OPTICAL FILTERS, MODULATORS AND INTERCONNECTS FOR
OPTICAL COMMUNICATION SYSTEMS
By
SANGKOOK 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. WooYoung 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 electrooptic 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
SangKook 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 multiquantum well (MQW) structures. This study encompasses the
fabrication and characterization of passive ridge waveguides, efficient phase
modulators using the quadratic electrooptic 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 impurityinduced layer disordering (IILD) technique
essential for the implementation of highly dense wavelengthdivisionmulti
plexers/demultiplexers (WDM) in multiwavelength 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 integratedoptics 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 roomtemperature 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, optoelectronic integrated
circuits (OEIC's) consisting of highspeed 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 lowloss 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 electrooptic coefficients of this material by developing and testing
ridge waveguide phase modulators in this material system.
The usage of wavelengthdivisionmultiplexing/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 lowloss window available in optical fibers. A case in
point is the proposed all optical multiwavelength optical network [Bra93],/
shown in Fig. 1.1. In this system, the WDM crossconnect is a key component
which requires the narrow bandwidth, wide tunability and the flattop
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 multiwavelength operation, by
extending the concepts of the discrete filter devices, e. g. arrays of wavelenth
WDM crossconnect
Access node A
Figure 1.1 The schematic diagram of all optical multiwave
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 lasermodulator 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 multiquantum 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 electrooptic (LEO) and
the quadratic electrooptic (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 electrooptic effect (LEO) coefficient is
estimated to be 1.2 x 1012 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 cm3
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 cm2 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 MachZehnder
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 nnlantI7nInn Paco Tc.;cihlfrlk+ +_ __ 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 bandgap can be tuned over a rela
tively large wavelength range (0.851.67 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 longwavelength 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
ireemode 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 metalsemi
conductormetal Schottky photodetector [Gri90] on a semiinsulating 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 16layer 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 longwavelength system
have been grown by MOVPE. The 40layer 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, twophoton absorption [Vil90]
was measured in InGaAlAs/InP ridge waveguides. This material showed a
relatively large twophoton 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
MachZehnder interferometric technique. For the first time, the quadratic /
electrooptic 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 guidedwave optical devices can be optimized
only through an accurate knowledge of the refractive index and material dis
persion. Recently, we presented a semiempirical 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 FabryPerot 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 filmsubstrate 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 semiinsulating Fedoped InP substrate
by Prof. Bhattacharya and his coworkers at the University of Michigan. The
material is latticematched, 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 bandgaps 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 PerkinElmer Lambda9 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 semiempirical relations for,/
ternary and quatenary optoelectronic materials reported in the literatures
[Afr74, Bro84, Han9la]. We fitted the measured transmission data with Eq.
(2.4), piecewise 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 singleoscillator model [Afr74] in each narrow spectral
(k)= B EEd 1 0.5
,o, Ed are the two parameters of the singleoscillator 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.(24).
)
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 singleoscillator
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 2E2E2E2'
n 2 =1 E d d p In g p (2.8)
E E3 2E3(E2E2) E2 E2
o o o g g P
where Eg is the bandgap 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.47yAlyAs. The solid curves represent the fit to
modified singleoscillator model.
Table 2.1: Numerical values of parameters used in
modified singleoscillator 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 140017 or 23 are normally used. Spin rate 4500 rpm for
40 sec. results in 0.4 and 0.8 pun thick PR for 140017 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 nearfield 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
leastsquares 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 mLockin
amplifier /
Figure 2.7 Near field intensity measurement set up.
*rl
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 ElectroOptic 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 highspeed signal processing. The semi
conductor waveguide phase modulators are typical optical devices utilizing
the refractive index change. These phase modulators usually employ a pn
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 electrooptic 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 ElectroOptic Effects
2.4.1.1 Linear electrooptic 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 electrooptic effect (or Pockel's effect) and is
proportional to the applied electric field. Manba [Man61] has studied the lin
ear electrooptic (LEO) effect in zincblende 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 zincblende 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 << n2, the refractive indices along the [110] and [110] direc
tions are given by
n3
n = n + r41F for [110] (2.10)
n3
S= nr41F 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 electrooptic 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 FranzKeldysh 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 FranzKeldysh effect
was shown to have a quadratic dependence on the applied electric field
[Alp87]. The refractive index change due to the quadratic electrooptic (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
rentvoltage(IV) 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 IV 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 CurrentVoltage (IV) 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 MachZehnder 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 electrooptic coefficient
For zincblende 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 freespace wavelength.
Since the background carrier concentration is very low (< 1015/cm3 ) in
the guiding region, onesided 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 builtin 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 metalcontact and the maximum
field strength located at the metalcontact.
Eop(x) was obtained using a step index 3layer 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 builtin 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 (CV) 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 CapacitanceVoltage (CV) characteristics of the
Schottky barrier junction.
Nd value by using the Eq.(2.16) is 6 x 1014 cm3. 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 1012 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 electrooptic 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 1012 m/V) is comparable to that of GaAs while the QEO coefficient (3.7
x 1019 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 PpinN 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 electrooptic (QEO) effect was demonstrated. The obtained
value of QEO coefficient from the measurements is 3.7 x 1019 m2V2 at 80
meV below the band edge. In addition, the linear electrooptic effect(LEO)
coefficient was estimated to be 1.2 x 1012 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 wavelengthdivisionmultiplexing/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), gratingassisted 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 gratingassisted 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
striploaded 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
striploaded 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 twodimensional 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 striploaded 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) esxds (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 _(sp21)/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_ (f82s2)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(yD)} (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 na1 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 nahbdv wh; xx r nvrball, ,n 4..a .' ;41, ,,,,
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 coupledwaveguide 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(Pbab 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) E2Kab1
Ya = a (3.42)
[K=bb + (b a) E2kba (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, CS 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 e2sinhl 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*.47y y
0.30 "
7
0.35
", \ "... S
S0.40 U ..
a
7 .
0.45 ''.. ".
'1 2*11111 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 2D 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 fullwidth halfmaxi
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.
