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Optical Studies of Subwavelength Structures

Permanent Link: http://ufdc.ufl.edu/UFE0022133/00001

Material Information

Title: Optical Studies of Subwavelength Structures
Physical Description: 1 online resource (111 p.)
Language: english
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: electromagnetic, enhanced, lithography, modes, optics, plasmon, rigorous, subwavelength, surface, transmission, trapped
Physics -- Dissertations, Academic -- UF
Genre: Physics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In this study we have studied optical properties of subwavelength structures. There is still a debate about possible mechanisms responsible for enhanced optical transmission of subwavelength structures. Two different works have been produced to better understand the physics of enhanced optical transmission: hole arrays in silver films and bullseye structures. In hole arrays, the period of the grating and hole size are systematically varied to give peak transmittances at different wavelengths. The spectra coincide when scaled using the array geometry and this shows independence of the dielectric function of the metal. We conclude that the spectra can be explained by interference of diffractive and resonant scattering. The resonant contribution is due to electromagnetic modes trapped inside the structures. In bullseye structures we have shown enhanced transmission without apertures due to trapped modes and cavity resonances.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Hebard, Arthur F.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022133:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022133/00001

Material Information

Title: Optical Studies of Subwavelength Structures
Physical Description: 1 online resource (111 p.)
Language: english
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: electromagnetic, enhanced, lithography, modes, optics, plasmon, rigorous, subwavelength, surface, transmission, trapped
Physics -- Dissertations, Academic -- UF
Genre: Physics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In this study we have studied optical properties of subwavelength structures. There is still a debate about possible mechanisms responsible for enhanced optical transmission of subwavelength structures. Two different works have been produced to better understand the physics of enhanced optical transmission: hole arrays in silver films and bullseye structures. In hole arrays, the period of the grating and hole size are systematically varied to give peak transmittances at different wavelengths. The spectra coincide when scaled using the array geometry and this shows independence of the dielectric function of the metal. We conclude that the spectra can be explained by interference of diffractive and resonant scattering. The resonant contribution is due to electromagnetic modes trapped inside the structures. In bullseye structures we have shown enhanced transmission without apertures due to trapped modes and cavity resonances.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Hebard, Arthur F.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022133:00001


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OPTICAL STUDIES OF SUBWAVELENGTH STRUCTURES By SINAN SELCUK 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 2008 1

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2008 Sinan Selcuk 2

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To my Mom, 3

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ACKNOWLEDGMENTS So many people I have to thank and acknowle dge for this work. First, Prof. Arthur Hebard has been a continuous source of knowle dge, direction and support. I cannot thank him enough. I want to thank my committee members for their time for reading the manuscript and their suggestions. I want to thank my lab member s, present and past for helping me. I would like to thank my coworkers in Prof. Tanner's lab for th eir help and time. I need to especially thank Kwangje Woo. Also for their tech nical support I am thankful to UF Nanofabrication facility personnel and UF High Performance Computing Ce nter, machine shop and Jay Horton. I also thank Prof. Sergei Shabanov for his ideas and discussions. I am grateful to my parents for their neve r-ending support. I want to thank my brother and Basak Hakanoglu for supporti ng me during this work. 4

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TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF FIGURES.........................................................................................................................7 ABSTRACT.....................................................................................................................................9 CHAPTER 1 INTRODUCTION..................................................................................................................10 2 THEORY................................................................................................................................13 2.1 Introduction............................................................................................................... ........13 2.2 Electromagnetics of Metals..............................................................................................13 2.3 Surface Plasmons..............................................................................................................14 2.4 Dynamical Diffraction......................................................................................................16 2.5 Composite Diffracted Evanescent Waves........................................................................16 2.6 Trapped Modes.............................................................................................................. ...18 2.7 Cavity Resonances.......................................................................................................... ..19 3 EXPERIMENTS.....................................................................................................................22 3.1 Fabrication........................................................................................................................22 3.1.1 Sample Cleaning.....................................................................................................22 3.1.2 Photolithography....................................................................................................23 3.1.3 Electron Beam Lithography...................................................................................26 3.1.4 Focused Ion Beam Lithography.............................................................................28 3.2 Characterization........................................................................................................... .....29 3.3 Measurement.....................................................................................................................29 4 COMPUTATION...................................................................................................................32 4.1 Introduction............................................................................................................... ........32 4.2 Rigorous Coupled Wave Analysis....................................................................................33 4.2.1 Projection-slice theory............................................................................................36 4.3 Finite Difference Time Domain........................................................................................36 5 HOLE ARRAYS.............................................................................................................. .......41 5.1 Introduction............................................................................................................... ........41 5.2 Zinc Selenide....................................................................................................................43 5.2.1 Transmission...........................................................................................................43 5.2.2 Reflectance.............................................................................................................4 6 5.2.3 Absorption..............................................................................................................47 5

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5.3 Fused Silica............................................................................................................... ........49 5.4 Annular Arrays............................................................................................................. ....49 6 BULLSEYE............................................................................................................................66 6.1 Introduction............................................................................................................... ........66 6.2 Results...............................................................................................................................68 6.2.1 Peak Positions.........................................................................................................69 6.2.2 Dielectric Thickness...............................................................................................71 6.2.3 Central Aperture.....................................................................................................72 6.2.4 Sidewalls................................................................................................................ .73 6.2.5 Silver Thickness.....................................................................................................74 6.2.6 The Role of Missing Rings.....................................................................................75 6.2.7 Different Open Area Fractions...............................................................................75 6.2.8 Polarization.............................................................................................................76 6.2.9 Separation of bullseye into two components..........................................................77 7 CONCLUSIONS AND FUTURE WORK..............................................................................99 7.1 Conclusions.......................................................................................................................99 7.2 Future Work................................................................................................................ ......99 APPENDIX GALLIUM AR SENIDE EXPERIMENT...............................................................101 LIST OF REFERENCES.............................................................................................................105 BIOGRAPHICAL SKETCH.......................................................................................................111 6

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LIST OF FIGURES Figure page 2-1 Electric field distribution on th e interface of a dielectric and a metal...............................21 3-1 Silver film during after focused ion beam etching.............................................................31 3-2 Effect of dry etch ing of fused silica substrate....................................................................31 4-1 Planar diffraction grating............................................................................................ ........39 4-2 Yee cell.............................................................................................................. .................40 5-1 Optical transmittance of zinc selenide................................................................................ 51 5-2 Index of refraction of zinc sele nide as a function of wavelength......................................52 5-3 Transmittance of hole arrays with different a and Dg on zinc selenide substrate..............53 5-4 Transmittance of hole arrays as a function of scaling variable..........................................54 5-5 Reflectance of hole arrays as function of scaling variable ...............................................55 5-6 Transmittance and reflectance data for two hole arrays.....................................................56 5-7 Transmittance and reflectance fo r hole arrays with six micron periodicity.......................57 5-8 Computation vs. experiment for hol e arrays with different open area fractions................58 5-9 Electromagnetic field distribution inside the holes for two different arrays.....................59 5-10 Energy density inside the holes with different open fractions............................................60 5-11 Transmittance of fused silica as a function of wavelength between 2.5 m up to 5.0 m......................................................................................................................................61 5-12 Transmittance of hole arra ys on fused silica substrate .....................................................62 5-13 Transmittance of hole arrays on fused silica substrate as a function of scaling.................63 5-14 SEM micrographs of hole arrays........................................................................................6 4 5-15 Transmittance of the annular arrays as a function of wavelength......................................65 6-1 SEM pictures of bullseye structures................................................................................... 79 6-2 Fabrication step s of a bullseye structure............................................................................. 80 7

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6-3 Optical transmission of Indium oxide film on fused silica.................................................81 6-4 Optical transmission of a flat 35nm-thick silver film on fused silica ................................82 6-5 Optical transmittance of the bullseye structure as a function of scaling parameter...........83 6-6 Different pe riodicities of bullseye......................................................................................84 6-7 Transmittance vs. wavelength for bulls eyes with different dielectric thicknesses.............85 6-8 Simulation results for transmittance vs. wavelength for bullseyes with different dielectric thicknesses......................................................................................................... 86 6-9 Bullseye structur e with central apertures............................................................................87 6-10 Transmittance of bare holes in silver flat films..................................................................87 6-11 Transmittance vs. wavelength for a bullseye structures of different silver thicknesses.....89 6-12 Computational transmittance versus. wa velength of 1D grating for different silver thicknesses.........................................................................................................................90 6-13 Bullseye structure with missing rings.................................................................................9 1 6-14 Computational results for different ratios of a to Dg..........................................................92 6-15 Optical transmittance of the bullseye structure as function of wavelength for different polarizations.......................................................................................................................93 6-16 Computational results for different polarizations...............................................................94 6-17 Separation of bullseye structure into two components.......................................................95 6-18 Transmittance of dielectric-metal grating with and without substrates..............................96 6-19 Transmittance of metal grating......................................................................................... ..97 6-20 Transmittance of bullseye structure as a sum of transmittance of two individual gratings and as the average of tran smittance of two indi vidual gratings...........................98 A-1 Gallium arsenide reflect ance as a function of wavenumbers...........................................102 A-2 Transmittance of gallium arsenide and gallium arsenide on silicon.................................103 A-3 Reflectance of a hole arra y on GaAs on Silicon wafer....................................................104 8

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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 OPTICAL STUDIES OF SUBWAVELENGTH STRUCTURES By Sinan Selcuk May 2008 Chair: Arthur F. Hebard Major: Physics In this study we have studied optical properties of subwavelen gth structures. There is still a debate about possible mechanisms responsib le for enhanced optical transmission of subwavelength structures. Two different works have been produced to better understand the physics of enhanced optical transmission: hole arra ys in silver films and bullseye structures. In hole arrays, the period of the grating and hole size are systematically varied to give peak transmittances at different wavelengths. The spectra coincide when scaled using the array geometry and this shows independence of the dielectric function of the metal. We conclude that the spectra can be explained by interference of diffractive and re sonant scattering. The resonant contribution is due to electromagnetic modes trappe d inside the structures. In bullseye structures we have shown enhanced transmission withou t apertures due to tr apped modes and cavity resonances. 9

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CHAPTER 1 INTRODUCTION The ability to concentrate, localize and control the distribution of electromagnetic energy in micro and nanostructures offers fundame ntal research opport unities and numerous applications. An important field in optical rese arch, called plasmonics or subwavelength optics, has been stimulated by work on optical transmi ssion through subwavelengt h periodic hole arrays by Ebbesen and coworkers.1 In that work it was shown that transmission of hole arrays is larger than the area occupied by the holes at some certa in wavelengths. In their case, the area occupied by the holes was only 2.2 %, and the transmission at 1.5 m was about 4 %. This was a surprise considering the classical calcula tion given by Bethe which predicted that transmission would be proportional to (d/ )4 where d is the hole diameter.2 For Ebbesen et. al. Bethe's calculation would correspond to practically zero transmission. In itially this extraordinary transmission was attributed to resonant excitation of surface plasm on polaritons at the metal/dielectric interface. Since then, a lot of work has been produced to understand and explain this mechanism and exploit it for possible promising applications. Diffe rent explanations other than surface plasmons are suggested. These explanati ons involve Composite Diffracted Evanescent Waves (CDEWs), dynamical diffraction, cavity modes and/or trapped modes.3-6 However, the explanation of enhanced transmission still remains controversia l. If we can understand the mechanisms behind all these effects, we can manipulate the distri bution of electromagneti c energy in micro and nanostructures for possible app lications in near field microscopy, photolithography, display systems and thermal emission sources. Subwavelength optical structures in the near field are not necessarily limited by diffraction and smaller size st ructures can be fabricated to replace bulky optoelectronic components.7,8 These applications can be us ed in all-optical information processing which is necessary for fa ster computation and communication.8,9 10

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To further understand extraord inary optical transmission, in this work, we have fabricated and characterized two different se ts of structures where optically enhanced transmission can be observed. In the first set of structures we have fabricated hole arrays in silver metal films deposited onto fused silica and zinc selenide su bstrates and measured optical transmission and reflection. For 44 % open area fraction samples, we get extraordinary transmission on the order of 60 %. The results are then compared with numerical simulations. By changing the hole size and periodicity of the ho le arrays, the optical transmission and reflection measurements together with numerical simulations have shown that en hanced transmission can be explained without surface plasmon polariton excitati ons and therefore is independent of metal properties. The enhanced transmission is attributed to the role of diffraction in additi on to the role of the solutions of the Maxwell equations with peri odic boundary conditions, wh ich are called trapped electromagnetic modes. The resonant scattering due to trapped modes and their interference with diffracted modes leads to extraordinary optical transmission. Trapped mode s are quasistationary, long lifetime, localized elec tromagnetic modes inside the structures. In the second set of the structures we have fabricated and analyzed bullseye structures and we have shown apertureless transmission due to the presence of trapped modes and cavity resonances. In this work we study the effect of metal thickness, dielectric thickness, groove periodicity, number of grooves, groove width relative to the pe riodicity, polarization and the presence/absence of a central aperture. This thesis is organized as follows, first th e theoretical background (review of literature) is given in Chapter 2 and then in Chapter 3 the experimental proce dures are presented, and this is followed with the introduction of computational methods used in Chapter 4. In Chapter 5 and 6, 11

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our experimental and numerical results are given for hole arrays and bullseye structures respectively. And finally conclusions are given in Chapter 7. 12

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13 CHAPTER 2 THEORY 2.1 Introduction In this chapter, the theoretical background that will be used to explain the effects observed in the experiments will be discussed. There are different theories that claim to explain the physics of enhanced optical tran smission of subwavelength hole arrays. Here, we will review some of those theories with th eir strengths and the drawbacks. Chronologically, the explanations are, excitations of surface waves (mostly surface plasmon polaritons, but different versions of it have been suggested), dynamical diffraction, Composite Diffracted Evanescent Waves (CDEW) and as many others also claime d diffraction enhanced by resonant character of lattice or surface waves. We will not go to a detailed discussion about the theories, but summarize some of the important claims. The reader is directed to review papers given in the references. 2.2 Electromagnetics of Metals For a linear, isotropic, nonmagnetic medium Ma xwell's equations in CGS units are given as, 4 D (2-1) 0 B (2-2) 1 B E ct (2-3) 14D HJ ctc (2-4) where D is the electric displa cement field, given as, DE and the induction field B is given as B H In SI units, 4 is replaced with 1/ 0 and c is set to unity.

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2.3 Surface Plasmons Surface plasmon polaritons are electromagnetic excitations that occur between at the interface of a metal and a dielectric.9 Electrons in a metal couple w ith the electric field of the incident radiation, giving rise to surface waves that decay into the metal. Only p-polarized (transverse magnetic, TM) light, (electric field is in the plane of incidence) can couple to surface plasmons.10 Wavevectors of surface plasmons are given as 0 dm sp dmkk (2-5) where 0/kc is the wavenumber of the incoming light. For a metal, the dielectric function can be expressed with the Drude model result as, 2 2()1p m (2-6) Since surface plasmon polaritons are excited only fo r TM mode (electric field is in the plane of incidence), it is important to have phase matchi ng; gratings (and corrugati ons make this possible) so that energy can be transferred to the excitations. The electric field di stribution (blue curves) on the interface of a dielectric (air) and a metal (gray color) is shown in Fig. 2-1. To be consistent with an alternating surface charge di stribution, the electric field has to be in xdirection here (has to be in th e plane of incidence, TM polariza tion, here magnetic field is into the page). The field distribution falls off more rapidly inside the metal than it does within the dielectric layer above. The dispersi on relations for the light line (/ kc ) and surface plasmons are shown in the figure. To gene rate surface plasmons, the reciproc al lattice wave vectors of the periodic structure must be included in the mome ntum conservation equati ons. Incident light can only couple to surface plasmon polaritons if there is a grating. 14

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sppkkG (2-7) where is the wavevector of light pa rallel to the film surface, kspp is the wavevector of surface plasmon and G is the reciprocal lattice vector given as, k 2 ()gGx D y (2-8) At low k values, the dispersion rela tion of surface plasmon polaritons is linear, because at long wavelengths dielectric function of metal is much larger than the dielectric constant of the dielectric, so dispersion equati on approaches the light line. Th eir momentum does not match to the phase match they need co rrugation (momentum conservation). The surface plasmon is essentially an evanescent wave traveling para llel to the interface with intensity rapidly diminishing within the metal. Enhanced optical transmission (EOT) is attr ibuted to surface plasmon polaritons (SPPs). According to theory, they are excited and resona ntly decay through the metal film, or through the hole arrays. There are two different types of surface plasmons: propagating surface plasmon polaritons, and localized surface plasmons. Propagating surface plasmons are usually on patterned films like hole arrays. Localized surface plasmons are associated with voids and/or metal particles and they do not propagate.11 Resonant absorption of light by SPPs and thei r decay is claimed to be the reason for extraordinary optical transmission. Even today, this is the most co mmonly accepted hypothesis of EOT. Near-field considerations and the difference between localized and propagating surface plasmons is given by Smolyaninov et. al.11 A new field, involving app lications that depend on surface plasmons is called plasmonics.8 15

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However the surface plasmon explanation ha s drawbacks. It only works for TM polarization case, and fails to explain TE polarization. There are experimental results for 1D gratings and 2D hole arrays for the TE polariz ation case, and extraordinary transmission is shown. Also numerically, for perfect electric conductors extraordinary transmission is shown, where perfect electric conductors cannot support surface waves and surface plasmons. Also for tungsten thin films at visible wavelength extraordinary transmissi on is shown, but tungsten is a dielectric in visible wavelengths.12 The dispersion relation for surface plasmons is obt ained for flat films, but it is not known to modify it for corrugated surfaces. Still surf ace plasmon explanation is the most commonly accepted theory. 2.4 Dynamical Diffraction Another explanation for extraordinary optical transmission is an explanation by Treacy.3 In that work it is claimed that surface plasmons are a part of the diffracted light but they do not play an important role in enhancement. The enhan cement comes from the Bloch waves that peak inside the holes are strongly excited, but the Bl och waves that peak on the metal are absorbed strongly and decay. 2.5 Composite Diffracted Evanescent Waves Composite diffracted evanescent waves (CDE Ws) are a descriptio n based on scalar diffraction theory. The theory is developed to overcome problems with the surface plasmon explanation.4 It does not rely on surface plasmons but on interference of diffracted evanescent waves, which are claimed to predict the right amount of transmission amplitude, and suppression as well. The authors also claimed that in the first work of Ebessen et. al.1 larger values of transmission ratios of enhancement were repor ted because Ebbesen et. al. underestimated the aperture sizes. 16

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Incident light is sca ttered both into radiative modes a nd evanescent modes. The collection of all evanescent waves is a surface wave, whic h is named as composite diffracted evanescent wave (CDEW). The CDEW propagates with the wavevector of the incident light, and its amplitude decays with a reciprocal dependence (1/x) on distance as it propagates together with a phase that is shifted by /2 compared to the excitation at the source.4 When the CDEW arrives at another scattering center (for hole arrays it is a neighboring hole) it interferes with the light that is directly hitting that hole, giving rise to elec tric field enhancement at the aperture entrance when the interference is constructive, or field suppression when the inte rference is destructive. The grooves, or corrugations are only a means of increasing the amplitude at the entrance of the hole. As the light emerges from the aperture on the backside of the film, some of it again is diffracted into radiative modes and some of it w ill diffract as evanescent modes, the collection of evanescent waves on the backside also forms another CDEW.4 The total intensity transmitted through the hole is expressed as TC( ) = A1( ) TH( ) A2( ) fC (2-7) where A1( ) is the field enhancement at the entrance of the aperture, TH( ) the intrinsic transmission coefficient of the aperture, and A2( ) the effective collection enhancement due to scattering off the corrugation on the exit side of the film, and fC is the fraction of the total light emerging from the aperture exit.4 According to the author's claim, the CDEW explanation can replace the SPP explanation because it predicts the correct peak positions of the transmittance observed in hole arrays and also includes enhancement and supp ression effects. And it is more general than surface plasmons in the sense that the enhanced transmission effe ct seen on dielectrics an d perfect conductors can be explained. Another paper where these effects are observed is by Gay et. al.13 Results of this 17

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work have been controversial and it seems is th at the CDEW explanation has some shortcomings in its interpretation. There are two papers anal yzing the CDEW interpre tation. The first of these14 showed that CDEWs are not adequate for ha ndling s-polarization ca se, and mishandles ppolarization case, even though it is a scalar theory. Also the authors pointed out that, omitting radiative modes in calculations is a serious mi stake because the radiative modes can cancel the contribution of evanescent modes. They also claimed that the CDEW description only works after several fitting parameters have been included. They conclude that the CDEW explanation is physically and mathematically flawed.14 Another work also concludes that there are flaws in CDEW picture.15 2.6 Trapped Modes Trapped modes are solutions of the Maxwell equations when th ey are expressed as in the same form as the Schrodinger equations. When these Schrdinger-like equations are solved, for our structures and similar subwavelength structures, the solutions are in the form of eigenstates. These eigenstates solutions are electromagnetic modes trapped inside the structures.5 The trapped modes explanation of extraordinary transmission of subwavelength structures solves all the problems with TE, TM polarization cases; it works with metals (and perfect conductors, numerically shown) and the dielectric structures The trapped modes are shown to have long lifetimes. To convert the Maxwell equations into Schrdinger equations we start with the relations16, DcxH (2-8) B cxE (2-9) 18

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for no current or free charge case. In these equations B and D are inductions and E and H are fields. Their relations to each other are given as, DE (2-10) B H (2-11) The time-dependent Schrdinger equation is iH t (2-12) Here E H and the Hamiltonian, H is given as, 0 0ic H ic (2-13) The initial value problem is solved a nd propagated with th e time operator, ()()eiHtttt (2-14) Trapped modes are independent of the choi ce of the materials, and the only thing important is geometry. Space dependency is included in the dielectric constant The solution of Maxwell's equations in periodic boundary conditions will impose these solutions. This dependence on geometry is shown in th e scaling results of Selcuk et. al.17 2.7 Cavity Resonances Cavity resonances (Fabry Perot) type resonances18 are shown to exist in 1D and 2D structures for perfectly conducting structures, s-polarization case.19 When a wave is inside the resonator, it will reflect back and forth and will form a standing wave inside the cavity structure. For our bulleye structures, to be discussed in Ch apter 6, with thick dielectric structures beneath 19

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the metal layer, we will show that cavity res onances, which are localized and hence similar to trapped modes5, play a role in optical transmission enhancement. 20

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21 Figure 2-1. (left) Electric field distribution (blue curves) on the in terface of a dielectric (air) and a metal (gray color). (right) Dispersion curves for the light line (dashed) and surface plasmon (solid).

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CHAPTER 3 EXPERIMENTS 3.1 Fabrication The following summary gives an overview of fa brication procedures. The procedures for fabrication are determined by the mi nimum feature size in the struct ure. If the structures are on the order of 1.5 micron or above, photolithogr aphy rather than Elec tron Beam Lithography (EBL) or Focused Ion Beam (FIB) lithography is preferred for patterning. Photolithography techniques have limitations since it is inherently diffraction limited.20 EBL and FIB lithography techniques require conductive laye rs in the sample for charged particles to flow from source to ground. Otherwise excess charged pa rticles at a local poi nt will deflect or repel the beam and will distort the pattern. Also low throughput of EBL and FIB lithography is one of the main reasons it is not a widely employed lithographic process, because each element is scanned serially, whereas optical lithog raphy has a significantly higher throughput. Another consideration in this study is the wavelength ranges over which optical data wi ll be collected. As will be discussed later, the wavelengths where enhanced optical transmission occurs can be controlled with the design of the structures. Our measurements in near infrar ed (NIR) and far infrared (FIR) require bigger pattern sizes to get enough signal. Since it will ta ke long time to pattern bigger areas with EBL or FIB, photolit hography is the pref erred method for most of the samples. Solution to this might come from imprint lith ography, which could be an important tool to fabricate submicron structures with large areas.21 But its drawback is the fabrication of the mold, which requires large areas to be written again with EBL; so it is not commonly used yet. 3.1.1 Sample Cleaning The very first thing is to remove the contam ination on the sample. Contamination can be in the form of organic and inorga nic particles or the thin films. For polymeric particles deionized 22

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(DI) water sonication is the most efficient method for cleansing whereas acetone:ethanol (1:1) mixture is very efficient for removing inorganic particles.22 Fused silica and zinc selenide (ZnSe) substrates are cleaned sequentially with sonication in deionized water, acetone, isopropanol and meth anol at least five minutes for each. Samples are then dried with nitrogen blow. Th ey are inspected visibly and th en with optical microscopy for cleanliness. Acetone leaves a residue if it evaporat es from the sample; to prevent that methanol must be used right after acet one without letting acetone evapor ate. To remove residues of polymers dry cleaning procedures might be need ed: these are oxygen reactive ion etch (RIE) (O2 plasma), barrel asher and UV/ozone cleaning. 3.1.2 Photolithography Photolithography also known as optical li thography is a common microfabrication technique. It involves a light source emitting at UV wavelengths, which is used to change the chemistry of a radiation sensitiv e polymer, photoresist, which is coated on top of a sample and exposed through a chrome mask. The change in th e chemistry of photoresist with light makes it soluble or insoluble in a chemical called the developer depending on the type of the resist. Positive (negative) photoresist becomes solubl e (insoluble) when exposed to UV light. A Karl Suss MA-6 mask aligner is used in our experiments. It s mercury bulb's light is filtered at 365 and 436 nanometers. Even though different photoresists are used for different purposes, mostly Shipley S1813 thinned with P-Thinner with a ratio of 3:1 (Thinner : Photoresist)23 is used in our experiments. S 1813 is produced by Shipley (now owned by Rohm-Haas) and distributed by Microchem Corporation. The photoresist is spin coated onto the samples without any adhesive layer. Spin sp eed is 4000 rpm for 40 seconds after an initial spin of 100 rpm to dispense the photoresis t. The photoresist is prebaked at 115 0C for 90 seconds on a hot plate or in an oven for 30 minutes for 90 0C to dehydrate the surface. Baking in 23

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an oven gives a more uniform photoresist film. The thickness of photoresist is about 550nm after baking as determined by atomic force microscopy m easurements. If it is not diluted with thinner, S181324 photoresist has a thickne ss of approximately 1.3 m if it is spun 4000 rpm and it has optimal sensitivity near the mercury g-line at 436nm. For samples with feature sizes in the 1.5 m range, even thinner photoresists can be used. Usually, for a successful liftoff, the thickness of photoresist should at l east be twice that of the meta l layer to be evaporated or sputtered. If thinned photoresist (3:1) is us ed, it is exposed through a chrome mask for 12 seconds (with light power of 8.0 Watt/cm2). Exposure time depends on the pattern; it can be up to 30 seconds. There are different types of contacts made with the sample and the mask in MA6 mask aligner: these are hard, soft and vacuum contac ts. In soft contact mode there is an air gap between the sample and the mask. This exposure type does not give the best resolution but it is used if the mask is fragile, because this give s the least damage to the mask. Also, if the resolution is not critical soft cont act is preferred. In hard contact mode, nitrogen gas is used to push the sample against the mask. In vacuum c ontact mode, the separation between the sample and the mask is under vacuum during the exposure; this is the closest th e sample and the mask can get. This contact mode gives the best reso lution. Sometimes there is a need to expose the sample without the mask; this is called flood exposure, and it is on e of the modes of Karl Suss MA 6 mask aligner used in this study. Exposed photoresist developed for about 14 seconds with AZ 300 MIF (metal ion free) or MF 319 develope rs without dilution with DI water at room temperature. These two developers have the same chemistry, but are supplied by different companies. Samples are rinsed in DI water an d nitrogen blown dried. Karl Suss MA 6 has another mercury light line, whic h is 365 nm (mercury i-line), which is preferred for other 24

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photoresists. Channel 2 of MA6, with a light of wavelength 436nm (mercury g-line) is used for S1813. Photoresist is used without thinning but must be postbak ed if the next step is an aggressive dry etching process. In some of applications Lift off Resist B (LOR B)25 is used. When exposed photoresist on top of LOR is deve loped, LOR will give an undercut even though it is not UV sensitive. LOR gives an undercut, wh ich helps liftoff process. It is baked at 200 0C on hot plate for 2 minutes after it is spin coat ed usually with 3000 rpm. LOR is soluble in Remover PG by Microchem.25 Metal-ion-free developers such as MIF 319 contain tetramethylammonium hydroxide (TMAH) as the active material. Its chemical formula is (CH3)4NOH and it is a strong base. MF 319 and MF 322 can be used for same pur poses; difference comes from the amount of TMAH in their unit volume. MF 322 will develop faster but with less control over developing process. The photoresist can be postbaked at 115 0C for 3 minutes if the next step involves dry etching. For different applica tions different types of photoresis ts are employed. Photoresist is removed with acetone, but sometimes after dry etch ing, if it became carbonized, more aggressive methods are necessary to remove it from the su rface like oxygen plasma or heating the Remover PG. Also there are special photoresist strippers from Microchem. If photoresist is used without thinning exposure time is about 28 seconds and developing is 30 seconds. To get slower developing, DI water can be mixed with the developer. If there is no negative pattern on the chrome mask, it may be necessary to use a positive photoresist as a negative resi st. The recipe for this is, using AZ 5214 E photoresist26, it is an image reversal photoresist. The su ccessful recipe used in this study is to expose for 10 seconds 25

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with the mask and then bake 2 minutes on a hotplate at 110 0C followed by a 30 second exposure without the mask (flood exposure). 3.1.3 Electron Beam Lithography In Electron Beam Lithography (EBL) electro ns are accelerated towards the sample, which is coated with a polymer, called resist that is sensitive to electron ra diation. This process is similar to photolithography in the sense that it uses a coated layer, resist, to be patterned, from which the pattern will be transferred to the samp le with metallization or etching. But they differ in the sense that, structures are patterned seri ally, one by one, whereas optical lithography is a parallel process. Polymethylmethacrylate (PMM A) with 950K molecular weight is the electron resist used. It is a positive electron beam resist It has a long shelf life and has a resolution of 10 nm.27 It is spin coated on to th e substrate with different spin speeds to obtain different thicknesses. After coating it is baked on a hotplate at 180 0C for 1 minute. It could also be oven baked at the same temperature with longer time, which would yield a more uniform coating. In our experiments, most of the cases we have used insulator substrates to start with and then coated conducting layers to prevent ch arging during EBL, oven baking affected our conducting layers, so we used hotplate baking usuall y. This baking evaporates the solvent for the PMMA. There are two different solutions solid PMMA can be dissolved in: chlorobenzene or anisole.28 In our experiments we have used anisole as the solvent to dilute PMMA and obtain different concentrations for different thicknesses. There are two types of electron beam lit hography systems: commercial systems and systems modified from a Scanning Electron Microscope (SEM) using proprietary Nabity software. In this study, we have used both of them: Raith 150 as a commercially available EBL system and NPGS29 installed XL40 FEI SEM. Compared to the Raith 150, the Nabity system using FEI XL40 microscope is much faster, be cause the large field of view(more than 1mm 26

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1mm accommodates large exposure areas. But the uni formity all over the samp le is an issue for such large areas. As a solution to this the Raith 150 wr ites the whole pattern by dividing it into smaller square-area writing fields. By doing so, it can produce same quali ty all over one writing field because electromagnets can focus the beam ev en at the edge of the field. But from write field to write field, even though stage positi on is controlled interferometrically, there are sometimes stitching field errors. The reasons for these errors arise from misalignment of writing fields (due to user) or shifts between cons ecutive write fields as the patterning proceeds (sometimes due to software/hardware). The usual acceleration voltage is varied be tween 10 to 30 keV. Higher voltages give smaller spot size and better resolution but more energetic secondary el ectrons as well. Lower voltages give less contrast bu t less number of secondary el ectrons with lo wer energies.27 The number and the density of elements will determine the total time for exposure. Samples are grounded with colloidal gr aphite or carbon tape or metal clamps. Focusing, stigmation, aperture alignment and write field alignment must be done reasonably well for a successful exposure. With good focusing, stigmati on and aperture alignment, 20 nm diameter spots can be easily exposed. 30 m aperture size is usually used with 10 keV it gives a current of about 0.18 nA. Bigger apertures will give higher currents (doubling the ap erture will quadruple the current) so that exposure tim e can be significantly reduced. Th e dose is usually kept between 100 C/cm2 and 300 C/cm2. Proximity effects occur if two elements are t oo close to each other. The smallest feature size needed in our experiment is a square array with 300 nm sides and 600 nm spacing in between them. In such a close an d dense pattern, proximity effect s start to become important. For developing exposed PMMA, MIBK:IPA (3:1) mixture is used and the time of 27

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development depends strongly on the metal layer underneath the PMMA and the density of elements in the pattern. If thic k silver (100 nm or thicker) laye r is underneath, 7 seconds is sufficient, whereas on silicon wafer with PMMA, 30 seconds is sufficient for development. Developed PMMA is rinsed with IPA and blown dried with nitrogen. Another mixture that is commonly used is MIBK:IPA (1:1), which develops faster and is very se nsitive but gives less contrast. After developing, there may be so me PMMA residue on the surface, which can be removed with oxygen plasma in a barrel asher with a power of 100 Watts. If the next step is metallization, the liftoff is done with a mixture of methylene chloride and acetone (9:1). PMMA has a natural undercut, which makes liftoff easier. But sometimes still copolymer might be needed underneath PMMA. Copolymer similar to LO R develops faster and gives an undercut. If it is coated on top of PMMA, after developing and metallizat ion it gives mushroom-shaped T gates.28 To fabricate structures on insulating substrates, for example on fused silica, a very thin but conducting layer of silver (20 nm) is evaporated. This layer is enough to prevent charging in EBL. After exposure, silver metallization and lift off, this thin layer is etched away with argon ion etch. 3.1.4 Focused Ion Beam Lithography Focused Ion Beam (FIB) lithography simila r to electron beam lithography, involves charged particles, this time ions instead of el ectrons. FIB processing does not require a mask or a resist as in EBL and photolithography even t hough masks could be used. It is real time processing of the sample. This removal of material has the disadvantage of being irreversible. In contrast, in EBL and photolithograp hy the resist can be removed after an unsuccessful exposure, and then re-coated to start over. FIB does not o ffer this flexibility in most of the cases. FIB lithography systems are starting to be commercially available30 even though FIB was first 28

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developed to be used a tool to detect and fi xed broken microchips in semiconductor industry. Gallium is the common source of the ions in FIB sy stems because it is easy to extract ions from the low melting point liquid metal. The melting point of gallium is around 30 0C. Ga+ ions from liquid metal ion source are accelerated towards th e sample. This charge must be grounded with a conductive layer on the sample. This conductive laye r is usually grounded with colloidal graphite applied on the corner of the sample. Simultaneously there is gallium contamination as material is being removed from the sample. The acceleration energy of ions is 30 keV. The ion current used in the experiments is in the order of 50 pA. This is the lowest current that can be extracted from the system and has the least damage on th e sample during imaging and aligning. An FEI DB 235 system is used in the experiments31. This system has dual beams: an electron beam (SEM) for imaging and positioning the sample and an ion beam for patterning. The etching time depends on the thickness of the laye r, but it is usually in the orde rs of a few minutes. For metals focused ion beamed surfaces often become rough, because differently oriented grains have different etching yields.27 Fig. 3-1 shows this ion-beam i nduced roughness for a 100 nm thick silver film. 3.2 Characterization After each process, quality of samples in terms of defects, surface roughness, and uniformity is examined using atomic force mi croscopy (AFM), optical microscopy, scanning electron microscopy, surface profilomete r and Wycko optical profilometer. 3.3 Measurement Our collaborators in Dr. Tanner's lab perfor med some of the measurements, mostly midinfrared measurements. A tungste n bulb is used for near infrar ed (NIR) and de uterium bulb for UV and visible range of spectru m. Most of the measurements are performed with Fourier 29

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Transform Infrared (FTIR) spectroscopy and optical microscope attached spectrometer. Reflection measurements are done with a conical angle of 8 degrees. 30

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31 Figure 3-1. 100 nm Silver film during FIB, different grains have diffe rent etch rates. Figure 3-2. AFM images of a dry etched Fused S ilica substrate a. Dry etched Fused Silica with CF4 and O2, 150 nm deep, leaves a rough su rface with photoresist mask. b. Same sample O2 plasma to smoothen the surf ace, 500 Watts, 20 minutes, 350 sccm of O2. c. Argon ion etch of the same sample, 10-4 Torr, 15 minutes, surface gets better but there is lateral etching, depth is ar ound 200 nm. Image is 5micron X 5micron.

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CHAPTER 4 COMPUTATION 4.1 Introduction To fully understand the physics of optical enhanced transmission in subwavelength structures, numerous experiments have to be done systematically. There are many parameters in the experiment to vary, including the metal film and its thickness, aperture size, shape and depth in the structures, periodicity, superstrate mate rial, and the substrate. Along with the possible variations in the fabricat ed structures there are also variations in the measurement setup as well: polarization, angle of incidenc e and the measurement of reflection and transmission in higher orders. It is not possible to perform all these ex periments because of limited resources. But help comes from the field of computational electroma gnetics. In recent years with the advent of computers and with the availability of fast er and more robust algorithms, computational electromagnetics has come a long way. There are different numerical methods applied to different electromagnetics problems each with unique advantages and disadvantages. Some of those methods are Rigorous Coupl ed Wave Analysis (RCWA),32 Finite Difference Time Domain Method (FDTD),33 Frequency Domain Method (FDM), Finite Element Method (FEM), Boundary Element Methods (BEM) and Method of Moments (MoM). This list is not complete. Here I will only review briefly the methods that we used in this study, RCWA and FDTD. These methods are often used in theoretical stud y of the enhanced optical transmission field. When feature sizes in the structure become comparable with the wavelength, sometimes called rigorous domain, vectorial ra ther than scalar solutions of Maxwell equations are required, because effects like multiple scattering become important. RCWA and FDTD are implemented vectorially and thus are capable of solving rigorous domain problems. 32

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4.2 Rigorous Coupled Wave Analysis RCWA is a commonly used method for the analysis of diffraction gratings. It functions by dividing the structure into multiple layers and ex pressing dielectric permittivity and fields inside the layers with Fourier expansion in spatial coor dinates in each layer. Eigenmodes in every layer are calculated independently from the other la yers. These eigenmodes are the solutions of Maxwell's equation in each layer. At the end of the calculation, far field values of the electric field are calculated with the corresponding Fourier transforms giving transmittance and reflectance information. RCWA is claimed to be a fast method and is widely used for optimization of diffraction grating design.34 But it is a monochromatic method because fields are expressed in terms of the singl e wavelength of the interest. Consider the one-dimensional lamellar diffraction gr ating in Fig. 4-1. To calculate the field intensities, reflected and transmitted, the field in side the grating has to be calculated. There are three regions of interest with index of refractions n1, n2 and n3: region I is the superstrate, region II is the periodic rectangular grating (sometimes called bina ry or lamellar grating) region and region III is the substrate. Rectangular gratings are some times called binary or lamellar gratings. In region I, there are two contributions to the total electric field: the incident electric field and the electric field due to reflected orders. Th e sum of these contributions, can be written in terms of traveling wave solutions, 11exp[())]inc j jEERjikr (4-1) where is the incident electric field, incE R j is the complex diffracted dielectric field of the jth order, 1() j kis the wavevector of the reflected light and r is the displacement vector, which is, 33

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rxizk (4-2) Inside region II, the total electric field can be expressed as, 2 0()exp()()exp[()]jjjx j jjESzikrSzikxk zz (4-3) where kxj=kx0-jK, kx0 is zero order wavevector, j is the diffraction order and K is the magnitude of grating vector, given as K=2/Dg. Similarly the magnetic field can be expande d as a function of unknown vector field functions, 2()exp()jj jHUzikr (4-4) and the dielectric function of Region II is expanded in terms of Fourier series, (,)(,)()exp()gm m x zxDzzimKx (4-5) where m(z) are the Fourier coefficients. The permittivity (dielectric function) is a periodic function of the lattice periodicity Dg, which is inversely proportional to K, magnitude of grating vector, as 2 g K D (4-6) With the Maxwell equations, x EBH (4-7) 0 x BDE (4-8) and assuming exp(-it) time dependence on the fields, the wa ve equation for Region II is of the form, 22 222()(,)0 EkxzE (4-9) 34

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If equation 4-3 is substituted into equation 4-9, we get, 2 222 0 2()() 2()()()jj zo xjxj mjm mdSzdSz ikkkSzkzSz dz dz()m (4-10) These are second order-coupled wave equations.35 Each term j in the expansion is coupled to the other j-p terms in the expansion. The solution of this large number of coupled equations can be obtained using a state variables method.35 Solutions are expressed in terms of eigenvalues and eigenvectors as, ()exp()jm j m mSzCz (4-11) And finally similar to region I, fields in region III can be expressed as, 33 exp[()()]j jETjikrd z (4-12) where we have assumed that the substrate is lossless. These 3 equations (eq. 4-1, 4-3, and 4-12) for fields in regions 1, 2 and 3 are phase matched along the interfaces, thus providing solutions for far-field transmission and reflection data. In this study, RCWA is used with co mmercially available software GSolver.34 In GSolver when light is incident on the su rface, there are five input parame ters of the numerical calculation: these are the wavelength, the two angles for incident and transmitted light and the two angles for polarization angle. In the simulation, the number of Fourier harmonics determines the resolution. If a sufficient number of Fourier components ar e involved in the solution, the results will converge. Usually increasing the number of Four ier harmonics in the expansion is a good check of convergence if the results are stable. The details of GSolver parameters that are used in this study will be given in Results and Discussion chapter. 35

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4.2.1 Projection-slice theory The bullseye structure fabricated in this work is analyzed as a one-dimensional grating. Even though the bullseye structure is circularly sy mmetric, its side view is a 1D grating. If bullseye structure's reflection and transmission is measured with polarized light, it can thus be comparable to a 1D grating. This idea is justified with the Projection-slice theorem, which states that one-dimensional Fourier transform of a parall el projection of an object is equal to a slice passing through origin of the two-dimensi onal Fourier transform of the same object.36 In Chang et. al.37 it is shown that 1D gratings can be used as a model to simulate the bullseye structure. Similar conforming results are obtained in this study; a nd the details will be presented in Chapter 6. 4.3 Finite Difference Time Domain In the FDTD method, Maxwell's equations are approximated by discretization of continuous field values into discrete values at certain points in space and time. To divide space and time into discrete values a mesh composed of cells is used. FDTD belongs to a more general class of Finite Difference Methods where discre tization is used. The fi eld progression and its values are calculated at every grid point. This provides a possibility of r ecording fields behavior as it propagates or as it interacts with the structures giving a possibility of animation of field as it propagates through the computational domain. Anothe r advantage of FDTD is that structure can be excited with a broadband pulse, so that ma ny wavelengths can be simulated simultaneously. The FDTD method originat ed with Yee's work.38. Maxwell's equations are expressed as difference equations. Once again, the Maxwell equations in SI units are, for an isotropic media, 0B E t (4-13) 36

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B HJ t (4-14) B H (4-15) DE (4-16) where J, and are functions of time and space. The equations above can be expressed as coupled finite difference equations, as follows, y x zE B E ty z (4-17) y x zB E E tz x (4-18) y x zE E B ty x (4-19) From here each of these equations can be expanded, or approximated if we replace their continuous values with discrete values taken at the midpoint of spacing that has been determined when the computational domain is defined. We can approximate field values as given by, 1 1/2 21111111 [1/(,,)(,,)][(,,1)(,, 2222 2 2 111 [(,1,)(,,)] 22n nn xxyy nn zz1 )]n B ijkBijkEijkEijk tz EijkEijk y (4-20) Equation 4-20 states that, time derivatives can be approximated by differences between adjacent points. The working space is divided into gr id cells and values are taken at the center of 37

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the cell. This cell in FDTD is sometimes called the Yee Cell.39 All Yee Cells make up the lattice throughout the computational domain. Any numerical solution of a partial differe ntial equation requires that the equations should be transformed into algebraic equations similar to what we ha ve seen in RCWA. And time intervals are expressed as finite time steps. From each step, or from each cell, the field values are evaluated and progressed with Leap Frog schemes. The computational FDTD algorithm used in this study is the freely available Meep version 0.10.38,40 At the moment Steven G. Johnson of Massachusetts Institute of Technology is maintaining Meep. Usually 3D FDTD with disper sive materials needs a bout 8 processors and around 8 Gb memory to run about a few hours, so supercomputing facilities might be needed for such heavy computations. The FDTD code (M eep) is run in High Performance Computing Center of University of Florida (UF HPC). Th e author acknowledges th e UF HPC for providing computational resources and support.41 38

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39 Incident light Figure 4-1. Diffraction grating with reflected and transmitted orders for a planar grating. X I II III Z Y T0

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Figure 4-2. 3D Yee cell, the elect ric field values (blue) and ma gnetic field values (green) are calculated at the center of the cell.39 40

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41 CHAPTER 5 HOLE ARRAYS 5.1 Introduction Bethe has calculated transmission of for a subwavelength hole with radius r, on a perfectly conducting thin film as 4~(/)Tr (5.1) in 1944.2 But in a recent work it has been shown that the transmission per hole of an array of subwavelength holes in a metal f ilm is higher than what Bethe ha s predicted and also bigger than the area occupied by the hol es at certain wavelengths.1 Since then much work has been produced to understand this phenomenon. As discussed in the theory chapter (Chapter 2) many authors have suggested different models. The explana tion of enhanced optical transmission through subwavelength holes remains c ontroversial. Here for simplicity, we will denote a specific hole array with parameters (a, Dg) where a is hole diameter (if it is a circular hole) or si de of a square hole and Dg is the periodicity of the array. Another definition th at we will be using is 2(/)g f aD (5.2) where f is the open area fraction. We will use f to designate different hole arrays because we have observed that the difference in terms of p eak amplitudes comes from the different open area fractions, f, for our samples. Obviously peak amplit udes in transmittance depend strongly on the hole size and the peak positions depend on the latt ice constant. A hole array is characterized by geometrical parameters, such as the hole size, the lattice (square, triangular, hexagonal, etc), the hole shape (rectangular42, circular42,43, annular44,45, elliptical46), the hole depth47 and the periodicity 17,47. Also there are parameters that are coming from different materials used, like

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different metals48,49 or the semiconductors like gallium arsenide50 and silicon carbide51 and the substrate or the superstrat e and finally the materials filling inside the holes52. So far, in all the works produced since 1998 with different explanations, one thing that is certain is that the periodicity of the hole array is the most important parameter of all the listed parameters above in terms of determining the peak position in wavelengths. Here our results, optical transmission, refl ection and absorption of square hole arrays with periods ranging from 1 to 8 m with different hole sizes, will be presented and comparison with numerical calculations will be given. We ha ve used two different substrates, zinc selenide (ZnSe) and fused silica. Our numerical calculatio ns use Finite Difference Time Domain (FDTD) techniques as well as freque ncy domain techniques, which in clude the calculation of the electromagnetic field distribution inside the holes. We will show scaling in the hole arrays, i.e. within the studied arrays, if we plot waveleng th axis with respect to dimensionless scaling variable, the spectra of different samples with di fferent holes sizes but with same periodicities will have similar features. Also we will show that enhanced optical transmission is due to diffraction and resonance of trapped modes. Trapped modes are the electromagnetic modes inside our structures. These mode s have finite lifetimes and are solutions of Maxwell's equations with periodic boundary conditions. A dip in R + T spectra will show existence of a trapped mode at the wavelength dip occurs. The resonance of the trapped modes happens close to the diffraction threshold. And depending on the hole size, the contributions due to the trapped modes and diffraction will be different. This is due to the fact that bigge r holes interact strongly with the surrounding environment and due to this interaction they have a larger damping so they cannot support trapped modes. As the hole size gets smaller, th is behavior changes, trapped electromagnetic 42

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modes inside the holes have longer lifetimes and they do not decay as fast as the ones in the bigger holes. 5.2 Zinc Selenide 5.2.1 Transmission Commercially available chemical vapor deposition (CVD) grown ZnSe substrates with 25 mm diameter and 2 mm thickness are used as the substrates in the infrared region experiments. As shown in Fig. 5-1, Zn Se is optically transparent between 2.5 m and 20 m as much as 60 %. The index of refraction, nd, of ZnSe is a function of wavelength. Its dependence on wavelength is given as, 2 2 2 dB nA C2 (5-3) with the parameters, A=4.00, B=1.90 and C2=0.113.53 As can be seen in Fi g. 5-2, the index of refraction of ZnSe is decreasing for increasing wavelengths. nd is 2.49 at 1 m and 2.34 at 17 m. In our study we have ignored this change a nd assumed a constant value of 2.4. We could have made a correction for the change in nd of ZnSe, and we checked that for calculation of the peak positions and it did not make much differen ce. Also in this work mostly we will compare structures with the same periodicity but different filling fraction, which means that the change in nd will be same for all. So it is reasonable to ignore the change in n. To prevent the differences that might result from the processing of diffe rent samples, all hole arrays used in the transmission measurements are fabricated on the same substrate. For reflection experiments we needed a much larger area of the sample to get enough signal in measurement so each hole array is fabricated on a different ZnSe substrate. The fabrication of hole arrays is discussed in the experiment chapter (Chapter 3). But fabrication steps are patterning with electron beam 43

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lithography or photolithography exposure and development, silver metallization and the liftoff in acetone or methylene chloride. Square hole arrays with squares of side a and periodicity Dg are fabricated. Silver thickness is around 100 nm. The skin depth of any metal is given as54, 1/2 212 1(/)1 (5-4) where which is a function of frequency is the dielectric function of the metal and is the conductivity. At near infrared (NIR ) frequencies, the skin depth of silver is around 20 nm. So our films are optically thick. The dependence of the dielectric function on th e frequency is given by the Drude formula as, 2 2()pi (5-5) where p is the plasma frequency of silver, its value is 9.1 eV 55 and is 3.70 and is 18 meV. Using this equation we get at 1 m (1.23 eV), = -51 and at 10 m (123 meV) =-5470. This change in should be observed in the behavior of the hole arrays if their transmittance depends on the metal properties. To test this notion, we have fabricated different samples with different periodicities and different hole sizes such that the periodicities span from 1 m up to 10 m. Within this range the dielectric functi on of silver changes by a factor of about 100. In Fig. 5-3 the transmittance data for 9 diff erent hole arrays are shown. The measurements are performed with a Bruker FTIR spectrometer. A ll of these 9 samples have different hole radii and/or periodicities, (a, Dg). In the figure around the highest peaks for each curve the corresponding a and Dg within parentheses are shown. Thr ee different colors are used: blue, green and red for different periodicities of Dg= 4 m, Dg= 6 m and Dg= 8 m respectively. Also for clarity each of the curves is labeled with a letter, just belo w the letter in the figure, in 44

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parentheses (a, Dg) is shown. Curves labeled with C and F are also shown with an arrow. The diffraction thresholds are indicated by vertical dashed lines. The positions of diffraction thresholds can be calculated as, 22()d dgnDij (5-6) where nd is the index of the refraction of the substrate, Dg is the periodicity, i and j are indices of the diffraction order. All the blue curves have their highest peak at around 10 m. The difference between these three blue curves is the hole size. The smallest amplitude blue curve (the one on the bottom) has a hole size of 4/3 m. The open area fraction for this curve is f = 0.11. As the hole size gets bigger, (as the open area fraction, f increases) the transmittance amplitude increases. The blue curve with transmittance amplitude of around 25 at around 10 m has f=0.25 with a=2 m. Finally the blue curve that is higher th an the others is the one with the highest open area fraction f=0.44. Three green curves, which have peaks at longer wavelengths than the blue curve, correspond to hole arrays with 6 m periodicity. As the hole size gets bigger for these different arrays, the transmittance amplitude increases. The three green curves have open area fractions of f=0.11, 0.25 and 0.44. All the red curves, Dg =8 m have their highest peak at around 20 m. The data set shown in Fig. 5-3 can be replot ted if we define a dimensionless variable called scaling variable, s, as, / s dgnD (5-7) The result of plotting with respect to this sca ling variable is shown in Fig. 5-4 with the corresponding diffraction thresholds shown by th e dashed lines. The positions of diffraction thresholds for this curve is, 45

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221/()dij2 (5-8) where i and j are indices for the order of diffraction. In Fig. 5-4, in parent heses the indices are shown, the positions of thresholds are at 1, 0.7 and at 0.45. Every time diffraction threshold opens up, transmittance goes down, because light is scattered into higher diffraction orders and out of the normal direction. Here in this figure f=0.25 samples are shown, with three different colors, the blue curve (C) is for (2,4), green (B) is for (3,6) and the red curve (A) is for (4,8). The importance of this figure is that the transmittanc e of different samples with same periodicity and with different hole sizes but w ith the same open area fraction, f, when plotted against the scaling variable will have similar features in their spec tra, i.e. peaks and dips, at similar wavelengths. This result is called scaling. Scaling means that enhanced optical transm ission of hole arrays is independent of metal properties, and it implies that the enhanced optical transmission effect is mostly a geometrical effect. 5.2.2 Reflectance In Fig. 5-5 the reflectance spectra for three arrays with different open area fractions are shown. The three arrays (a, Dg) are (8/3,8), (4,8) and (16/3,8) with blue (A), green (B) and red (C) colors respectively. Also in the figure with the dashed lines, diffraction thresholds are shown for (1,0) and (1,1) orders. At the diffraction threshold the transmittance of the hole array in specular direction goes down, because light is scattered into higher orders. This also results in a drop in reflectance spectra for the corresponding hole array. In the figure this is best observed for the sample with f=0.25 (the green curve). For these curves the behaviors can be explained with two different phenomena, diffraction and the trapped modes. As will be discussed below, for different open area fractions, their contribution is different. As th e open area fraction gets bigger, the diffraction dominates, the structure is not able to hold the trappe d modes long enough, and 46

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the trapped modes thus have a short lifetime and decay faster. As for the smaller open area fraction, for example for f=0.25, the contributions from both trapped modes and diffraction is observable. As the open area fraction gets even smaller, here for array shown with (8/3,8) f=0.11 (blue, A curve), the diffraction does not play an important role as much as the trapped modes. There is an angle of about 10 2 degrees of incidence in the measurement setup; this makes the analysis of the reflection data more complicated. But even with this complication, two samples are shown in Fig. 5-6. In this figure, reflectance and transmittance data for two samples with (3,6) (blue curves) and (4,6) (red curves) are shown. In the figure with A and B letters reflectance and with C and D letters transmittance is shown. Instead of having a reflectance minimum where transmitta nce is a maximum, they are shifted with respect to each other. Right at s= 1.0 reflectance for the two curves goes down whereas transmittance decreases at longer wavelengths. This difference can be attributed to the above-mentioned angle of incidence in the reflectance measurement. At the moment, a new stage with capability of rotation is being built to measure transmittance at an angle of 10 degrees. 5.2.3 Absorption With the reflectance together with transmittance measurement we can calculate the absorption in the structures. All of the absorbed light goes to ohmic losses. Absorption can be calculated from, (5-9) 1ATRwhere A is absorption, T is transmittance and R is the reflectance amplitude. In Fig. 5-7, the result of such a calculation is s hown for a sample with (3,6) with f=0.25. The red curve (C) is for transmittance, the blue curve (B) is for reflectanc e and the black curve (A) is for absorbance. The dashed lines show the diffraction threshold a nd their orders are give n in parentheses. 47

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In Fig. 5-8 the numerical (blue curves or B, D & F) and the experimental (red curves or A, C & E) results are shown for different open area fractions, f. There are two panels, in the upper panel f=0.25 and f=0.44 are shown, in the bottom panel f=0.11 is shown. The numerical calculations are performed by time dependent Lanczos-split algorithm.16 For silver the values to be used in numerical simulation are obtained from Ordal et. al.56 There is a very good match with the numerical and experimental results. In the numerical results the peaks are sharper and their amplitudes are little bit higher than the corresponding experimental results. The experimental results are broader due to impe rfections, such as film roughness and hole size irregularities, in the samples. The diffraction thre sholds are shown as vertical dashed lines. In Fig. 5-9, electromagne tic field distribution of By is shown, magenta is for positive By, and red is for negative By on the top, for f=0.11 and on the bottom it is for f=0.44. These figures are plotted as a function of z/Dg in x-axis and x/Dg in x-axis. The direction of the field is By. The fields are localized in the vicinity of the holes. In Fig. 5-10, the electromagnetic energy (intensity E2 + B2) is shown for different hole sizes (different open area fractions of 0.11, 0.25 and 0.44) for Dg=4 m. In the figure, the leftmost panel represents the smallest holes with a=4/3 m, the middle panel a=2 m, and the rightmost panel a=8/3 m. The color orange is for the highest field intensity. As can be seen from the figure field intensities are localized differently for different hole sizes. For the smallest hole, the fields are stronger on the metal circumference of the hole. For the hole size with f=0.25 (the middle panel in the figure) the modes are weaker, and some of the energy is localized in the center. Incoming light here is polarized in y-direction that results an asymmetry in the figures. In Fi g. 5-10c, the field intens ities are shown for the biggest hole. Again fields are localized around the circumference and in the center. 48

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5.3 Fused Silica Fused silica is used as a substr ate for experiments in near infr ared regions. It is index of refraction as a function of wavelength (in microns) given by57 22 2 222220.6960.4080.897 1 (0.0684)(0.116)(9.90)n 2 2 (5-10) In Fig. 5-11, transmittance of fused silica as a function of wavelength is shown. The transmittance is 80% up to wavelengths of 3.5 m and at longer wavelengths transmittance decreases. Beyond 5 m fused silica is opaque. The water and the metal content determine its optical transmission, which is usually comes fr om its production. But ou r purposes and over the wavelength region in which we are interested, th e optical transmittance spectra are good enough. In Fig. 5-12, the optical transmittances of two array structures fabricated on fused silica substrates are shown. The red curve (A) is for 0.5 m side square holes in 70 nm thick silver film with 1 m periodicity. The blue curve (B) is for (1 ,2). Diffraction thresholds are shown with dashed lines. This figure shows that scaling holds in the near IR region with good overlap of the scaled peak and dip positions. In Fig. 5-13, the data for Fig. 5-12 is scaled with the scaling parameter s. 5.4 Annular Arrays In Fig. 5-14 SEM pictures of two hole arrays are given. In Fig. 514a square arrays, in Fig. 5-14b square arrays with sq uare holes filled with a metal annular structure are shown. The periodicity of the structures shown here is 4 m, for the annular struct ure on the right, inside there is a silver square symmetrically spaced at the center of each hole. It was first shown numerically by Labeke et. al. that the annular structures will lead to much higher transmission th an a regular hole array.58,59 The stated reason for this enhanced transmission is that an annular structure will support the TEM mode of a waveguide, whereas a 49

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regular hole will not. Accordingly, an enhancement is expected for annular arrays. With the following experimental works, this expected result is not observed. There are two reported experimental studies of annular arrays. Th e first study, taken in the visible region60, there was not much a difference between the annular array a nd regular hole array. In the second work, a negligible difference in transmission amplitude s is observed, but the peak positions for the annular arrays were red shifted with the shift being attributed to cylindrical surface plasmons.61 For us, when we have fabricated square annular structures, we also have not observed any further enhancement than that which occurs in a regular hole array. Our results are shown in Fig. 5-15 for regular hole arrays (the black curve, also la beled as A) and hole ar rays with metal square (with inside square having a side of 1.0 m) annular structures in the center (the red curve, B), both arrays with Dg=4 m. Both structures have about 30 % transmission. So in our study, we also have not observed any enhancement or peak shifts due to annular arrays. 50

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Figure 5-1. Optical transmittance of ZnSe substrate up to 25 m. 51

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Figure 5-2. Index of refrac tion of CVD grown ZnSe as a function of wavelength. 52

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Figure 5-3.Transmittance of hole arrays with different a and Dg on ZnSe substrate. In parentheses (a,Dg) are shown. The blue curves are for Dg=4 m (also labeled with A, B and C), the green curves for Dg=6 m (D, E and F) and the red curves are for Dg=8 m (G, H and I). 53

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Figure 5-4. Transmittance of hole arrays with f=0.25 vs. scaling variable s. Dashed lines show diffraction thresholds. The red curve (A) is (4,8 ), green (B) is for (3,6) and blue (C) is for (2,4). 54

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Figure 5-5. Reflectance vs. scaling variable for 3 different hole arrays with (8/3,8) blue A with f=0.11, (4,8) green (B) with f=0.25 and (16/3,8) red (C) for f=0.44. These 3 arrays have different open area fracti ons but the same periodicity. 55

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Figure 5-6. Transmittance and reflectance data for tw o hole arrays with (3,6) for blue curve, A is reflectance and D is for transmittance, and (4,6) the red curve, B is for reflectance and C is for transmittance. Dashed lines show diffraction thresholds. 56

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Figure 5-7. Red curve (C) is for transmittance, the blue (B) reflectance, the black curve (A) is for reflectance and transmittance added togeth er for an array of (3,6) (f=0.25). 57

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Figure 5-8. Computation vs. expe riment for hole arrays with different open area fractions, f, are shown in the figure. The red curves (A, C & E) are for the experimental; the blue curves (B, D & F) are for computational results. 58

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Figure 5-9. Electromagnetic field distribution for Ey for f=0.11 (top figure) and for f=0.44 (bottom figure). 59

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Figure 5-10. Energy density inside the holes with different open fractions, f=0.11 (left), f=0.25 (middle), and f=0.44 (right). 60

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Figure 5-11. Transmittance of fused silica as a function of wavelength between 2.5 m up to 5.0 m. 61

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Figure 5-12. The blue curve is for a=0.5 0.5 m with Dg=1 m and the red curve is for a=1 1 m with Dg=2 m. 62

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Figure 5-13. Transmittance of two hole arrays with (0.5,1) blue (B) and (1,2) red (A) on fused silica substrate as a func tion of scaling variable, s. Diffraction orders are shown with the dashed lines with the orde rs shown in the parenthesis. 63

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Figure 5-14. SEM micrographs of two hol e arrays with same periodicity (Dg= 4 m) and same hole size (a=2 m). In the annular structure on the righ t, inside of the holes, there is a silver metal square thereby giving an annular shape to the aperture. 64

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Figure 5-15. The red curve (B) is for the annular array with 2 m hole size, inside 1 m metal square and with Dg=4 m, the black curve (A) is for (2,4) hole array. 65

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66 CHAPTER 6 BULLSEYE 6.1 Introduction The bullseye structure is composed of concentr ic circular rings as shown in Fig. 6-1a. The rings, comprised of metal (Ag) and dielec tric (PMMA) components, are periodically spaced As can be seen in Fig. 6-2b, where the side view of a bullseye structure is shown, the structure is composed of mesas and steps with finite hei ghts. Structures with this geometry can be considered as circular diffracti on gratings. Their optical propert ies have been studied in the literature; enhanced optical transmission (EOT) is shown in the near infrared (NIR)62 and microwave regions.63 At terahertz frequencies the transmitted light amplitude64 depends on the phase between the light emitted from the central aperture and the light associated with the resonances (trapped modes) set up within the grooves. The net effect can be either enhancement (constructive interference) or suppression (destruc tive interference). In a ddition to enhancement, beaming is shown if the exit aperture is patterned concentric with the grooves.65 This opens a possibility of using a bullseye st ructure as a near field lens. Al so it is shown that the surface waves are propagating towards to center.66 In another work, surface plasmons are excited with a near scanning optical microscope (NSOM) on a bullseye structure and interference effects with these surface waves are shown.67 According to Steele et. al. as the surface plasmon polaritons propagate across each groove they gain 0.07 phase shift.67 All these works mentioned above have used optically thick metal grooves. Recen tly a numerical study claimed that dielectric periodic structures on top of a thin flat silv er film would lead to EOT 68 as well. In this work we have fabricated bullseye structures of silver metal films on quartz substrates with thick PMMA diel ectric grooves. On top of the groove s we have evaporated a thin

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metal silver layer. The silver metal is thick enoug h to reflect most of the light in the NIR, which is the region of interest for us in this study. Our initial intent was to show resonant light tunneling through optically thick metal films69-70-71 and associate this tunneling with the excitation of surface waves. In addition to that, we also wanted to understand the interaction between the central aperture and the surface wa ves in a circularly symmetric structure. Basically, in a bullseye structure, the incident lig ht would have a direct path through the aperture and an indirect one through the genera tion and transmission of surface waves. In our study, with th e grating structure we are able to couple to trapped modes.5 Due to the presence of the trapped modes, our structures have EOT even without apertures. The peaks in transmittance spectra of our structures are very close to the diffraction thresholds and their positions are determined primarily by the periodicity of the bullseye structure, but as the thickness of the dielectric is increased secondary peaks due to cavity modes are observed. It is shown by other authors that thick dielectric grooves surrounded by metal will support cavity modes.72 When the grooves are thick enough, we clearly observe these cavity modes as well at longer wavelengths. We emphasize in this chapter the distinction between the trapped modes and their associated diffraction thresholds, which are sensitive to lattice periodicities, and the cavity modes, which are associated with the dielectric-filled grooves and are sensitive to changes in geometrical parameters like the dielectric th ickness and the ratio of dielectric width to periodicity. We also observe that when the central apertures are drilled, the transmittance amplitude of the peaks that are due to trapped modes increases but the peak amplitude due to cavity resonance does not change. In addition, if some of the rings are removed from the structure, transmittance amplitude is decreased. These experiments, which are described below, thus help distinguish the re lative contributions of the trapped and cavity modes. 67

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To numerically analyze our st ructures, we have used rigo rous coupled wave analysis (RCWA) implementing software GSolver73 demo. This software can numerically simulate the behavior of 1D subwavelength diffr action gratings. The justification for the use of 1D gratings to simulate bullseye structures is discussed in Ch apter 4, in accordance with the Projection-slice theorem. 6.2 Results When the PMMA is thick enough (around 200 nm) EOT is observed. If the PMMA is even thicker (400nm), a 2nd peak is observed. We attributed the first p eak, which is in close proximity to the diffraction threshold, to trap ped modes and diffraction as discussed in the previous chapter for hole arrays, and the second peak to cavity resonances that take place within the metal cavity surrounding the thick PMMA diel ectric. To understand the interactions between different electromagnetic modes, the band gap of th e structure has to be measured or calculated; this can be done if we can measure or calculate reflection as a function of angle of incidence.74 Fabrication steps are shown in Fig. 6-1; the details of th e processes are discussed in Chapter 4. Briefly, a very thin, 3 nm thick, InOx layer is sputtered onto quartz substrates; this film has an optical transmission of about 75 % starting from 800 nm towards longer wavelengths as shown in Fig. 6-3. The elec tron resist (PMMA) is applied by spin coating and electron beam lithography (EBL) is used to patt ern the bullseye structure. A s ilver film is then thermally evaporated onto the developed bullseye structures. Fig. 6-2a shows an SEM of a typical structure. After the optical tran smission and reflection of this st ructure is measured, the central aperture is drilled through us ing a focused ion beam (FIB). The optical transmission and reflection can then be again measured and changes associated with the aperture noted. Flat (surface roughness is around 5-10 by AFM) silver films of 35 nm thick are optically opaque at 800 nm and longer wavelength s as shown in Fig. 6-4. In Fig. 6-4 the bulk 68

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surface plasmon mode, at 323 nm (3.84 eV) is giving the transmittance maxima shown. In the literature the bulk plasma of s ilver is stated to be 3.80 eV55 and 3.78 eV75. From the plasma frequency, the number of free electrons can be calculated as, 2 24pm n e (6-1) where m is electron mass and n is volume number density of free carriers. From this formula, which is in CGS units, n is calculated to be 1.06x1022 cm-3, which is smaller than the reference value of 5.8522 cm-3.76 6.2.1 Peak Positions Opening of a diffraction threshold leads to a drop in transmittance of the structure, giving a transmission minimum at the threshold. The di ffraction threshold is defined in the previous chapter in the discussion about hole arrays. Th e transmission maximum is always on the longer wavelength side of the threshold. Opening a diffraction threshold, basically, enables the structure to couple to higher diffraction orders or surface m odes leading to a sharp drop in transmission in the direction normal to the film. With this the peak positions lie right next to the diffraction threshold, just on the longer wavelength side. Scaled diffraction threshold positions are given as, 221/1 ()sthreshold dgnDij2 (6-2) where the integers i and j denote the diffraction order, nd is the refractive index of the substrate and Dg is the periodicity of the structure. Equation 6-2 basically determines the peak positions. We have fabricated bullseye structures with different periodicities; Dg=2 m is shown in the Figure 6-5 and Dg = 1, Dg = 1.2 m are shown in Figure 6-6. The dimensionless thre sholds are shown with a dashed line in Fig. 6-5 and 6-6 and in pare ntheses the orders (i,j) are marked. The longest wavelength threshold 69

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corresponds to (1,0). In these figures, the tran smittance data are plotted against a dimensionless scaling variable, s, which is defined as, / s gdDn (6-3) The peak positions, which depend on periodicity of the structure, are then calculated by the equation, peaksgdDn (6-4) where peak is the wavelength of the peak. In Fig. 6-5, there are two peaks; corresponding peak 's are approximately 2400 nm and 3275 nm with s=0.845 for the first peak (i=1,j=0) and s=1.137 for the second peak (i=1,j=1). We can compare peak positions ratio (ratio of first peak position to the second peak) with the ratio of positions of corresponding diffraction thre sholds. It is difficult to identify the exact location of the peaks, because th e peaks are very broad. We es timate a ratio of 1.14/0.85=1.35. Using the corresponding di ffraction thresholds at s =1, 0.7 and 0.45 we calc ulate the ratio of the position of the first diffraction th reshold to second threshold to be 1.4, in good agreement with the observations. In Fig. 6-6, the red (A) curve corresponds to a bullseye with Dg=1 m, the peak positions are approximately at s=0.9 and s=1.25. Their ratio gives 1.39. From the same figure, for Dg=1.2 m (the blue curve (B)), the peak positions ar e 0.80 and 1.15, and their ratio gives 1.44. These two spectra when plotted as a function of the scaling variable, s, will have similar features in their spectra; this is called scaling. Basically this means, the physics of these two structures is only dependent on geometry but not on the ot her parameters like metal properties. The peaks in our experimental data are very broad compared to calculations. This is in all likelihood due to irregulari ties of the sample like grating hei ght not being constant all over the 70

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total sample area and the presence of imperfections in the metal films. Also simulation assumes normal incident plane waves (zero incident angle) at a single wavelength. In the measurement the light beam has an angular cone of incide nce, about 10 degrees, wh ich may couple to higher order surface modes. In Fig. 6-6 the peak po sitions are marked with arrows. There are two distinct peaks in each curve. Beyond 3.3 m the peaks are beyond our spec trometer's range. Also at 5 m there is a cutoff due to the fused silica substrate. In all our measurements the structures are illuminated from the quartz side. 6.2.2 Dielectric Thickness Dielectric thickness is an important parameter in our experiments. As can be seen in Fig. 6-7, which compares experiment with simula tion, for a sufficiently thick enough dielectric (300 nm) shown with light green color (also la beled with letter A), tra pped modes are excited and enhanced transmission is observed. In the figur e dark green color (label C) is for simulation for a 300 nm thick PMMA dielectric. When dielectr ic thickness is a factor of three thinner (100 nm), there is no peak observed as shown in th e figure where the cyan curve (label B) is experimental and the blue curve (label D) is for numerical result. Here th e results are shown for a bullseye with Dg= 1.0 m fabricated with a 35 nm thick silver film. Dielectric thickness is measured with AFM (atomic force microscope ) and surface profilometer. The AFM gives a result around 350 nm. The PMMA da tasheet for the spin speed used for this sample gives the thickness to be 300 nm. AFM scanning is done w ith a very slow scan speed giving a high resolution with good reproducibility. The metal layer on top of the grooves provide s coupling as well as it might be supporting surface waves. If the metal layer is made too thick (100 nm or so) the peaks disappear. We have also observed this in simulations. 71

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In Fig. 6-8 numerical results for different PMMA thickness are shown. For the 300 nm thick PMMA sample there is only one peak formed around 1 m, which is very close to the diffraction threshold, shown as a dashed line in the figure. As the dielectric thickness is increased, there is a second peak formed as s een in the figure with ma genta color (the curve denoted with letter C). And as the thickness of the dielectric increas es further there is a red shift in second peak's position but first peak's position does not change much with the thickness. The first peak's position is determined by the diffraction threshold and is independent of the dielectric thickness. The strong dependence of position of th e second peak with respect to dielectric thickness suggests that this peak is due to a cavity mode inside the dielectric. As the cavity increases in size the mode it supports moves to longer wavelengths as would be expected. 6.2.3 Central Aperture In Fig. 6-9 the transmission of Dg=1.2 m bullseye after drilling the central hole with different diameters, is shown. The central hole will contribute to transmission with zero phase shift. If the two peaks result from different processes, and any of those processes would add a phase to the transmitted light, they will interfere w ith the light coming out of the central hole. In our experiments, with the central hole, transmi ssion always goes up for both of the peaks, thus implying a constructive interference. As shown in Fig. 6-1, the central aperture is circular. Opening the central hole, increases the overall transmission more than the relative area increase associated with the hole opening. Accordingly, the light coming out of the bullseye structure and the light coming out of the central hole interfere constructively. To make sure that results are repeatable and to minimize concerns about the effect of the focused ion beam on sample quality, at least four of the same bullseyes with same hole size are fabricated. Bare holes have a very low transmittance as shown in Fig. 6-10. Cao et. al.64 showed the position of the central hole with respect to grooves can lead to enhancement as well as 72

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suppression of the transmitted light. In our experime nts we have not observed this effect even though we have changed the relative position of the hole with respect to the grooves. In Fig. 6-9, optical transmission of a singl e bullseye structure with different diameter center holes is shown. The same hole is widened with the FIB after each measurement. Here, as can be seen from the figure, as the hole size increases, the transmission goes up. The dielectric thickness of this sample is around 350 nm. In this figure the green curve is for the case without any holes, the cyan curve (also labeled as E) is for 2 m, the black curve (label F) is for 5 m, blue (D) is for 7 m, magenta (C) is for 10 m, yellow (B) is for 12 m hole and red curve (A) is for 16 m diameter hole. Bullseyes with 2, 5 and 7 m central holes have the same transmittance amplitude. The first peak, peak around 1200 nm show s the largest relative increase compared to second peak (peak around 2000 nm) for all hole si zes. As can be seen in Fig. 6-9 the transmittance of the first peak increases with the widening of the central hole whereas the second peak amplitude does not change. These observations suggest that the s econd peak is a cavity mode, which is only dependent on the dielectric thickness and thus does not shift in position since the dielectric thickness remains constant. Fig. 6-10 shows the transmission of corres ponding bare holes on th e same 35 nm-thick flat silver film. The coloring is the same as used in Fig. 6-9. The same behavior can be observed here as well; at longer wavelengths, the16 m diameter hole has the same transmission as much as 2 m diameter hole. All of the curves in Figure 6-10 collapse to the same curve for wavelengths greater than 1800 nm. 6.2.4 Sidewalls We presented our results for specular tran smission measurements. Light coming out of the sidewalls will be contributing more to higher or ders. It's hard to say how thick the sidewalls are. Grooves being very tall, silver film being ve ry thin, it might be safe to assume there are no 73

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sidewalls, or they are very thin and very leaky. In simulation electric field is perpendicular to slits. More work and analysis might be needed to assess the role of sidewalls on overall optical behavior of our structures. 6.2.5 Silver Thickness During fabrication of the bullsey e structure silver is evaporated to cover everywhere on the sample uniformly. This coating goes on top of the grooves and onto the mesa between them and has the same thickness for both. The amount of this silver is varied and optical transmission measurements are performed for different thicknesses. Experiment al results are shown in Fig.611. As can be seen for the blue curve with silv er thickness of 17 nm, a peak does not form. This film is too thin and the structure transmits wit hout a well-defined diffract ion threshold. When the silver thickness is doubled (the red curve for 35 nm thick silver) the diffraction threshold peaks are observable. This is the standard thicknes s used in all other bullseye experiments where thickness of silver was not a parameter, i.e. when for example thickness of the dielectric is varied for different samples, a 35 nm-thick silver film is used for all the samples. In Fig. 6-11, yellow and navy curves correspond to thicke r silver films, 50 nm and 65 nm respectively. In other words the diffraction threshold does not change. After the peaks are formed, we did not observe much of a change in the peak positions within the thickness values varied here. In the computation without the metal on top, light woul d not be coupled to the dielectr ic layer and if the metal layer is made too thick, enhanced tran smission will not be observed. In Fig. 6-12 the numerical results for the silver thicknesses used in the expe riment are shown. In the simulation program thicknesses can be made multiples of 20 nm. The results shown in Fig. 6-12 are for 20, 40 and 60 nm thick silver film with the colors of blue, red and navy respectively. 74

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The thickness of the silver has to be right to couple the light into the dielectric PMMA, but if it is too thick, then light will not pene trate through this metal la yer and cavity modes will be not be observed. The ideal thic kness of the silver film is f ound to be between 30 nm to 70 nm. 6.2.6 The Role of Missing Rings If some of the rings are missing in a bullseye structure, its overall transmission will go down as shown in Fig. 6-13. In Fig. 6-13, gree n curve (A) is for a bullseye with all the rings. Starting from the 10th ring from the center, we ha ve removed some of the rings. The red curve (C) is for one ring (eleventh) missing, blue (D) is for 3 rings (11-13th rings), cyan (E) is for 5 rings (11-15th rings) and yellow (B) is for 10 (11-20th) rings missing. Magenta (F) represents the case when the first ten rings are missing. As can be seen from the figure, as we take out some of the rings the overall transmission goes down. The overall area occupied by the rings is 100 100 m and it contains 50 rings. From the data it seems that the biggest contribution to transmittance comes from the first 20 rings. Also the effect is most drastic if the rings are taken from the center. This experimental result justifie s in our simulation of FDTD where we can use a finite number of rings to simulate this structure. The details of this will be discussed in Results and Discussion chapter. When a ring is removed, it is replaced with a flat silver film. Transmission drop shows that light only passes th rough a part where there are grooves. In a recently published paper it is shown that a hole array composed of 9 9 holes will be enough to saturate the transmittance enhancement.4 6.2.7 Different Open Area Fractions Bullseye with different ratios of groove widt h to periodicity other than 0.5 can be fabricated to understand more about the nature of resonances insi de the dielectric. The calculated behavior for different fractions of a/Dg is shown in the Fig. 6-14 where a is the width of the dielectric PMMA. Different ratios of a to Dg (for Dg=1 m), a=0.3 m red (A), a=0.4 m blue 75

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(B), a=0.2 m cyan (C), a=0.5 m black (D) and green (E) is 400 nm thick silver film. Dielectric thickness is 300 nm. The highest transmi ssion is observed for a=0.3 m. For the computed groove widths here, only 0.5 m ones are fabricated and measured. To further progress this work, some of the different groove widths should be fabricated to confirm the simulation results. Also in this figure the 40 nm-thick flat silver film's transmittance at these wavelengths is shown with the green curve. 6.2.8 Polarization The optical measurements shown up to this point are perf ormed with unpolarized light. For the bullseye structures, since they are circularly symmetric, the polarization will not make any difference. In Fig. 6-15 two curves are show n, the blue curve corres ponds to case with NIR polarizer whereas the red curve corresponds to unpol arized light. As can be seen from the figure, the blue curve is very noisy because with the po larizer, the light intensity gets lower. The peaks are at the same position in both of the curves for polarized and unpolarized light. Since polarized and unpolarized light in the experi ment (the blue and the red) have the same spectral shape we conclude that we can use unpolar ized light in our measurements and can compare results with numerical calculations performe d with polarization. All the num erical results are shown up to now only for TE modes. TE (also labeled as s) pola rization is defined as the case where electric field is parallel to slits, perpe ndicular to plane of incidence. Within the polarization choices of TE and TM, TE polarization fits better to our experimental results. This is shown in Fig. 6-16 where there is a comparison of tw o different polarizations and the experimental result. The black and the yellows curves are for the experiment with unpolarized light for two different samples with same dielectric thickness, the blue (E) curv e is for TE polarization, the red (A) curve is for TM polarization and finally the green (B) curv e is the average of the cases TM and TE polarizations. (the average of the blue and the re d curve). The average is shown here because for 76

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a similar structure to ours in their work, Cha ng et. al. showed a comparison of average of two polarizations for unpolarized light incident on a circularly symmetrical structure.37 With TM polarization computation there se ems a numerical instability because the transmission calculation result s are growing up to 0.8 after 1600 nm and remain as high. Our conclusion out of this is that, in the bullseye st ructures TE polarization will couple and dominate the transmission characteristics. 6.2.9 Separation of bullseye into two components Can bullseye structure be considered to be co mposed of two components, i.e. as the sum of two different diffraction gratings? In this section we will decompose bullseye structure into two di ffraction gratings and investigate the behavior of these separate st ructures, and compare them with the bullseye structure. Separation into these two components is shown in Fig. 6-17. In the figure a sideview of bullseye structure is shown which can be divided into two components. Corresponding transmittance data for these two diffr action gratings is given in Fig. 6-18 and Fig. 6-19 with their structure shown just above the figures. In Fig. 6-18 optical transmittance for the structure shown above the graph is shown for self-standing (the black curve) and structures with substrates (the green curve is for 400 nm th ick PMMA and the blue curv e is for 600 nm PMMA). In Fig. 6-19, the transmittance of the second di ffraction grating with 35 nm thick silver is shown. The black curve is for self -standing, and the blue curve is for structures with the substrate (fused silica, n=1.44) is shown. In the blue curve there is an additional peak at 1440 nm as a difference from the case of self-standing metal f ilms. For each interface there is a diffraction threshold. But in the previous structure of Fig. 6-18, there is no peak formation at 1440 nm, but there is a small kink in the spectra. The sum structure transmittance of separate diffraction gratings is shown in Fig. 6-20 with comparison of the transmittance data for bullseye structure. 77

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In Fig. 6-20, with the red curv e (A) the summation of transmittan ce of two individual gratings is shown, with the black curve (B) transmittance of bullseye structure is shown. And the blue curve (C) is the average of sum of transmittance of two individual diffraction gratings. Even though individual behavior of two diffraction gratings is not able to predict th e peak positions, the sum of their transmittance or average of transmittances is able to predict peak positions as can be seen from Fig. 6-20. 78

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Figure 6-1. SEM pictures of bullseye structures a. (top left) Bullseye structure with Dg = 1 m before a central hole is drilled. b. (top ri ght) Bullseye structure with the central hole. c. (bottom) Bare hole in silver f ilm. Silver thickness is about 100 nm. 79

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FUSED SILICA PMMA Figure 6-2. Fabrication steps, side view of bullseye structure, figures are not to scale, they are exaggerated for illustration purposes. a. (top left) InOx (purple color) and PMMA (green) are coated onto the fused silica substrate. b. (top right) After EBL development and silver liftoff. c. (bottom) After a central hole is drilled with FIB. 80

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Figure 6-3. Optical transmi ssion of Indium Oxide (InOx) 3 nm thick flat film on fused silica. (experiment) 81

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Figure 6-4. Optical transmission of a flat 35nm-thick silver f ilm on fused silica. (experiment) 82

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Figure 6-5. Optical transmittance of the bullseye structure (Dg =2 m) versus scaling parameter, s. Dashed lines show diffraction th resholds. In parentheses indices (i,j) corresponding to diffraction threshold ar e shown. (1,0) threshold is at 1 m, (1,1) threshold is at 0.7 m, and (1,1) is at 0.447 m. (experiment) 83

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Figure 6-6. Different pe riodicities of bullseye, red curve is for Dg =1 m and blue is Dg =1.2 m. Arrows indicate peak positions for the corresponding data with the same colors. (experiment) 84

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Figure 6-7. Transmittance vs. wavelength for bullsey es with different dielectric thicknesses. If the dielectric thickness is on the order of 100 nm, there is no peak around 1200 nm. Light blue curve (B) is for the experimental result, blue (D) is for computation of 100 nm thick gratings. But if th e dielectric is made thick enough (400 nm) as can be seen from light green curve (A)(experiment) and dark green curve (C) (computation) the peaks associated with the diffractive threshol d (vertical dashed line) are observed and have approximately the same transmi ttance. (experiment + computation) 85

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Figure 6-8. Transmittance vs. wavelength for bullsey es with different dielectric thicknesses. The simulations are done for 1D slits with Dg = 1 m, a = 0.5 m. The respective PMMA (dielectric thickness ) thicknesses are 200 nm (green) (E), 300 nm (red) (D), 400 nm (magenta) (C), 500 nm (blue) (B) and 600 nm (yellow) (A). Numerical results are for zero order transmission with TE polarization. The vertical dashed lines represent the first and second diffraction thresholds. (computation) 86

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Figure 6-9. Dg=1.2 m bullseye with A6 PMMA spun with 3000 rpm. The green curve (label G) for no central hole case, the cyan curve (label E) 2 m, the black curve 5 m (F), the blue curve 7 m (D), the magenta curve (C) 10 m, the yellow curve 12 m (B) and the red curve (A) is for 16 m diameter hole in the cen ter. Because of the space limitation only labels A, B and G are shown in the figure, labeling starts from top with A and goes down to G. The first or der diffraction threshold is shown by the dashed line. (experiment) 87

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Figure 6-10. Bare circular holes with diameters 16 (red), 12 (yello w), 10 (magenta), 7 (blue) and 5 m (black) on a 35nm flat silver film. (experiment) 88

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Figure 6-11. Transmittance vs. wavelength for a bullseye structure with 300 nm dielectric thickness, with Dg=1 m. Different curves represent different silver thicknesses. Blue curve is for 17 nm, red is for 35 nm, yello w is 50 nm and navy is for 65 nm. Two bottom ones are, green 35 nm flat silver film and cyan for 70 nm flat silver films. (experiment) 89

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Figure 6-12. Transmittance vs. wavelength of 1D grating for different silver thicknesses. The blue curve is for 20 nm (A), red 40 nm (B) and the navy curve (C) is for 60 nm thick silver film. Above in Fig. 6-11 experimental results for similar thickness bullseye structures are shown. (computation) 90

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Figure 6-13. Bullseye with defects, green (A) with highest transmission is for the case when all the rings are present, i.e., no ring defects. The other curves represent cases (see text) when some rings are missing. Note that the lowest transmissi on (magenta,F) occurs when the innermost ten rings are remove d. A6 PMMA (300 nm thick), 3000 rpm, Dg=1 m. (experiment) 91

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Figure 6-14. Different ratios of a to Dg ( its value (periodicity) is fixed, Dg=1 m), a=0.3 m red (A), a=0.4 m blue (B), a=0.2 m cyan (C), a=0.5 m black (D) and green is 40 nm thick silver film (E). Dielectric thickness is 300 nm. (computation) 92

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Figure 6-15. Optical transmittance of the bullseye structure as function of wavelength. The blue (upper) curve is for polarized light. Re d (lower) curve is unpolarized light. (experiment) 93

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Figure 6-16. The blue curve (E) is for TE polarization, the red curve (A) is for TM polarization, green (B) is for average of TE and TM. A nd the black curve (D) and the yellow curve (C) is for the experiment for 300 nm thic k dielectric. (experime nt + computation) 94

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Figure 6-17. Separation of bullseye st ructure into two components. 95

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Figure 6-18. First grating with its optical transmission. The black curve (A) is for the selfstanding (without substrate), green (C) is for 600nm thick PMMA and the blue curve (B) is for 400 nm thick PMMA case. 96

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Figure 6-19. The grating only with metal structure on top of it. Th e black curve (A) is for selfstanding (without substrate) a nd the blue curve (B) is with the substrate. The metal thickness is 35nm thick silver. 97

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Figure 6-20. The transmittance of bullseye structure (400 nm P MMA on a substrate) is shown with the black curve (B). The red curv e (A) is for sum of transmittance of two individual gratings (of Fig. 6-18 (B) and Fig. 6-19 (B)). A nd the blue curve (C) is for the average of transmittance of two individual gratings (of Fig. 6-18 (B) and Fig. 6-19 (B)). 98

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99 CHAPTER 7 CONCLUSIONS AND FUTURE WORK 7.1 Conclusions In this thesis we have presented the re sults of our work on subwavelength optical structures. Enhanced optical tr ansmission is shown for two diffe rent systems, hole arrays and bullseye structures. By varying the hole size and periodicity of the hole arrays, it has been shown that enhanced transmission can be explained wi thout surface plasmon po lariton excitations. By scaling geometrical parameters of the system it is shown that transmission spectra depend only on geometry but not metal properties. This exclud es the role of surface plasmons. The enhanced transmission is attributed to diffraction and tr apped modes. The resonant scattering due to trapped modes and its interference with diffr acted modes leads to extraordinary optical transmission. Also in bullseye structures apertu reless enhanced transmission due to the presence of trapped modes and cavity resonances is shown. 7.2 Future Work To our knowledge enhanced optical transmission of periodic arrays of dielectric structures, hole arrays or cylinders have not been shown experimentally. This kind of work will further assure that trapped modes do not require metallic structures. Al so another work will be on differentiating material resonanc es in materials (like SiC, Ga As, GaP) from trapped modes by characterizing hole arrays made in these polar materials.16 For the bullseye stru ctures some of the results we have shown are only for numerical calculations. To further check validity of our numerical results, additional experiments, such as varying the width of the grooves to the periodicity, need to be performed. Also no nlinear effects using tr apped modes have been predicted.77 We have shown that electric field st rengths can be significantly enhanced in

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subwavelength structures. Accordingly, nonlinear ma terials can be strategi cally placed within the structure for second harmonic generation and possible use in applications. 100

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101 APPENDIX GALLIUM ARSENIDE EXPERIMENT In this section, briefly failed experiments on Gallium Arsenide (GaAs) wafers will be given. We tried to fabricate GaAs free standing hole arrays. We ha ve used three different wafers, GaAs wafers, GaAs on Silicon wafers and GaAs on AlGaAs/GaAs wafers. Initial works are performed with GaAs wafers In Fig. A-1 reflectance of a square hole array on GaAs wafer as a function of wavenumb ers is shown. The range of wavenumbers are from 100 cm-1 to 600 cm-1. The red curve is only for GaAs without any pattern and the blue curve is for 18 m periodicity (a=9 m) square hole arrays. The peak around 300 wavenumbers is due to ionic material resonance of GaAs due to its polar character. In these structures we were not able to observe diffraction effects. These wafe rs were not backside etched and were not free standing. In the second part we have used GaAs (2 m) thick grown on Silicon wafers for our measurements. The transmittance as a function of wavelength for these type of wafers are shown in Fig. A-2. As a comparison with the red curve in this figure transmittance of GaAs wafers is shown. And with the black curve the transmittance for silicon wafers are shown. As can be seen from the figure silicon is not transparent be tween 5 and 20 m range. The reflectance curve as a function wavelength for GaAs on Silicon wafers is shown in Fig. A-3. The pattern is 18 m periodicity (a=9 m) hole arrays. All these three curves, red, green and black correspond to same structure measured for different times. Also for the red curve a larger shutter is used in the measurement to increase the amount of incident light on the sample. But these samples were not self-standing, so we have tried to etch this silicon layer using different wet and dry etches. This part of the experiment did not work well. So we have used another wafer, which is GaAs on AlGaAs/GaAs. The concentration of Al in AlGaAs is 0.6. This work is still in progress.

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Figure. A-1.GaAs reflectance as a function of wavenumbers. The red curve is for GaAs substrates and the blue curve is for 18 m periodicity hole array with a=9 m. 102

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Figure A-2. Transmittance of GaAs and GaAs on Silicon. The red curve is for GaAs wafers and the blue curve is the transmittance of GaAs on silicon wafers. 103

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Figure A-3. Reflectance of a=9, Dg=18 hole array on GaAs on Silicon wafer. The black and the green curve is for smaller shutter in the m easurement setup and the red curve is for a larger shutter. 104

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111 BIOGRAPHICAL SKETCH I was born in Ankara, Turkey. I lived there for 26 years. I have graduated from Mimar Sinan High School in Demetevler. I have attended Middle East Technical University in Ankara. Initially I have studied geology for one year before I have realized that I enjoyed physics more. In 2000, I have graduated with B.Sc. degree in physics. My interests were experimental condensed matter physics so I have attended to Bilkent University in Ankara for 2 years to get master's degree but before finishing that I moved to Florida to start Ph.D. studies at the University of Florida. I graduate from University of Florida in May 2008.