modal distortions. ............. ...............78.....

4-16 M2 meaSurement for an uncompressed amplified beam of average power 5W at 5
k
5-1 Amplified output power as a function of pump repetition rate (square points)
measured before compression; the red-line is a guide to the eye. ............. ...................82

5-2 Amplified v/s pump pulse energy with increasing repetition rate. ................. ...............83

5-3 Measured M2 for an uncompressed amplified beam of average power of 9 W at 8
k
5-4 Amplified spectrum (blue-curve) for the corresponding oscillator spectrum (red
curve) as measured using a fiber spectrometer. .............. ...............85....

5-5 Emission spectra for Ti: sapphire. ............. ...............86.....

5-6 Free-running spectrum for the regenerative amplifier cavity at 5 k
5-7 Shot-to-shot pulse energy measured for more than 600, 000 shots. ................ ...............87










5-8 Histogram of the amplified output pulse energy. The black dots are the
experimentally measured data with 20 bins and the red curve is a Gaussian fit to the
data. .............. ...............88....

5-9 Thermally induced optical path difference versus crystal length for a Eixed radius of
2.5 mm for Tboundar=103 oK (left axis) and Tboundary=77 OK (right axis). ..........................90

5-10 Thermally induced optical path difference versus crystal radius for a fixed length of
6 mm for Tboundar=103 oK (left axis) and Tboundary=77 OK (right axis) .............. ...............91

5-11 3 -mirror folded astigmatically compensated cavity ................. .............................93

A-1 Schematic of the experimental set up of the FROG apparatus in our laboratory. ...........101

A-2 Raw SHG-FROG spectrograms recorded using (a) 150 g/mm and (b) 300 g/mm
grating. The horizontal axis is the wavelength axis and the vertical axis is the delay
axis. ............. ...............102....

A-3 Raw SHG-FROG spectrograms indicating (a) unfiltered (b) filtered traces. The
horizontal axis is the wavelength axis and the vertical axis is the delay axis. .................1 03

B-1 Bragg vector diagram and physical configuration for (a) retreating and (b) oncoming
sound waves. ................. ................. 107........ ....

B-2 Schematic of the AOPDF ..........._ ..... ..__ ...............108.









Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

DEVELOPMENT AND CHARACTERIZATION OF A HIGH AVERAGE POWER, SINGLE-
STAGE REGENRATIVE CHIRPED PULSE AMPLIFIER

By

Vidya Ramanathan

December 2006

Chair: David Reitze
Major Department: Physics

Ultrashort pulses have revolutionized the field of optical science making it possible to

investigate highly nonlinear processes in atomic, molecular, plasma and solid-state physics and

to access previously unexplored states of matter. Although ultrashort pulses make an extremely

useful tool, the generation of these highly energetic but short pulses is by no means trivial.

Amplified ultrashort pulses are generated by the technique of chirped pulse amplification (CPA).

Pulses with peak powers of the order of 1012 W from the CPA lasers when focused down to a

surface area that correspond to a few square-microns generates high intensities capable of

ionizing the medium or generate spectacular non-linear electromagnetic phenomena.

This dissertation details the design, fabrication and complete characterization of a high

average power, high repetition rate, and single-stage chirped pulse amplifier system capable of

delivering 40-45 fs pulses in the milli-joule range at multikilohertz repetition rate. In order to

achieve millijoule level pulses from a single amplifier stage, the CPA systems need to be

pumped with high average power sources. This introduces a host of thermal issues and thermal

management then becomes necessary to increase the efficiency of such systems. In this work, we

have carried out a systematic investigation of the thermal loading effects in a high average power,

regenerative CPA system. We experimentally characterize the thermal aberrations using a variety









of different techniques interferometryy, pump-probe thermal lens power, and M2 analysis). We

compute the temperature distribution, the optical path deformations (OPDs) and the

corresponding thermal lens focal powers using Finite Element Analysis (FEA) for different

pumping conditions. The validation of the experimental results with the FEA model allowed us

to use the model to design an effective regenerative amplifier cavity that is stable over a wide

range of thermal lens focal length and hence over a wide range of repetition rates. The model

could also predict optimal pumping conditions for minimizing thermal aberrations for a variety

of geometries and pumping schemes.

The regenerative amplifier is capable of generating 40-45 fs, ~ ImJ pulses at 5 kHz

repetition rate and ~ 300 CIJ at 12 k
pulse energy) in the shot-to-shot pulse energy and good beam quality (average M~2 Of 1.42 at 5

k








CHAPTER 1
INTRODUCTION

Light is everywhere in the world. It has always been a carrier of information: from the real

world to our brains through our eyes. Our vision defines a sense of perception, which in turn

governs the way we look at the world. With the help of modern instruments, light has enabled us

to see closely and understand phenomena beyond our limited visibility. From scrutinizing

astronomical obj ects thousands of light years away from us to delving into the microscopic world,

light has in many ways helped us achieve the impossible.

Much of this achievement witnessed accelerated growth after the invention of lasers, which

have undoubtedly been one of the greatest inventions in the history of science. Since their arrival

in the 1960s (Maiman, 1960) they have found themselves useful in almost all areas of science

today. Barely years after the first laser was demonstrated DeMaria and coworkers (1966)

generated ultrashort pulses which were picoseconds long from a modelocked Nd: glass laser.

Atomic and molecular processes occur on time scales as short as a few picoseconds (10-12 SOCS)

to a few femtoseconds (10-"5 secs). The generation of short laser pulses has made it possible to

observe such effects with very high temporal resolution. The shorter the pulse duration, the

greater are the prospects of investigating highly nonlinear processes in atomic, molecular, plasma

and solid-state physics and gain access to previously unexplored states of matter.

Through the 1970s picosecond pulses were generated from flash lamp pumped solid state

materials such as ruby, Nd: glass and Nd: YAG using passive modelocking schemes such as

saturable absorbers in the laser cavity. But the major drawbacks of these systems were the large

fluctuations in the shot-to-shot output from the laser, and the instability of the saturable dye

solution whose quality degraded with exposure to light. As a result focus shifted from solid state

gain medium to organic dye lasers which were capable of generating pulses shorter than 10-ps.









The field of ultrafast laser development has seen rapid progress since the generation of

high quality sub-picosecond (0.1-ps) laser pulses by Richard Fork, Benjamin Greene and Charles

Shank in 1981. Pulse durations quickly dropped to the femtosecond regime (Shank et al., 1982)

using colliding pulse modelocked lasers. With the invention of solid state laser material such as

Ti3+ doped sapphire (Ti: Al203) by P. F. Moulton (1986) renewed interest in solid state lasers as

they offered higher stored energies and unlimited operating and 'shelf' lifetimes as compared to

organic dye liquids.

The discovery of self-modelocked Ti: sapphire lasers by Spence et al in 1991

revolutionized the field of ultrafast laser development. It now became possible to generate pulses

as short as 5 fs (Jung, et al., 1997; Morgner et al., 1999) directly from a laser oscillator without

the use of saturable absorbers. These table top lasers easily generate peak power levels of the

order of a few megawatts (106 W) (Huang et al., 1992a; 1992b; Asaki et al., 1993).

Ultrashort pulses allow for fast temporal resolution. One now has the capability to 'freeze'

motion of fast moving electrons and molecules, facilitating the study of molecular dissociation

dynamics, complex chemical reaction dynamics, etc. thus paying way for the field of

femtochemistry (Zewail, 1996), which deals with the nature of transition states and their control.

Following the development of milli-joule level picosecond pulses by Strickland and

Mourou in 1985, it became possible to generate millijoule level femtosecond pulses via the

technique of Chirped Pulse Amplification. This saw an increase in peak power by six orders of

magnitude 1012W)over those generated by the Ti: sapphire laser oscillators. Current table top

laser systems can generate peak powers in the petawatt range (10'5W) (Perry et al., 1999;

Pennington et al., 2000, Kitagawa et al., 2004).These lasers have found a variety of applications

over the past decade and continue to do so as our understanding develops.









Peak powers of a megawatt are however insufficient for many experiments. Several

nonlinear optical processes like high harmonic generation, ultrashort surface science, generation

of extreme ultraviolet radiation (EUV) (to name a few) are limited by the availability of

ultrashort pulse energies and the average flux, making it necessary to amplify pulses from a self-

mode-locked Ti: sapphire oscillators. The technique of chirped pulse amplification has

progressed significantly since the amplified picosecond pulses from the system developed by

Strickland and Mourou (1985). Amplification of ultrashort pulses by a factor of 106 to generate

peak powers in excess of 1012 W (1 TW) at a repetition rate of 10 Hz was easily achieved (Maine

et al., 1988; Kimetec et al., 1991; Sullivan et al., 1991; Zhou et al., 1995; Chambaret et al., 1996).

S. Backus et al. (2001) extended the chirped pulse amplification technique to generate millijoule

level, femotsecond pulses at multikilohertz repetition rate in a single stage chirped pulse

amplifier system. Advantages of liquid nitrogen cooled Ti: sapphire crystal (Moulton, 1986;

Schulz and Henion, 1991) were incorporated into a multipass amplifier cavity.

The advent of such high intensity, ultrafast lasers has facilitated many experiments in

'high-field' science. Matter exposed to intense ultrashort laser light undergoes ionization as the

electronic wave packet is set free to oscillate in a laser electric field that is strong enough to

overcome the effective binding potential. Nobel gases such as neon, argon, etc. when exposed to

such intense electric fields, ionize generating electromagnetic waves at much higher frequencies.

Also free electrons in plasma can be accelerated over 100 MeV in a space of only a few

millimeters (Umstadter, 2001) using strong laser electric fields. As a specific example, millijoule

level amplified pulses are essential for non-linear processes such as generating sub-nanometer

range radiation, which are harmonics of the fundamental laser beam (L'Huillier and Balcou 1993;

Bartels et al., 2000; Reitze et al., 2004). When a high-energy ultrashort laser pulse is tightly









focused the intensities created corresponds to an electric field that often exceeds the binding

energy of a valence electron to the core of a noble gas atom. Within the first laser period the

ej ected electron from the parent ion is accelerated and it may return to the parent ion with a finite

probability releasing harmonics that are coherent, directional and shorter in duration as compared

to the driving laser pulse (Figure 1-1). Coherent soft and hard X-rays produced due to the

harmonic up-conversion are used to conduct frequency interferometry in the ultraviolet to probe

thin solid films and dense plasmas (Salieres et al., 1999; Descamps et al., 2000) and study

electron transport dynamics in semiconductors (Rettenberger et al., 1997).







20 25 30 35 40






al.,ap 200)




matuerials thatudrgo fbic ratedn mic rostrcue using fe 6mto 0-secn a0nd ioscn pulses s1




muc eteril tha n thgos parodcaed mcotcue using nanseodan iosecond pulses (iXeta.197VodrLind e


al., 1997). Such fast 'cold' ablation technique where the solid is changed directly to the gas









phase is highly desirable as it reduces effects caused by heat conduction and interaction of the

pulse with the ablated material.

In addition, amplified ultrashort pulses can further be compressed to sub-10 fs duration by

self-phased modulation of these pulses in hollow core waveguides and pulse compression

(Steinmeyer et al., 1999). Harmonics generated by such short and intense pulses give rise

coherent x-rays with pulse duration as short as 10-1 s (100 attoseconds) (Paul et al., 2001;

Hentschel et al., 2001) to study electronic state transition processes that occur faster than

femtosecond timescales.















(a) (b)
Figure 1-2: A sheet of invar micromachined with (a) 10 nsec pulses and (b) 100-fs pulses.
(http://www. cmxr. com/Indu stri al/Handb ook/Chapter7 .htm)

Femtosecond pulses with high energy and faster repetition rates are also utilized to perform

surface non-linear spectroscopy (Ostroverkhov et al., 2005; Liu et al., 2005). As a second order

nonlinear optical effect, second harmonic generation and sum-frequency generation are

forbidden under the electric-dipole approximation in media with inversion symmetry. But at the

surface or an interface this symmetry is necessarily broken. Thus non-linear surface spectroscopy

is surface specific. As described in Figure 1-3 (a), two laser beams at frequencies my~ and @2~ When

mixed at an interface generate surface-specific sum frequency (or second harmonic,









when mi, = mi, ) output in transmission or reflection. The signal is proportional to the square of the


nonlinear susceptibility j' ms) = my + m,: of the interface. Scanning m, over the vibrational

resonances of the molecules or adsorbates on the surface, gives rise to a vibrational spectrum,

which is unique to that particular surface/interface. When mi, and mi, are high energy pulses

derived from a high brightness femtosecond chirped pulse amplifier, the peaks in the vibration

spectra are well enhanced making it possible to detect surface abnormalities with ease.








Figure 1-3: ~ Schemaic-~ of surac spcrsoy()adatpclSmfeunyGnrto
spo,~ ectra (b).[ernd with permisonfo Supriee l,(91]

An ntese ltrshot lserpule a aailbletody, ithpea poers> 1 Wcm r
capable~ ofgnrtn lcrcfed ta xes f1"Vccnpoueawk fpam









A voume, w-Sherea is h avlnt of sra pe thesop lase randia tionscapal oum frq c generatinatoeond









pulses and electron bunches (Naumova et al., 2004; Ness et al., 2005). These laser-based

radiation sources may someday be used for cancer radiotherapy and as injectors into

conventional accelerators, which are critical tools for x-ray and nuclear physics research.

The above examples present but a few of the applications of ultrafast lasers in physics,

materials science, and chemistry. There is an ever-increasing need for ultrashort pulses at high

pulse energies and faster repetition rates driven by these applications. The generation of these

pulses is by no means trivial: the simultaneous requirement of high pulse energies (> 1 mJ) and

high repetitions rates (> 5 k
then becomes the key to the operation of these highly pumped lasers. Improved thermal

properties of sapphire at 77 oK (Moulton, 1986) allows for much efficient extraction of energy

from the crystal in an amplifier making it possible to achieve millijoule pulses at k
rates in a single amplifier stage (Backus et al., 2001). Lowering the crystal temperature way

below the ambient only reduces and does not eliminate the deleterious thermal effects. Thus in

order to increase the overall efficiency of the chirped pulse amplifier system an extensive

thermal analysis and characterization of the crystal in the amplifier becomes inevitable as it

provides a better understanding of these thermal effects.

In this thesis we develop and characterize a high average power, single-stage, chirped

pulse amplifier system that generates 40-45-fs pulses with pulse energies close to a 1mJ at 5 k
repetition rate. We present a systematic investigation of the thermal loading effects in such

amplifier systems. We experimentally characterize thermal aberrations in a regenerative

amplifier using a variety of techniques. Using Finite Element Analysis (FEA) we compute the

temperature distributions, optical path deformations (AOPD) and corresponding thermal focal

lengths for a variety of pumping conditions. Excellent agreement between the FEA modeling and









the experimental results allow us to predict optimal pumping conditions for minimizing thermal

aberrations that could further increase the efficiency of the system. The usage of the acousto-

optic programmable dispersive filter (AOPDF) as a pulse shaper makes this a unique and a

compact system capable of delivering ultrashort pulses in the millijoule range. High brightness

sources such as this is ideally suited for high harmonic generation which is essential for the

generation of attosecond pulses, plasma generation and acceleration of free electrons in plasma.

Applications such as femtosecond micromachining and surface characterization using nonlinear

frequency conversion techniques will benefit from the amplifier's high average powers for the

high signal-to-noise measurements via lock-in detection.

The layout of the dissertation is as follows: in Chapter 2 we discuss the principles of

ultrashort pulse generation and characterization. The design and construction of the various

components of a high average power, single-stage chirped pulse amplifier is described in detail

in Chapter 3. Chapter 4 deals with issues relating to the design, modeling and characterization of

the host of thermal effects in a regenerative CPA system. The experimentally measured results

are validated numerically using Finite Element Analysis (FEA). The characterization and the

optimization of the pulses from the amplifier system are elaborated in Chapter 5 along with

techniques that can further improve the efficiency of the CPA system. Finally we conclude in

Chapter 6.









CHAPTER 2
ULTRASHORT PULSE GENERATION AND CHARACTERIZATION

Before we begin to delve into the details of the construction and performance of a high

average power chirped pulse amplification system, it is beneficial to understand more about the

fundamentals of generation and characterization of femtosecond pulses. This chapter discusses

the various aspects of femtosecond pulses that are extremely crucial to the work described in this

thesis.

Beginning with a mathematical relationship between pulse width and the spectral

bandwidth the chapter discusses dispersion of broad bandwidth pulses. Principles of nonlinear

effects such as the second and third order effects that are crucial for pulse characterization and

the generation of ultra board brand sources respectively are discussed in the Einal sections of this

chapter.

2.1 Relationship between Duration and Spectral Width

A plane monochromatic wave of frequency 4i, (Figure 2-1 (a)) has an infinite spread in the

time domain.


E (t) = Re (E, exp (iw,t)) (2.1)

A light pulse can be generated from a sinusoidal electric field as in equation (2.1) by multiplying

it with a bell shaped function for the amplitude modulation. Choosing a Gaussian function the

above equation then transforms as


E(t)= Re E, exp (-Tft+ im,t) (2.2)

The time evolution of equation (2.2) is shown in Figure 2-1(b). r is the shape factor of the

Gaussian envelope. The spectral content of the two kinds of light pulses can be obtained by









performing a Fourier transform to the temporal domain. Figure 2-2 (a) and (b) are the numerical

Fourier transforms for the cosine and the Gaussian function in equations (2.1) and (2.2).

The monochromatic plane wave oscillates with a single frequency 4i~ whereas the Fourier

transform of the Gaussian function is also a Gaussian, with the width proportional to r .











tt
(a) (b)
Figure 2-1: Evolution of a plane monochromatic wave in time (a) and a plane wave with
Gaussian amplitude modulation in time (b).












(a) (b)
Figure 2-2: Fourier transform of the (a) cosine function in Figure 2-1(a) and (b) Gaussian
function in Figure 2-1 (b).

From the empirical relationship between the spectral width and the pulse duration of the

pulse, we can now derive a more formal relation (Seigman, pp.331). For a Gaussian electric field

as in equation (2.2), the instantaneous intensity can be expressed as


Ift)- = Elt) 2 = E2 ep- (41n, 2)1 t (2.3)









where r is the duration of the pulse measured at half the maximum intensity and is known as the

Full Width at Half Maximum (FWHM).

r, = Ju2(2.4)

The Gaussian spectrum in frequency is the Fourier transform of equation (2.2)


E (mi) = exp ( ~) (2.5)
4r


The power spectrum of the Gaussian pulse can be written in the same form as the instantaneous

intensity as in equation (2.3)



IS) E ()2= Bp-(1n ) (2.6)


The FWHM bandwidth of the Gaussian pulse is


Af = (2.7)





If in equation(2.2) C = (a ib), where b is known as the chirp factor, then the pulsewidth r,

and Af, undergo the following modification

~21n 2
Sa
b (2.8)



Incorporating the E in the expression for electric field equation(2.2), in the time domain









E (t) = E, exp(-at )exp i met + bt 1]
(2.9)
E (t) ac exp ig, (t)]

where,
40, (t) = mi,t + bt2 (2.10)

is the time varying phase of the Gaussian pulse. An instantaneous phase gives rise to an

instantaneous frequency 0i,.

dio, (t)
0 (2.11)

For the Gaussian pulse described above this instantaneous frequency is given as


m,(t) = mil,t+ bt = 4i, + 2bt (2.12)

Thus a Gaussian pulse with a time-varying instantaneous linear frequency is known as

being chirped with the parameter b being a measure of this chirp. Figure 2-3 demonstrates a

chirped Gaussian pulse.













Figure 2-3: Time evolution of a Gaussian electric field with a quadratic chirp (b = 10O) on it.

2.2 Time Bandwidth Product

The product of pulsewidth and spectral bandwidth is known as the time bandwidth product

(TBP). Multiplying equations (2.4) and (2.7) we get









21n 2
Afpr, = -_ 0.44 (2.13)


According to the uncertainty relation the time bandwidth product for a Gaussian pulse cannot be

less than 0.44. Chirp on a Gaussian pulse increases the TBP.


~ (2 1n 2 fb 2 fb 2
Af r= x +I- ~0.44 x 1+ (2.14)



Thus for a Gaussian pulse the minimum TBP is 0.44 and such a pulse is known as

'transform-limit' as the linear chirp-factor b = 0 .

The TBP depends on the shape of the pulse and the definitions of Af and At (rms, FWHM,

etc.). The table below compares the TBP for 3 fundamental pulse shapes suitable for laser beams,

for other forms of intensity profiles such as square, triangular, exponential etc. the reader is

urged to refer Sala et al (1980).

Table 2-1: Time bandwidth product for different pulse shapes (Figure 2-4)

Pulse Shape Intensity I(t) Afe At dit rdc

Gaussian _-20.4413
-e
Hyperbolic Secant = sech2X 0.3148
Lorentzian 1 0.2206
1+ x2
Note: Adapted from Sala et al. (1980).









Figure 2-4: Intensity profile for a Gaussian pulse (solid blue curve), hyperbolic secant (dashed
blue curve) and a lorentzian (red curve).

2.3 Dispersion

Ultrashort pulses, with its broad spectral content undergo dispersion as they propagate in

air, materials, etc. Dispersion is said to occur when the phase velocity of the wave depends on its

frequency (Born and Wolf). The vacuum dispersion relation is given as: m,= ck where 0i is the

angular frequency of the radiation, k is the wave number and c is the velocity of light in free

space. For such a dispersion relation the phase velocity (v, and the group velocity vg) are the

same. In a dispersive medium, the dielectric constant is a function of frequencye(mi) with the

consequence that v, + vg Different components of the wave travel with different speeds and tend

to change phases with respect to one another. An ultrashort pulse propagating through such a

media will undergo changes in its shape ultimately leading to temporal broadening.














Figure 2-5: Schematic relationship between phase and group velocities for a transparent
medium (v < v ).

The electric field of an ultrashort pulse, in the frequency domain is given by equation (2.5).

After the beam propagates through a distance x its spectrum is modified accordingly as

E(B) = E, (w)exp +ik (w)x] (2.15)









where k (m) = n/cul is a frequency dependent propagation constant, with n2 being the refractive

index of the medium. If the propagation constant k (mi) is a slowly varying function of a ,: it can

expanded in a Taylor series expansion about a central frequency mi, as long as As I .

dk 1 8 k 2 1 8 k 3
8m ~2!8 3! Sm"'


The frequency dependent propagation constant k (mi) will modify the pulse as it propagates

through the medium. Substituting the above expression in equation (2.15)


E m)= x -k,(m -ikx m- ,)- k~ ( -m) +.. (2.17)


where, k'= (8k/8m/co~ csandk" = (8k/8d~),0= ,,. The temporal evolution of such a pulse can be

obtained by a Fourier transform of its spectral shape (Rulliere, pp.33).


E(t)= 1 E(w)exp(-imt)ds (2.18)
2 x

E (t = xp s, t- F(x)t -(2.19)


The first term in the exponent produces a time delay by an amount x/v:, after propagation though

a distance x The quantity v, (c,) = (m/k)0 is the phase velocity of each of the plane wave

components of the pulse in the medium. vg (e ) = (d'k/dw)l is known as the group velocity and

determines the speed of the pulse in the medium. For cases where el, 0i, vg < v and the


pulse is said to undergo normal dispersion. Now F(x) =1/ + 2ik~x, where" = d/de v, (mc)l

is known as the group velocity dispersion. Figure 2-5 is a schematic of the dispersion effect in a









medium with a dispersion relation m = ck (c() Thus the equation (2.19) demonstrates that a short

pulse propagating through a transparent medium undergoes delay, a broadening of its pulse

duration accompanied by a frequency chirp.

2.4 Nonlinear Effects

2.4.1 Second Order Susceptibility

Light intensities generated by an ultrashort pulse can change optical properties of the

medium that they pass through. The intensity dependent changes to the optical properties of the

material constitute nonlinear optics. Many of these nonlinear optical effects tend to be useful

while generating and characterizing ultrashort pulses.

On expanding the polarization in a Taylor series expansion

P = X' E + X'mEE + X'3EEE +... (2.20)

The first term in the above equation is the linear term whereas it's the higher-order terms that

account for the nonlinear optical effects.

Second-order optical effect or second harmonic generation (SHG) is caused due to the second

order susceptibility term Xc: It is characterized by the second-order polarization P(2 (t) .


Pm' (t) = X'mEE*~ (2.21)

Two photons of frequency ai combine in a medium to give rise to a single photon of

frequency 2mi (Figure 2-6). But the process of second harmonic generation is dependent on the

orientation of the crystal axis and the polarization of the incoming light. If the medium posses an

inversion symmetry, X(2 vanishes uniformly over the bulk of the medium. SHG in such cases

can be observed either at an interface or on the surface of the medium. For an impinging

intensity I(mi) of frequency ai with a propagation constant k, the intensity of the second









harmonic signal I(2mu) with the propagation constant k, = 2k, through a nonlinear crystal of

length Iis given as (Boyd)


I (2m) ='Z 2~~1 I2 (0)~ l2)] (2.22)


where, Ak = k, 2k, is known as the wavevector mismatch. The SHG process is most efficient

for the perfect phase matched condition where Ak = 0 .













Figure 2-6: Geometry of second-harmonic generation (a) and schematic energy level diagram (b).

As the SHG signal for a given crystal length, orientation and polarization of the incoming

light is directly dependent on its intensity, it is extensively used to measure the pulsewidth of an

ultrashort pulse as described in detail in appendix A.

The second order susceptibility is also responsible for a variety of other effects that involve

3 photons such as the sum-frequency generation (SFG) where two incoming photons of

frequency my~ and ai~ combine in a nonlinear crystal and generate a signal at the sum

frequency 03,= my,+m ~. Difference frequency generation (DFG) is a process where the two

incoming photons generate a signal at the difference frequency 03~ = mi~ my~ where 0i~ > 0i, The

satisfaction of the phase marching condition Ak = k, + k, k, determines the efficiency of all

these process within a non-centrosymmetric crystal.









2.4.2 Third Order Susceptibility

Three photons mix to generate third order nonlinear effects due to the third order

susceptibility X(3) term equation(2.20). The third order polarization term can be written as

P(3) X(3)E.E*.E
(2.23)
P(3) __ (3)I.E

Some of the third order effects include third harmonic generation (as in Figure 2-7) where

three photons of frequency ai combine to generate a photon of frequency 3m ,. Unlike the second

order effect, the third order effect can occur in any media irrespective of the symmetry and can

also occur in liquids and amorphous materials such as fused silica.

The number of effects increases as the order of nonlinearity increases. The primary focus

of this chapter will be to discuss the effects related to generation and characterization of

ultrashort pulses.














Figure 2-7: Geometry (a) and schematic of third order generation (b).

2.4.2.1 Nonlinear index of refraction

The intensity of the ultrashort pulse in a medium changes its optical properties. The third

order polarization in equation (2.23) when combined with the linear polarization term becomes

P = '1'E + 3. g(3)I.E = X, E(m)
(2.24)
where, Xpt = X(1 + 3.g(3)1









where I = E2 is the intensity of the incident ultrashort pulse. The second order term can be

made to vanish in the above equation due to symmetry conditions in the crystal. For a

centrosymmetric medium X(2) VaHishes and for non-centrosymmetric medium the second order

effects can be eliminated by orienting the crystal in such a way so as to satisfy the phase

matching condition only for X(3) effects. The refractive index of the material is defined

as: n2 = 1+4. 3 c. Substituting for X74, the refractive index can be expressed as


n2 = 1+c4nXrf c +12.:? IE(co) 2 (2.25)

The refractive index of a material, when a high intensity laser beam is incident on it, can also be

described by the following relation

n2 = no0 +n12 IE 2 (2.26)

where no and n2 are the linear and nonlinear index of refraction respectively.

Comparing the relations (2.25) and(2.26), one can obtain expressions for no andn2


n0 = 1+ 4g 111/2

n2_6q(3)j (2.27)


For an ultrashort pulse the intensity is a function of both space and timelI(r, t) Both the spatial

and temporal dependence of intensity leads to interesting effects such as Kerr lens effect, self-

phase modulation, self-focusing, filamentation etc. Effects that lead to the generation of

ultrashort pulses are discussed in the following sections.

2.4.2.2 Kerr lens effect

The spatial intensity profile of a Gaussian laser beam propagating in a X(3) material is










I(r)=exp(-gr ) (2.28)

The refractive index of the material also gains a spatial gradient given as

n2(r) = nlo +nI2(r.) (2.29)

This generates a refractive index gradient as in Figure 2-8 that follows the gradient in the

intensity profile of the incident ultrashort pulse. For a nonlinear index of refractionn, > 0, the

refractive index is greater at the center of the medium as compared to the sides. The amount of

nonlinear phase accumulated by the ultrashort pulse as it passes through this graded index

material is

2xi 2xi 2xi
O(r) = n,1ol- n IIl(r) = -0o Y n I(r) (2.30)


This effect similar to a static lens, increases the focal power of the material due to the spatial

variation in the phase of a traversing beam such that beam focuses into the material. This effect

known as Kerr lens effect is of utmost importance in understanding self mode-locked Ti:

sapphire laser oscillators.


nz>0






Figure 2-8: Schematic representation of the Kerr lensing effect. The KLM effect leads to the self-
focusing of the intense ultrashort pulses.

2.4.2.3 Self phase-modulation

The temporal profile of a Gaussian pulse incident on a X3 material is


Ir) t = x (2.31)









Thus the refractive index is then transformed as


n(t) = no + n2,I 0 Xp (2.32)


The time varying intensity leads to a time varying refractive index as the pulse propagates

dn dl t 2 ii2 t
dt = 2 dt ~r x 722 (2.33)



An instantaneous refractive index brings about a change in the total phase ( = -2xinl/Al)

accumulated by a pulse or a phase delay as it propagates through such a medium.

2xi 2xi 2xi
O(t)= nol n 0 21(t) (2.34)


where ii is the vacuum wavelength of the carrier and nolis the optical length traversed by the

pulse. This generates a time varying shift in frequency

dO 2xi dl
mi(t) -m n
dt jl dt

a~(l)~ In,(2.35)



A plot of Am ~(t) (Figure 2-9) shows that the leading edge of the pulse shifts towards the

lower frequencies ('red' shift) and the trailing edge shits towards higher frequencies ('blue' shift),

generating an overall increase in the bandwidth of the pulse.

Although the spectral content of the pulse is increased as it passes through such a crystal

the temporal structure remains unaltered by the self-focusing effect. But natural dispersion

occurring within the crystal tends to broaden the pulse.










Ti: sapphire-based laser oscillators make use of the Kerr-lensing effect to generate pulse as

short as 6-fs (Jung et al., 1997) directly from an oscillator which is described in detail in the

following chapter.


2 oi








23500 -50 0 50 100




time fs
Figure 2-9: Schematic of Self-phase modulation. (a) A Gaussian pulse propagating through a
nonlinear system undergoes self focusing effect (b) which gives rise to additional
frequency components which when compensated for material dispersion generates a
short pulse.

2.5 Summary

We briefly discussed in this chapter the essential theoretical background needed to

understand the various nonlinear process such as the generation of femtosecond lasers through

the Kerr lensing effect. Also processes such as the second harmonic generation which is a

commonly used tool to characterize ultrashort pulse widths, were discussed in considerable detail.

More on the technique of measuring ultrashort pulses are elaborated in Appendix A at the end of

this dissertation.









CHAPTER 3
DESIGN AND CONSTRUCTION OF A HIGH AVERAGE POWER, SINGLE STAGE
CHIRPED PULSE AMPLIFIER

3.1 Introduction

Strickland and Mourou (1985) developed the first ultrashort laser in the year 1985, capable

of delivering millijoule pulses at picosecond time scales (2x10-12 Secs) at a wavelength of 1.06

Clm, by the technique of chirped pulse amplification. Ultrashort pulses by definition support a

large spectral bandwidth(Av~r= const) Amplification of ultrashort pulses enforces certain

minimum requirements on an amplifier system. First, the amplifier bandwidth must be wide

enough to accommodate the spectral bandwidth of the seed or the un-amplified pulses. As a wide

range of Fourier components is required to produce an ultrashort pulse, a gain medium with a

narrow emission bandwidth could not possibly support ultrashort pulses. The central wavelength

l, of the seed pulses must efficiently extract the stored energy in the amplifying medium, i.e the

fluence of a pulse must be close to the saturation fluence of the amplifying gain medium

J,, = hu/a, where o, is the gain cross-section of the gain medium. Finally the peak intensities

generated within the amplifier must be well below a certain critical level above which nonlinear

effects as discussed in chapter 2 can distort both the spatial and the temporal profile of the

amplified beam and in some cases can damage the optical components within an amplifier as

well.

3.2 Why Chirped Pulse Amplification?

While amplifying femtosecond pulses, the phase shift experienced by a propagating

ultrashort pulse in an amplifying medium can be both linear and nonlinear









2xi 2xi
hToal =,ZI nl~ (n, + n,I(r, t))1
Ai A (3.1)


The linear phase 2n.,;-7~/Al arises due to the linear index of refractionn,. The nonlinear phase

shift arises from the nonlinear response (distortion) of the electron cloud surrounding an ion

subjected to an intense electric field. As can be seen from equation (3.1), the peak intensities

associated with an ultrashort pulse introduce additional phase delay (n,2 > 0) and therefore

experience enhanced nonlinearities, which are manifested both in temporal as well as spatial

distortions of the laser pulse. One can calculate the nonlinear phase accumulated by an ultrashort

pulse along an optical path L as (Koechner, 1976)

~L L
2Oz i= nIrtd (3.2)


where n, is the nonlinear index of refraction of the lasing medium and I (r, t) is the instantaneous

pulse intensity within the amplifier cavity. A peak value of 5 for the nonlinear phase Oz (for

historical reasons also known as the 'B integral') corresponds to a critical intensity (Maine et al.,

1988) above which only high spatial frequencies are preferentially amplified, reducing the

spectral bandwidth of the amplified pulses that ultimately results in longer pulses. As noted in

the previous chapter a host of nonlinear effects are associated with the spatial as well as the

temporal variation of the intensity of an ultrashort pulse. And if the accumulated nonlinear phase

exceeds this critical value, the ultrashort beam becomes distorted due to these nonlinear

processes (Boyd, 2003). Thus keeping the amount of nonlinear phase that an ultrashort pulse can

gather, much below the threshold value is of utmost importance in amplifying these pulses to

high energy levels.









Given a suitable gain media like Ti3+:Al203 (which shall be discussed in the following

section), the technique of chirped pulse amplification circumvents the generation of excess

amplified intensities capable of damaging amplifier materials or causing nonlinear effects. Figure

3-1 illustrates a schematic of a chirped pulse amplification system.

This technique relies on increasing the duration of the pulse being amplified by introducing

a controlled amount of dispersion ('chirping' the beam) and then optically compressing (Treacy,

1969; Martinez, 1987; Martinez, et al.,1984) the amplified beams to its original pulse duration.










Fs-Laser I M Stretcher I Amplifier 1 Compressor *

Figure 3-1: A schematic representation of a Chirped Pulse Amplifier system. The pulse cartoons
represent the temporal structure of the pulse at each stage in the amplification process.

Temporally lengthening (or 'stretching') the pulses reduces the peak intensity, enabling

efficient energy extraction from the amplifier gain media by distributing the total energy content

of the pulse over a broader time scale. Chirped pulse amplification becomes particularly useful

for amplifiers utilizing solid-state gain media with high stored energy densities (1--10 J/cm2)

well above the damage threshold of several optical components, in order to efficiently extract the

entire stored energy in the gain media.

The following sections contain an in depth discussion of the various components of a

single stage, CPA system in our laboratory.










3.3 Ti: Sapphire as Gain Medium

Ultrashort pulse amplification needs very broadband gain media. Femtosecond amplifiers

in the past relied heavily on broadband laser dyes and excimer gain mediums as the amplifying

material (Ippen and Shank, 1986; Downer et al., 1984; Knox et al., 1984). Due to the low

saturation fluences offered by these media, the amplified output powers were severely limited by

the size of the amplifying medium. But solid-state media such as Nd: glass, Cr3+ doped BeAl204

(Alexandrite), Cr3+ and Ti3+ doped Al203 (Sapphire) not only posses much higher stored energies

(~ 1J/cm2) but also display extremely broad emission bandwidths to support ultrashort pulses

(Moulton, 1992).

1.0














---Absorption \ -Fluorescence

0.0
400 500O 600 700 800 9100

Figure 3-2: Absorption and emission spectra for Ti: sapphire. [Adapted from Rulliere (1998)].

Of all the solid state materials available, Ti3+ doped Al203 (COmmonly referred to as Ti:

sapphire) emerged to be the most promising material (Moulton, 1986). The early nineties saw a

boom in the use of Ti: sapphire as an active medium to produce femtosecond pulses due a

number of its features that were desirable as a laser host material. With a damage threshold of 8-

10 J/cm2 (COmparable with metals), high saturation fluence of 0.9 J/cm2, a peak gain cross-









section og of 2.7 x 10-19 /cm2 (Backus et al., 1998) and an extremely broad gain bandwidth of

230 nm (Moulton, 1986), there is little doubt as to why Ti: sapphire is a favorite among

femtosecond-laser developers! Ti: sapphire exhibits a peak absorption maximum at 500 nm.

Figure 3-2 indicates the absorption and emission bandwidths for Ti3+ doped Al203. With the

availability of high average power diode-pumped solid-state lasers, such as the frequency

doubled Nd: YAG and Nd: YLF laser source (laser emission at 532 nm), Ti: sapphire quickly

became the obvious choice in the development of table-top terawatt sources (Backus et al., 2001).



P, 8I~00 nm, 30 fs




2 n/e~n nPump Laser
HR

Ti: Al Os L

Figure 3-3: Self-mode-locked Ti: sapphire laser oscillator. The cavity is formed by a high
reflecting mirror (HR) and an output coupler (OC). The pump beam is focused on to
the crystal which is placed in a sub-resonator formed by mirrors M1 and M2.
Dispersion compensation is achieved by prisms P1 and P2.

There has been a tremendous amount of progress in the generation of femtosecond pulses

since the construction of the first self mode-locked Ti: sapphire laser by Spence et al. in 1991

generating 60-fs pulses. With further improvisations to their optical design (Figure 3-3), it

became possible to generate pulses as short as 6 fs (Jung et al., 1997) directly from a laser

oscillator. Short pulses were achieved by the process of Kerr-Lens mode-locking (discussed in

the previous chapter), wherein an inherent nonlinearity of the Ti: sapphire crystal was creditably

exploited, which is yet another reason why Ti: sapphire is the most revered material for

ultrashort pulse generation!









3.4 Mode-locked Laser

Mode-locking is the essential mechanism to generate pulses from a laser oscillator. A laser

cavity allows oscillation only for di screet resonance frequencies that sati sfy the

condition = mc/2L where cis the velocity of light and L is the length of the laser cavity and

m is an integer. The longitudinal modes of a laser cavity oscillate freely and the output intensity

consists of different modes with no specific phase relation with respect to each other and the

laser is said to be operating in a 'continuous wave' or cw mode. These modes which initially

possess random phases, when forced to oscillate with a well defined phase constitutes a pulse

and the laser is then said to be lasing in a pulsed mode with a finite bandwidth spectrum as in

Figure 3-4.

Mode-locking in dye lasers and in certain solid state media was achieved either by an

external modulation (active mode-locking) or by placing saturable absorbing medium in the laser

cavity (passive mode-locking).











Figure~ ~ 3-:Gneain futrsot uss yte ehnimo md ocig

Ti: sapphire laser does not require either extrnatmlatino strbl borest







Fgu 34 enerateo o ultrashort pulses. Thi ise knowns asse f mode-locking. A icse ntepeiu









chapter, an intensity dependent variation of the refractive index of the Ti: sapphire crystal,

arising from a non-uniform power density distribution in Gaussian beams gives rise to an

intensity dependent phase-shift that leads to the generation of multiple modes within the

oscillator cavity. The amplitude of the short pulse is modulated in such a way that intense pulses

experience less loss than weaker pulses and can therefore sustain within the cavity.

Figure 3-3 is a schematic of a self-mode-locked Ti: sapphire laser oscillator. The laser

cavity is formed by two plane mirrors, one a high reflecting mirror (HR) and an output coupler

(OC) which is partly transmitting. The Ti: sapphire crystal is placed in a sub resonating cavity

formed by two identical spherical mirrors of radii of curvature 10-cm, which are dichroic in

nature, transmitting 532-nm and reflecting 800-nm. Two fused silica prisms placed in the longer

arm of this asymmetric cavity provide the phase compensation necessary to achieve mode

locking. The Ti: sapphire crystal is pumped by a 5 W Coherent Verdi which is a diode pumped

Nd: YVO4 laSer system.

The refractive index of sapphire varies with the intensity of the incident pulse

as n = no + n2I(r) The crystal behaves like a converging lens asn2 > 0 The Kerr lensing effect

in conjunction with the self-focusing of the laser beam within the crystal gives rise to the

broadening of the spectral content of the pulse.

Although the spectral content of the pulse is increased as it passes through the Ti: sapphire

crystal the temporal structure remains unaltered by the self-focusing effect. But natural

dispersion occurring within the crystal tends to broaden the pulse. The prism pair inside the

oscillator cavity generates negative dispersion to compensate for the positive dispersion

introduced by the crystal (Martinez et al., 1984; Fork et al., 1984), enabling the generation of

femtosecond pulses from the oscillator. Careful balancing of the self-phase modulation effects










and the group velocity dispersion due to the prism pair causes all the modes in the oscillator to

have the same optical path length through the crystal, forcing them to oscillate in phase to

generate a train of mode-locked pulses with a repetition rate 1 aR where zR is the round trip time

around the cavity.

The peak intensities inside the Ti: sapphire crystal must be high enough to induce

nonlinearity but well below a critical level, which can distort the beam within the cavity. In order

to favor the high intensity pulsed operation of the laser over the continuous-wave (cw) mode, old

designs of the Ti: sapphire oscillator used a hard aperture blocking out the large waist modes that

correspond to low intensity levels.









Waeant (m

Figure;8 3-5:LZ ~ Osiltrsetu s esrdb ie p ecrmtran t orertasom
Inst s hecacuatd empra pofle(tmpra bndwdt o 1 f) ssmig
consant haseacrss te enire pecral andwdth











Fi The m-.odltos inathemesre spectrum as ered an ariactoh fiber spectrometer. The itempora roiler wrans
calulaed nfrset fitrn the meascured sepecrum w oith a avtzky-orl a sooting funto and then perfoming
aninereourertransfr on the arsmoothedetr spectrum.adidh









stroking the prism next to the high reflecting mirror. The oscillator routinely generates 300-400-

mW mode-locked pulses at the repetition rate of 90 MHz (defined by the cavity length), centered

at 800-nm and a full width of half-maximum bandwidth (FWHM) of 80-90-nm, an average pulse

energy of 2-5 nJ depending on the alignment. A pair of razor edges that form a slit allows tuning

of the mode locked spectrum. In order to stabilize the laser in the mode locked state, the Ti:

sapphire crystal is maintained at a constant temperature of 20 oC by a circulating water chiller.

Also for prolonged stability, the laser is isolated from the environment by enclosing it in a

protective case. Due to the absence of an external compensator to generate transform limit pulses

from the oscillator, the temporal FWHM is always greater than calculated as in the inset of

Figure 3-5.

The seed pulses from the oscillator are then introduced into a pulse stretcher to temporally

broaden the pulses before they can be inj ected into the amplifier.


3.5 Dispersion

The phenomenon of dispersion is very important to the Hield of ultrafast optics. As

ultrashort pulses, with their broad spectral content undergo dispersion as they propagate in air,

materials, etc., dispersion management then becomes the key to developing really short pulses.

As previously noted, dispersion is said to occur when the phase velocity of the wave depends on

its frequency (Born and Wolf). Different components of the wave travel with different speeds

and tend to change phases with respect to one another. An ultrashort pulse propagating through

such a medium will undergo changes in its shape ultimately leading to temporal broadening. The

electric field of an ultrashort pulse is represented in the frequency domain as

E~m)= E~) ex (iq(m))(3.3)









where E(co)is the amplitude modulation for a finite beam and #(0) is the phase of each of the

frequency components present in the beam. If the spectral phase #(0) is a slowly varying

function of ai (this does not hold true in regions of 'anomalous dispersion' where n~i) varies

rapidly over narrow intervals of mi) then it can expanded in a Taylor series expansion about a

central frequency mio.

8 ~1 82~ 2
(m) = + (0 G (C( -~ o)? +- (m G) +... (3.4)
8m 2!cm 802 3! 3

where 8 /80i, 82 l~i2 and 83 l~i3 are the derivatives of phase with respect to frequency and

are known as group delay, second-order dispersion or group velocity dispersion (GVD), third-

order dispersion (TOD), fourth-order dispersion (FOD) and so on. The variation of the group

delay r = 80/80i with frequency is





From the above expression, it is clear that the #"(mo), known as frequency-sweep rate linearly

chirps the pulse and #"(mo~) generates a quadratic chirp on the pulse, etc. Figure 3-6 (a) and (b)

illustrate a Gaussian pulse with a second-order and third order phase on it that generates a linear

and quadratic chirp on it respectively.

For pulses that undergo normal dispersion in materials, the phase change is given

by ma, (mi) = La,n(mi) m/~c Thus longer wavelength components in the pulse travel faster than the

shorter wavelength components i.e 'red' travels faster than 'blue', introducing a positive chirp. A

pulse compressor then becomes inevitable to compensate for this positive chirp.

The management of spectral phase is thus of utmost importance in the design of a chirped

pulse amplifier system. The next section deals with the broadening or the chirping of the pulses









in order to effectively amplify them in an amplifier and their recompression back to femtosecond

time scales.










t









Figure 3-6: A Gaussian pulse possessing (a) linear chirp (#"(co,)) on it and (b) quadratic chirp

(#"'(w,)) on it.

3.6 Pulse Stretching and Recompression

As an ultrashort pulse propagates through the different optical components in an amplifier

cavity, the material dispersion accumulated must be compensated for in order to achieve shorter

pulse durations. Also in order to reduce the risk of damaging the amplifier components and to

keep the amount of accumulated non-linear phase [equation(3.2)] well below the threshold level,

femtosecond pulses obtained from the Ti: sapphire oscillators must be temporally broadened

before they can be injected into an amplifier. Also, in order to generate ultrashort pulses in a

mode-locked Ti: sapphire oscillator it becomes necessary to compensate for the group velocity

dispersion (GVD) such that all the spectral components of the pulse can travel with the same

group velocity around the oscillator cavity. Thus dispersive components become an integral part

of a chirped pulse amplifier system.









Pulse stretching can simply be accomplished by material dispersion. As beams traverse

through material they tend to broaden temporally owing to normal dispersion. But for most

materials significant lengths are needed to achieve stretch factors of 104 which are required to

amplify nanojoule level femtosecond pulses to the millijoule level. In addition, one cannot avoid

beam distortions due to the increased B-integral.










M,







Figure 3-7: Dispersive delay lines. (a): A pair of anti-parallel gratings forms a pulse compressor
(Treacy, 1969) and (b) Pulse stretcher formed by anti-parallel gratings with a unit
magnifieation telescope between them by Martinez et al. (1984).

In 1969 E. B. Treacy showed an extremely clever way of broadening pulses in time by

using an anti-parallel grating pair (Figure 3-7(a)). Significant stretch factors could be achieved

with this arrangement, although as originally conceived the Treacy configuration was designed

to produce negative group delay dispersion that could compensate for positive material

dispersion. The grating pair disperses the spectrum of the pulse, such that the 'blue' edge of the

spectrum travels faster than the 'red' edge through the grating arrangement. The first grating

serves the purpose of dispersing the spectral content of the pulse and hence the negative GVD,

and the second grating recollimates the different wavelengths. Martinez (1987) designed a

compressor with dispersion opposite to that of the Treacy's design (Figure 3-7(b)). A telescope










placed between a pair of anti-parallel gratings modified the effective length between them

yielding positive group velocity besides providing a high magnification yielding compression

factors as high as 3000.

The phase shift across the spectrum of the pulse as the beam propagates though the grating

pair can be calculated as (Treacy, 1969)





where Lg is the perpendicular distance between the gratings, 7 is the incidence angle, B is the


angle between the incident and the diffracted beams, ii is the central wavelength of the spectrum

of the pulse and d is the grating constant. One can derive the group velocity dispersion (GVD)

from the above equation

824 87 4;~cL,/cos(7-6)
2(3.7)
m~d smyv


The expression for GVD for the Martinez stretcher (Figure 3-7 (b)) is the same as eq.(3.7)

except with an opposite sign. The above expression is for a single pass through the grating pair.

The beams are made to pass once again through the arrangement to remove the wavelength

dependent spatial walk-off, by reflecting them off a retro-reflector or a pair of mirrors used in a

roof geometry. Due to the ease of their construction the stretcher and the compressor are

designed in such a way as to exactly reproduce the input pulse temporally.

Martinez et al. (1984), showed that negative GVD can also be generated from a pair of

prisms arranged in parallel. While the reflective grating geometry as in Figure 3-7 (b) is not an

easily adjustable design the prism arrangement in Figure 3-8 provides both low loss as well as

tunability from negative to positive values of GVD and hence is incorporated into the mode-









locked Ti: sapphire oscillator to compensate for the varying pulse GVD which is alignment

dependent. It is based on the idea that wavelength dependent phase delay caused by angular

dispersion always yields negative GVD.













Figure 3-8: Prism delay line. A pair of parallel prisms generates negative GVD that can be varied
by changing the distance between the prisms (Martinez, 1984; Fork, 1984).

In the Figure 3-8, the optical path between the points A and B is

A = ~c/mi = nL eos B (3.8)

The GVD term is given as

d2 A'3 dA8
(3.9)
dei, 27r c2 dA1

Substituting for A from equation (3.8) in equation (3.9) and calculating the GVD along the

direction of the wave vector (6 = 0) yields

dA dn d 3.0
-2d1 = n d L (3.10


The above expression yields a negative GVD regardless of the sign of the term d8/dAl The first

prism, as in the case for the grating pair, causes the angular dispersion and the second prism

serves to recollimate the different wavelengths. The net dispersion is also easily adjustable by









translating one of the prisms normal to the incident beam without altering the optical alignment.

This allows for the introduction of material dispersion without changing the negative GVD.

For amplified pulse duration < 35-40 fs, getting rid of the residual phase over a large

spectral bandwidth becomes a formidable task due to the mismatch of the compressor i.e when it

is not able to compensate completely the chirp introduced in the stretching and the amplification

process. The all-refractive stretcher design by Martinez et al. (1987) introduces strong chromatic

aberrations (a wavelength component that diffracts from the first grating at an angle of 6 must

arrive at the second grating at the same angle) inevitably causing a mismatch between the

dispersive delay lines in a CPA. A. Offner (US Patents, 1971) came up with an all-reflective

triplet combination that reduces the effects of chromatic aberration. When used as a stretcher,

this design makes it possible to recompress amplified pulse to near transform-limit. The Offner

triplet consists of a single grating and the refractive unit magnification lens telescope in the

traditional stretcher design by Martinez is replaced with two concentric spherical mirrors, one

concave and the other convex. The use of spherical mirrors reduces the aberrations to only

spherical order, which in turn are further reduced owing to the fact that the ratio of their radii of

curvature is two and they are of opposite signs. Although any deviation of the grating from the

center of curvature (Gill and Simon, 1983) of the two mirrors, causes astigmatism leading to

degradation in the temporal pulse profile.

Cheriaux et al. used a slightly modified version of the Offner triplet in their stretcher

design for their CPA system (1996). Although they had to place the grating out of the plane of

curvature for stretching purposes, the spherical aberrations as a result of this arrangement were

calculated to be very small such that the temporal shape of the pulses remained unchanged. Their

calculations also indicated that the spherical aberrations were significantly less severe than a











slight misalignment of the components in Offner's triplet design. Further improvisation to the

stretcher design by Cheriaux et al., (1996) M. B. Mason et al. (2000) came up with an all-

reflective doublet geometry (Figure 3-9) that lets the diffraction grating lie at the aberration-free

position in a stretcher configuration, enabling nearly perfect recompression of the broadened

pulses. It has the capability of achieving large stretch factors with over-sized optics while totally

eliminating any aberrations to the pulses.

Concave
Input Mirror, R= 120-cm
Grating



Convex Mirror Plane
R- 101-cm Mirror
L=115-cm


Figure 3-9: Schematic of the stretcher layout. Oscillator pulses of duration ~20 fs are stretched to
~ 200 ps without any chromatic aberrations.

















Wavelength (nm)
Figure 3-10: Spectrmm measured from the oscillator and after propagation through the pulse
stretcher. Spectral clipping on the red side of the spectrmm is due to insufficient width
of the optics in stretcher.

The stretcher in our CPA system uses the Mason doublet design to achieve stretch factors

as high as 104. The pulses from the oscillator are broadened to ~200-ps. Pulses are incident into

the stretcher at an angle of 8.240 (close to Littrow angle). We use an 8-inch diameter concave









mirror of radius of curvature of 120-cm to set a band-pass limit of ~100 nm on the spectrum of

the seed pulses. A convex mirror of radius of curvature 101-cm is placed about 70-cm from the

concave mirror. This arrangement produces an effective length (Lg, as in eq.(3.7)) of 121-cm. A

schematic of the stretcher setup is given in Figure 3-9. Some spectral clipping (Figure 3-10) is

observed in spite of the use of large optics in the stretcher.

For ideal compensation the incident angles and the effective lengths for the stretcher and

compressor must be close. But the incident angle for the compressor in our setup is 180 and the

effective length is about 125 cm. This is to account for the material dispersion and the higher

order dispersion terms added to the total phase of the pulse due to the amplification process.

3.7 Ti: Sapphire based Laser Amplifier

Amplifying femtosecond pulses in the milli-joule range was once only possible using dye-

amplifiers (Knox, 1988). Ti: sapphire based regenerative amplifier was first introduced in 1991

by J. Squier, et al. following the introduction of Ti: sapphire based laser oscillators by Spence et

al. (1991). These systems demonstrated a two-fold increase in the pulse energies. Also due to

their wide tunability and low background as compared to the dye amplifiers, it was possible to

generate more than 2 W of average power from Ti: sapphire amplifiers at a repetition rate of 10

k
repetition rate pump lasers, low repetition rate systems soon grew more popular as pulse energies

as high as a joule were available at a repetition rate of 10 Hz (Sullivan et al., 1991; Zhou et al.,

1995). A few millijoules of amplified pulse energy were attainable at 1 k
(Vailliancourt et al., 1990; Backus et al., 1995). When high average power pump sources

became available, pumping water-cooled Ti: sapphire crystal in the amplifier cavity generated

huge thermal loading which then limited the pulse energies to a few micro-joules in high









repetition rate CPA systems. As the pump power is increased to achieve large amplification

factors, the residual heat in the Ti: sapphire crystal gives rise to deleterious effects that influence

pulse energies and mode quality, limiting the overall efficiency of the system. Specifically, the

thermal gradient generated within the crystal due to the pump beam, consequently gives rise to a

gradient in the index of refraction of sapphire that causes the crystal to act as a positive lens (De

Franzo and Pazol, 1993; Moulton, 1986).

Moulton (1986) and later Schulz and Henion (1991) observed that the thermal properties of

sapphire improved upon cooling to 93 OK. They noted that calculations of the thermo-optic

aberrations indicated an increase in the output power capabilities of a Ti: sapphire laser by 200

times at 77 oK than at room temperature. Several groups have since developed high brightness,

high repetition rate ultrafast laser systems which mitigate or circumvent these thermal effects.

Backus et al. (2001) produced a millijoule level, femtosecond single-stage multi-pass chirped

pulse amplifier at 7 kHz repetition rate utilizing cryogenically (LN2) COoled Ti:sapphire crystal.

By cooling the crystal to temperatures near 77 K, a forty-fold increase in the thermal

conductivity (Touloukain et al., 1973; Holland, 1962) and five-fold reduction in the temperature

dependent refractive index term (dn/dT) at low temperatures (Feldman et al., 1978) is obtained.

Zhavoronkov and Korn (2004) demonstrated single-stage regenerative Ti: sapphire amplification

at multi-kilohertz repetition rate to powers of 6.5 W at 20 k
210 K and a cavity design that takes into account the strong astigmatic thermal loading of the Ti:

sapphire rod. Zhou, et al. (2005) have used two stages to avoid large thermal loading present in

single-stage systems to generate 7 W of average power at a repetition rate of 5 k








3.7.1 Process of Amplification

Optical amplification occurs in a medium where the equilibrium configuration of the

system comprises of its atoms or molecules in a state with higher energy content as compared to

the ground state of the system. This electronic exchange between the two energy states is

achieved by an external pump source. Amplifieation occurs when an electromagnetic wave of

appropriate frequency passes through such an 'inverted' medium, resulting in a release of

photons as the atoms drop back to a lower energy state, thereby extracting energy from the

system. The gain of the amplifying medium is defined as the ratio of the output intensity to that

of the input intensity. For a gain curve or emission line shape goof a laser medium of lengthL,

the gain in energy through a single pass is expressed as


Go = ez^(3.11)
go = no

where n is the population density in the upper energy level of the system and o is the gain cross

section. For successive passes through the amplifying medium, the energy content in the seed

pulse grows exponentially. This exponential increase in the gain with increasing paths through a

laser medium with limited gain bandwidth leads to narrowing of the amplified spectrum as the

central portion of the spectrum experiences more gain as compared to the spectral components

on the wings. Figure 3-11 (which is a schematic) illustrates an amplified pulse that undergoes

gain narrowing in the amplifier upon multiple round trips within the laser cavity. To circumvent

this, the amplifying medium should have a very broad gain bandwidth, such that in spite of the

gain narrowing effect, the amplified pulse bandwidth is still quite significant.

Just as the amplified bandwidth depends on the gain narrowing effect, the gain saturation

effects in the amplifier limit the maximum energy of the amplified pulse. As the energy of the

input pulse increases with each pass through the amplifying medium, the number of photons









extracting energy from the medium becomes comparable to the population density in the upper

level of the host material. Consequentially the amplifier's gain falls lowering the energy of the

amplified pulses after it reaches the peak attainable gain in the cavity.

For a homogeneously broadened medium, the gain saturation is expressed as


g = (3.12)
1 + E Es~t

where, go is the small signal gain coefficient, E is the signal fluence and Es, is the fluence of the

amplifying medium.

This effect is less pronounced for materials with large saturation fluence such as the Ti:

sapphire (Es,,t= 0.9 J/cm2). While gain narrowing determines the amplified bandwidth and hence

the pulse duration, gain saturation effect determines the pulse energy and these effects often

dictate the type of amplifiers (either regenerative or multipass) one may need.

















Figure 3-11: Effect of gain narrowing in amplifiers, the red curve is the fundamental laser
spectrum and the blue curve is after five passes through the laser medium.

3.7.2 Types of Amplifiers

Amplifiers can be classified into two broad categories: Multipass and Regenerative

amplifier systems.










In a multipass amplifier as in Figure 3-12 (the exact geometry may vary from system to

system) (LeBlanc et al., 1993; Zhou et al., 1994; Backus et al., 1995; 2001; Lenzer et al., 1995)

the seed pulse is made to pass through the gain medium just a few times and each time it follows

a different path through the laser medium everytime. For media with a high gain co-efficient and

where the pump power is not an issue, the multipass system is often the best scheme of

amplification. One can get around the effects of gain narrowing with just a few roundtrips within

the multipass amplifier cavity while achieving a high output power. This configuration limits the

amount of gain that can be extracted from the medium and hence is suitable only when the

energy of the input pulse is high enough to begin with.

Amplified
Output







Figure 3-12: Schematic representation of a multipass amplifier system. The seed pulses pass the
gain medium several times but through a different path each time.

On the other hand a regenerative amplifier allows one to achieve very high gain factors on

the order of 105-106 (Wynne et al., 1994; Barty et al., 1996; Zhavoronkov et al., 2004;

Ramanathan et al., 2006). Hence pulse energies of the order of a millijoule can be realized with

input seed pulse energy as low as a few nanojoules, as is obtained from a mode-locked Ti:

sapphire oscillator. Figure 3-13 is a schematic representation of the regenerative amplifier in our

lab. One of the main advantages of a regenerative amplifier is it's a laser cavity configuration

which determines the spatial profile and the pointing of the amplified beam. It is capable of

delivering highly energetic pulses with excellent beam quality. Although one of its major

drawbacks is that due to the high gain per pass and since the number of passes is usually large to










obtain high factors of amplification, the effect of gain narrowing restricts the bandwidth of the

amplified pulses. In addition, amplified spontaneous emission can deplete the gain faster than the

seed pulse. Thus systems that generate ultrashort pulses in the 1-10 mJ range often use a high

gain preamplifier followed by one or two power amplification stages.

Seed pulse

Amplified
Output
TFP


M, Ti:sapp Pump Beam 1/4


Figure 3-13: A schematic representation of the regenerative amplifier in our laboratory. The seed
pulses are injected through a Faraday Isolator (FI) and reflected off a Thin film
Polarizer (TFP). The pockel cell (PC) and the h/4 waveplate confine the seed pulses
for ~250 ns (15-16 roundtrips) in a cavity formed by mirrors M1 and M2. The
amplified output is obtained through the other exit in the FI.

But with the advent of high average power pump lasers such as the diode pumped solid

state lasers, using high thermal conductivity crystals such as the Ti: sapphire, it is now possible

to generate millij oule level pulses at k
2001; Zhavoronkov and Korn, 2004; Ramanathan et. al., 2006).

The effects of gain narrowing and gain saturation could be curbed to a certain extent by

shaping the spectral amplitude of the seed pulses before injection into the amplifier cavity or

during the amplification process. For positively chirped pulses in the amplifier, the leading edge

or the 'red' edge of the pulse spectrum can experience a higher gain as compared to the 'blue' or

the trailing edge of the spectrum. In the past etalons were placed within the amplifier cavity to

compensate for the gain narrowing effects. Barty et al (Barty et al., 1996) used 3-Clm thick air

spaced etalon in their regenerative amplifier cavity to obtain a ~15% increase in the amplified

bandwidth thereby measuring 18 fs pulses on compression. Specialized filters have been used in









the amplifier cavity to generate spectrally dependent losses such that the maximum gain around

800-nm is reduced and distributed over the wings of the gain curve. Bagnoud and Salin (2000)

used a 580-Clm thick birefringent filter to increase the spectra of the amplified pulses from 30-nm

to ~50-nm. More recently Takada et al (2006) designed a multilayer dielectric fi1m to introduce

losses near the peak of the gain curve of Ti: sapphire, generating 12-fs pulses directly from a

1k
they rely on gain losses to increase the bandwidth of the amplified pulses.

3.8 Pulse Shaping

Pulse shaping techniques wherein an input pulse with a slight 'lean' in its spectral content

towards the wings of the gain curve could offset the gain narrowing effect and lead to broader

bandwidth with low pulse energy losses. Spatial light modulators (SLM) that serve as amplitude

and or phase masks when placed in a zero-dispersion standard 4f stretcher, serves as a pulse

shaping devise for ultrashort pulses (Omenetto et al., 2001; Efimov and Reitze, 1998; Efimov et

al., 1995). The SLM placed in the Fourier plane between the two lenses of the stretcher setup as

in Figure 3-7(b), allows one to write complex amplitude and phase masks that when applied to

an ultrashort pulse can generate arbitrary amplitude and phase profile.

Verluise et al (2000) demonstrated an acousto-optic programmable dispersive filter

(AOPDF) or commonly known as the Dazzler as a pulse shaping device. Unlike the SLM pulse

shapers, the dazzler is based on the acousto-optic interaction and does not need to be placed in a

Fourier plane of a zero dispersion stretcher setting, making it a highly compact device. When

placed between the stretcher and the amplifier, the dazzler can pre-compensate for gain

narrowing and saturation effects in the amplifier. Pittman et al (2002) applied spectral and phase

correction to the pre-amplified pulses using the dazzler to generate an amplified bandwidth of 51









nm. Figure 3-14 indicates an optimally shaped input pulse spectrum with the dazzler that

generates the broadest bandwidth pulses from our amplifier. For more on the principles of

operation of the dazzler system, consult Appendix B.













,,.,Waveengt (~nm) Lm





Figure 3-14: Amplified pulse spectrum shows a FWHM of 33-nm. Inset, blue curve is the shaped
oscillator spectrum using an AOPDF, which yielded an amplified bandwidth of 33-
nm, obtained from the original oscillator spectrum (red curve).

3.9 Ultrashort Pulse Measurement

Since electronic devices have response times that span a few nanoseconds to few

picoseconds, they cannot be used to measure the temporal characteristics of an ultrashort pulse.

In order to measure an event as short as few femtoseconds, we need a probe that is either shorter

or the same duration as the event itself. The only way then to measure a femtosecond pulse, is to

use the pulse to measure itself! The most common method to measure ultrashort pulse has been

the auto-correlation method devised by Maier et al. (1966). The ultrashort pulse to be measured

is split into two using a 50-50-beam splitter. The optical set up is similar to the Michelson

Interferometer where one of the beams traverses a fixed path length through one of the arms of

the interferometer and is known as the reference beam, the probe beam on the other hand passes

through a delay stage (Figure 3-15). The two beams are then focused and spatially overlapped









on to a nonlinear crystal that generates a second harmonic generation (SHG) signal. The SHG

signal which is twice the frequency of the fundamental beams is then measured as a function of

the delay time z between the two pulses. The field envelope of the second harmonic signal is

then the product of the electric fields of the two pulses

EG (t, z) ac E (t) E(t r) (3.13)

If the two beams have an intensity distribution as I(t) and I(t z), the auto-correlation of the

two pulses is


-> It,(r) c CI (t)I(t r)dt(.4




The measured auto-correlation signallI,(r) then gives us an estimate of the duration of the

measured ultrashort pulse. It is evident from the above equation that the auto-correlation

technique cannot uniquely determine the temporal phase structure of the pulse. For a given

intensity profile as measured by the auto-correlation technique, one can construct several

different pulses with different phase structures (Chung and Weiner, 2001).

To be able to determine the temporal phase of the pulse, one needs to know the frequency

domain phase of the pulse along with its magnitude. But as the auto-correlation yields only the

Fourier-transform magnitude, it represents a classic case of the unsolvable 1-D phase retrieval

problem (Akutowicz, 1956; 1957).























crystal
Figure 3-15: Experimental auto-correlator set up. The pulse to be measured is split into two; the
pulses that are delayed with respect to each other are focused on a SHG crystal and
measured in a detector.

Experimental FROG trace Retrieved FROG trace








(a) (b)





time (s) Wa elengh (nm
(c)~ (--ml~d)pcm
Figure~ ~ ~ 3-6 FRG a xeietlsecrga,()Rtivdsecrga ihaFo ro
of002 c 3f uswdt n d pcrmfo h reree Frgtae
In the eal 190s Trbn an ae(93 rsre omketepaertrearbe
a -iesoa n heeni ol il acuaeifrmto bu the phs of thulea
well~~~~~~~~~~~~~ (Strk 197.Ti ehiu nw steFeqec eovdOtclGtn FO)
spectallyresovd h SH siga in anat-orltradtepcrga bandte
uniuel deemnstetmorlplewdhadth orsodn haeb sn hs









retrieval algorithm. The spectrogram is a 2-dimensional representation of the pulse as a function

of frequency and time delay(S'(m, )) For a more detailed explanation of this technique refer to

appendix A at the end of this dissertation.





Figure 3-16 (a) and (b) is the experimental and retrieved FROG traces respectively for a

compressed pulse from the CPA system in our laboratory and (c) and (d) is the retrieved

temporal and spectral profie with the phase structure in the respective domains for a 43-fs pulse.

3.10 Chirped Pulse Amplifier system

The single stage chirped pulse amplifier system in our laboratory (Figure 3-17) employs a

Coherent Corona laser, capable of generating 12-mJ pulses at an average power of 80 W at a

repetition rate that can be varied from 1-25 k
30 fs pulses from a home-built Ti: sapphire oscillator is stretched to ~200 ps before inj section into

the amplifier. The crystal in the regenerative amplifier is placed in a cryogenic vacuum chamber

and cooled to 87 oK by the use of liquid nitrogen. Two Faraday isolators placed in the beamline

prevent the backtracking of the amplified pulses into the oscillator. Two spherical mirrors of

radii of curvature 1 and 2m (high damage threshold custom coating from Rocky Mountain Inc.)

form the regenerative amplifier cavity. The seed pulses are introduced into the amplifier via

reflection off a thin film polarizer (Alpine Research Optics). A sol-gel coated Pockels cell (KD P)

and a quarter waveplate combination help retain the amplified pulses for ~240-ns (15-16

roundtrips) within the amplifier cavity. The Pockels cell helps switch the amplified pulses out of

the amplifier. The crystal is double pumped with roughly a total of 60 W of 532-nm light from

both sides. An average amplified power of 6 W (1.2 mJ pulse energy) at 55 W of pump power










and 9 W (1.8 mJ pulse energy) at 80 W of pump power at 5 k
pulses are then magnified by an 8f-telescope system before compression to minimize the risk of

damage to the compressor gratings. The energy of the compressed pulses drops to 0.7 mJ and 1.3

mJ at 55 W and 80 W of pump power respectively due to an efficiency of about 70%, of the

compressor gratmngs.

The amplifier exhibits a variety of temperature related effects such as thermal lensing,

thermal birefringence, and stress. Thermal management within the amplifier cavity is of utmost

importance in developing a high power, high repetition rate CPA. The next chapter is hence

devoted to the understanding of these issues and some techniques adopted to develop a state-of-

the-art CPA system.






Stretcher
Ti: Al O, Oscillator








~2 mJ,Q 45 fs M
Clryogenic Vacuum chamber PC 4


Figure 3-17: Schematic representation of CPA.

3.11 Summary

This chapter was devoted to the discussion of the design and construction of the various

components that make a chirped pulse amplifier system in our laboratory. Since the system is a

single-stage amplifier, the Ti: sapphire crystal is pumped with a high average power pump









source that gives rise to deleterious thermal issues. The following chapter characterizes these

temperature related effects and its effect on the performance of the amplifier.









CHAPTER 4
THERMAL EFFECTS IN HIGH POWER LASER AMPLIFIER

As discussed briefly in the previous chapter, temperature related effects in the regenerative

amplifier cavity causes detrimental effects to its performance. This chapter is dedicated to

discussing these effects in detail and the steps undertaken to mitigate them to increase the overall

efficiency ofthe system.

4.1 Introduction


600 ---
550
g 500
450




0.5
5 5

S-8.5013
leng~th mm
Figure 4-1: Simulation of the resultant temperature gradient in an end pumped Ti Al203 laSer rod
at room temperature when pumped by 70 W of 532 nm laser light. Courtesy Jinho
Lee.

The output of a Ti sapphire (Ti: Al203) laSer when pumped by 80 W of frequency- doubled

Nd: YAG laser of wavelength 532 nm Apump,,) giVCS rise to a laser output peaked at 800 nm


(iasmg,). Ti: sapphire has a wide absorption band in the green spectral region with significant

absorption at 532-nm (figure2-2) due to which it absorbs 85-90% of the incident pump light (the

absolute absorption is dependent on the doping levels of Ti3+ in Sapphire). The quantum defect or

the Stokes shift which is the energy difference between the pump photon and the lasing photon

'7( = Aasmg ipurmp) i S deposited as heat in the crystal. The radial intensity dependence of the beamn









is translated into a spatial temperature gradient along the transverse axes in the crystal. This

results in a 'hot' area at the center of the crystal as compared to its edges. As an example of the

severity of this effect, Figure 4-1 is a numerical simulation of the temperature rise within a

crystal whose boundary is maintained at room temperature, when a Gaussian beam of 532-nm

source at an average power of 70 W is incident on it. For the sake of simplicity a 6-mm long and

2.5-mm radius cylindrically symmetric crystal was assumed for the simulation which was

performed using a Finite Element Analysis package by Comsol Multiphysics or commonly

referred to as Femlab. The spot size of the pump beam on the crystal was 500-Clm and the

absorption parameter a, L was 2.2. As Figure 4-1 indicates the center of the crystal is about 150

oK above room temperature. This spatial variation in the temperature along the two transverse

radial axes alters the refractive index leasing to the following thermal effects (Koechner, 1976)

















Figure 4-2: Refractive index changes to a crystal incident with 80 W of pump beam. The thermal
gradient causes optical path deformation for a beam traveling along the : -axis.

1. Thermo-optic effect: The temperature gradient in the crystal changes the refractive

index of the laser material along the axes perpendicular to the propagation axis'z' as in

Figure 4-2. A laser beam traversing through the crystal experiences a change in the

optical path length (OPD) due to the position dependent refractive index n2 (r, z) .










AOPD = A~d:= A~d:(4.1)


where AT = T (r, z) T (r,, z, ), An, is the temperature dependence of refractive index.

2. Thermo-elastic deformations (Thermal Expansion): The heat generated by the

absorption expands and leads to radially curved end-faces because of the heat generated

temperature gradients. The former effect does not affect the focal characteristics of the

crystal, but the thermal gradients generate increased focal power (Figure 4-3). This end-

face curvature causes a change in the optical path length of a transmitting laser beam.

AOPD, = a A Td: (4.2)

where a is the thermal expansion co-efficient.







Al Al

Figure 4-3: Radially curved end-faces due to increase in temperature caused due to absorption of
incident pump beam.

3. Elasto-optic effect: The temperature distribution T (r) also causes the center of the

crystal to expand more rapidly as compared to the cooler outer edges. This generates

mechanical stress in laser rod as the center is constrained by the edges of the crystal.

The optical path length changes induced due to this effect is given as

AOPD,, = 'An,,d: (4.3)

where Ane, is the photo-elastic coefficients of the crystal.

Thus, the total optical path difference can be calculated as









AOPD = AOPD, + AOPDe + AOPDe (4.4)

These various thermal effects coupled with the fact that thermal constants of

sapphire (a,r, dn/dT) are functions of temperature, induce modal distortions in the lasing beam,

which restrict the output power from the amplifier cavity besides distorting the shape of the

beam. Table 4-1 gives a quantitative comparison of these thermal effects in sapphire indicating

that the elasto-optic effects can be safely neglected while calculating the net thermal effects in

the Ti: Al203 CryStal (Lawrence, 2003). The comparison made in Table 4-lassumes that the heat

incident on the crystal is absorbed uniformly over the entire length of the crystal whose radius R

is much larger than the beam diameter a Considering only radial heat flow between the points

r = 0 tor = mi, the temperature differences where there is no appreciable change in the thermal

constants of the crystal is thus calculated as


sT = A T[ -a ATa (4.5)
=w K (27ts~ih)

where, Pa is the absorbed power by a crystal of length h r is the thermal conductivity.

Integrating this quantity over the entire length of the crystal yields

3Tdz = a(4.6)


The relative strengths of the various thermal effects can now be calculated and compared

as equation (4.6) indicates that r/PJ3Td~z is a constant for any material for small changes in

temperature.

In order to achieve beam quality close to the diffraction limit and higher amplified pulse

energies, these optical distortions in the cavity must be eliminated as much as possible. In the









past, numerous methods have been proposed that can lower these distortions (Schulz and Henion,

1991), including:

1. Pumping the crystal at lower powers such that the available heat limits the thermal

distortions in the system.

2. Using a slab geometry for the crystal rather than a cylindrical rod design in the amplifier

(Koechner, 1976) reduces the heat flow to a one-dimensional problem, which then

simplifies the removal of heat.

3. Reducing the quantum defect n (which may be defined as i4 1,,,li,,, or i4 ,, 1,,,,,, by

pumping the crystal with a higher wavelength source (Moulton, 1986).

Table 4-1: Quantitative estimate of thermal effects in sapphire.
Thermo-optic effect 1
Thermal expansion 0.8
Elasto-optic effect 0.2
Note Adapted from Lawrence (2003)

For several reasons, the above mentioned measures cannot be easily implemented when

designing high average power systems. Pumping the crystal at lower powers reduces the output

power of the amplifier. Although a slab geometry produces lower optical distortions, is it found

(Miyake et al., 1990) that the cylindrical rod geometry for Ti: Al203 prOduces higher powers

when cooled to liquid nitrogen temperature. Besides a slab geometry can also give rise to various

parasitic modes that can lower the useful stored energy in the crystal (Koechner, 1976). Special

coatings to suppress these parasitic modes and to enhance the thermal coupling to the cooling

unit can add to the cost and the design complexities of slabs. In addition slab geometries are not

easily implementable in regenerative amplifier systems.

The heat generated in the crystal is given by the product of the amount of heat absorbed by

the crystal and the quantum defect(H = P, x 77). Pumping Ti: Al203 at 600 nm instead of 500 nm









reduces the quantum defect by a factor of two (Schulz, 1991). In order then, to achieve the same

absorbed power at 600 nm, the concentration of Ti3+ ions has to be increased in the crystal as, the

absorption coefficient of Ti: Al203 is lower for 600 nm as compared to 500 nm (figure 2-2)

(Moulton, 1986). Thus high quality crystals must be used to limit losses due to the absorption of

the crystal at the lasing wavelength. Most significantly the availability of high-powered pump

sources at 600-nm restricts operation at this regime.

This prompts a more detailed study and analysis of the two most damaging thermal effects

in Ti: Al203 to gain a better understanding of the problem so as to be able to suggest remedial

measures.

4.2 Theoretical Background

As explained above, refractive index changes of Ti: sapphire with incident pump beam

leads to optical distortions. These changes can be separated into temperature- and stress-

dependent changes

n(r) = no + An(r), + An(r), (4.7)

where n (r) is the radial variation of refractive index; no is the index at the center of the laser rod

and Anz(r),~ and An (r.) are the temperature and stress dependent coefficients of refractive index

respectively. Ignoring the effects of the stress-dependent changes (Lawrence, 2003) as per

explanation above, n (r) can be expressed as

dn dn
An~),= T~r -T~o) = AT(x, v y, z) (4.8)
dTI \dTI

This results in an OPD change as given in equation (4.1).









As sapphire exhibits peak absorption at 532-nm, there usually is some physical distortion of the

flatness of the rod ends that result in a change of the optical path length of a laser beam that

traverses through it. This deviation can be calculated as

L(r) = aoLoA T(r) (4.9)

where, so is the coefficient of expansion and La is the original length of the laser crystal. This

results in an OPD change as per equation (4.2) Thus the transverse optical path difference for

propagation along the z-direction can be written in general as


AOPD(x, y)= (n[T(x, y,z)]-1)dz (4.10)


Expanding n and dz in powers ofAT, using equation (4.8) and (4.9) equation (4. 10) becomes


AOPD(x, y) (no +~ -AT 1)(dz + ao ATdz)
L L L(4.11)
= n ATdzo +I naoTdzo coTdzo +(no -1) +O([AT]2)



Neglecting the constant term and terms in(AT)2, the integrated optical path length is then given

by

dn
AOPD~x~y)= +a(n -1)I AT(x. y.z~dz (.2
\dT U I(.2

Analytical solutions to the above equation for cylindrically symmetric crystal geometry can be

obtained by solving the steady-state heat diffusion equation with the appropriate boundary

conditions.

-V *[KcVT(x, y, z)] = Q








M. E. Innocenzi et al. (1990) solved the heat diffusion equation for an axially heated cylinder

with a thermally conductive boundary at the periphery. For an incident pump beam that is

Gaussian in nature, the steady state temperature difference is calculated as

aabs n exp(-aoz) r02:: 2r0P2 : 2r2 (.4
AT(r, z)= x In +l 2 E1 2(.4


where, 14 is the incident pump power, aab s I the absorption coefficient that results in the

heating, w, is 1/e2 radius of the Gaussian pump beam, ro is the radius and r is the thermal

conductivity of the laser rod. The expression for AT(r,z) can be obtained by neglecting

E, 132r0,2m ,;as it mall for most practical cases andl epuandi~ng E, 12r2/m2 (Abramawitz andl

Stegun, 1965) as a power series and retaining only the terms quadratic in r. Plugging it into

equation (4.1) (their calculations do not include the thermal expansion of the crystal) yields the

resultant phase change or the transmitting laser beam of wavelength ii through the crystal

2xi
A # = AOPD(r)

2i7y (dn/dT) 245
Af = 2 [1- eXp(-aabs)]r


comparing the above equation to the phase changes that occur in a lens like medium with a

quadratic variation in its refractive index (Kogelnik, 1965)

2xir2
A # = (4.16)
Af

where, f is the effective focal length. Comparing equation (4.15) with equation (4.16) the

effective focal length for the laser rod can be written as

f= ~i 1 (4.17)
th n (dn/dT) 1 -exp(-aabsn)









This effect known as thermal lensing because it alters the modal properties of a beam that

transmits through it, just like a static lens but unlike a static lens, it's dynamic in nature due to its

implicit dependence on pump power. In an amplifier cavity formed by two spherical end mirrors,

this effect can destabilize the cavity as the modal properties of the lasing beam starts to exhibit

the same dynamism as the thermal lens in the crystal for various pump power levels. A positive

value of dn/dT for a material generates a converging thermal lens and a negative value

generates a diverging lens. Although the above equation is calculated for a cylindrical crystal

pumped with a continuous laser source, we can nevertheless use it to obtain an estimate of the

focal length for a Brewster cut Ti sapphire crystal pumped with a pulsed laser source (Coherent,

Corona). The thermal constants for sapphire at room temperature are: ic = 0.33 W/cm2 (Holland,

1962), dn/dT = 1.28 x10 /K (Feldman et al., 1978). For a crystal with its boundaries at room

temperature and pumped with 60W of green light with a spot of 500-Clm on the crystal and a

constant pump absorption-length product, absL = 2.2 yields a thermal lens of focal length

f, = 4cm !

To increase the thermal lens focal length or conversely to decrease the thermal lens power

(defined asl/,), the pump power can be decreased or alternatively the pump spot size on the

crystal can be increased. Recalculating the focal length for a pump spot of radius 1-mm and a

decreased incident pump power of 30 W, increases the focal length to ~ 30-cm. Although

reducing the pump power increases f,, but this necessarily decreases the amplified output power.

Since a high overlap integral between the pump spot and the lasing beam spot sizes on the crystal

is required for efficient energy extraction from the Ti: sapphire in the amplifier. This integral is a

maximum when the pump beam is smaller or equal to the amplified beam. Increasing the spot










size my~ of the pumping beam may alter the overlap integral, again bringing about a reduction in

the extracted energy from the amplifier.

Thus to be able to achieve high average amplified power from a regenerative Ti sapphire

amplifier cavity the thermal lens effect needs to be either eliminated (ideal solution) or at least

minimized (practical solution).

4.3 Methods to Reduce Thermal Effects

In the past, researchers have used various methods to reduce thermal effects in their laser

systems. A quick review through some of these measures brings about a deeper understanding of

this issue.

The most intuitive method of eliminating or reducing thermal effects in a laser cavity

would be to introduce a diverging lens in the beam path to compensate for the induced positive

or converging thermal lens generated by the crystal. Due to the variable nature and broad range

of the thermal lens, a fixed focal length passive optical element cannot compensate for a range of

incident pump powers. Also such an optical element will change the beam diameter on the

crystal with each pass, increasing modal distortions in the laser beam.

Salin et al. (1998) introduced the concept of thermal eigenmode amplifiers. A thermally-

loaded multipass amplifier is equivalent to a series of lenses separated by a distance L that

corresponds to the beam round trip length inside the cavity. An unfolded resonator with two

spherically curved mirrors with radii of curvature 2 fherm, With the crystal at the center is

equivalent to a series of lenses of focal length ftherm Separated by a distance L. An eigenmode of

this resonator, calculated from the paraxial Gaussian beam propagation relations, reproduces

itself for each round trip, which for a multipass is equivalent to re-imaging the beam onto itself

after each pass. If the input beam has the same size and characteristics of the eigenmode of the










resonator then the amplified output beam characteristics are similar to those of the input beam

producing diffraction limited amplified pulses. This is suitable when the incident pump power is

maintained at a constant value, as any change in this parameter causes a change in the focal

length thus changing L This is also based on the assumption that the host medium is cylindrical,

such that the thermal lens is mostly spherical over the entire pump beam diameter and the length

between the successive passes is a constant. A Brewster cut rod (Figure 4-4) instead of a

cylindrical laser rod generates an aspherical thermal lens and it then becomes difficult to

calculate the thermal eigenmode accurately. MacDonald et al. (2000) have reduced the thermal

lensing effect in diode-pumped Nd: YAG laser with multiple composite rods. These rods had

undoped end caps to remove the part of thermal lens formed due to the bending of the end faces

of the laser rod.

Zhavoronkov and Korn (2004) thermoelectrically cooled a 3-cm Ti sapphire crystal in a

three-mirror astigmatic regenerative amplifier cavity to 210 OK that took into account the huge

positive thermal loading of the sapphire rod. Their single-stage, multi-kilohertz laser was able to

generate 6.5 W of average amplified power at 20 k
were obtained, the thermal and thermo-optical constants did not differ significantly from their

room temperature values, and it is likely that higher order spatial aberrations were present in the

output beam.




Q =60.5 2.



Figure 4-4: Brewster cut Ti sapphire crystal.









Zhou X et al. (2005) used two multipass amplification stages after a regenerative amplifier

cavity in order to avoid large thermal loading present in single-stage systems. They were able to

generate 7W of average amplified output at a repetition rate of 5 k
to solve the thermal-loading problem in their CPA system, managing multiple amplifier stages

can get cumbersome.

An often used technique to reduce thermal lensing in high power continuous wave

Nd:YAG laser systems (Graf et al., 2001; Wyss et al., 2002; Mueller et al., 2002) can be

incorporated to compensate for thermal effects in single-stage high repetition rate systems. The

idea is to use self-compensating (adaptive) methods to thermo-optically compensate for the

thermal lens effects that change with changing power. This technique essentially uses adaptive

optical devices such as self-adjusting lenses within the laser cavity that can compensate for every

single pass of the lasing beam through the cavity. A material with a negative thermal dispersion

coefficient is placed in the cavity that generates a power dependent thermal lens that

compensates for the positive dn/dT induced by the temperature gradient in the laser crystal. Th.

Graf et al. (2001) were the first to successfully use an adaptive negative thermal lens to

compensate for the positive thermal lens in a transversely diode-pumped Nd: YAG laser rod. The

compensating element must absorb a small fraction of the incident laser power and hence should

posses a strong thermal dispersion dn/dT to effectively compensate for the positivedn/dT This

technique has also been extended to correct thermally induced optical path length changes

induced by absorption of transmissive optical components such as electro-optic modulators and

Faraday isolators, of gravitational wave interferometer (Mueller et al., 2002).

We attempted to extend the concept of thermo-optical compensation to our regenerative

amplifier. Curing gels or index matching fluids such as the OCF-446 (Nye Opticals) possesses









the combined advantages of solid materials (no convection) with a strong negative dn/dT With

a negative thermal dispersion value as high as 3.5 x 10-4 o -1 and a large expansion co-efficient

of 8 x 10-4 it seems like an ideal candidate as a compensating material with the added advantage

of low absorption at the lasing wavelength of 800-nm (< 2x 10-4 O/o/pm). Although numerical

simulations by Jinho Lee seem to suggest that the thermo-optical compensation method should

work for an OCF thickness of ~ 3mm for a pump power of 80 W, but preliminary experiments

have revealed the high intracavity peak powers in the regenerative amplifier cavity causes

damage to the cell containing OCF 446. It is not clear from these experiments if the damage

occurred to the cell holding the OCF or if the OCF itself burns due to the absorption at the lasing

wavelength. Redesigning the cavity taking into consideration the OCF or changing the location

of the OCF could potentially solve this problem but has not yet been experimentally verified and

could possibly be one of the avenues that could further be explored to increase the efficiency of

the present amplifier system.

Meanwhile the most efficient and convenient means of reducing thermal effects in Ti

sapphire laser crystal in a chirped pulse amplifier is by cooling it to cryogenic temperatures

(liquid nitrogen temperature (770K) or below) (Moulton, 1986; Schulz and Henion, 1991).

Sapphire exhibits excellent thermal properties on cooling to low temperatures. The next section

delves on how the thermal properties of sapphire can be exploited to reduce the temperature

related effects.

4.4 Liquid Nitrogen Cooled Ti Al203 Laser Amplifier

P.F. Moulton (1986) was the first to demonstrate the advantages of cooling the sapphire

laser crystal to liquid nitrogen temperature in a quasi cw laser. He reported an increase in the

output power of the laser from 45 mW to 150 mW when the crystal was cooled to 80 OK. He









attributed this effect to an increase in the thermal conductivity of sapphire with decreasing

temperature. This idea was then extended by Schulz and Henion (1991) where they investigated

the effects of thermal loading on a single-transverse-mode of Ti: sapphire laser cooled to 93 OK

and reported a reduction in the thermo-optical refractive index changes by more than two orders

of magnitude. They realized an output power from the Ti: sapphire laser that was 200 times

larger at 77 oK than at room temperature!

Table 4-2: Thermal properties of sapphire at 300 and 77 oK.
Property At 300 oK At 77 oK
Thermal conductivity it 0.33 W cm K- 10 Wcm K-
Thermal dispersion dn dT 1.28 x 10-5 K1 0.19 x 105 K-1
Thermal expansion co- 5.0 x 10-6 K-1 0.34 x 10-6 K-1
efficient oc
Note: Adapted from Schulz and Henion (1991).

Table 4-2 compares the thermal properties of Ti sapphire at room temperature and liquid

nitrogen temperature. Figure 4-5 (a) and (b) show the variation of thermal conductivity r and

dn/dT with temperature, the key parameters in minimizing thermal distortions.

The thermal lens focal length as given by equation (4.17) is directly proportional to the

ratio r/(du/dT) Figure 4-5 indicates that as the temperature is decreased, the thermal

conductivity rises steeply, and the coefficient of refractive index with temperature decreases

thereby making the ratio of thermal conductivity to dn/dT increase with increasing temperature.

This leads to a decreasing thermal power (or an increasing thermal lens focal length). Backus et

al. (2001) were able to generate 13 W of amplified output power at 7 k
cryogenically cooled single-stage multipass amplifier with good beam quality (measured M2 Of

1.2 and 1.36 along the X and Y axis).

We can now calculate the effective thermal lens focal length [equation (4.17)] of a Ti

sapphire crystal at LN2 temperature using the constants in Table 4-2 for an input pump power of



































8000
600
400
2001


60 W and a spot size of 500-ypm as mentioned above. On doing so, an f, of ~8m is obtained!


Thus we find that there is a tremendous decrease in the thermal lens power of about two orders


of magnitude on cooling the crystal to 77 oK!


1.8



0.2
0.0



200
1.


50 100 150 200 250 300 350 400 450

Temeperature K




Figure 4-5: Dependence of (a) Thermal dispersion (dn dT) (Feldman et al.,1978) and (b) Thermal
conductivity ic (Holland, 1962) of Ti sapphire with temperature.

In order to design an effective regenerative amplifier cavity we accurately need to know


the positive thermal lens generated by the crystal with changing pump power. We have made a


very detailed study of this, which is elaborated in the remaining sections of this chapter. The next

section deals with the construction of a regenerative chirped pulse amplifier since all the


experiments and numerical calculation on thermal analysis were performed on this high average


power CPA system.


4.5 Construction of a Regenerative Amplifier Cavity

The entire below mentioned discussion has been based on the current amplifier system in


our CPA and this section delves into the details of the construction of this amplifier.


s

-J









A 5-mm diameter and 6-mm long Ti sapphire crystal is the host material in our

regenerative amplifier cavity. The crystal is cooled to 87 oK in a vacuum chamber that' s placed

underneath a liquid nitrogen dewar. The vacuum chamber was designed after extensive

consultations with our in-house mechanical engineer Luke Williams. The LN2 dewar is separated

from the crystal by a thin copper wall of thickness ~100-Clm. The crystal is held in a copper

holder, and a 127-Clm Indium foil is sandwiched between the crystal and the thin copper wall for

better thermal contact between with the LN2 in the dewar. A thermocouple placed along one of

the edges of the crystal senses the temperature of the crystal at all times. The temperature sensor

has an in-built relay circuit to automatically facilitate the turning off of the pump laser when the

crystal temperature exceeds 185 oK. Figure 4-6 is a CAD drawing of the vacuum chamber-

dewar assembly in our CPA system. As can be seen in the Figure 4-6 (a), the vacuum can has 2

extended arms on either side with brewster windows on it as entrance and exit for both the pump

beam and the amplified IR beam. A view-port right in front of the crystal allows one to position

the pump beams on the crystal. Figure 4-6 (b) is the copper holder in which the Ti sapphire

crystal is placed.

This particular assembly generates almost 0.6 OC rise in temperature per Watt rise in the

pump power (Figure 4-7). At zero watts of pump power the crystal temperature as measured by

the thermocouple is 90 oK. With almost 65 W of pump power at 5 k
temperature rises to about 127 oK when the lasing action within the regenerative amplifier cavity

is inhibited and 108 oK when the cavity is in the lasing mode. The higher temperature rise when

the cavity is not lasing is due to the absorption of fluorescence by the thermocouple which is

considerably decreased during the lasing action. This allows for continuous operation of the

regenerative amplifier to repetition rates as high as 12 k













































= cavity lsn
125

120

115

110

105




90


0 10 20 30 40 50 60 70


J





W


E
a
E
a


0.3 mJ at 12 k

amplified pulses (Figure 4-15).






















(a) (b)
Figure 4-6: CAD drawings depicting (a) Vacuum dewar assembly and (b) copper crystal holder.
Drawings by Luke Williams.


Pump Power (W)


Figure 4-7: Boundary temperature rise as pump power is increased when lasing action is
inhibited (red points) and when the cavity is lasing (blue points). The lines are guides
to the eye.

4.6 Measurement of Thermal Lens


A laser beam transmitted through a material that acts as a thermal lens undergoes modal


changes in its divergence angle relative to the input beam. By measuring these changes, one can









estimate the thermal lens power of the material. The design of an optimum regenerative amplifier

cavity necessitates the need to characterize accurately the thermal lens in the Ti sapphire crystal.

To be able to measure the thermal lens in our laboratory we used a He-Ne laser to probe

the Ti: sapphire crystal as a function of pump power. The He-Ne laser was mode matched to the

pump beam spot on the crystal. The changes in the divergence angle of the beam after traversing

the crystal were determined for a series of pump powers by measuring the position dependent

spot sizes with a CCD camera. By comparison with the He-Ne beam waist position at zero pump

power, the measured waist positions for the non-zero pump powers enabled us to calculate the

thermal lens focal length within the thin-lens approximation using the ABCD matrix formulation.

In Figure 4-8 is plotted the measured thermal lens power for the two transverse axes as a

function of power. For a pump power of about 50-55 W the measured thermal lens focal length is

about 1.1 m along the vertical axis on the crystal and 0.2-0.3 m along the horizontal axis. The

asymmetry in the thermal lens is immediately evident as the thermal lens power along the

horizontal axis rises much sharply as compared to the vertical axis.

An effective amplifier is one where the cavity maintains stability over a wide range of

thermal lens power. The ABCD formalism was used in which the crystal was treated as a thin

spherical lens. The cavity stability or the g-parameter was calculated for various combinations

and permutations of the radii of curvature of the two end mirrors and the distance between them.

The most suitable cavity was one that exhibited stability (-1<; g<;-1) for a large range of thermal

lens, where 'g' is the stability factor. This essentially translates as minimum changes to the spot

size of the amplified beam on the crystal. The regenerative amplifier cavity currently being used

is 2-m long, comprised of two spherical mirrors of radii of curvature 1-m and 2-m. Figure 4-9 is












a plot of the g-parameter calculated for different values of thermal lens power using the ABCD


matrix formulation.

s.o
SX-Axis
4.5 -1 Y-Axis
4.0 -1 o

E 3.5 -I /

$3.0-


1.5-
1~ .0-


0.5-
0.0
15 20 25 30 35 40 45 50 55 60

Pump Power W


Figure 4-8: Measured thermal lens and thermal power for the two transverse axes; the boundary
temperature was measured to be 87 K at zero pump power and 103 K at 55 W of
pump power.

0.4

0.2

0.0






S-0.6

-0.8

-1.0
0 1 2 3 4
Thermal Lens focal length (m)


Figure 4-9: Cavity stability parameter as a function of measured thermal lens.

From the above plot, it's clear that the cavity is most stable for a thermal lens focal length


values from 0.6-m to 5-m. Also the calculated laser beam spot size (1/e radius) on the crystal


shows a variation of about 15% from its minimum value of 343-pLm at about 1-m thermal lens


focal length. The imaging system of the pump beam on the crystal let us vary the pump spot










from a 1/e radius of 200-Clm to 800-Clm. This ensures a good overlap of the pump beam with the

varying mode sizes of the amplified beam on the crystal, for a great range of pump powers.

In order to validate the thin lens approximation in calculating the thermal lens of the

crystal as a function of pump power, we invoke the simple lens maker' s formula for the effective

focal length for both thin and thick lenses.

1 11
fthn R,
(4.18)
1 ---1 1 (nzens no)d
Phlck lens 0'L)
fthlck R 4 nzensR,

where nzens and no are the refractive index of the lens medium and the medium in which the lens

is placed. R, and R2 are the radii of curvature of the two curved surfaces of the lens of thickness

d The difference in the thermal lens power resulting from the thin lens and the thick lens

treatment of the sapphire crystal is given as


A e""(4.19)


For a Ti: sapphire of thickness d = 6mm in vacuum and with refractive index, n =s1.76 and

assuming R, = 0.5m and R2 = -lm the change in the focal length is 3.4 x 10-3. Due to the

insignificant difference between the two treatments of the crystal thermal lens, it suffices to use

just the thin lens approximation in all the calculations using the measured modal changes with

pump power.

4.7 Calculation of Thermal Lens

Although cooling to 77 oK brings about a drastic reduction in the thermal lens power of the

crystal, it is in practice difficult to achieve boundary temperatures close to the LN2 temperature

when pumping with high laser powers. For a 6-mm thick Brewster-cut sapphire crystal the thin









lens approximation does not accurately describe the thermal lens. Hence to validate the use of the

thin lens approximation, we compared the measured thermal lens power with that obtained from

a Finite Element Analysis (FEA). An accurate knowledge of the temperature gradient inside the

crystal determines the thermal lens accurately.

The temperature gradient is obtained by solving the heat diffusion equation (4.13) with the

appropriate boundary conditions. For cylindrically symmetric geometries, pumped with

continuous sources, analytical solutions to the heat equation are intuitive (Quetschke et al., 2006).

Analytical solutions have also been obtained for crystals pumped with pulsed sources (Lausten

and Balling, 2003), however the crystal geometry was again a cylindrically symmetric one. For

more complicated geometries such as Brewster cut crystals (Figure 4-4) numerical methods are

needed to calculate the temperature gradient inside the crystal. Additionally, the physical

quantities in these equations (a, c, dn/dT) are temperature and therefore spatially dependent, and

not analytically tractable. Hence we use a finite element analysis package (Comsol Multi-Physics)

to model the pump pulse-induced temperature changes and numerically integrate equation (4.12)

to compute AOPD Calculations by Jinho Lee show that for a Brewster-cut geometry the source

term on the RHS of the 3-D heat equation (4. 13) takes the form

2Pa, 2o L, xx
Q2~~) cosy ex 2 -a 8r) 2COSB,2 2 _- abs L
O~xFr) mo +2 cos 8, cos 8,


(4.20)

where P is the incident laser power, aabis ISthe absorption coefficient for the pump, mi is the

pump waist (1/e in field), L is the crystal length, and 8,,, are the incident and refracted angles in

the crystal, respectively. Even though the pump source is pulsed the steady state equation

perfectly describes the situation as the thermal relaxation constant for Ti: sapphire laser rod is










measured to be ~0.5-secs (Ito et al., 2002) which is much longer than the repetition rate of the

laser. Therefore, for pump repetition rates of > 1 k
of the thermal gradient.

120
x 10 11
4-1
116






108

5 5 1106
x~~ 103 x 109 104
Horizontal Axis Crystal length (m)


Figure 4-10: Computed temperature profie in a 6 mm long, 5 mm diameter Brewster-cut Ti:
sapphire crystal single end-pumped by 50 W in a 0.4 mm pump spot waist radius for
and absorption corresponding to adb = 2.2 and a boundary temperature of 103 K.

The geometry (shown in Figure 4-10) consists of a 3D-tilted cylinder corresponding to our

Brewster cut crystal. Temperature dependent thermo-optical and mechanical constants were

obtained from Touloukain et al. (1973) and Holland (1962) were fitted over 50 300 K. The

absorption at the Ti: sapphire emission wavelength was not included as this has a negligible

effect on the temperature for Ti: sapphire crystals with high Eigures of merit

(FOM~ = as,,,,,/as,,,,,, = 200; a being the absorption coefficient). The boundary conditions were

specified as a temperature T, along the barrel of cylinder as either a Eixed or variable temperature


(corresponding to contact with the bath) and on the ends as dT/dni = const (corresponding to the

radiation). This allowed us to explore more physically realistic scenarios in our amplification












































--q dratic lfit



fs1ea a s


system. Calculating the temperature profile within the crystal, we can now estimate the changes

in the optical path length or AOPD through the crystal.


The simulated AOPD were calculated for an ideal thin lens of the same focal length f~~ in


vertical and the horizontal transverse dimensions as that obtained from the simulated temperature


gradient within the crystal (Figure 4-11)The experimentally measured thermal lens values from

the previous section were then compared to the thermal lens values obtained from the computed

OPDs.




(a) Hron axis -=-cal uated OPD
-10 -q dratic 1it


a-400 ,., ~f-en as" u
500 .
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
crystal radius (mm)


0
-100
E`-200



-600


-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
crystal radius (mm)


Figure 4-11: Plots (a,b) are the corresponding AOPD as a function of the transverse coordinates,
for the computed temperature profile in figure (3-6).

These values were also compared with the analytical solution to thermal lens focal length


[equation(4.17)] derived by Innocenzi et al. (1990), associated with the phase changes that occur


inside a cylindrical laser rod due to temperature dependent refractive index An (r, z).Figure 4-12,


is a plot of the measured thermal lens focal lens power as a function of pump power, compared

with the values obtained from the FEA calculations and the expression (4.17) The ic and


dn/dT values used in equation (4. 17) corresponded to the maximum computed temperature rise











at the center of the crystal at each pump power. While the FEA calculations agree reasonably


well with the measured values along the vertical crystal axis and quite well along the horizontal


axis, the focal lens power calculated from Innocenzi's analytical equation significantly

underestimates the lens power along both axes.

1.0
0. a rical Axit
0.8 measured
fmnite eleme it method
0.7anltali



0.3
0.2


S10 20 30 40 50
% Pump Power (W)

1.6
(b6 ) Horizontal Axis
1. rit element mto
1.0 anaiticalformua
0.8
0.6
0.4
0.2 -
0.0
10 20 30 40 50
Pump Power (W)


Figure 4-12: Comparison of experimentally measured thermal lens powers (squares) against
numerically predicted values using finite element analysis (circles) and an analytical
expression for thermal lensing (triangles). Formula derived from Innocenzi et al
(1990).

The underestimation by the analytical expression is somewhat surprising, since treating


r and dn/dT as a constant over the entire crystal volume underestimates the effective thermal


conductivity and over estimates dn/dT since r ( dn/dT ) increases (decreases) as the


temperature decreases away from the beam propagation axis. However, equation (4.17) neglects


the physical expansion of the crystal, which can increase the thermal lens power by a factor of

1.8 over a pure thermo-optic lens (Lawrence, 2003). Nonetheless, the FEA lens power estimates










agree with experimental data when using boundary temperatures consistent with the

experimentally measured boundary temperature values.

This present regenerative amplifier cavity designed with the above measured thermal lens

measurement and the FEA analysis has been performing exceptionally well producing average

powers as high as 9 W (before compression) when pumped with 80 W of green light at 5 k
repetition rate.

4.8 Direct Measurement of the Optical Path Deformations

To directly measure the pump induced path length changes and further corroborate our

simulations, the LN2 COoled Ti: sapphire crystal was placed in one of the arms of a Michelson

interferometer. A single frequency 1064-nm Nd: YAG laser (Lightwave Corporation NPRO) was

split into two arms with the crystal in one arm and free space through the other. The interference

pattern was recorded as a function of power on the WinCam CCD beam analyzer. Figure 4-13 is

the recorded spatial interference pattern as a function of pump power.

PPMP=OW PPM = 6W PPM = 22W





PUP= 41W PPM = 54W PPM = 56W








Figure 4-13: Spatial interference pattern in the Michelson interferometer recorded in a CCD
camera as a function pump power.

The zero intensity frame corresponds to zero path difference at 0 W of pump power. As the

pump power was gradually increased, the change in the intensity of the interference pattern











indicated the increase in the OPD through the crystal. Figure 4-14 is the measured optical path

difference obtained from the recorded interference pattern, in the crystal as a function of pump


power.

700
600 +--T = 93
-T~ = 103K 3
500 -T =13
Experlliental oi tical
400 pt 1frn




3 0 10 2 30 4 50 0
PupPwe W
Fiue41:Maue PD coprdwt h E acltdfrtredfeetbudr




Tb ~ ~ ~ ~ ~ Pm = 03K thihe pm pwes




At the highest pump power (56 W), a AOPD of 350 nm +/- 80 nm was measured (or


approximately 0.45 Ai at 800 nm), decreasing as the pump power was lowered. The intensity


fluctuation of the NPRO laser (102 103) as well as path fluctuations caused by acoustic


perturbation of the interferometer optics most likely caused the large error bars at lower pump

powers. Experimentally, a boundary temperature of 93K was recorded at the boundary for zero

pump power. As the pump power was increased to 55 W, a boundary temperature rise of 20K

was recorded, but a fraction of this rise was experimentally attributed to the absorption of

scattered Ti: sapphire fluorescence by the thermocouple; only a portion of the experimentally

recorded temperature rise was due to physical heating at the boundary. Thus, we simulated the


AOPD for a range of constant boundary temperatures Tb displayed in Figure 4-14. At the


highest pump powers, we see good agreement between the predicted and measured optical path










length for Tb =103"K (corresponding to 10 OK rise on the boundary), although the data and

simulations deviate somewhat at lower temperatures and most severely at the lowest temperature.

As expected, the AOPD is less severe as the boundary temperature is reduced due primarily to

the strong temperature dependence of ic. Figure 4-10 and Figure 4-11displays the computed

temperature rise and AOPD for a particular boundary temperature Tb = 103"K respectively.

4.9 Effects of Thermal Aberrations on Beam Shape

5kHz, EF 1.56 ml 6kMz, Er=1.44 ml 7k~, Er=1.44 ml SkMz, 57-0.96 ml
















Figure 4-15: Beam shape as a function of repetition rate. Increasing the repetition rate of the
pump beam introduces modal distortions.

The spatial quality of the amplified beam is highly sensitive to temperature changes within

the crystal. The amplified beam shapes were measured using a WinCamD-UCM CCD beam

analyzer after ample attenuation Figure 4-15 is a far field measurement of the spatial profile of

the beam with increasing repetition rates.

As the pump power is increased the temperature within the crystal increases leading to

increased spatial distortions to the beam profile. The boundary temperature as measured by a

thermocouple on the crystal rose from 103 oK at 5 k
repetition rate. Astigmatism due to the geometry of the crystal is evident in the elliptical shape of




















(a) Ve tical A> is


200

1000
M 1.62
800

600 I-.

400 R

200


the amplified beam even at a repetition rate of 5 k

was measured (5W output power) using the beam analyzer by attenuating it suitably and


focusing with a 1 m focal length lens.


I___


-1


1400

1200

S1000
v,800


S400


1


E
7


20 -


;0 -40 0 40
Distance (cm)


) 1;


40 0 40
Distance (cm)


Figure 4-16: M2 meaSurement for an uncompressed amplified beam of average power 5W at 5
k

A common measure for the beam quality is known as M It is defined as the ratio of


divergence of the amplified beam to the divergence of an ideal Gaussian beam of equal beam

wai st.


M' = OR"measured
0Gausslan


(4.21)


where 00R, and Inteasured are the waist and the divergence respectively of the laser beam of


unknown quality and me~ and 0Gaussan are the waist and the divergence of a fundamental laser










mode (TEMoo mode). The transverse profile of the beam (mi)R, ) WaS measured as a function of

the propagation distance using a CCD camera. If mi)R, = )~ then


M = easuect(4.22)
9Gausslan

These results are shown in Figure 4-16. We observed that at lower repetition rates (5 k
corresponding to 5 W average power, the amplified beam M2 ValUeS deviated from the ideal

TEMoo mode by a factor of only 1.62 and 1.14 in the vertical and the horizontal axes respectively.

The thermal astigmatism of the crystal geometry is evident in the measured M2 value (a ratio of

1.42 in the divergence angle along the two axes). For higher repetition rates (8 k
amplified power output of 9W and a boundary temperature T, = 108"K ) this ratio increased

further to 1.73 (measured M2 ValUeS of 2.12 and 1.22 in the vertical and the horizontal axes

respectively). The rise in the astigmatism of the beam shape can be attributed to the changes in

the temperature related thermal constants for sapphire crystal as the boundary temperature

increases at higher repetition rates.

4.10 Summary

Summarizing the contents of this chapter, we detailed the various temperature related

effects in a high average power laser system and more specifically to liquid nitrogen cooled Ti:

sapphire crystal in a regenerative chirped pulse amplifier. We thoroughly characterized these

thermal effects using both experimental techniques (such as interferometry, M~ analysis and

measurement of focal power) as well as Finite Element Analysis. These measurements helped us

in designing a suitable cavity for the regenerative amplifier that generates 5 W of 40fs, amplified

output. The good agreement between the measurements and the numerical methods allowed us to

extend the numerical methods to predict an optimal cavity configuration to further minimize









these thermal aberrations which are detailed along with the present status of the amplifier in the

next chapter.










CHAPTER 5
CHARACTERIZATION AND OPTIMIZATION OF HIGH AVERAGE POWER CPA

Having fully investigated the fundamental aspects of designing and constructing a chirped

pulse amplifier and the thermal issues inherent with high powered systems in prior chapters, this

chapter concentrates on the characterization and performance of the amplifier and discusses

methods to further enhance its efficiency.

5.1 Amplifier Performance

5.1.1 Average Power, Pulse Energy

The cryogenic amplifier cavity based on the extensive thermal analysis is capable of

delivering 9 W of amplified power at 5 k
lis a plot of the measured average output power as a function of the pump laser' s repetition rate.
















4 5 6 9 10 11 12 13
Repetition Rate ktz
Figure 5-1: Amplified output power as a function of pump repetition rate (square points)
measured before compression; the red-line is a guide to the eye.

As the repetition rate is increased the output power of the system drops. This drop

coincides with the drop in the pulse energy of the pump laser (from 14.7 to 6 mJ). The boundary

temperature around the crystal increases from 110 oK at 5 k
indicates the amplified and the pump pulse energy with increasing repetition rate. The efficiency






























12




6

4


of the regenerative amplifier (defined as Eamph~fiedlEpump ,) is approximately 14% at 5 k
drops to 5% at 12 k
which no lasing action is observed as the cavity ceases to be stable. By altering the cavity g-

parameter, the amplifier can be made operational for repetition rates above 12 k
amplified output power of 4.5 W is generated at 12 k
recovered from the compressor. This could easily go up by the usage of gratings with improved

efficiency in the compressor setup.

61c t~


Repetition Rate (kd~z)
Figure 5-2: Amplified v/s pump pulse energy with increasing repetition rate. Amplified pulse
energy is indicated by the red points and the pump pulse energy by the blue points.
The solid lines are guides to the eye

5.1.2 Spatial Beam quality

The increasing thermal loading effects as a result of the increasing repetition rate also

bring about degradation of the spatial profile of the amplified beam as in Figure 4-15. This is

evident in the measured M~ of the beam at 8 k
chapter, M~ is a measurement of deviation of a laser mode from the fundamental TEMoo mode.

A boundary temperature of 115 oK was recorded for an input pump power of 75 W at 8 k









M2 Value Of 1.22 and 2.12 was recorded in the vertical and the

An average output power of 9 W uncompressedd) was obtained.

(a)
1400-
12nn 1- aucal i
lo \I *


repetition rate. A measured

horizontal axes respectively.


distance (cm)


-120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120
distance (cm)
Figure 5-3: Measured M2 for an uncompressed amplified beam of average power of 9 W at 8
k
The ratio of the divergence angle along the 2 axes is thus 1.73, which is a nearly 22%

increase from its value at 5 k
If the only source of astigmatism in the cavity is due to the Brewster crystal geometry, then

increasing the repetition rate should have little or no effect to beam astigmatism. But the rise in

the astigmatism of the beam shape with increasing pump power can be attributed to the changes

in the temperature related thermal constants for sapphire crystal as the boundary temperature

increases at higher repetition rates. Figure 5-3 is a plot of the measured M2 along the two

transverses axes plotted along with the respective divergence for a Gaussian beam of same waist.










5.1.3 Spectral Characteristics

The bandwidth of the amplified pulse is 25-30 nm (without any amplitude shaping)

depending on the bandwidth of the seed pulses. The amplified spectrum is shifted to the 'blue'

end of the spectrum as compared to the oscillator spectrum (Figure 5-4).





0.8- -w r l10.8






0.2 0.2~



0.0 0.0
700 7 0 740 760 7240 800 8 0 840 860 8140 900
Wavelength (nm)
Figure 5-4: Amplified spectrum (blue-curve) for the corresponding oscillator spectrum (red
curve) as measured using a fiber spectrometer.

Figure 5-5 is the emission spectra for Ti: sapphire at two different boundary temperatures:

87 oK and 300 oK. We observe that the emission spectrum is narrower at a crystal temperature of

87 oK than at room temperature. As the oscillator spectrum (Figure 5-4) is red-shifted with

respect to the emission spectrum the gain of the amplifier (Figure 5-5) is pulled to the bluer edge

of the spectrum due to which the amplified spectrum peaks at 780-nm as compared to 820-nm

for the oscillator spectrum. The spectrum for the free-running laser for the regenerative amplifier

cavity confirms the reason for this spectral shift towards the blue end (Figure 5-6). By reshaping

the oscillator spectrum as in figure 3-14 using the dazzler towards the blue end not only increases

the amplified output power from the regenerative amplifier but also reduces the amount of time

the seed pulse needs to stay within the cavity to be able to extract gain from the crystal. This is

since the gain of the sapphire crystal peaks at 775-nm (Figure 5-5), sculpting the spectrum of the








































































7 0 740 760 780 800 820 840
Wavelength (nm)

Figure 5-6: Free-running spectrum for the regenerative amplifier cavity at 5 k

0.8


=


seed pulse towards the bluer edge of the spectrum leads to efficient extraction of the energy by


the seed pulse from the crystal that in turn leads to a reduction in the number of roundtrips the


seed pulse needs to make to be able to gain the same amount of energy as a pulse with its


spectrum shifted towards the red-edge.


The amplified spectrum in Figure 5-4 generates 40-45 fs compressed pulses in a grating


based compressor with an efficiency of about 60%.


1













630 700


Figure 5-5: Emission spectra for Ti: sapphire.


1.0


800 900 1000 1100
Wavelength (nm)


a
e,
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