• TABLE OF CONTENTS
HIDE
 Title Page
 Dedication
 Acknowledgement
 Table of Contents
 Abstract
 Introduction
 Waveguide characteristics and efficient...
 Vertical directional coupler wavelength...
 Tapered waveguide interconnect
 Effect of impurity induced layer...
 Integration of an electroabsorption...
 Conclusion and future works
 Reference
 Biographical sketch
 Copyright














Title: Optical filters, modulators and interconnects for optical communication systems
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Table of Contents
    Title Page
        Page i
    Dedication
        Page ii
    Acknowledgement
        Page iii
        Page iv
    Table of Contents
        Page v
        Page vi
        Page vii
    Abstract
        Page viii
        Page ix
    Introduction
        Page 1
        Page 2
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    Waveguide characteristics and efficient phase modulation in InGaAlAs on InP
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    Vertical directional coupler wavelength filter
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    Tapered waveguide interconnect
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    Effect of impurity induced layer disordering on the refractive index of GaAs/AlGaAs MQW
        Page 146
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    Integration of an electroabsorption modulator with a tapered waveguide interconnect
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    Conclusion and future works
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    Reference
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    Biographical sketch
        Page 209
        Page 210
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    Copyright
        Copyright
Full Text










OPTICAL FILTERS, MODULATORS AND INTERCONNECTS FOR
OPTICAL COMMUNICATION SYSTEMS









By


SANG-KOOK HAN













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


UNIVERSITY OF FLORIDA


1994


















DEDICATED TO MY FATHER AND LATE MOTHER














ACKNOWLEDGMENTS



If this work is judged to be a success in some small fashion, I would be

remiss not to thank all the people who have helped me throughout my time at

the University of Florida.

First and foremost, I wish to express my deep gratitude to my advisor

Professor R. V. Ramaswamy, for his guidance, encouragement, and support

throughout the course of this work. His high standard in academic achieve-

ment really inspired me to do my best for the completion of this work.

I would like to thank Professors P. Zory, T. Anderson, A. Neugroschel,

and M. Law for their participation on my supervisory committee. I would

also like to thank Prof. P. K. Bhattacharya at the University of Michigan and

Dr. Woo-Young Choi at MIT for providing the InGaA1As samples used in this

study.

Thanks are extended to all the students that I have worked with or

studied with while at the university. Particular thanks go to Dr. Sang Sun

Lee, Dr. Young Soon Kim, Dr. Hsing Chien Cheng, Dr. Hyoun Soo Kim, Chris

Hussel, S. Muthu, W. Li, S. Xie, Dr. Young Soh Park, Dr. Mike Grove, Craig

Largent and fellow researchers Dr. Robert Tavlykaev, Dr. Sanjai Sinha and
T'M- XTr l r-- * -_ _- .1_ - f I I I I I- ..









tion, I wish to express my appreciation to my friends, Dr. Hyun Deok Lee, Dr.

Jinho Park, Dr. Sung Min Cho, Dong Wook Suh, Tae Hoon Kim, and Minbo

Shim, who have provided many unforgettable memories throughout all the

years I spent in Gainesville.

Last, but certainly not least, I want to thank my family for their end-

less love, patience, and support during all the years of this study. Special

thanks go to my father and late mother for showing me the importance of a

good education. In particular, her devotional care and love will be kept in my

mind forever. I want to thank my wife and a lovely daughter. Often the

hours spent on this work were hours I should have spent as a husband and a

father. Through their sacrifice and patience, they are responsible for what-

ever success this work attains.



















NOWLEDGEMENT ..............................................................................

TRA CT ........................................................................................................

PTERS

INTRODUCTION ..................................................................

1.1 Motivations ..................... ...............
1.2 Outline of Dissertation.................................................

) WAVEGUIDE CHARACTERISTICS AND EFFICIENT
PHASE MODULATION IN InGaA1As ON InP ..........................

2.1 Introduction ......................................................................
2.2 Refractive Index of MBE grown InGaAlAs on InP..............
2.3 Passive Ridge Waveguides on InGaAlAs/InP ..................


z.4.1.z quadratic electro-optic ettect...................
2 Fabrications and Measurements ........................
3 Results and Discussion .......................................










3.1 Introduction ............................................................................... 60
3.2 Principle of Operation .......................................................... 63
3.3 Analysis ............................................................................... 65
3.3.1 Spectral Index Method ............................................ 66
3.3.2 Coupled Mode Theory............................... .......... .. 73
3.3.3 Characteristics of Wavelength Filter Devices.............. 80
3.3.3.1 Power coupling and the bandwidth of filter..... 80
3.3.3.2 Array of several filter devices ....................... 93
3.4 Experiments ............................................................................ 96
3.4.1 Fabrications ............................................. ........... .... 96
3.4.2 Measurements .......................................... ........... ... 98
3.4.3 Discussion ................................................................... 107
3.5 Tunability of Filter .................................................................110
3.5.1 Reverse Bias Condition ...............................................110
3.5.2 Forward Bias Condition..............................................113
3.6 Summary ............................................................................ 120

FOUR TAPERED WAVEGUIDE INTERCONNECT.............................. 121

4.1 Introduction ............................................................................. 121
4.2 Fabrication............................................................................... 124
4.3 Results and Discussion ......................................................... 126
4.3.1 Photoluminescence Measurements ............................ 126
4.3.2 Near Field Intensity .................................................. 133
4.3.3 Analysis...................................................................... 135
4.3.4 Propagation Loss ........................................................ 142
4.4 Summary .............................................................. .................. 144

FIVE EFFECT OF IMPURITY INDUCED LAYER DISORDERING
ON THE REFRACTIVE INDEX OF GaAs/AlGaAs MQW............ 146

5.1 Introduction ....................................................................... 146
5.2 Experim ents ........................................................................ 147
5.2.1 Fabrications ............................................................ 147
5.2.2 Interference Measurements....................................... 150
5.3 Results and Discussion ..................................................... 154
5.3.1 PL Measurements ................................................. 154
5.3.2 Diffusion Characteristics ........................................... 157
5.3.3 Analysis.................................................................... 161
5.4 Sum m ary ............................................................................ 165









SIX INTEGRATION OF AN ELECTROABSORPTION
MODULATOR WITH A TAPERED WAVEGUIDE
INTERCONNECT ............................................................................ 168

6.1 Introduction ............................................................................. 168
6.2 MQW Electroabsorption Modulators ..................................... 169
6.2.1 Quantum Confined Stark Effect................................ 169
6.2.2 Fabrications and Characterizations.......................... 173
6.2.3 Results and Discussion ............................................. 177
6.3 Integration of a Modulator with a Waveguide Interconnect. 182
6.3.1 Fabrications and Characterizations.......................... 182
6.3.2 Results and Discussion .............................................. 185
6.4 Summary ................................................................................. 190

SEVEN CONCLUSION AND FUTURE WORKS ..................................... 192

7.1 Conclusion ............................................................................. 192
7.2 Future Works ........................................................................... 196

REFERENCES ................................................................................................ 199

BIOGRAPHICAL SKETCH ...................................................................... 209













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


OPTICAL FILTERS, MODULATORS AND INTERCONNECTS FOR
OPTICAL COMMUNICATION SYSTEMS


By

Sang-Kook Han

August, 1994



Chairman: Ramu V. Ramaswamy
Major Department: Electrical Engineering


This dissertation describes the theoretical and experimental studies on

the guided wave optical devices in the InGaA1As/InP material system and the

integration of the optical devices which utilize single quantum well (SQW) as

well as multi-quantum well (MQW) structures. This study encompasses the

fabrication and characterization of passive ridge waveguides, efficient phase

modulators using the quadratic electro-optic effect, as well as efficient, narrow

bandwidth wavelength filters. For the purpose of the monolithic integration of

an SQW laser diode with an MQW modulator in GaAs/A1GaAs without a com-

plex regrowth process, an impurity-induced layer disordering (IILD) technique










essential for the implementation of highly dense wavelength-division-multi-

plexers/demultiplexers (WDM) in multi-wavelength optical networks and sys-

tems. The vertically stacked directional coupler structure wavelength filter

device operating at 1.55 pm which permits the maximum asymmetry possible

in directional coupler devices to achieve a narrow bandwidth is presented.

The quaternary InGaA1As layers grown on InP substrate are used and it

facilitates larger tunability due to material dispersion. The spectral index

method and coupled mode theory are used for theoretical calculations of the

filter response. The characteristics of the filter are measured and the tun-

ability of the device is discussed. An array of many filters with different cen-

ter wavelength in a single chip is studied and a relatively broad range of

center wavelength is easily obtained by a small variation in the design of the

structure.

To achieve an integration of a high gain SQW laser diode and an MQW

electroabsorption intensity modulator with an high on/off ratio, we utilize a

tapered waveguide interconnect using an IILD technique which permits

transfer of the energy generated in an SQW laser region to an MQW modula-

tor region. The refractive index variation of the MQW region due to an IILD

is obtained from the interference measurements. Finally, the integration of a

tapered waveguide interconnect and an MQW electroabsorption modulator is

achieved with high modulation efficiency.













CHAPTER ONE
INTRODUCTION


The guiding of light beams along dielectric layers, experimentally real-

ized in the early sixties, has stimulated the growth of a new class of passive

and active components using guided light. Because of their small dimension

and low power requirements, it was then projected that such optical compo-

nents would replace electrical circuitry in integrated electronics equipment.

In addition, the optical elements would provide the advantages of greater

bandwidth and immunity from electromagnetic interference. In addition,

since the transmission of information (voice, video and data) continues to

require huge bandwidths, it has been largely responsible for the stimulation

and the progress of the integrated-optics technology. Of course, this develop-

ment has been helped immensely by the realization of low loss optical fibers,

without which the explosion in optical communications of the recent past

would not have occurred.

The advent of room-temperature semiconductor diode lasers has pro-

vided the necessary impetus in the development of passive and active semi-

conductor optical devices such as different types of waveguides, modulators,

couplers, splitters, wavelength filters, and photodetectors. This has lead to

the incorporation of these devices into monolithic, opto-electronic integrated









circuits (OEIC's) consisting of high-speed optical and electronic devices on the

same semiconductor substrate. In these integrated circuits, a number of dif-

ferent optical signal processing functions are often combined, e. g. generation

(diode lasers), modulation (optical modulators), transmission (waveguides),

detection (photodetectors). In addition OEIC are also used to convert optical

signals into electric signals (phototransistors) and vice versa. Their perfor-

mance in most cases is superior to both the electronic integrated circuits and

hybrid OEICs since optical circuits are characterized by small size, lower

power requirements, efficient operation, low noise and considerably larger

capacity of information bandwidth. Moreover, recent advances in the mate-

rial growth technologies such as molecular beam epitaxy (MBE) and metalor-

ganic chemical vapor deposition (MOCVD) have rendered realization of these

devices more realistic with the availability of high quality semiconductor /

films and precisely controlled super fine microstructures.


1.1 Motivations


For the ultimate OEIC implementation, one of the most important

decisions is the choice of the material system so that the operating

wavelength of OEIC devices correlates with the low-loss region of the optical

fiber. Currently, the InGaAsP quaternary is widely used for various optical

devices operating at 1.3 to 1.55 pm. As a promising alternative to the









InGaAsP system for the fabrications of longer wavelength laser diodes,

optical modulators, photodetectors, etc., the InGaA1As system is being

currently investigated. Unfortunately, not much work has been done in this

material system. In this dissertation, therefore, we propose, as part of a

number of tasks, to investigate the waveguide characteristics of this material

and compare them with that of InGaAsP, and determine the linear and

quadratic electro-optic coefficients of this material by developing and testing

ridge waveguide phase modulators in this material system.

The usage of wavelength-division-multiplexing/demultiplexing (WDM)

techniques at 1.55 um in optical communication networks provides a means

of increasing the transmission capacity of existing systems, thus taking full

advantage of the broad low-loss window available in optical fibers. A case in

point is the proposed all optical multi-wavelength optical network [Bra93],/

shown in Fig. 1.1. In this system, the WDM cross-connect is a key component

which requires the narrow bandwidth, wide tunability and the flat-top

response of the wavelength filter devices. Toward meeting this requirement,

we design and demonstrate a narrow bandwidth, widely tunable wavelength

filter device based on the vertically stacked directional coupler structure.

The InGaAlAs quaternary layers are used to achieve the wide band gap vari-

ation essential for larger tunability. For multi-wavelength operation, by

extending the concepts of the discrete filter devices, e. g. arrays of wavelen-th

































WDM cross-connect


Access node A


Figure 1.1 The schematic diagram of all optical multi-wave-
length optical network.









One of the most demanding tasks in an OEIC is the integration of the

laser diode and optical modulator. Instead of using directed modulated laser

diodes which suffer from considerable chirping at high bit rates, often an

external modulators with tens of GHz bandwidth [Wak90] is used. Unfortu-

nately, to date very few laser-modulator integration schemes have been

implemented [Kor88]. This is perhaps due to the complex fabrication proce-

dures essential in order to meet a number of challenges including wavelength

detuning between laser and modulator, small coupling loss, and good electri-

cal isolation between laser and modulator. In order to integrate a high gain

single quantum well (SQW) laser diode and an multi-quantum well (MQW)

electroabsorption modulator with a high on / off ratio due to the quantum

confined stark effect (QCSE) [Woo88], we need an interconnect which trans-

fers the energy generated in an SQW region by laser diode to an MQW modu- /

later region. For the purpose of this interconnection, a tapered waveguide

interconnect is utilized. The integrated structure is shown in Fig. 1.2 where

an SQW layer and an MQW layer are grown on the same chip in a single

growth. Through the use of the impurity induced layer disordering (IILD)

technique [Tho88] to the MQW region, the refractive index of the MQW can

be changed due to the variations of the well shape and the quantized energy

levels inside wells. This effect is utilized in an interconnect structure so that

the normal mode of the structure evolves from the SQW laser region to the

MQW modulator region.















SQW MQW
Laser Interconnect Mod
Laser Modulator


Impurity diffused
region V m

Il


MQW

SQW


Figure 1.2


Schematic diagram of a SQW laser and a MQW
modulator integrated structure where Vm is the
modulation voltage and IL is the injection current.









1.2 Outline of Dissertation


In this dissertation, the theoretical and experimental guided wave

optical devices in the MBE grown InGaA1As on InP substrate as well as the

integration of the optical devices which utilize the SQW and MQW structures

in GaAs/AlGaAs are presented. This study encompasses characterization of

the passive ridge waveguides and the application of these ridge waveguides

to phase modulators. In addition, we investigate both theoretically and

experimentally the wavelength filter devices based on this material system

operating at 1.55 pm toward the realization of the dense WDM system. Also,

for the purpose of the monolithic integration of an SQW laser diode and an

MQW electroabsorption modulator, an IILD technique is used to facilitate a

novel tapered waveguide interconnect developed in our group [Sin92] which

transfers the beam generated from an SQW laser to the MQW modulator

region.

In chapter 2, the waveguide characteristics and properties of an

efficient modulator using the MBE grown InGaA1As compound semiconductor

layers lattice matched to InP substrate are investigated. A simple technique

for measuring the refractive index and the material dispersion of InGaAlAs

layers in the transparent wavelength region is presented. Even though the

accuracy of this technique is limited by the accuracy of the film thickness,





8


transparent substrate (most ternary and quaternary systems are grown on

InP substrate). Also, this technique can be used as a quick and routine

characterization of the grown films. We fabricated ridge waveguides in this

material and measured an average propagation loss of about 1.5 dB/cm for a

single mode operation. With the refinement of the growth technique, we

believe that the waveguide structure using this material may become quite

useful for optoelectronic system applications. A single heterostructure

InGaAlAs/InP phase modulator utilizing the linear electro-optic (LEO) and

the quadratic electro-optic (QEO) effects is demonstrated. For the first time,

the QEO coefficient of this material at 80 meV below the band edge is

obtained. In addition, the linear electro-optic effect (LEO) coefficient is

estimated to be 1.2 x 10-12 m/V which is comparable to that of GaAs. The

measured single mode phase shifts due to the QEO and LEO are 5.5 and 2.8

/Vmm for TE and TM polarizations, respectively. These values are the

largest values reported so far in InGaAlAs system. Combining the large QEO

effect and wide band gap variation available (0.85 to 1.67 pm), a highly

efficient, optical modulator can be accomplished at longer wavelength regions

(e. g. 1.3 to 1.55 mu) useful in low loss optical communication systems.

In chapter 3, we study both experimentally and theoretically the very

narrow bandwidth wavelength filter at 1.55 pm and its tunability. The

quaternary InGaAlAs semiconductor layers grown on InP substrate are used

in vertically stacked directional coupler structures in order to have a wide










selection of filter wavelengths and possibly wide bandwidth tunability. The

maximum possible asymmetry of two vertically stacked waveguides is

utilized to achieve the narrow bandwidth of filter. The spectral index method

is used to calculate the mode index and the field profile of the two-

dimensional ridge waveguides. Then the coupled mode analysis is used to

obtain the coupling coefficients between the ridge waveguide and planar

waveguide which has a wide loaded strip for the purpose of the beam

confinement in the lateral direction. We have measured the characteristics

of the wavelength filter and compared them to the theoretical calculation. An

array of many filters with different center wavelengths in a single chip is

proposed and a relatively broad range of center wavelengths for the filter can

be obtained with a small variation of the ridge width. Wavelength tuning of

this filter device by using LEO and QEO effects under the reverse bias /
/
condition, as well as resulting from band shifting associated with carrier

injection, is studied. An 88 nm tuning was obtained with 1.4 x 1018 cm-3

carrier injection. Since the refractive index changes due to both QEO effect

and band shifting are strongly dispersive, the bandwidth of the filter can be

varied. Calculation shows that the bandwidth becomes two times larger as a

result of an 88 nm tuning.

In chapter 4, for the potential application of an interconnect between

optical devices, we demonstrate a waveguide taper transition where energy

from a MQW region is transferred to a SQW region [Sin92, Kim93]. The









adiabatic index tapered structure is achieved by intermixing of AI/Ga using

fluorine implantation induced disordering of GaAs/A1GaAs MQWs [Han93b].

PL measurements verify the gradual change in disordering as well as the

bandgap of the tapered MQW structures. The normal mode analysis is used

to explain the power transfer from an MQW region to an SQW region.

Numerical calculations show excellent agreement with near field intensity

measurements. The propagation loss due to fluorine (1 x 1015 cm-2 dosage)

implantation is measured and turns out to be 18 dB/cm which is rather

higher than we expected. From the above loss measurements, an averaged

propagation loss of the tapered waveguide is estimated to be around 9 dB/cm.

This structure thus permits the interconnection of two different guided wave

devices, one using an SQW and the other involving the MQW as the guiding

layer (for example, integration of an SQW laser and an MQW modulator),

without using a complex regrowth process.

In chapter 5, the variation of the refractive index of GaAs/AIGaAs

MQW, near its band edge, caused by IILD of MQW is studied. The

information on the variation of the refractive index is essential to utilize the

IILD technique in optical device design and fabrications. We employ a

structure consisting of several uncoupled, MQW ridge waveguides with

tapered disordering across the transverse direction. The extent of

disordering along the transverse direction is varied by using a tapered SiO,









determining the refractive index variation is appropriate to other impurity

sources as long as the interdiffusion characteristics are known. The effective

index variations in ridge waveguides are measured by the Mach-Zehnder

interference technique. Variational technique is used to calculate the energy

levels on the interdiffused quantum wells. The results of the PL

measurements are used to convert the SiOx barrier thickness to the

corresponding interdiffusion length, Ld. The interdiffusion lengths of 0 to 10

nm in quantum wells are obtained and they correspond to bandgap values of

1.61 to 1.90 eV. The maximum changes in the refractive index (An =

nundisordered ndisordered) of 0.083 and 0.062 are obtained at 35 and 100 meV

below the band edge of the undisordered MQW, respectively. The knowledge

of An is very important in the design of the photonic/optoelectronic devices.

In chapter 6, the monolithic integration of an MOCVD grown tapered /

waveguide and a GaAs/AlGaAs MQW electroabsorption intensity modulator

in a single chip without regrowth is presented by exploiting IILD. First, the

characteristics of a discrete electroabsorption intensity modulator are pre-

sented. A 24 dB on/off ratio is measured near the band edge. Also, the varia-

tions of the absorption spectra with different reverse bias voltages are

nrPQpnftdr fnr T. nind TM nnlantI7nIn-n Paco Tc.;cihlf-rlk+ +_ __ OTI ,,




















r region in the fabrication process. The diffusion of Zn i

r region is verified by the shift in the PL peak of the

n optimum integrated structure that tailors a low 1

e transition and at the same time obtains a high on/off

ry precise two step Zn diffusion must be used

i last chapter of the dissertation summarizes the resu


SMQW. r

oss tapered













CHAPTER TWO
WAVEGUIDE CHARACTERISTICS AND EFFICIENT PHASE
MODULATION IN InGaAlAs GROWN ON InP

2.1 Introduction


Recently the InGaAlAs quarternary semiconductor system has

attracted considerable attention since its band-gap can be tuned over a rela-

tively large wavelength range (0.85-1.67 pm) by varying the ratio of Ga to Al.

With the indium composition fixed at 53 %, this quaternary material is lattice

matched quite nicely to the InP substrate. Figure 2.1 shows the lattice con-

stants and the band gaps of various binary and ternary compound semicon-

ductor where Ino.s5Gao.47.yAlyAs is located between Ino.52Alo.4As and

Ino.53Gao.47As keeping the lattice constant at about 5.87 angstrom. The

waveguide devices in this material system are especially interesting for appli-

cations in long-wavelength communication systems. Moreover, this material

system is a promising alternative to InGaAsP for the fabrication of long-

wavelength laser diodes. Since this material system has a small valence

band offset (28%) in the MQW structures formed with InAlAs which results

in less hole accumulation in the valence band. This property is considered

important for high speed photodetector applications. Furthermore, the pres-





















2







)







































uctures. Also, Chang et al. [Cha91] reported a


knA1As/InG:


AlAs DH structure grown on InP substrate [Cro90] v

iree-mode interference within the multimode waveg


the e,

ral sti

in pa

,r dioc

guide

SThe

ation

00me

90] hz

rnn1ahi









1.5 pum LKas91a, Kas91bJ with very low threshold current density have

already been reported. Moreover, InGaAs/InGaA1As MQW lasers emitting at

1.517 gm [Kaw91] have been grown by Gas Source MBE where InGaAsP and

InP were used as guiding and cladding layers, respectively. A metal-semi-

conductor-metal Schottky photodetector [Gri90] on a semi-insulating InP sub-

strate was fabricated by using a nominally lattice matched InA1As/graded

InGaA1As/InGaAs structure grown by MBE. On the average, the graded

quarternary layer enhanced the responsivity by about 35% compared to an

identical device without the graded region. In another experiment,

InGaA1As/InAlAs MQWs were used as reflectors [Chi91] for the resonance

enhanced absorption in a high speed photodetector with a thin absorption

layer. Using a 16-layer QW in a Schottky diode structure, 50% enhancement

of quantum efficiency was experimentally demonstrated for a 475 nm thick

absorbing layer at 1.52 pm. On the other hand, high reflectivity InGaAlAs/

InP multilayer mirrors [Mos89] for application in the long-wavelength system

have been grown by MOVPE. The 40-layer structures exhibit reflectivities

as high as 95% in the wavelength range 1.55 to 1.70 pm. Yet in another study

for the nonlinear optical device applications, two-photon absorption [Vil90]

was measured in InGaAlAs/InP ridge waveguides. This material showed a

relatively large two-photon absorption which is a limiting factor in an all-

optical switching device.









In spite of the growing interest in this material system, very little

work has been reported to date on the refractive index and material disper-

sion which are essential in the design of optical devices. Bernardi et al.

[Ber90] used modal cut off spectroscopy (MCS) to determine the refractive

index of InGaAlAs. But this technique gives the refractive index only at few

wavelength which correspond to the modal cutoff of the waveguides. In this

chapter, a simple and accurate technique for measuring the refractive index

and material dispersion [Han91b] in the transparent region is presented. We

have fabricated ridge waveguides on InGaA1As grown on InP substrate by

MBE and also measured the waveguide propagation loss on this material sys-

tem. It appears to be comparable to that of other material systems. Finally,

efficient phase modulators were fabricated and characterized by using the

Mach-Zehnder interferometric technique. For the first time, the quadratic /

electro-optic coefficient of this material near the band edge has been mea-

sured [Han92, Han93a].


2.2 Refractive Index of MBE Grown InGaA1As on InP


The performance of the guided-wave optical devices can be optimized

only through an accurate knowledge of the refractive index and material dis-

persion. Recently, we presented a semi-empirical relation [Han91a] based on









InLUaAlAs in the transparent region as a function of composition and tested

its validity by comparing our results with the scant experimental data avail-

able [Ber90].

In this section, we present experimental determination of the refrac-

tive index of InGaA1As (lattice matched to InP) in a wide wavelength region

for several aluminum compositions. Our experimental measurement is based

on the Fabry-Perot transmission technique and can easily be implemented

using a commercial spectrophotometer. Unlike the previous reports where

the index is determined from absolute measurement of the reflectivity at the

peaks of the reflection spectrum, we determine the refractive index by accu-

rate measurement of the wavelengths corresponding to the extrema in the

transmission spectrum. Thus the method is independent of the surface qual-

ity of the film or film-substrate interface. For example, the results would not

be sensitive to an oxidation layer on the InGaAlAs surface. However, the

method used here requires an accurate knowledge of the film thickness.

The quaternary Ino.53Ga0.47yAlyAs films (y=0.10, 0.20 and 0.30) were

grown by MBE on a ~ 400 pm thick semi-insulating Fe-doped InP substrate

by Prof. Bhattacharya and his coworkers at the University of Michigan. The

material is lattice-matched, as depicted by the photoluminescence peak with

FWHM of around 20 meV at the temperature of 13K. Based on the absorp-

tion edge measurements, the band-gaps occur around 1.10 pm, 1.22 pm and

1.43 pm for y=0.3, 0.2 and 0.1 respectively at room temperature. Figure 2.2



















Al =0.2














, , I , , I , ,1 . . l . .


1000


" "i"l.... "I *


I.. .i


1200 1400 1600
Wavelength (nm)


1800


Figure 2.2


Transmission characteristic of Ino53Gao.27Alo.2oAs
where the absorption begin around 1220 nm.









shows that the transmission characteristic of the sample with Al = 0.20

where the absorption begins around 1.22 pm. The back surfaces of the sam-

ples were polished to reduce possible scattering losses.

The Perkin-Elmer Lambda-9 spectrophotometer with slits adjusted for

less than 2 nm resolution in the 1.2 to 1.7 gm region was used for the trans-

mission measurements. Figure 2.3 shows the spectral transmission of the

y=0.30 sample. Since the InGaA1As films grown on InP substrates have a few

percentage variation in thickness from the center to the corners, we used a

sample holder which has a small hole (~ 1.5 mm) such that there is the least

variation of thickness where the optical beam passes through. The refractive

index at the peak and valley transmission wavelengths can be determined if

these wavelengths and the film thickness are precisely known. To obtain

accurately the wavelengths corresponding to the maxima and minima in the /

transmission, the following procedure was adopted.

In a transparent film of index n and thickness t, supported on a sub-

strate of index ns less than n, the spectral transmissivity for radiation of

wavelength ,, incident normal to the film, is expressed as



1 (2.1)














1'1' *~*I 1 I' jSS 55


1300 1500

Wavelength(nm)


1700


Figure 2.3


Transmission spectrum of 2240 nm thick
Ino.53Gao.17Alo.3oAs grown on InP substrate.


0
.2
*r*


30


29


28


27


1100


I I I I I I I I I I I I I I I I I I a I I


I









where F depends on the reflectances of the two interfaces and 8 = 47mt/X. If

the thickness of the substrate is much smaller than the coherence length of

the incident light such that the reflections on both interfaces of the substrate

affect the overall transmission interference pattern, we have to consider a 4-

layer transmission case instead of a 3 layer one. However, in deriving Eq.(2-

1), it is assumed that there is no absorption and the substrate thickness is

sufficiently large (comparable to the coherence length of the incident light).

As a result, the reflection from the back surface of the substrate does not con-

tribute to oscillations in the spectral transmission pattern. The latter condi-

tion can easily be satisfied in practice by substrate thickness of the order of a

few hundred micrometers and spectral resolution of a few nanometer in the

1.2 1.7 pm wavelength region. Although n and n, are wavelength dependent

in the transparent region, F can be considered to be fairly constant in narrow

spectral regions between two consecutive intensity maxima or minima. On

the other hand, if the film or the substrate absorbs weakly, it is likely that

the absorption coefficient would decrease monotonically as the wavelength

increases such as shown in the data presented in Fig. 2.2. In this case, the

transmission spectrum, between two consecutive peaks or valleys, can be

written as


Ta = K(a)To (2.2)









where K(X) can be assumed to be linearly dependent on X, i.e.,


K(W) = Ko +D% (2.3)


where Ko and D are constants to be determined experimentally. Using Eqs.

(2.1) and (2.3), Eq.(2.2) can be written as


1
T = (Ko +DX) (2.4)
a ( (+ F sinA ))2


where A(X) = 27n(X)t. Although the absolute value of n is not known a priori,

for the purpose of describing the transmission spectrum in a narrow spectral

interval between two transmission extrema, the spectral dependence of n can
/
be predicted with reasonable accuracy using the semi-empirical relations for,/

ternary and quatenary optoelectronic materials reported in the literatures

[Afr74, Bro84, Han9la]. We fitted the measured transmission data with Eq.

(2.4), piece-wise for each peak and valley, assuming F to be constant in such a

narrow spectral region where A(%) / X equals mn (m is an integer) for the max-

ima and (m + 1/2)i for the two neighboring minima. K and D are obtained by

joining two adjacent peaks by a straight line and t, the film thickness, is mea-

sured independently. The only fitting parameters, therefore, are F and A(X).

We further assume that the functional dependence of n(X) can be expressed

approximately by the single-oscillator model [Afr74] in each narrow spectral




















(k)= B EEd 1 0.5




,o, Ed are the two parameters of the single-oscillator model wt

ilated by interpolation from the ternaries [Bro84] and Ep is the

(Ep =hc/). B is a constant for each segment which now becol

tting parameter along with F. The thickness of the film, t, i

independently by a DEKTAK II surface profiler.

figuree 2.4 shows the results of fitting one of the transmission

[.(2.4) where we have used Eo = 2.81 eV and Ed = 25.63 eV. W(

ng procedures for the various maxima and obtain the peak p

Iculate the refractive index from


n(I )f. = m I





















.* I I .. .









- 1 1 I I 1 I i. I I
390 1430 1470 1510 155

Wavelength (nm)


ure 2.4 An example of fitting one of the transmission peaks of
2.2 with Eq.(2-4).


)




4
4
4





I.
| (











2n(X,)t = m'Xm. (2.7)


where m' = (m + 1/2). We must emphasize that by the fitting procedure

described here, the value of m is uniquely determined; i.e., once we know B

from the fitting of Eq.(2.4) to the measured transmission, there is unique m

or m' value which satisfies the relation A(W) / X = mn or m'c at each extrema

position. For example, we have m=12 and m'=11.5 for the lowest peak and

valley wavelengths in Fig. 2.3. Using t= 2240, 1761 and 1724 nm for the

samples with y=0.30, 0.20 and 0.10 respectively, the values of the refractive

index obtained from Eqs.(2.6) and (2.7) are plotted in Figure 2.5. The solid

curves represent the fitting curve obtained by the modified single-oscillator

model [Afr74] (see Eq.(2.8)) using the appropriate parameters. Table 2.1 lists

the corresponding parameters used in the model.




2 E EE2 E4 2E2-E2-E2'
n 2 =1 E d d p In g p (2.8)
E E3 2E3(E2-E2) E2- E2
o o o g g P



where Eg is the band-gap energy and Eg = 0.73 + 1.49y (y is Al composition)

[Noj88].














3.6
y=0.10
3.55

S 3.5 y=0.20

ti 3.45

3.4
S: y=0.30
C| 3.35

I: 3.3

3.25

3.2 I I , I I I I
1100 1300 1500 1700 1900

Wavelength (nm)












Figure 2.5 Wavelength dependence of the refractive index of
Ino.53Gao.47-yAlyAs. The solid curves represent the fit to
modified single-oscillator model.


























Table 2.1: Numerical values of parameters used in
modified single-oscillator model.
Aluminium
fraction E(eV) Ed(eV) Eg(eV)
fraction (y)
0.10 2.52 25.4 0.87
0.20 3.01 29.2 1.02
0.30 3.14 28.2 1.13 /
/


















In

mat

subs

c. TI

char


ial <

-ate

spe

:teri



2


Naveguide Fabrication


We used the quaternary Ino.53Gao.nAlo.aoAs layer grown by M

a is undoped with a free carrier concentration of less than 11

*ocessing steps involved in the fabrication of the ridge wavegi

mple are quite simple. Clean areas and hoods are generally

d contamination from the environment during the process. Th









4. Dip in warm acetone for 2 4 min.

5. Dip in the methanol for 2 min.

6. Rinse in DI water and blow the remained water by N2 gun.

The sample must be baked at least 5 min. at around 100 C before the

photolithography begins. If the surface of the sample is not dried completely,

the photoresist may not be properly spun and become adherent. The follow-

ings are steps in the photolithography process to define the stripes on the sur-

face of the sample.

1. Put the photoresist (PR) on the sample by spin coating. The positive
PR Shipley 1400-17 or 23 are normally used. Spin rate 4500 rpm for
40 sec. results in 0.4 and 0.8 pun thick PR for 1400-17 and 23,
respectively.
2. Soft bake the sample at 90 100 C for 30 min.
3. Using the mask aligner, place the desired patterns on top of the PR
coated sample. Notice that the right side of the mask has been
placed to the sample to avoid the possible gap which may cause the
interference pattern on the sample.

4. Expose the sample to the UV light for about 3 sec.

5. Dip into the developer (Shipley 319 or diluted 331) at least for 40
sec. Hold the sample with tweezers and stir the sample slowly and
regularly.
6. Check with the microscope to see whether the desired pattern has
come out.






















Fil

ridgi

(wh


control of the etching rate. This etchant gives 0.24 pm / min. 1

good looking surface. The height of the etched ridge is 0.9 "n

ige waveguides are formed, both ends of the sample need to be

'e mirror like facets. In the case that a very short device leng

and some of optical modulators) is needed, the back surface of

should be lapped until the thickness of the substrate becomes b

















W


In0.53Gao.17A10o.3As


[001] SI InP Substrate

[110]


S0.9 pm
1.3 Mm


Figure 2.6 The schematic cross section of the InGaA1As/InP ridge
waveguide.









2.3.2 Waveguide Characterization


The waveguides were characterized by using an 1.3 pm InGaAsP laser

diode as the light source. Figure 2.7 shows the near field measurement set

up. The measurements of the near-field intensity profiles showed that the

ridge waveguides support only the fundamental mode (Fig. 2.8). The conven-

tional cutback method was used to measure the propagation loss. The mea-

sured relative transmissions of the waveguides of w = 5 and 6 pm are plotted

in Fig. 2.9 as a function of waveguide length for the TE polarization. Each

data point represents the average of at least three measurements. Due to a

slight power fluctuation of the semiconductor laser, there is an error of 0.1

dB in the measurement of absolute power. Average propagation losses were

obtained by fitting the measured data points to the straight line by using the

least-squares method. The propagation loss for w = 5 and 6 pm is 1.68 and

1.55 dB/cm, respectively. For the TM case, we anticipate slightly higher prop-

agation loss. These losses mainly come from the scattering from the surface

and the walls of the ridge waveguides as well as the interface between the

guiding region and the substrate. The propagation losses reported here are

the lowest thus far obtained in this material although it might still be higher

compared to other materials such as InGaAsP [Aug89]. With the refining of

the growth technique, the waveguide structure using this material may

become quite useful for system applications.



















1.3 upm InGaAsP Compensator
laser Waveguide
lase Single mode fiber Wav uid
Ge
detector


Chopper Objective lens


UDT
power meter


d mLock-in
amplifier /











Figure 2.7 Near field intensity measurement set up.

















*r-l




-1.3 gun


SAir Substrate







/



(a)






Figure 2.8 Measured near field intensity profile of 5 pm wide
ridge waveguide in the case of TE polarization
where (a) for vertical direction and (b) for horizon-
tal direction.





Figure 2.8 Continued.

















-2

-2.2

-2.4

-2.6

-2.8

-3

-3.2

-3.4

-3.6


0 1 2 3 4 5 6

Length(mm)


Figure 2.9


Transmission versus length, for 5 and 6 pm wide
waveguides in the case of fundamental TE mode at 1.3
um. Average propagation losses are represented by the
slopes of the straight lines.









2.4 Efficient Electro-Optic Modulator in InGaA1As/InP


The refractive index change induced by external electric fields (electro-

optic effect) has very important applications for optical devices such as cou-

plers, switches, and modulators. These devices are essential components for

optical communication system and high-speed signal processing. The semi-

conductor waveguide phase modulators are typical optical devices utilizing

the refractive index change. These phase modulators usually employ a p-n

junction in order to inject or deplete free carriers from the junction. Most of

them are operated in the reverse bias condition because of the potential high-

speed. By applying a reverse bias voltage, free carriers are depleted from the

junction. The electric field across the depletion region causes local refractive

index to change by the linear or/and quadratic electro-optic effects and,

hence, the phase of the propagating wave changes. Here, we present the effi-

cient phase modulator in quaternary InGaA1As /InP optical waveguides oper-

ating at 1.3 gm.


2.4.1 Electro-Optic Effects


2.4.1.1 Linear electro-optic effect

When we apply an electric field to certain optically isotropic but non-

centrosymmetric crystals, they become birefringent. The induced birefrin-

gence is the result of the linear electro-optic effect (or Pockel's effect) and is









proportional to the applied electric field. Manba [Man61] has studied the lin-

ear electro-optic (LEO) effect in zinc-blende crystals by using an index ellip-

soid with the electric field applied along various crystal directions. In the

presence of the electric field for crystals of the zinc-blende such as GaAs, the

perturbed index ellipsoid can by expressed by



(x2 + y2 + z2) + 2r41 (Fxyz + FyXz + Fzxy) = 1 (2.9)


where r4l is the LEO coefficient, and Fx, F, and Fz are the x, y, and z compo-

nents of the applied electric field, respectively.

For an applied electric field F along the [001] direction as shown in Fig.

2.10, which is the most practical direction for compound semiconductor

devices, the principal axes (x', y') of the perturbed index ellipsoid are rotated /

by 45 2 from the major axes (x, y) of the unperturbed index ellipsoid. The

directions x' and y' are the [110] and [110] crystal directions, respectively.

Assuming F-'r4 << n-2, the refractive indices along the [110] and [110] direc-

tions are given by


n3
n = n + r41F for [110] (2.10)


n3
S= n--r41F for [110]













z [001]




--' 110]












x' [110]
x [100]







Figure 2.10 Principal axes of index ellipsoid and corresponding
crystal directions. The new axes of the perturbed
index ellipsoid are rotated by 45 2 from the major
axes of the unperturbed index ellipsoid.









Therefore, the refractive index change due to the LEO effect is given by


n3
AnLE = r41F (2.11)


The plus and minus signs corresponds to the [110] and [1101 crystal direc-

tions, respectively, as seen in Eq. (2.10).

A propagating optical field experiences a different refractive index

depending on its polarization and the propagation direction. For example, if

we consider a TE mode propagating along the [T10] direction, it experiences

an increased refractive index ( the plus sign in Eq. (2.11)) since its electric

field is parallel to the [110] direction. On the other hand, a TE mode propa-

gating along the [110] direction sees a decreased refractive index indicated by

the minus sign in Eq.(2.11). For a TM mode with its electric field polarized

along the [001] direction, no refractive index change due to the LEO effect

occurs for an electric field applied along the [001] direction.

2.4.1.2 Quadratic electro-optic effect

If the electric field is applied, the conduction band and valence band

are tilted in the depletion region. This increases the probability of finding an

electron within the band edge and consequently absorption increases below

the fundamental absorption edge. The absorption edge appears to shift to

lower energies, but actually broadens, which is known as the electroabsorp-

tion or the Franz-Keldysh effect [Cal63, Tha63]. It is a companion effect of











relation, making the refractive index increases at photon energies below the

bandgap.

Recently, the refractive index change.due to the Franz-Keldysh effect

was shown to have a quadratic dependence on the applied electric field

[Alp87]. The refractive index change due to the quadratic electro-optic (QEO)

effect can be expressed by


3
AnQEO(E) = -R (E)F2 (2.12)


where R is the QEO coefficient. Experimental and theoretical values of R

near the GaAs bandgap [Fai87, Men88] show that the QEO effect is indepen-

dent of both the propagation direction and polarization of the guided mode.

The QEO coefficient depends on the photon energy as strongly as the band

shifting effect caused by carrier injection. As the photon energy move toward

the bandgap, the QEO effect will increase dramatically. Since the QEO effect

in compound semiconductors is normally larger that the LEO effect near the

band edge, the information on R as a function of wavelength will be useful in

designing the optical modulators.









2.4.2 Fabrication and Measurements


A single heterostructure InGaA1As/InP phase modulator utilizing the

quadratic elecrooptic (QEO) effect is made for the first time. A single mode

planar waveguide structure was used. For the metal contacts, a 500 ang-

strom Ti and 2000 angstrom Au were evaporated on 1.0 mun thick

Ino.53Ga.27Al.2oAs (band gap = 1.22 gm) grown on an n+-InP substrate to

form a Schottky barrier. After lapping and polishing the InP back side rea-

sonably well, 1500 A Au was evaporated as the back side contact. A gold

deposited ceramic plate was used as a mount for the modulator. The bottom

of the sample which is n* contact attached to the mount by using a conduct-

ing silver epoxy. Therefore, to apply the voltage bias, one probe goes to top

schottky contact and other one touches any place of mount plate. The cur-

rent-voltage(I-V) characteristic (see Fig. 2.11) measurements yield a reverse-

bias breakdown voltage of ~ 7 V with about hundred nA leakage current for

the Schottky diode. We observed that the I-V characteristic became worse

after the sample was annealed at low temperature (~ 85 OC) for an hour to

make the silver epoxy hardened. We think the possible defects in the contact

region diffuse such that the schottky contact becomes worse. A Mach-

Zehnder interferometer setup was used for the phase shift measurements at

1.3 pm. Figure 2.12 shows the interferometer set up. TE and TM polarized







































Figure 2.11 Current-Voltage (I-V) characteristic of the Schottky
diode.
MENE.











BS
Lase Phase Modulator Mirror
-Mirror
Laser


Bias Voltage



BS
Mirror





S00 -- I

Oscilloscope TV Monitor IR Vidicon






Figure 2.12 Mach-Zehnder interference measurement set up.









respectively, with the direction of propagation along [110]. The interference

fringe pattern was viewed on a video monitor using an infrared vidicon with

an oscilloscope and a frame synchronizer connected to the video monitor. A

suitable horizontal video frame scanning line was selected.

Phase shift measurements were performed for TE and TM polariza-

tions on a 3.2 mm long waveguide. Figure 2.13 shows the fringe shifts for

TE mode corresponding to 0, -2, -4, and -6 V bias from top to bottom. The

bias dependence of the phase shift efficiency in degrees/mm is plotted in Fig.

2.14 for each polarization. Since the operating wavelength is just 80 meV

below the band edge, significant contribution to the refractive index change

comes from the QEO effect and possible free carrier effects, in addition to the

LEO effect in the case of TE polarization. The wave is propagating along the

[110] crystal direction. Therefore, we do not expect any phase changes due to

the LEO effect for the TM case (optical field polarized along the [0011 crystal

direction). On the contrary, the phase changes due to the QEO effect and car-

rier effects are independent to the polarization.


2.4.3 Results and Discussion


2.4.3.1 Linear electro-optic coefficient

For zinc-blende structure crystals, when an electric field E(x) is applied

along the [001] crystal direction, the refractive index changes for the TE

polarized wave due to LEO effect is given by
















..iiillEli













Figure 2.13 Line scanned interference fringes patterns for TE
mode (0, -2, -4, and -6 V bias from top to bottom).














i u, I ,,I is *I *1 .11. I, 1 . I

TE
O TM O






0-


0





0 1 2 3 4 5 6 7 8


Reverse Bias (-V)










Figure 2.14 The bias dependence of the phase shift efficiencies
for the TE and TM polarization.


C,)



Cl)











AnLEO = -r4E (x) (2.13)


where r41 is LEO coefficient and n is the refractive index. The plus and

minus signs correspond to the polarization of the optical field along the [110]

and [110] crystal directions, respectively.

Since the TM polarized mode does not exploit the LEO effect, the phase

shift AZILEo due to the LEO effect can be extracted from the difference in the

phase shift for the TE and TM modes. It can be written as


7n3
A(LEO = r41L [(E ()) (E (x))o] (2.14)


Here, the overlap integral v is defined by




EE (V, x) IEo (x)12dx
(E (x)) op (2.15)
JJ Eop (x)l 2dx



Here Eop(x) is the optical mode field profile along the [001] direction, E(V,x) is

the electric field across the junction as a result of the reverse bias voltage V, L

is the waveguide length, X is the free-space wavelength.









Since the background carrier concentration is very low (< 1015/cm3 ) in

the guiding region, one-sided abrupt p+-n junction model is applicable to this

Schottky barrier device. Then the depletion width W is given by [Sze81]


Es Vi Va)
= (2.16)
qNd


where E, is permittivity of InGaA1As. Nd is background carrier concentration.

Vi is built-in potential and V, is a bias voltage.

Also the electric field distribution in the depletion region is given by


qNd (W x) qNdX
E(x)= =Em (2.17)
8 s
ES M CS


where x and Em are the distance from the metal-contact and the maximum

field strength located at the metal-contact.

Eop(x) was obtained using a step index 3-layer slab waveguide model

where we assumed a perfect metal as the top cladding layer so that the opti-

cal field drops down to zero at the interface. The built-in potential of

Ino.53Gao.27Alo.2oAs [Tiw92] with Au is ~ 0.5 V, the refractive index [Han91b]

at 1.3 pm is 3.450. To get an accurate value of Nd, we made the capacitance-

voltage (C-V) measurements in the schottky barrier junction. Figure 2.15

shows the variation of the capacitance as a function of the reverse bias.

Assuming that the junction was fully depleted around 0.5 V, the calculated

















6.5


6


5.5


5


4.5


4


a>
01N



P4-

Cd
Pc
CT
0


0.5 1 1.5 2


Reverse Bias (V)








Figure 2.15 Capacitance-Voltage (C-V) characteristics of the
Schottky barrier junction.









Nd value by using the Eq.(2.16) is 6 x 1014 cm-3. With Eqs. (2.15), (2.16)

and (2.17), the overlap between the optical field and the electrical field across

the junction has been calculated. The calculated as a function of the

reverse bias is represented in Fig. 2.16. From the fitting of Eq. (2.14) to the

measured phase shift difference between the TE and TM modes, the LEO

coefficient was estimated to be r41 = 1.2 x 10-12 m/V. Even though dispersion

near the band edge is rather small, the r41 coefficient (at 80 meV below the

band edge) is a factor of two larger than that of Pamulapati and Bhatta-

charya [Pam90] (at 400 meV below the band edge). This value of r41 of

InGaAlAs is comparable to that of GaAs [Fai90].

2.4.3.2 Quadratic electro-optic coefficient

In the case of the TM polarization, the refractive index changes are
/
caused by the QEO and the free carrier effects only. However, since the back- /

ground carrier concentration of the guiding region is rather low (6 x 10 14/

cm3), we can neglect the carrier effects and consider only the QEO effect for

estimating the refractive index change. In this case, the presence of a strong

electric field changes the shape of the fundamental absorption edge of a semi-

conductor which leads to correlated changes in the refractive index. The

phase shift due to the QEO effect can also be written, similar to Eq. (2.14), as



AQEO = LR [(E2 (x))- (E2 (x)0] (2.18)
QEO = X







































I . I


v -r U U I U


srse Bis


Figure 2.16 The calculated as a function oft


L. I


r


j









where R is the QEO coefficient and v is defined by


fE2(V,x)lEO (x)12dx
(E2(x)),= (2.19)
2 E op l 2dx


The same overlap integral calculation has been done in the QEO case

except the electric field E (V, x) was replaced by E2 (V,x). Figure 2.17 shows

the calculated . From the measured phase shifts in the TM case, the

QEO coefficient R is estimated to be 3.7 x 10 -19 m2/V2 at 1.3 um in this

material system. This value is almost three times larger than that of GaAs

[Fai90]. To calculate the QEO coefficient of the GaAs, we used the theoretical

dispersion of the QEO coefficient R ~ exp(3/-3) [Men88]. The QEO coefficient

of the GaAs was estimated at the same 80 meV below the band edge so that

the comparison is valid. At this time, we are not sure why this material has

much larger QEO effect. One of the possible reason for that is this material

may have very steep absorption edge which causes large refractive index

changes like the MQW structures. Using the theoretical dispersion [Men88],

the dispersion of the QEO coefficient in In0.53Ga.27Alo.20 As is represented in

Fig. 2.18. The phase shift efficiency due to the QEO effect ( 2.8 /Vmm) is not

as large as that of TE mode even though the QEO coefficient is large. The

primary reason is that the overlap between the square of the electric and the

optical fields is relatively small (less than 10 %). The measured individual
























A

CV


0 2 4 6 8 10

Reverse Bias (-V)








Figure 2.17 The calculated as a function of the reverse
bias voltage.

























rl

X


2


1.
1.2


' ' I ' ' I ' ' .1 I I ' 1


1.3 1.4 1.5 1.6 1


Wavelength (pm)








Figure 2.18 The dispersion of the QEO coefficient of
Ino.53Gao.27Al0.2oAs below the band edge where the
square represents the measured point.














25 .... i '
O LEO(Meas.)
O QEO(Meas.) QEO(Calc.)
20 *.


,O 10<. -
S15




C)
S10 LEO(Cal.) -







0 1 2 3 4 5 6 7 8

Bias (-V)





Figure 2.19 Comparison of the measured and theoretical phase
shift efficiencies due to LEO and QEO effects. The
solid and dotted curves represent the calculated
LEO and QEO effects, respectively, and open circles
and squares represent the measured LEO and QEO
effects, respectively.









presented along with the theoretical estimates where the solid and dotted

curves represent the calculated LEO and QEO effect, respectively.

For the first time, a phase modulator on InGaAlAs/InP waveguides has

been demonstrated near the band edge to exploit the QEO effect. The mea-

sured phase shifts due to LEO and QEO as a function of reverse bias have

been presented and they are quite large, viz., ~ 5.5 "/Vmm and 2.8 "/Vmm for

the TE and TM polarizations, respectively. The estimated LEO coefficient

(1.2 x 10-12 m/V) is comparable to that of GaAs while the QEO coefficient (3.7

x 10-19 m2/V2) at 80 meV below the band edge is larger than that of GaAs.

Modulator structures with larger overlap between the electric and optical

fields (e g. PiN [Mar85] or P-p-i-n-N structure [Lee91]) rather than Schottky

barrier devices, will enhance the phase shift efficiency due to the QEO effect

considerably.


2.5 Summary


In summary, the waveguide characteristics as well as the efficient mod-

ulators fabricated on MBE grown InGaAlAs compound semiconductor layers

lattice matched to InP substrate have been investigated. A simple technique

for measuring the refractive index and the material dispersion of InGaAlAs

layers in the transparent wavelength region was presented. Even though the

accuracy of this technique is limited by the accuracy of the film thickness,





59



this technique can be applied to any material system which has a transpar-

ent substrate (most of ternary and quaternary systems grown on InP sub-

strate). Also, this technique can be used for quick characterization of grown

films. We fabricated ridge waveguides on this material and measured the

propagation loss which was about 1.5 dB/cm for single moe operation. With

the refining of the growth technique, we believe that the waveguide structure

using this material may become quite useful for optoelectronic system appli-

cations. A single heterostructure InGaAlAs/InP phase modulator utilizing

the quadratic electro-optic (QEO) effect was demonstrated. The obtained

value of QEO coefficient from the measurements is 3.7 x 10-19 m2V2 at 80

meV below the band edge. In addition, the linear electro-optic effect(LEO)

coefficient was estimated to be 1.2 x 10-12 m/N which is comparable to that of

GaAs. The measured single mode phase shifts due to the QEO and LEO were

5.5 and 2.8 ONmm for TE and TM polarizations, respectively. These values

are the largest values reported so far in InGaA1As system. Availability of the

large QEO effect and wide band gap (0.85 to 1.67 im), highly efficient optical

modulator can be achieved at long wavelengths (e. g. 1.55 pm), quite useful in

low loss optical communication systems.













CHAPTER THREE
VERTICAL DIRECTIONAL COUPLER WAVELENGTH FILTER

3.1 Introduction


Use of wavelength-division-multiplexing/demultiplexing (WDM) tech-

niques in optical communication networks will increase the transmission

capacity of existing fiber links, taking full advantage of the low loss win-

dows available in optical fibers. Narrow band width, wavelength selective,

broadly tunable filters based on compound semiconductors are potentially

useful as wavelength and optical switching devices in optical communication

systems. In addition, these devices could be monolithically integrated with

other optoelectronic components, such as optical amplifiers or photodetectors.

In current WDM systems, discrete gratings and interference filters are com-

monly used with bulk microoptic components to perform the demultiplexing

and multiplexing functions (see Ishio et al. [Ish84] for an overview of WDM

technology).

As a monolithic WDM light source, several DFB lasers emitting at dif-

ferent wavelengths have been integrated [Aik77, Oku84]. Monolithic detec-

tor arrays are already commercially available. However, a crucial problem

remains unsolved, namely, its achievement of an integrated optical, narrow









band wavelength filter compatible with the lasers and detectors. The best

approach to this problem is to selectively couple light between waveguides,

e.g., conventional directional although its wavelength selectivity is far too

poor for most applications. However, if the two waveguides of the coupler are

made with different refractive indices, the wavelength selectivity can be

enhanced significantly. Wavelength filters using this principle have been fab-

ricated in LiNb03 [Alf78]. Due to the small refractive index change possible

in this material, the wavelength selectivity is limited, thus, the demonstrated

wavelength filter is capable of demultiplexing only one channel. Also, LiNb03

is not compatible with optoelectronic integrated circuits (OEIC's).

Recently, a narrow bandwidth (2.0 nm), grating-assisted directional

coupler filter with a broad band tunability (21.5 nm), with a central wave-

length around 1.5 pm has been demonstrated [Alf92a]. Using quantum well

electrorefraction, wavelength tuning in a grating-assisted vertical coupler fil-

ter has also been observed in A1GaAs / GaAs [Sak91]. A large tuning range

should be expected when used in conjunction with the quantum confined

Stark effect (QCSE); however, a value of only 2.0 nm was achieved with a 3

dB bandwidth of 1.7 nm. An ultranarrow bandwidth of ~ 8 A in a directional

coupler filter [Wuc91] at 1.3 pm was demonstrated by using InGaAsP / InP.

Monolithic integration of an optical amplifier with a grating assisted direc-

tional coupler filter [11191, Alf92b] as well as an intracavity tunable laser has









been achieved with tuning range of 57 nm and bandwidth of 3.0 nm at 1.5

im, using both forward and reverse biases[Alf92b].

In this chapter, we present both the theoretical and experimental

study of the very narrow bandwidth wavelength filters at 1.55 pm where the

loss of optical fiber is minimum. The quaternary InGaAlAs semiconductor

layers grown on InP substrate are used providing a wide selection of filter

wavelengths and possibly wide bandgap variation for large tunability. This

filter structure is fairly easy to integrate with other optoelectronic devices, an

important consideration for WDM system applications. The maximum possi-

ble asymmetry of two vertically stacked waveguides, namely, ridge and strip-

loaded waveguides, is utilized to achieve the narrow bandwidth filter. Cou-

pled mode analysis is used to obtain the coupling coefficients between the

ridge waveguide and planar waveguide which has a wide loaded strip on top./

The spectral index method is used to calculate the mode index and the field

profile of the two dimensional ridge waveguides. The coupling of power

between two waveguides along the length will be discussed in relation to the

bandwidth of the filter. The study of an array of many filters with different

filter wavelength in a single chip also be presented. Tunability of the wave-

length filter will also be discussed for both the reverse and forward bias con-

ditions.















filter consists of two vertically coupled waveguides of dis

and different quaternary compositions. The upper wave

thin and made of a high refractive index material while 1

is designed to have a thicker layer, but with a lower re

upper waveguide is a ridge waveguide whereas the lo

strip-loaded planar waveguide. The propagation const-

individual upper and lower waveguides, respectively, arn

tain o,, at which wavelength the light launched into the

completely transferred to the upper waveguide after tre

one coupling length, Lc. As I .o I increases, the co

waveguides becomes weak rapidly due to phase misma

power transfer from the lower to upper waveguide will be

pling become weaker. This is the basis for a directional ci

a wavelength filter. According to the coupled mode theor

width at half maximum AXBW is given by


A 5















































Substrate













Figure 3.1 A schematic diagram of the wavelength filter
device.


...............



:Bj1;.... ......


-










= L b~]d dX = Xo
(3.2)

As seen form Eq. (3.2), the filter bandwidth will become further narrower if

the dispersion in one waveguide is large compared to the other. This condi-

tion can be satisfied with the use of a well (top) and a weakly (bottom) con-

fined waveguide mode in the two waveguides. Therefore, in our case, the

maximum differential dispersion is obtained by having a well confined ridge

waveguide and a weakly confined strip loaded waveguide.


3.3 Analysis


In this section, we will present the method used to calculate the char-

acteristics of wavelength filter devices as well as the results of simulation.

First, the mode index and field profiles of top ridge waveguide and the bottom

strip-loaded waveguide must be calculated. The spectral index method (SIM)

[Ken89, Mci90] is used to obtain the mode index and the field profile of the

ridge waveguide; the two-dimensional effective index method is used for the

strip loaded waveguide. After normalization of each of the field profiles, cou-

pled mode theory is used to derive the coupling coefficient of the directional

coupler structure. The evolution of field amplitude in the beam propagation

direction has been calculated at different wavelengths to evaluate the charac-

teristics of filter devices.









3.4.1 Spectral Index Method (SIM)


The conventional effective index method [Ram74] is well known for its

excellent performance when the etch depth is small in the ridge waveguide

structure, i. e., for well guided ridge, rib and strip-loaded structures. But it

fails completely when the outer slab is cut off. The SIM [Ken89, Mci90] gives

much more accurate results at the expense of requiring a slightly longer com-

puting time. We use the SIM to obtain the mode index and the field profile of

the ridge waveguide and an effective index method is used in the case of a

strip loaded waveguide.

The main idea of the SIM is as follows. Let us consider a rib structure.

The Helmholtz field equation is solved exactly both in and below the ribs.

Simple trial functions are chosen in the ribs. These are then linked across

the bases of the ribs, to the Fourier transformed solution of the wave equa-

tion below the ribs by a variational technique.

In Fig. 3.2, we show a rib waveguide of width 2W, rib wall height H,

and slab thickness D. Region 1 is the cladding (usually air), region 2 is the

guiding region, and region 3 is the substrate. Except on the line at the base

of the rib (y=0, -W < x < W), we can solve the exact field equations. Thus,

within the rib and guiding layer


2 2
DE DE
x2 E + (K2 -2)E = 0 (3.3)
5x2 Wya





Figure 3.2 Typical rib waveguide structure.











where K = (2n / %)n is the propagation constant in the medium of refractive

index n, X is the free space wavelength, and 3 is the propagation constant of

mode.

In the rib, we solve Eq.(3.3) exactly by writing

E = F (x) G (y) (3.4)
The equation for F(x) is then a symmetric slab equation whose constants

determine G(y). An approach that deals with this approximation easily is

obtained by using the concept of an effective width [Ada81]. In the case of TE

mode, the effective width is



WE =W+ + (3.5)


since E is normal to the rib sidewalls where i, = (27/d)nl is the free space

propagation constant in air. The effective depth of the outer slab is



DE = D + (3.6)


since E is parallel to the slab / cladding interface.

We define the spectral index technique and derive the form of the dispersion

equation that is used to determine p. Using a Fourier transform with respect










to x, we convert the wave equation below the plane of the base of the rib (y=0)

to yield


2
+ {K2(y) s2 p2} = 0 (3.7)
ay2


where
00
S(s, y) = E (x, y) esxdx (3.8)

and



E(x, y) = (s, y) e-sxds (3.9)
-00

The solution of Eq.(3.7) is similar to that for a slab waveguide with a spectral

index ns, which is defined by



r2 2 1/2
ns = (n2S (3.10)



where Ko is the plane wave propagation constant in free space. This reduces

the difficulty of the problem by one dimension.

Therefore, for any layered structure, we can define a transfer function

F(s) such that on the plane of the base of the rib
l18
r(s) (3.11)
Cay


















case

le ent

y and

lives I

varia


- 4.2- A'L -1


Ld the star denotes its complex conjugate. Using the Parseval ty

we can rewrite Eq.(3.12) to link the spectral and real space soluti




JE -E*dx = -1 a E *ds (3.
Dy 2n- Fy
-w o


the transfer function defined by Eq. (3.11), this further simplifies


a E d x


_ _1-









As E, E, and F depend implicitly on P via Eqs. (3.3), (3.7) and (3.11), respec-

tively, Eq. (3.14) is the dispersion equation to be solved for P.

Equation (3.14) represents a variational form, and as a consequence,

the value.of p derived from it will be insensitive to small errors in E or C.

Hence, we expect to arrive at accurate values of 0 from a simple trial function

E. Based on the fact that E = F(x)G(y) within the rib, we can choose for the

fundamental symmetric mode

F (x) = cos (six) (3.15)

where

81 = 2W (3.16)


Then, by defining

Y 2 _(-s-p21)/2 (3.17)
we have


sin {7y (y + H) }
G (y) = (3.18)
sin {y7H}

at the base of the rib


cos (sW)
s = 2 s 2 2 (3.19)
S -S i


The dispersion relation, Eq. (3.14), can be simplified as










4s3 (s) cos2 (s W)
ycot(yH) = r(ds (3.20)
n2_ (f82-s2)2


The mode index P can be obtained from Eq.(3.20) using an iterative

computer analysis. The value of F(s) is obtained from a general solution of

Eq. (3.7) and Eq. (3.11). Once the value of p is known, we can use Eqs. (3.15)

and (3.9) to calculate the field profile inside the rib and below the rib, respec-

tively. The calculated spectral field profile below the base of the rib is as fol-

lows.

a) when 0 y D

E = Asin (F2y) + Bcos (F2y) (3.21)
b) when D 5 y

E = Cexp {-F3(y-D)} (3.22)
where


r2sin (F2D) -r3 cos (F3D)
A = -C (3.23)
r2

F2cos (F2D) + 3 sin (F2D)
B = C (3.24)
F2


where 2 = (K2 2 2)1/2 and F3 = (p2 + s2 K32)2.

To obtain the mode index and the field profile of a strip loaded

waveguide (used in our filter) which has a weak confinement in the lateral (x)




































ofile of the fundamental mode


LLMLLLoULAe d WTLo

3C- ,,- 3 --


nuerent


presented b

n x and y I


3.2 Coupled Mode Theory


:oupled mode theory has be

.conductor laser arrays or

n i n-a1 nlnA ,.n,- -. I, ........


en very useful in the

microstrip coupled t

-. -1 1 . .. -.-. -.e


field of inte


Ile Dower c


conservationn argument for the powers in indii

the fact that the two coupling coefficients Kab an

fta n ph na-hbdv wh; xx r nvrball, -,n- 4-..a -.' ;4-1, ,,,,


7.1






74


Region 1 Region 2 Region 1


Ws

air



ni





n2

Guiding layer


n3
Substrate








Figure 3.3 Schematic of a strip loaded waveguide.









waveguides are not identical. A more rigorous approach has been recently

proposed and very good numerical results have been presented [Har85,

Har86]. However, there is still considerable ambiguity about the reciprocity

and the power conservation in the coupled mode theory. We know that both

the reciprocity and the power conservation laws are basic that must be

obeyed. Often, they are usually used in electromagnetics as necessary condi-

tions to check the numerical accuracy of the results. In this section, we use

the modified coupled mode theory proposed by Chuang [Chu87] to calculate

the coupling characteristics of the wavelength filter structure.

Consider the first two Maxwell's equations in a medium of the dielec-

tric constant E(1 (x, y)



VxE(1) =icogH(1) (3.25)



VxH(') = -ioe(1)E(1) (3.26)


where the fields (E(1), H(1)) satisfy all the Maxwell's equations and the bound-

ary conditions in the medium E()(x, y). For a different medium E(2)(x, y), the

fields (E(2), H(2)) satisfy a similar set of equations and also the boundary con-

ditions in E(2). Following similar procedures for the Lorentz reciprocity theo-

rem, we obtain


7Fi






7R


ve ap

metr



(El





div(

exact

e box

()(x,,

eciprn


sing e''(X,y) = E(


,y) and


E') =a (z) EtJ ) (x, y) +b(z)E D) (x, y) (



H() a (z) H(a) (x, y) + b (z) H(b) (x, y) (



a(z) and b(z) express the z dependence of the individual guide

+-vnorn... "on., rA... tv.(a) TT (a) ..4 T (b) T.T (b) ml. -L- ....





77


of solutions to the Maxwell equations in the coupled-waveguide medium
E(x,y) and the radiation mode has been neglected. Both waveguides a and b
are assumed to support only a single TE (or TM) mode. For the second set of
solutions, we choose either e(2)(x,y) = e(a)(x,y) or E(2)(x,y) = e(b)(x,y). By using
the reciprocity equation Eq. (3.28) with Eqs. (3.29) and(3.30) in the cases of
both e(2)(x,y) = E(a)(x,y) and E(2)(x,y) = e(b)(x,y), the following relations are
obtained (see Chuang [Chu87] for details)


a (z) +CabCba db(z)= ia +aa)a(z)
Tz 2 dz


+i(Pa 2 +kbab (z) (3.31)


and
Cab + Cba da (z) +db (z)
2 dz dz


= i(Pb-ab ba +Kab)a (z) + i(b+ Kbb)b (z) (3.32)


where Kpq is the conventional coupling coefficient given by


Kpq = A^( )^ EEq) )- E(P) E (4))dxdy (3.33)










00
Cpq = ZJ J t~q t ~) dd
-00


(3.34)


and


(3.35)


Ae(q) (x, y) = e(x, y) -E(q) (x, y) q = a, b

where Ez is the longitudinal component of the field.


Based on the Eqs. (3.31) and (3.32), we obtain the coupled mode equa-


tions


Sd (z) = iS (z)
dzb (zJ (z)]


(3.36)


where the matrix elements for U and S are


C +C
c = pq qp
Opq = qp = Cpq +2Cqp
2


Skp (Cp + Cqp
Spq = Kqp+Jp p 2


Kpq+Cpqfq


We note that C11 =C22 = 1, and matrix C is symmetric.

Let


Cab + Cba
2


(3.37)


(3.38)


(3.39)





79


We invert the matrix U and obtain the coupled mode equations


da
= iaa + iKabb (3.40)


db
d= ibb + iKbaa (3.41)


where


[Kaa+ (Ja- b) E2-Kab1
Ya = a (3.42)


[K=bb + (b a) E2-kba (3
Yb [b 2+P (3.43)
1 -C




Kb [kb J ^Kb).]
Kab [ab+(b a j (3.45)
Kba 1 -C2


Please note that even though the matrix C and S are both symmetric, C-S is

not symmetric in general. That is Kab Kba, unless we have two identical

waveguides.





80


3.3.3 Characteristics of Wavelength Filter Devices


3.3.3.1 Power coupling and the bandwidth of the filter

Once we can calculate the coupling coefficients Kab and Kba by using

Eqs. (3.44) and (3.45), the power transfer characteristics between ridge and

strip loaded waveguides can easily be studied. Instead of using Eq. (3.1) to

obtain the bandwidth of the filters, we calculate the power transfer character-

istics of the coupler structure as a function of wavelength so that a more

accurate analysis is possible. We use Marcatili's approach [Mar86] to calcu-

late the power transfer characteristics. In the case that all of the light is cou-

pled into the waveguide 'a' (we launch all the light into the lower strip -

loaded waveguide), the power in both waveguide as a function of the propaga-

tion distance (z) are written as
/


P = 1- e-2sinh-l Ssin2z (KabKb ( 2) (3.46)



S= 2 + s2z(KbKba) (1 + 2) (3.47)
b 1 +82


where c is defined in Eq. (3.39) and 8 is normalized asynchronism parameter

between the guides, defined as 8 = (Pa Pb) / 2(KabKba)1/2

As studied earlier, the quaternary InGaA1As layers grown on InP sub-

strate are used to achieve a wide selection of filter wavelength and wide






81


: of the

3 methc


y tne 1:


lts (


ults [Me

3re usei

onal ave

7yAlrAs

Srefrac


[nGaAsAs layers. Even though we have already

d (in chapter 2) to obtain the refractive index an

material system, the accuracy of the results of

Formation on the film thickness. Therefore, v

-active index of Ino.63Ga .47.yAlyAs based on the rei

on92] in the following discussion. The reflection

d with Ino.52Gao.48As/In.53Gao.47As superlattice,

rage was used to find the corresponding val

layer.


ti.


I ---


___----y- -.


--


i














We used the

e of TM moi

region due

vith, the mc

obtained by i

ing IMSL s

ire. In the c

FT) routine

effective in

lide to obta


i the mode index and the field profile. The sch

r structure is drawn in Fig. 3.5 where the compc


3624 at 1.55 pm. The variations of the mode index o

own in Fig. 3.6.


82














3.55


3.5


3.45


3.4


3.35


3.3


3.25


3.2


3.15


1000110012001300 1400150016001700 1800

Wavelength(nm)








Figure 3.4 Refractive index and material dispersion of
Ino.53Gao.47.yAlyAs layers.


.*. I.. .... I .....I..I. II .... I * i. II ... S
25 0.20 y=0.15
0.25 In 53Ga047- A As
". 53Oo 0*.47-y y


0.30 "
7

0.35
", \ "--... -S

S0.40 U -..

-a
7 .

0.45 ''.. "--.

'1 2*111---11 1
........



S I I ". i "I l ..l . ." .















W
y=0.10
H

G L I

y=0.30 S



y=0.20 D




y=0.30


/

InP substrate








Figure 3.5 The schematic of the filter device where all the lay-
ers except the substrate are Ino.53Gao.47yAlyAs with
different Al compositions (y).


R4





85


3.366 .



3.364 -..


Plan
3.362
(strip-


3.36


1.54 1.545 1.55 1.555 1.56

Wavelength in pm






Figure 3.6 Variations of the mode index of 3 x 0.66 ipm ridge
and 2.78 pm planar waveguides.


C
rc
c


3









ridge waveguide is a form of 2-D data set and the interpolation routine in

IMSL library was used to obtain the magnitude of the field at certain point.

A cosine function was used in both the transverse and lateral direction in the

field profile of the strip loaded planar waveguide. In the case of H = 0.66 pm,

W = 3.0 pm, D = 2.78 pm, L = 20.0 pm and G = 0.6 pm, the coupling coeffi-

cients Kab (coupling from planar to ridge waveguide) and Kba (coupling from

ridge to planar waveguide) were calculated by using Eqs. (3.44) and (3.45),

respectively, as a function of separation S between two waveguides. Figure

3.7 shows the variation of the coupling coefficients at 1.55 pm as a function of

S. To have a coupling length Lc of 5 mm, S was determined as 1.5 pm. A

coupling length can be calculated from coupling coefficients by using the fol-

lowing relation

/
L 2(3.49)


The parameters used in the calculation are set as follows: H = 0.66 pm,

W = 3.0 pm, D = 2.78 pm, L = 20.0 pm, S = 1.5 pm and G = 0.6 pm. Before we

start the evaluating the power transfer in the propagation direction, the cou-

pling coefficients and the joint interaction of the individual waveguide modes,

c = Cab Cba, need to be determined as a function of wavelength near the fil-

ter wavelength. The variations of the coupling coefficients (Kab, Kba) and c

near 1.55 pm are shown in Fig. 3.8 and Fig. 3.9, respectively.















450

400

350

a0 300
0
S250

200

0 150

100

50 I I I * I * I t i
1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1

Separation S (gm)







Figure 3.7 The variation of the coupling coefficients at 1.55 gm
as a function of separation between two waveguides
where H = 0.66 .m, W = 3.0 pm, D = 2.78 pm, L =
20.0 pm and G = 0.6 pm.


61
















4 2 ----4 >
42

40 -

38

36

34 '

32 -.*'

30
1.549 1.55 1.551 1.552

Wavelength (gm)








3 3.8 Variations of the coupling coefficients near the filter
wavelength where S= 1.5 pm, H = 0.66 pm, W = 3.0
pm, D = 2.78 pm, L = 20.0 pm and G = 0.6 pm.






Rq


.549 1.55 1.551 1

Wavelength (gm)


.'iL ULt 0.u V lvaUiII ULi UIUle JOIIIL nieracuoi
.... ... . --* ._ ._ l i





Ain


Since we have already obtained the Pa, Ob, the two coupling coefficients

Kab, Kba and c, the power coupling characteristics between two waveguides in

the direction of propagation direction can be calculated by using Eqs. (3.46)

and (3.47). The light was launched into the planar waveguide and the powers

in both ridge and planar waveguides after 100 mun propagation were calcu-

lated for the purpose of checking the conservation of total power in the sys-

tem. The powers in ridge and planar waveguides after 100 gm propagation

was used as an initial condition and the powers after another 100 am was

calculated in the same manner. This process was repeated until the total

propagation length reached a value of 10 mm. We observed that the total

power (power in ridge + power in planar waveguide) was well conserved and

the variation in the total power was less than 0.1 %. The coupling length of

our coupler can then be calculated by using Eq. (3.49) which turned out to be

~ 4.6 mm at 1.55 am. The evolutions of the power in ridge waveguide at sev-

eral different wavelengths in the propagation direction are shown in Fig.

3.10. In order to achieve complete power transfer from the planar to the

ridge waveguide, we chose z= 4.7 mm and evaluate the full-width half-maxi-

mum (FWHM) bandwidth of the filter. We obtained the 17 A FWHM band-

width at the center wavelength of 1.5504 gm. Figure 3.11 represents the

calculated bandwidth of the filter with the following parameters: H = 0.66

gm, W = 3.0 gm, D = 2.78 am, L = 20.0 gm, S = 1.5 am and G = 0.6 am. The






















(a
bbo




*r-


0.8


0.6


0.4


0.2


0 2 4 6 8


Propagation distance (mm)






Figure 3.10 The evolutions of the power coupled to ridge
waveguide in the propagation direction at different
wavelengths.




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