LOW LOSS ORIENTATION-PATTERNED GALLIUM ARSENIDE (OPGaAs)

WAVEGUIDES FOR NONLINEAR INFRARED FREQUENCY CONVERSION

Dissertation

Submitted to

The School of Engineering of the

UNIVERSITY OF DAYTON

In Partial Fulfillment of the Requirements for

The Degree of

Doctor of Philosophy in Electrical and Computer Engineering

By

Izaak Vincent Kemp

Dayton, Ohio

December 2012

LOW LOSS ORIENTATION-PATTERNED GALLIUM ARSENIDE (OPGaAs)

WAVEGUIDES FOR NONLINEAR INFRARED FREQUENCY CONVERSION

Name: Kemp, Izaak Vincent

APPROVED BY:

Dr. Andrew Sarangan Dr. Peter Powers Advisory Committee Chairman Committee Member Professor Professor Electrical and Computer Engineering Department of Physics

Dr. Partha Banerjee Dr. Guru Subramanyam Committee Member Committee Member Professor Department Chair Electrical and Computer Engineering Electrical and Computer Engineering

Dr. Rita Peterson Dr. Kenneth Schepler Committee Member Committee Member Adjunct Professor Adjunct Professor Electro-Optics Electro-Optics

John G. Weber, Ph.D. Tony E. Saliba, Ph.D. Associate Dean Dean, School of Engineering School of Engineering &Wilke Distinguished Professor

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© Copyright by

Izaak Vincent Kemp

All rights reserved

2012

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Distribution Statement A: Approved for public release, distribution is unlimited.

This dissertation contains information regarding currently ongoing U.S. Department of

Defense (DoD) research that has been approved for public release. Distribution of this dissertation is unlimited pursuant to DoD Directive 5230.24 subsection A4. Requests for further information may be referred to the author, Izaak V. Kemp AFRL/RYMWA.

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ABSTRACT

LOW LOSS ORIENTATION-PATTERNED GALLIUM ARSENIDE

(OPGaAs) WAVEGUIDES FOR NONLINEAR INFRARED

FREQUENCY CONVERSION

Name: Kemp, Izaak Vincent University of Dayton Advisor: Dr. Andrew Sarangan The mid-IR frequency band (λ = 2-5 μm) contains several atmospheric transmission windows making it a region of interest for a variety of medical, scientific, commercial, and military applications. Recently there has been a growing interest in using orientation-patterned semiconductors such as orientation-patterned gallium arsenide (OPGaAs) to achieve frequency conversion in this region. GaAs has a large nonlinear coefficient, broad transparency range, and a well-developed fabrication technology allowing for the manufacture of nonlinear integrated optical devices such as waveguides. By confining the nonlinear pump beam throughout the length of a waveguide one can achieve very high field intensities while at the same time overcoming the diffraction normally associated with tight focusing of Gaussian beams. However,

v device performance in OPGaAs waveguides has been limited by large propagation losses resulting from the unique nature of the material.

In this dissertation I report an OPGaAs/OPAlxGa1-xAs embedded ridge waveguide design which, combined with a new growth process using alternating MOCVD growth and chemical mechanical polishing (CMP), is capable of achieving the low losses necessary to function effectively as a nonlinear gain material. Our waveguide was designed to be single mode from 2-10 μm, based upon a series of numerical simulations to determine the effective indices of the waveguide across the mid-IR band, which was crucial for accurate calculation of the grating period Λ needed for quasi-phasematching.

Record low RMS surface roughness values of 5 nm were obtained using this new growth process. In addition, record low waveguide losses of 1.0 dB/cm were measured, validating our theoretical predictions, and nonlinear gain was investigated in an optical parametric amplifier (OPA) experiment.

vi

PREFACE

This work summarizes an effort to develop guided wave devices in orientation patterned gallium arsenide (OPGaAs) for nonlinear frequency conversion in the infrared.

This work was conducted at Wright-Patterson Air Force Base under the direction of the

Air Force Research Laboratory, and resulted in several original contributions to the field of nonlinear optical waveguide devices. We have established a working recipe for growing guided wave devices in OPGaAs with low loss, and constructed a theoretical model for designing such devices. We have thoroughly investigated this model by placing our finished waveguide samples in an OPA experiment, and laid the groundwork for future OPGaAs waveguide development. In addition we have constructed a temperature-tunable bulk OPGaAs OPO and shown that the tunability matches very closely what is predicted by theory.

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TABLE OF CONTENTS

ABSTRACT ...... v

PREFACE ...... vii

TABLE OF CONTENTS ...... viii

LIST OF TABLES ...... xv

CHAPTER 1 INTRODUCTION ...... 1

1.1 Motivations ...... 1

1.2 Current infrared sources ...... 4

1.3 Nonlinear infrared sources ...... 6

1.4 Infrared nonlinear optical materials ...... 7

1.5 Orientation patterned (OP) semiconductors ...... 9

1.6 Waveguides and integrated optics...... 13

1.7 Organization ...... 15

CHAPTER 2 THEORETICAL BACKGROUND ...... 16

2.1 The nonlinear susceptibility ...... 16

2.2 Nonlinear interactions (plane waves) ...... 17

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2.3 Phasematching and conversion efficiency ...... 21

2.4 Optical parametric oscillation ...... 28

2.5 Waveguide theory ...... 30

2.6 Frequency conversion in waveguides ...... 32

CHAPTER 3 WAVEGUIDE MODELING AND DESIGN ...... 34

3.1 2D computational mode solving ...... 35

3.2 OPGaAs waveguide tuning curves ...... 42

3.3 Template design ...... 46

3.4 Other design considerations ...... 48

CHAPTER 4 WAVEGUIDE FABRICATION, PREPARATION, AND ANALYSIS ...... 51

4.1 Waveguide MOCVD growth ...... 52

4.2 Template results and analysis ...... 56

4.3 Sample preparation and surface metrology ...... 60

4.4 Polishing and cleaving ...... 63

CHAPTER 5 EXPERIMENTAL PROCEDURE AND RESULTS ...... 68

5.1 Experimental setup ...... 68

5.2 Waveguide loss measurements ...... 72

5.3 Temperature tuning ...... 76

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5.4 OPA results ...... 78

5.5 Future Work ...... 81

REFERENCES ...... 83

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LIST OF FIGURES

Figure 1: Diagram depicting a nonlinear optical parametric generation (OPG) process ...... 1

Figure 2: Plot of horizontal atmospheric transmission (10 km) as a function of wavelength ...... 4

Figure 3: 3D illustration of the zincblende structure and two 2D cross sections...... 9

Figure 4: Illustration depicting how an orientation template is fabricated in the MBE process .... 11

Figure 5: Microscope image of a bulk OPGaAs sample, showing the periodic domains ...... 12

Figure 6: A GaInAsP/InP integrated optical circuit designed for use in a 1.55 μm optical communications system ...... 13

Figure 7: Plot showing the evolution of the output field magnitude, E3, for an OPG process(2.05μm -> 4.1μm) in GaAs as a function of propagation distance through the material for the case when Δk = 0 (dashed pink) and when Δk ≠ 0 (blue) ...... 21

Figure 8: Illustration showing a typical bulk QPM device ...... 26

Figure 9: Plot of signal power vs. crystal length for three different phasematching conditions .... 27

Figure 10: Illustration depicting the basic components of a confocal OPO...... 28

Figure 11: Propagation content spectrum of a waveguide ...... 30

Figure 12: Waveguide design used for modeling simulations, and corresponding structure as shown in LIGHTs ...... 35

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Figure 13: Results of our initial simulations in COMSOL ...... 36

Figure 14: LIGHTs generated mode profiles and corresponding field cross-sections for the pump beam (λ = 2.05 μm) ...... 40

Figure 15: Theoretical waveguide tuning curves based on our effective index calculations using six different AlGaAs Sellmeier equations ...... 42

Figure 16: OPGaAs orientation template grating mask design ...... 46

Figure 17: Detail of OPGaAs grating mask design showing how the spacing between waveguide ridges will be varied in order to allow for easy identification of grating period...... 47

Figure 18: Diagram illustrating the concept of numerical aperture in a waveguide with an asymmetric cladding ...... 48

Figure 19: Illustration of our OPGaAs waveguide structure (left) and a picture of the MOCVD chamber used at UW to fabricate it (right)...... 52

Figure 20: Diagram and photographs depicting the chemical mechanical polishing (CMP) system employed by UW ...... 53

Figure 21: Photos of the cleanrooms at UW where our waveguide etching was performed ...... 54

Figure 22: Scanning Electron Microscope (SEM) images of waveguide ridges made with ECR etching (left) and ICP etching (right) ...... 55

Figure 23: Photo of the first delivered waveguide template (left) and an SEM image of one of its ridges (right) ...... 56

Figure 24: Microscope image of the second template, showing a very large defect cluster ...... 57

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Figure 25: Nomarski micrographs of an OPGaAs orientation template (left) before and (right) after HVPE growth showing how this process seems to ‘heal’ over the defects in the template. . 57

Figure 26: Microscope images of the (left) third and (right) forth delivered waveguide templates. While the third template still exhibited a significant amount of pitting, it did not have the defect clusters seen in the second wafer. The forth wafer is nearly defect free...... 59

Figure 27: Photograph of the AFM used at UC (left) and an AFM image of a sample from the third wafer (right) ...... 60

Figure 28: SEM images taken at UC of waveguide ridges from the fourth template ...... 61

Figure 29: Photo of the Zygo white light interferometer (left) and an example 3D plot obtained from the scan of a waveguide ridge ...... 62

Figure 30: Microscope image of an OPGaAs sample after being diced ...... 63

Figure 31: Plot showing imput vs. transmitted power for a bulk OPGaAs sample before and after polishing ...... 64

Figure 32: Microscope images comparing the bulk OPGaAs polishing results from Blue Ridge Optics (left) and our own in-house efforts (right)...... 65

Figure 33: Photos of our Allied Multi-Prep polishing machine ...... 66

Figure 34: Photos of the Loomis automated cleaver. The sample is placed on a sticky matt (right) and a diamond scribe is used to make a very small incision (10 µm) in the crystal surface at a set pressure. A roller is then moved over the sample at a user set pressure to propagate this incision across a crystal plane...... 66

Figure 35: Photo of cleaved sample (left) showing how well the cleave propagates along the sample ...... 67

Figure 36: Diagram of our OPA experiment ...... 68

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Figure 37: Photos of our Tm:Ho:YLF pump laser ...... 69

Figure 38: Output spectra of our Tm:Ho:YLF laser ...... 70

Figure 39: Photos of the waveguide arm of our experiment ...... 71

Figure 40: Photo of our completed experimental setup ...... 72

Figure 41: Photos of our streak-imaging experiment ...... 72

Figure 42: The IR photo shown in Figure 42 with the contrast turned down (left), showing how the scattered light decays as it propagates through the waveguide. Also shown is a plot of the total pixel count (intensity) versus position, showing the exponential decay...... 74

Figure 43: Schematic design of our OPGaAs oven (left), and a photo of the OPGaAs sample with oven mounted in the OPO ...... 76

Figure 44: Output spectra of our OPGaAs OPO signal as a function of temperature...... 77

Figure 45: Plot comparing our measured signal peaks as a function of temperature to those predicted by theory ...... 78

Figure 46: IR camera image of the output of our waveguide (left) compared with the calculated mode profile for a waveguide with a 0.5 µm tall ridge...... 78

Figure 47: Plot comparing the tuning curves for the case where all three wavelength s propagate as TE modes (red), or the pump is TM polarized and the signal and idler are TE polarized (blue). The tuning curve is shifted by 2 µm, which could explain why we were unable to see gain (the red plot here corresponds to the purple plot in Figure 16)...... 80

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LIST OF TABLES

Table 1: Table comparing a variety of crystals used for nonlinear frequency conversion in the Mid-IR ...... 7

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CHAPTER 1

INTRODUCTION

Figure 1:Diagram depicting a nonlinear optical parametric generation (OPG) process. The pump photons

(ωp) interact with the nonlinear material and split into photons of different frequencies, called the signal

(ωs) and the idler (ωi). The relationship between the three frequencies is given by energy conservation, and the relationship between the two commonly used subscripts is shown. This dissertation covers the design, fabrication, and testing of orientation-patterned gallium arsenide (OPGaAs) waveguides for use in infrared frequency conversion. Our focus is on second-order optical parametric generation (OPG) obtained through quasi- phase matching (QPM) in the GaAs crystal. This chapter serves as an introduction to the problems motivating this research, a brief description of the scientific background to our approach, and a short description of the organization of the text.

1.1 Motivations

The field of photonics has expanded rapidly since the discovery of the laser in the early 1960s1, which has in turn increased the demand for coherent light sources across the

1 electromagnetic spectrum. Unfortunately, often there do not exist materials with the required properties to make a laser in the spectral region of interest. Alternatively, the existing materials might not provide the user with all the features (such as ease of use, portability, tunability, and low cost) desired for the end application. For these reasons, there is a great deal of interest in developing novel laser sources that provide greater flexibility in terms of spectral output than typical devices such as solid state, gas, and diode lasers.

One of these alternate techniques is known as nonlinear frequency conversion, where a laser beam of one frequency (often called the ‘pump’) is converted into another frequency through interaction with a nonlinear material (typically a crystal) as shown in

Figure 1. Governed by the strong dependence of nonlinear interactions on conditions such as temperature, material, and pump wavelength a frequency converting material can turn a fixed pump laser into a broadly tunable source centered on any wavelength the designer chooses, within the transparency and fabrication tolerances of the material and the boundaries placed by energy and momentum conservation.

In order for the frequency conversion process to be efficient, a condition known as phase-matching (equivalent to momentum conservation) between the interacting fields must be satisfied. This is typically a very strict requirement that limits the usable materials and tunability of a frequency converting device. There is, however, an alternative method to phase matching known as quasi-phase matching (QPM) that uses micro-fabricated structures to give the user greater control over the material properties and device output at the expense of a more complex fabrication process. QPM devices

2 have shown a great deal of promise in the mid to far-infrared (IR) region (3-10 μm)2, and since this is our spectral region of interest it is the technique we have chosen to employ.

The U.S. Air Force has an interest in high-power optical sources in the mid to far-

IR portion of the electromagnetic spectrum. Applications such as IR countermeasures

(IRCM) and battlefield remote sensing require high-power tunable sources which can be achieved using a combination of conventional and exotic laser materials3,4,5,6. The desired operating wavelengths for these applications lie in the regions where there is significant atmospheric transmission and, as shown in Figure 2, there are several so called

‘transmission windows’ (regions where the transmission approaches 100%) in the mid to far-IR region. QPM materials feature robust operation as well as compact size and conformability within existing systems7, and are capable of emitting coherent radiation in all of the atmospheric transmission bands. Part of this research includes the development of QPM waveguides, which can theoretically achieve increased nonlinear gain due to the waveguide confinement as well as enable direct coupling to a pump fiber laser making them ideal for compact integrated optical sources. While the focus of this work is on laser source development rather than systems development, these end applications are briefly mentioned as they are the major motivating factor behind this research.

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Figure 2: Plot of horizontal atmospheric transmission (10 km) as a function of wavelength. Note there are several ‘transmission windows’ in the 2-5 and 8-12 μm regions of the spectrum8.

1.2 Current infrared sources

In the near-infrared solid-state and semiconductor diode lasers are the dominant light sources used for commercial and military applications. 1.064 and 1.550 μm lasers in particular have seen an immense amount of development due to their usefulness in fiber- optic communication and can easily be found with a wide variety of beam, pulse, and power properties. These devices have proven to be highly efficient, small, long-lived and low-cost with a diverse range of applications9. One commonly used semiconductor laser diode material is gallium arsenide (GaAs), which boasts a very mature fabrication process and typically operates in the 0.6 μm to 1.550 μm range10. Reaching longer wavelengths with semiconductor lasers becomes difficult because to achieve such frequencies one must have a material with a very small band gap; in which case non- radiative processes such as Auger recombination begin to dominate and limit the device’s overall performance11.

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One alternative used to overcome the disadvantages of bipolar semiconductor lasers is the quantum cascade laser (QCL), which is based on intersubband transitions inside of specially engineered coupled quantum wells typically made of semiconducting materials12. Previously, quantum cascade lasers required cryogenic cooling in order to operate, however recent improvements have brought their operating temperatures to room temperature and they now cover a large part of the infrared spectrum13. However, QCLs are not currently capable of achieving the tuning range and power levels required for a number of applications, although this is an active area of research. QCLs have yet to see any widespread commercial or industrial use although it is speculated that they will begin to play a more important role in the mid-IR in the near future14.

In addition to semiconductor sources, there are a number of gas laser sources that emit in the infrared. These include a HeNe emission line at 3.39 μm, and CO2 emission lines at 9.2 and 10.8 μm15. While some of these lasers are capable of high powers, as mentioned previously they are typically very large, inefficient, fragile, and lack tunability. For these reasons infrared gas laser sources are typically limited to use in a laboratory environment. In addition to gas lasers, there are also a number of solid-state sources that can emit light in the infrared such as chromium doped semiconductors16, but they are also limited in terms of their tunability. For these reasons nonlinear devices are investigated as an alternative infrared source, as nonlinear generation is capable of achieving both high power and a wide range of tunability across the IR spectrum.

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1.3 Nonlinear infrared sources

As discussed in the previous section, generation of coherent IR radiation by nonlinear frequency mixing is an attractive alternative to direct laser sources. Some materials, when exposed to intense radiation, exhibit nonlinear terms in their induced polarization (dipole moment per unit volume). This nonlinearity can thus radiate an electromagnetic field at a frequency different than the field that drives it. While there are a large number of different nonlinear interactions, our focus is on optical parametric generation (OPG) which is illustrated in Figure 1. OPG is a second order nonlinear process whereby the intense field of the source/pump induces a polarization radiating at two lower frequencies (called the signal and idler, ωs>ωi) whose sum equals the incident frequency. The specific frequency pair generated depends on the phase matching conditions in the material, and is thus a user established quantity17.

An important distinction in the OPG regime is between what are called optical parametric amplifiers (OPAs) and optical parametric oscillators (OPOs). An OPA is a nonlinear device that takes pump and signal (or idler) photons from another coherent source (possibly an OPO) and amplifies either the signal or idler power through an additional nonlinear process such as difference frequency generation (DFG). In the process of generating the DFG, the signal (idler) input is also amplified. Nonlinear devices often consist of a series of OPGs and OPAs to maximize conversion efficiency18, which is limited in the case of a single OPG by what are known as the Manley-Rowe relationships (Equation 2.13). An optical parametric oscillator is a device where a nonlinear optical material is placed in a cavity that is resonant for at least one of the interacting wavelengths. This resonance enables multiple passes through the nonlinear

6 material, and this way the nonlinear material acts as a gain medium in a very similar fashion to a laser, although the fundamental physical phenomena are quite different.

Considering the wide range of solid-state and semiconductor lasers available for use as pump sources, a mid-infrared source based on an OPA or OPO configuration could easily be made portable by integrating them with an appropriate pump source. In this way the main limitation on the device output would be the properties of the nonlinear material itself.

1.4 Infrared nonlinear optical materials

GaAs GaP ZnSe ZnGeP2 AgGaSe2 LiNbO3 KH2P KTiO (PPLN) O4 PO4 (KDP) (KTP) Effective Nonlinear coefficient 57 45 38 75 33 17 0.5 13.7 (pm/V)* Transparency Range 1.8 - 0.55 - 0.5 - 0.8 - 12 0.5-15 0.4-4.5 0.2-1.7 0.35- (µm) 12 11 20 4.5 Phasematching type QPM QPM QPM BRF BRF QPM BRF QPM Thermal Conductivity 52 110 18 35 1 4.6 1.7 7.8 (W/m • K) Damage Threshold 3.1 5.4 5.0 9.0 0.5 2.5 50 15 (J/cm2)

*QPM materials have their nonlinear coefficients reduced by a factor of as discussed in

Chapter 2.

Table 1: Table comparing a variety of crystals used for nonlinear frequency conversion in the Mid-IR. GaAs boasts a number of advantages compared to other crystals in this class19-27. As previously stated, a major challenge in the field of infrared nonlinear optics is finding materials suitable for the desired application. Over the years a number of materials have been studied as candidates for use in the IR region. Those most commonly

7 encountered in the literature are listed in Table 1, for instance periodically poled lithium niobate (PPLN), which has seen widespread use in the past several decades not only in the IR region but also for generation of blue-green light at 532 nm28. While PPLN is a well-established nonlinear material, as can be seen from Table 1, it is opaque beyond 5

μm limiting its use in the mid-IR.

One class of crystals that is commonly used for mid-IR frequency conversion is the chalcopyrite family, which includes ZnGeP2 and AgGaSe2. ZnGeP2, for instance, has been used to build widely tunable OPOs covering the region from 3 to 10 μm29. These are usually available as bulk crystals with centimeter dimensions, and since they utilize birefringent phasematching they do not require the extensive materials processing described later for quasi-phasematched materials (although growing these crystals even in bulk form has its challenges). However the chalcopyrite family suffers from extrinsic problems like point defects generating excess absorption, and phonon-related absorption greatly limits their use beyond 9 μm. In addition chalcopyrites suffer from intrinsic problems due to the crystal’s birefringence such as beam walkoff and limitations on birefringent phase matching bandwidth (not all given interactions will phasematch in a birefringent crystal).

Given the limitations of these commonly used nonlinear materials, the need for alternatives with improved intrinsic properties becomes apparent. The main properties to consider are the nonlinear coefficient, which describes the strength of the nonlinear interaction, optical transparency, thermal conductivity (for tuning as well as heat management), and growth techniques. Zincblende semiconductors offer many attractive properties in these areas especially due to the ease of creating high quality, high purity

8 crystals using advanced semiconductor fabrication techniques. In addition, as can be seen from the table above, zincblende semiconductors such as GaAs, ZnSe, and GaP have very large nonlinear coefficients, although this is slightly offset by their high refractive indices

(as discussed in Chapter 2). While zincblende materials have major advantages over more commonly used infrared nonlinear materials they have historically not been used due to their lack of birefringence, which means that they require special fabrication processes in order to achieve the phasematching conditions necessary for efficient conversion. In recent years a great deal of effort has been devoted to developing fabrication techniques, such as orientation-patterning30,that will enable zincblende semiconductors to compete with existing nonlinear materials.

1.5 Orientation patterned (OP) semiconductors

Figure 3: 3D illustration of the zincblende structure and two 2D cross sections, one across the (011) and the other across the (01-1) crystal planes. Rotating the crystal about this plane (a 90° rotation about the central axis) results in a displacement of the positions of the two lattice sites.

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In order to take full advantage of the nonlinear and material properties of zincblende semiconductors, several methods for efficient nonlinear frequency conversion without using birefringence have been developed. The most common technique used is quasi-phasematching, which relies on periodic modulation of the nonlinear coefficient through rotation of the crystal. Since zincblende does not have a centrosymmetric unit cell, rotation of the crystal by 90° about the (011) plane changes the overall crystal structure, as shown in Figure, which in turn changes the sign of the second-order nonlinear coefficient. This has an effect similar to birefringent phasematching only in this case the crystal parameters (i.e. the grating period) are completely under the control of the crystal grower31.

The first method used to achieve QPM in GaAs was to use a series of discrete plates placed at Brewster’s angle66. While this method proved that QPM was possible, it was not very practical in terms of fabrication so the next attempt was to use diffusion bonded stack of plates that was periodically rotated along one axis32. While this approach was successful in generating nonlinear frequency conversion, it remains of limited usefulness because of the intensive labor involved in the stacking of these plates and the significant losses at the plate boundaries. The optical losses of the (bulk) material were measured to be 0.3 cm-1, which limited the conversion efficiency to less than 1%. For optical parametric generation in the mid-IR using OPGaAs one typically requires grating periods on the order of tens of microns, which would require a large number of very thin

GaAs plates to be bonded together by hand. Obviously this approach is not practical, so an alternate approach was developed called the orientation template method33.

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Figure 4: Illustration depicting how an orientation template is fabricated in the MBE process (a) First an inverted layer in deposited on top of an upright substrate (with a thin nonpolar layer of Ge) and then etched using photolithography. (b) Then epitaxial growth is performed, resulting in an orientation grating. The orientation template method is illustrated in Figure 4, and was originally developed in 1999 by Ebert and Koh et al34,35. Ebert and Koh observed that the crystal orientation of GaAs could be adjusted by manipulating the temperature of the growth process. Combining this technique with high purity growth processes like MBE and

HVPE they were able to obtain samples with losses as low as 0.025 cm-1, which proved more than adequate for nonlinear frequency conversion. The process works by using

GaAs of one orientation (polarity) as the substrate. A thin layer of non-polar germanium which is lattice-matched to both polarities of GaAs is then deposited epitaxially on top of it. GaAs of the other orientation is then deposited on the germanium, and this top layer is selectively etched away using standard photolithographic techniques and a mask

11 patterned with the desired nonlinear grating period, Λ. GaAs is then further epitaxially deposited on the surface of the GaAs stack, and since the growth follows the crystal orientation of the contacted surface the orientation patterning is preserved with each additional layer.

This technique can successfully grow orientation patterned gratings with periods as small as 20 μm and with hundreds of microns thickness, such as the sample shown in

Figure 5. Molecular beam epitaxy (MBE) is typically used to create orientation-patterned templates because it maintains the grating period better than faster growth techniques.

However MBE has a very slow growth rate, and is typically used only to fabricate the starting templates. Subsequent growth is performed using other processes such as hydride vapor-phase epitaxy (HVPE) or metal-organic chemical vapor deposition (MOCVD). In addition to flat surfaces, additional structures may be fabricated upon the template such as waveguides, and again, if the proper growth technique is chosen the gratings will propagate all the way through the structure. Our waveguide templates were grown using

MBE followed by HVPE, and the subsequent waveguide growth was performed using

MOCVD.

100 μm

Figure 5: Microscope image of a bulk OPGaAs sample, showing the periodic domains. The domains look very rough on the surface because the domains have different growth rates.

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1.6 Waveguides and integrated optics

Figure 6: AGaInAsP/InP integrated optical circuit designed for use in a 1.55 μm optical communications system36. These circuits contain many different devices all on one compact chip and are a key component of many modern optical sensing and communication systems. It is well known that an optical wave can be confined in a small region with a refractive index higher than that of the surrounding medium through the phenomenon of total internal reflection (TIR). Such a structure is commonly known as a waveguide, and is the basic building block of optical integrated circuits, which are compact and robust devices which perform complicated functions for specific applications by integration of several different optical elements. The study of optical integrated circuits, the field known as integrated optics, began in the late 1960s shortly after the invention of the laser, and since then has become a major area of research and development37. An extensive amount of work has been performed on waveguide theory, materials and fabrication, and various passive, active, and functional devices have been developed. Examples include devices such as optical couplers, filters, modulators, amplifiers, electro- and acousto- optic (EO/AO) switches, wavelength division multiplexers as well as many devices incorporating combinations of all of the above. While the vast majority of integrated optical circuits are designed for use in the fiber optic communications industry at near-IR

13 wavelengths (0.8-1.6 μm), such as the chip shown in Figure 6, they are beginning to find uses in a wide variety of applications spanning the electromagnetic spectrum.

There are several advantages to be obtained by confining a nonlinear process in a waveguide. A waveguide can confine a pump beam in a small cross-sectional area and thus maintain a high optical intensity over a long propagation length without the normal divergence associated with free-space propagation. This means that a nonlinear waveguide device can have a high conversion efficiency even with a moderate amount of input power, leading to a reduction in overall system size, weight, and energy consumption. In addition, a waveguide can be directly coupled to a fiber pump laser and its output can be coupled to an output fiber or another integrated optical element, eliminating the need for free-space optics which can greatly improve a device’s durability and mean time to failure. Another important advantage is that confining a nonlinear process in a waveguide offers new possibilities in phase matching. In addition to the conventional birefringent phasematching and quasi-phasematching used in bulk materials, one can phasematch through careful construction of the mode structure of the waveguide (so called mode-dispersion phase matching), which can extend the wavelength range and conversion efficiency of the material. The disadvantages of nonlinear guided wave devices are their increased complexity in terms of modeling, fabrication, and experiment and for these reasons no major commercial applications of nonlinear optics have incorporated waveguide structures yet.

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1.7 Organization

This dissertation is organized as follows. Chapter 2 presents the theory of nonlinear frequency conversion and waveguides. Chapter 3 covers the numerical modeling and theoretical calculations that went into our final OPGaAs waveguide design.

Chapter 4 covers the material processes used to fabricate our waveguides, and the metrology techniques we used to help facilitate this process. Chapter 5 covers the details of our OPGaAs waveguide OPA experiment and our measured device characteristics.

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CHAPTER 2

THEORETICAL BACKGROUND

In this chapter we present the electromagnetic theory necessary to understand the design parameters of our OPGaAs waveguides. There are a number of texts available on the subject of nonlinear optics17,38 as well as waveguide theory36,37,38, and obviously this chapter cannot cover the subject in the same amount of detail. The focus of this chapter is on second-order optical parametric interactions in embedded ridge waveguides, which are the interactions we are interested in for this effort. We begin by presenting the theory using plane waves and coupled-field equations, and then expand this theory to include nonlinear interactions involving waveguides and Gaussian input beams.

2.1 The nonlinear susceptibility

Nearly all introductory texts on electromagnetics introduce the related concepts of polarization and dielectric susceptibility. Because materials consist of charged particles the presence of an electric field induces a dipole moment per unit volume, called the polarization (P), related to the strength of the electric field (E) though the dielectric susceptibility (χ) by the relation:

⃑ ⃑

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Where εo is the permittivity of free space (using the standard SI notation). Equation (2.1), assumes that all materials have a linear response to field amplitude, however it turns out that materials do exhibit nonlinear responses under intense electric fields with field magnitudes comparable to inter-atomic electric fields (108 V/m), such as those created by a focused laser. By modeling the material response as an anharmonic oscillator, and assuming that the field dependence of χ is weak, one may write out the power series expansion:

⃑ ⃑

Here we have used the conventional notation where χ(1) is the first order dielectric susceptibility, χ(2) is the second order and so on. Using this expansion we may write out the total polarization as:

⃑ ⃑ ⃑ ⃑

The first term in equation (2.3) is often referred to as the linear polarization, while all the higher order terms are called the nonlinear polarization (PNL). For our purposes we restrict the discussion of the nonlinear polarization to second order, i.e. χ(2) processes, and thus our nonlinear polarization may be written as:

⃑⃑⃑ ⃑⃑⃑ ⃑

2.2 Nonlinear interactions (plane waves)

A plane wave propagating in an isotropic medium obeys the wave equation derived from Maxwell’s equations:

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⃑ ⃑ ⃑

where co is the speed of light in a vacuum, and μo is the free space permeability. Using equation (2.5) and splitting the polarization into linear and nonlinear parts we obtain the nonlinear wave equation:

⃑ ⃑ ⃑

Note here that we have replaced co with c, the speed of light in the medium (c = co / n).

Also note that equation (2.6) is a nonlinear partial differential equation in E, where the right hand side acts as a radiation source in the medium. We will now use the coupled- wave approach to solve for the various fields propagating through the medium.

For simplicity, we will take the example of three wave-mixing, which is the case we are most interested in for this work. Assuming that the total field E is a superposition of three fields of frequencies ω1, ω2, and ω3 propagating along the z direction with the same notation as defined in the first chapter:

∑

where En(z) in equation (2.7) is the complex amplitude of the field and c.c. denotes

“complex conjugate”. The nonlinear polarization may be written as:

⃑ ⃑

18

Where deff is called the effective nonlinear coefficient, and is commonly used in place of

χ(2) in writing equations for three wave mixing. Thus the resulting nonlinear polarization obtained is a sum of all the cross-product terms of the fields:

⃑ ∑

Equation (2.9) gives a series of different frequency components. Substituting equations

(2.7), (2.8), and (2.9) into the nonlinear wave equation (2.6) we obtain a single differential equation with all of these frequencies. If ω1, ω2, and ω3 are distinct (i.e. non- degenerate) then we can write three separate equations for the evolution of each associated electric field, called the Helmholtz equations. For particular cases of interest, for example OPG where ω1 = ω2 + ω3, the source term for one of the equations is related to the electric fields at the other two frequencies, thus coupling the three waves. In this particular case we obtain the following three coupled equations:

(2.10)

Where the * mark indicates the complex conjugate of the field. Before proceeding, it is convenient for us to normalize the complex envelopes of the plane waves by defining the

1/2 variables ap = Ap / (hωp/πεoconp) where np is the refractive index of the material at the corresponding frequency ωp, yielding:

19

⃑

We note that we may immediately write the corresponding intensities of the waves as:

| |

Which shows the justification for our choice of constants: in equation (2.12) ap represents the flux of photons at frequency ωp. We know that our frequency mixing process must exhibit energy conservation, and with this condition in mind we may derive equations describing the evolution of photon populations as the three waves propagate along z.

These are known as the Manley-Rowe relationships. Assuming a slowly-varying field envelope the relations we obtain from equations (2.11) and (2.12) are:

where:

⃑⃑⃑⃑ ⃑⃑⃑⃑ ⃑⃑⃑⃑ ⃑⃑⃑⃑

20

Δk is an important variable called the phase vector mismatch and represents how closely phasematched the driving field and the induced nonlinear polarization are. It will now be shown that nonlinear interactions are most efficient when Δk = 0, which is the so called phasematching condition.

2.3 Phasematching and conversion efficiency

Λ

Figure 7: Plot showing the evolution of the output field magnitude, E3, for an OPG process(2.05μm -> 4.1μm) in GaAs as a function of propagation distance through the material for the case of Δk = 0 (dashed pink) and Δk ≠ 0 (blue). Quasi-phase matching can be achieved in this case with a grating period Λ = 30 µm (shown with arrows), which corresponds to twice the coherence length of the non-phasematched ‘beat’.

21

As mentioned in the previous section the phasematching parameter Δk has a significant effect on the efficiency of the frequency conversion process. We can find the dependence of the output intensity I3on this parameter by solving equation (2.13) under the condition that a1 and a2 remain fixed. This is known as the “small-signal regime”, and results in the equation40:

This expression for the intensity given in equation (2.14) exhibits a periodic beat with a periodicity and amplitude dependent on Δk, as illustrated by the blue plot in Figure 8.

This beat-like shape represents the fact that as the three waves travel down the crystal radiation at frequency ω3 is at first generated by a spontaneous DFG process, but the intensity then decays as the newly generated ω3 photons are consumed by other frequency mixing interactions (back conversion). Looking at equation (2.13) we can see

why back conversion occurs: the sign of changes periodically in space due to the Δkz

term in the exponential. The periodicity of this function is 2π/Δk and hence the coherence length is:

From equation (2.15) we see that as Δk goes to 0 the coherence length Lc goes to infinity, meaning that the field will continue to grow exponentially throughout the entire crystal without experiencing significant back conversion. This case is represented by the pink dashed graph in Figure 8. Unfortunately Δk will normally not be zero because of the

22 dependence of k1, k2, and k3on the index of refraction at their respective wavelengths.

Under normal dispersion conditions Δk will always be nonzero.

Therefore, in order to make Δk zero (phasematch) one must somehow manipulate the index of refraction for each of the interacting wavelengths. This is normally accomplished by using birefringent crystals and controlling the polarization and incident angle of the interacting waves. As previously mentioned, birefringent phasematching is usually very limited by the dispersion of the nonlinear crystal and many crystals which possess desirable material properties in the infrared are not birefringent. In order to phasematch a material like GaAs one must develop an alternate scheme to birefringent phasematching.

That alternative is known as quasi-phasematching (QPM). The physics of quasi- phasematching can be understood if we recognize the fact that the nonlinear coefficient d can be a function of space, d(z). To represent any spatial variance in d, we may write the second order nonlinearity d in equation (2.4) as a rank 3 tensor17:

Let us now consider how this tensor behaves when it is rotated 90° about the x-axis (in other words x x, y -z, and z y) . The rotation matrix corresponding to this transformation in Cartesian coordinates is:

[ ]

23

The permittivity tensor, εij , and hence the index of refraction are given by rank 2 tensors.

These obey all of the transformation properties associated with tensors which may be found in any number of books on electromagnetics41:

where εij’ is the transformed tensor and the Einstein summation convention has been used. Since R90° has only one diagonal element(1), and since ε has only diagonal elements in the principal axis system, the only nonzero elements to the sum are i = j = α =

β and we may rewrite equation (2.18) as:

Thus the permittivity and other linear properties of the material remain unchanged under a 90° rotation, however since d is a rank 3 tensor it behaves slightly differently:

It can be shown using symmetry arguements17 that the only nonzero d-elements for GaAs are dxyz, dxxy, and dxxz. Under a 90° rotation about the x-axis, these transform as:

Equation (2.21) shows that under rotation certain elements of the d-tensor change sign, meaning that by periodically rotating the crystal we may obtain a periodic nonlinearity that changes sign while leaving the linear properties of the material unaffected.

24

A detailed understanding of QPM comes from the wave equation. We may rewrite the condition in equation (2.13) for the unrepeated pump case (where dE1 is negligible) as:

Thus the field E3 after passing through a crystal of length L can be obtained through integration:

∫

Let us now imagine that the crystal structure is periodically rotated as discussed above, such that d(z) flips sign from one domain to the next as shown in Figure 6. A one-half duty cycle square wave periodic structure like this lends itself naturally to Fourier analysis, and has the well-known series solution:

∑ ( )

Plugging this expression back into equation (2.23) and performing the integration yields:

∑

where:

25 and Λ = 2Lc is the grating period of the structure (the relation between Λ and Lc is shown in Figure 8). Assuming a fixed grating period Λ, this new Δk’ given by equation (2.26) will clearly be zero only for one given order m. Because the efficiency of the conversion process scales inversely with m, typically only first-order QPM is considered (unless the first order grating is too small to fabricate), whereby we have the relation:

Thus, in order to obtain first-order QPM we need to construct a grating period Λ that obeys the relation:

Lc

(a)

(b) Λ = 2L c

Figure 8: Illustration showing a typical bulk QPM structure, whose nonlinear coefficient is periodically modulated by inverting the crystal every coherence length Lc. The relationship between this length and the grating period Λ is also shown assuming a half-duty cycle.k = 0 1st order QPM k = 0; d =2d eff 0

26

SignalPower 2nd order QPM 3nd order QPM

No QPM

0 2 4 6 8 10

Distance (Lc)

Figure 5: Plot of signal power vs. crystal length for three diff A plot comparing the performance of birefringent phasematching and first-order QPM is shown in Figure 9. From equation (2.24) it is clear that the quasi-phasematched effective nonlinear coefficient for first order QPM is given by deff = (2/π) do. By using QPM we can obtain performance comparable to the birefringent case, only now the user has control over what nonlinear frequencies are generated through control of the grating period Λ. With the appropriate choice of pump wavelength and nonlinear crystal, quasi- phasematching allows us to engineer a material for frequency conversion in any range of wavelengths where the crystal is relatively transparent, and where the required QPM grating periods are suitable for fabrication.

k = 0 1st order QPM

k = 0; d eff =2d0 SignalPower 2nd order QPM 3nd order QPM

No QPM

0 2 4 6 8 10 Distance (L ) c

Figure 9: Plot of signal power vs. crystal length for three different phasematching conditions. Birefringent phasematching leads to quadratic growth in power with distance while quasi-phasematching results in quasi-quadratic increase of power with distance, with the effective nonlinear coefficient reduced by 2/π.

27

2.4 Optical parametric oscillation 1.1 Optical parametric oscillation

R R

L

Figure 10: Illustration depicting the basic components of a confocal OPO. The QPM material is placed in the center of two mirrors of reflectivity R, which resonate at one or more of the interacting frequencies. As discussed previously the field amplification obtained when pumping a nonlinear material is analogous to the optical gain exhibited by laser materials. Thus in a similar fashion to laser resonators nonlinear materials may be placed in a resonator to enhance conversion efficiency. As with laser cavities, there are many different ways to construct a resonant OPO structure. One of the most common configurations is the confocal resonator depicted in Figure 10, where the nonlinear material is located at the focal point between two resonant mirrors. If the reflectivity, R, of the mirrors is sufficiently large for both the signal and idler wavelengths we have what is called a doubly-resonant OPO (DR-OPO), and from equation (2.13) it is easy to derive the parametric gain in a nonlinear optical material42:

Obviously the gain depends on the intensity of the pump, and there is therefore a threshold intensity for which the gain equals the losses in the cavity similar to a lasing threshold. Of course this threshold intensity will depend on the beam profile throughout

28 the material since the intensity will not be uniform for a resonant structure. In addition, real laser beams will be Gaussian as opposed to plane waves, so this spatial profile must be taken into consideration as well. It can be shown that17 for a confocal resonator using

Gaussian beams the threshold condition is given by:

where R is the reflectivity of the OPO mirrors and δ is the degeneracy factor, a number that ranges from 0 to 1 and describes how far away one is from the degeneracy point (i.e. when ωs = ωi = ωp/2). An example calculation using the numbers for our OPGaAs OPO would have R ≈ 0.70, λp = 2.05 μm, n = 3.33, L = 1 cm, deff = 57 pm/V. This yields a threshold power of 50 W (cw), field strengths easily attainable with a focused pulsed laser. Depending on the spot size, these power levels can approach the damage thresholds of many nonlinear materials (see Table 1), so this becomes an important metric for judging which material is most suitable for a given application. This equation only considers the loss due to the mirrors, if one also includes the material losses one can show that the power output maximum is a function of length. Material losses thus limit conversion efficiency and increase threshold, and it is for this reason that material lengths longer than a few centimeters are rarely used.

29

2.5 Waveguide theory

Figure 11: Propagation content spectrum of a waveguide. Allowed modes (values of the propagation constant) are shown in red. So far we have covered the principles of nonlinear optics only in bulk materials, however the aim of this effort is to design OPGaAs waveguides so obviously we must mention the differences in this case. It turns out that the treatment of frequency conversion in waveguides is almost identical to the plane wave case, as would be expected from the plane-like behavior of waveguide modes. In general a waveguide is defined as a material with a refractive index n1 (called the core) surrounded by a material with a lower refractive index n2 (called the cladding). Total internal reflection of the core/clad interface leads to the creation of propagating standing waves called modes, which satisfy the wave equation:

⃑ ⃑ ⃑

The right side of equation (2.31) will equal zero if the electric field ⃑ does not lie along the direction of the spatial variation in the permittivity ε, in the case of a slab or a ridge waveguide this will be the case for the transverse electric (TE) modes. In this case we have the equation:

⃑ ⃑

30

Equation (2.32) is set up in the form of an eigenvalue equation, thus we might expect that the confinement of the waveguide leads to a set of discrete energy levels (modes) that can propagate through the structure. It can be shown that these modes have solutions of the form39:

⃑ ̃

Here ̃ represents the unchanging mode profile, Ai is the envelope of the field, and βi is the propagation constant of the ith mode given by:

where ni is called the effective index of the mode. This effective index turns out to be a very important parameter when discussing phasematching in waveguides. Looking at the form of equation (2.33) one can see that the field of the waveguide mode is functionally similar to that of a plane wave propagating in a material with a refractive index equal to ni. It can be shown that ni takes on discrete values when| | | | | |; these modes are called guided modes since the field exhibits a large degree of confinement within the waveguide core. If there is only one solution that lies in the region | | | | | | then the waveguide is known as single mode. Single mode waveguides boast a number of advantages over multi-mode waveguides and are desired for many applications27.

Alternatively, it can be shown that when ni lies outside this region the solutions to equation (2.33) are a continuum; these modes are known as radiation modes since they have large components present in the cladding and thus are very lossy. A plot of the

31 propagation constant spectrum is shown in Figure 12, where we have also included the consideration of negative ni (backward propagating modes).

If a component of ⃑ lies along the spatial variation of ε (quasi-TM modes for a planar/ridge waveguide), equation (2.31) does not simplify and one is left with a much more complicated problem to solve. Alternately, one may have a complex cladding geometry ε(z) such that there is no clear analytical solution to even the simplified equation (2.32). In practice these equations are almost always solved numerically by expanding the differentials using the finite-difference method. One assumes solutions of the form of equation (2.33) and makes a guess at the effective index ni. The numerical algorithm then iterates until it converges to a steady state solution, and the value of ni for this solution approximates the real solution for the effective index. Thus, the effective indices for even the most complex geometries can be found, assuming one has developed robust and accurate code.

2.6 Frequency conversion in waveguides

Looking at the form of equation (2.33) we see that waveguide modes propagate with a form almost identical to plane waves. It should be no surprise then that the results for quasi-phasematching in a waveguide are almost identical to the results for the plane wave. This is especially true when the waveguide supports only a single mode, which ensures one does not have to worry about mode overlap or the splitting of energy between modes. In this case the only difference between the waveguide and bulk case is that β’s show up in our expression for Δk37:

32

Here βi refers to the propagation constant corresponding to the idler wavelength, not the propagation constant of the ithmode. Thus, our expression for the grating period Λ in a single mode waveguide is given by:

Thus if one is able to calculate the effective indices corresponding to the pump, signal, and idler wavelengths one can calculate the appropriate grating period needed for quasi- phasematching. As we will see, actually calculating neff is not a simple task for waveguides with geometries like the ones we have chosen, and this calculation constitutes a significant part of the design of nonlinear waveguides.

33

CHAPTER 3

WAVEGUIDE MODELING AND DESIGN

The goal of our proposed experiment is to design an OPGaAs waveguide to use as a nonlinear infrared frequency conversion device. To function effectively, the waveguide should ideally be single mode across the entire frequency bandwidth of the device (2-10

µm). In addition, the waveguide needs the appropriate grating period Λ to phasematch the interacting wavelengths. In order to create our design, we used numerical methods to solve the equations derived from the theory discussed in the previous chapter. This allowed us to calculate the parameters for both the orientation template and the waveguides themselves. These designs were then sent off to their respective crystal growers for fabrication. Ultimately the success of this experiment rests on the accuracy of our initial design, making it a crucial step in the experimental process.

34

3.1 2D computational mode solving

W Optical Mode GaAs (1.5µm)

Al0.25Ga0.75As (0.5µm)

GaAs (3µm)

Al0.30Ga0.70As (5µm)

GaAs

Figure 12: Waveguide design used for modeling simulations, and corresponding structure as shown in LIGHTs. The fundamental mode propagates in the GaAs core, confined by the AlGaAs cladding and the GaAs rib. As mentioned in section 2.6 in order for our waveguide design to be efficient we require it to be single mode across the mid-IR band. As explained in chapter 2 a waveguide is considered single mode if it only has one solution for neff that lies between the values of the core and clad index (ncore

35

Figure 13: Results of our initial simulations in COMSOL. The shape of the fundamental mode is obtained (top) and we obtain a plot showing the waveguide is single mode (bottom). The circles on the right represent the effective indices of the fundamental mode, while the crosses represent the effective indices of the second order mode. The core and clad indices are indicated with the blue and red lines.

36

Several different waveguide models were initially studied, and finally the design shown in Figure 12 was settled upon. The waveguide in Figure 12 is an embedded ridge waveguide (meaning that the core is embedded under the ridge) with the dimensions and material composition shown. These parameters were chosen based on a series of 2D mode simulations run in COMSOL (specifically the RF module), a commercially available finite-element equation solver43, and adaptation of the waveguide structure reported by Oron et al51. These simulations showed that if the waveguide had our chosen parameters it would be single mode from 1.5 all the way to 14 µm. We determined that the waveguide was single mode by solving for the effective index of both the fundamental and second order modes as a function of various design elements. The plot in Figure 13 shows these effective indices as a function of rib width, and we see that at 2

µm the second order modes (red crosses) never rise above the bulk index of the cladding

(red line).

Similar simulations were run to look at the behavior of the waveguide as a function of x, layer thickness, and ridge height, and each of our parameters was chosen to be sufficiently single mode to account for any errors that might occur during our fabrication process. A thin layer (0.5 µm) of Al0.25Ga0.75As was chosen for the top cladding to ensure single mode operation as well as to allow the upper ridge to better confine the mode shape. The bottom cladding was made much thicker (5 µm) and given a slightly higher aluminum concentration to prevent the optical mode from leaking into the

GaAs substrate. The ridge width was also found to have some impact on the waveguide performance. When the width was 8 μm the beam was slightly more confined and was single mode up to 14μm wavelength, however a ridge width of 10 μm was found to yield

37 lower waveguide dispersion. Ultimately the final design incorporated both ridge widths, to ensure we could get both properties if desired. Credit for much of this early design work belongs to the researchers in Dan Botez’s group at the University of Wisconsin

Madison, however all of these calculations were independently verified by the author.

Once we were satisfied with our heterostructure design our next step was to calculate the effective indices for a wide range of signal and idler pairs in order to determine our phasematching grating period Λ. As mentioned in the previous chapter one cannot derive an analytic expression for the effective index in an asymmetric waveguide like ours, however a solution can be approximated using numerical techniques. To accomplish this we used the 2D mode solver software in the program LIGHTs. LIGHTs is an online software program developed by Dr. Andrew Sarangan at the University of

Dayton that uses a finite difference inverse power method to converge to a solution for the effective index44.

The inverse power method is a commonly used algorithm for solving differential equations in a number of different applications45, here we will focus on its use to obtain solutions of the wave equation. One of the main advantages of the inverse power method is that it converges quickly if one makes a sufficiently accurate guess to the solution.

Since we know β for the fundamental mode will be closest to βcore we can make an educated guess to the solution before we even start iterating. It can be shown that for piecewise-continuous refractive index distributions, equation (2.31) reduces to46:

38

where T is the transverse Laplacian ( , and we havechosen our coordinate

system such that propagation is in the z direction. The Ex/y designation signifies the difference between quasi-TE and quasi-TM modes. For our choice of coordinate system

(with y being along the direction of the waveguide layers) Ey designates a quasi-TM mode while Ex is used to solve for quasi-TE modes. This eigenvalue problem may be re- written in matrix form as:

[ ] [ ] [ ]

If we assume that the cross-terms between the quasi-TE and quasi-TM modes are small

(Rxy ≈ Ryx ≈ 0), we may rewrite equation (3.2) in generic form:

Where A is a pentadiagonal matrix (in the 2D case), and m and n represent positions in a predetermined (x,y) mesh-space. To solve for this matrix a reasonable initial guess for the field distribution (E0) and the mode propagation constant (β0)are made based on what is known intuitively about the problem. For our computations we assumed the initial field distribution was a uniformly filled core region, and the initial propagation constant was equal to ncoreko. These guesses keep iterating until they converge to a solution of equation

(3.3) using the inverse-iteration algorithm:

39 where I is the identity matrix and ηm is a normalization constant chosen such that the largest element in Em is equal to 1. When the gradient of η becomes sufficiently small between iterations of equation (3.4), an approximate solution for the effective index and field distribution is obtained.

Figure 14: LIGHTs generated mode profiles and corresponding field cross-sections for the pump beam (λ = 2.05 μm). Note the Gaussian symmetry of the x-cross section (left) vs. the asymmetry of the y-cross section (right). All of the above equations are built into the code of LIGHTs, so in order to obtain the effective index and mode profile the appropriate refractive index geometry, wavelength of interest, and guess functions are entered into the software. For our calculations the algorithm takes on average 3-4 minutes to converge to a solution, which allows us to calculate the effective indices for a large number of wavelengths in a short period of time. Examples of results from LIGHTs are shown in Figure 14. In addition to these plots of the field the program also gives a value for the effective index and several

40 movie files showing the convergence of the field. Once enough simulation data have been collected, we can generate tuning curves by using equation (2.35).

It turns out that the most difficult aspect of calculating the effective index in

LIGHTs is accurately estimating the bulk refractive index of the AlxGa1-xAs layers. The dispersion of GaAs in the infrared has been extensively studied and the Sellmeier equation given by Skauli47 has been verified by a number of authors over the

7,17,19,30 years . The behavior of AlxGa1-xAs is a little more difficult to model since the index of refraction is dependent on two variables, the wavelength λ and the aluminum concentration x. While several Sellmeier-like equations for AlxGa1-xAs can be found in the literature48,49,50 these references are typically only accurate to three decimal places.

This is simply not accurate enough for us to reliably determine the grating period Λ, if one looks at equation (2.35) it is apparent that since neff is in the denominator small changes in neff can cause large changes in Λ. We must also remember that although our pump will be traveling in the GaAs core, the bulk behavior of AlxGa1-xAs still has a significant effect on the modal effective index. Thus, in order to ensure the validity of our design we ran a series of simulations using slightly different equations for the bulk index of AlxGa1-xAs to see how much these changes affect our results when we calculate our nonlinear tuning curves.

41

Nf(x,) = nf(x,)*1.022 3.2 OPGaAs waveguide tuning curves

UW data, 10μm ridge UW data, 8μm ridge Soreq data(no multiplier), 10 μm ridge Soreq data (no multiplier), 8 μm ridge Soreq data (w/ multiplier), 10 μm ridge Soreq data(w/ multiplier), 8 μm ridge

Figure 15: Theoretical waveguide tuning curves based on our effective index calculations using six different AlGaAs Sellmeier equations (pump wavelength 2.05 μm).This graph indicates the significant effect even a slight difference in the Sellmeier equations can have on the grating period Λ. The red line indicates the range of grating periods present in our design. After compiling results from over 300 LIGHTs mode solver simulations our final result was the tuning curve plot shown in Figure 15. This plot shows the behavior of

Λ(λ), for each point on the y-axis there are two corresponding wavelengths representing the signal and idler pair (our pump stays fixed at 2.05 μm, so there is a degeneracy point at 4.1 µm). This conveys two important pieces of information, one it tells us what output wavelengths we can reasonably expect from these waveguides. According to equation

42

(2.30) conversion is most efficient when operated close to the degeneracy point. Looking at Figure 16 it is clear that we can reasonably expect output in the 3-5 μm range when operating near degeneracy. Secondly, this graph tells us what grating periods we will need to fabricate in order to obtain OPG. Looking at the tuning curves in Figure 15, it is clear that if the fabricated grating period is too small no frequency generation will occur.

Therefore we must select a reasonable range of grating periods based on our tuning curve results to obtain a working design. Based on the results seen in Figure 15 we selected the range of grating periods going from 33-42 μm, as indicated by the red line on the graph.

The three different Sellmeier-like equations we used for AlxGa1-xAs to generate the plots in Figure 15 were based on previous work by other research groups.

Our collaborators at the University of Wisconsin developed a model based on an exponential fit of the index of refraction data from one of the few extensive studies of

48 AlxGa1-xAs in the mid-IR available and matched it to the well-established results from ref. [47] (forcing an intersection of the two plots at the point where x = 0). This model was the basis for all of our COMSOL designs, but we also wanted to compare our model to one used by a group at Soreq51,52, who have recently published findings on OPGaAs waveguides.

The method used by the Soreq group first adjusted the values of the constants used in the modified Sellmeier equations given in47 in order to better fit the empirical measurements presented in the same paper. Then a linear correction was made in order to fit the AlxGa1-xAs index data to the GaAs data from ref. [47] at the point x =0, given by the equation:

43

nf(x,) = n(x,) – n(0,) + nGaAs() (3.5)

Where n(x,λ) are the values generated by the modified Sellmeier equation in ref. [48] and nGaAs are the values generated by the equation in ref. [47]. The research group at Soreq found that equation (3.5) predicted grating periods very close to the ones in which they observed second harmonic generation (SHG).There was however a slight difference between the predicted and measured SHG frequencies. In order to fit their model to their frequency measurements the Soreq group added a 2.2% correction, namely:

nfinal(x,) = nf(x,)*1.022 (3.6)

Figure 15 shows the calculated tuning curves for refractive indices obtained by the model from the University of Wisconsin, and the model from Soreq with and without this 1.022 multiplier. It is clear that all three tuning curves show the same basic shape, but are shifted along the Λ axis (as would be expected). The results of the Soreq model without the multiplier are close to those predicted by the UW model, and are well within the design tolerances of our OPGaAs wafer. However, when the 1.022 multiplier is taken into account the grating period changes dramatically (the degeneracy point goes from 38

μm to 48 for the 8 μm ridge). This illustrates the importance of correctly calculating the bulk indices of our waveguide materials, a 2.5% increase in the index of the cladding leads to a 26% increase in grating period size. While this finding is somewhat troubling, there are some issues with the1.022 multiplier used by the Soreq group as a fitting parameter.

44

First, there is no physical basis for this extra factor aside from three frequency measurements made in a single paper. Experimental error easily could account for this

2.5% margin quite apart from the index calculations. Secondly the Soreq group did not use this multiplicative factor for their waveguide simulations or grating period calculations. This is apparent when one notes that their published waveguide effective index is less than the bulk indices of both the core and cladding when this multiplicative factor is counted (and of course in order to have guidance one requires that ncore

Due to the questionable basis upon which this final step is made, we decided to neglect this factor for our design calculations. Even if the Soreq model is valid, we will at the very least have verified their method for calculating the refractive index and we can always use temperature tuning to try to get output even if our grating periods won’t work at room temperature. Regardless, these tuning curves have finally given us the last piece we need to complete our design, the desired grating period Λ.

45

3.3 Template design

Figure 16: OPGaAs orientation template grating mask design. Gratings are 1mm wide and have grating periods (Λ) ranging from 33-42 μm in 0.2 μm increments. Also shown is an overlay of the 2’’ wafer that the mask will be used for, to get a sense of how the grating periods will be distributed. With our theoretical calculations complete, we were able to finish a design for the orientation template and the waveguides. Not only were our computational results used to complete our design, but we also collaborated extensively with the crystal growers to make sure our layout was compatible with each of the materials processes involved. Our orientation patterning was done by P. Schunemann’s group at BAE systems in New

Hampshire30,53 using molecular beam epitaxy (MBE). The final template design sent to them for fabrication is shown in Figure 16. 47 Grating periods ranging between 33 and 42

μm were fabricated onto a 2’’GaAs wafer in increments of 0.2 μm. The wafer overlay is shown in the figure, and the central ring is the portion of the wafer that will actually be usable due to the way the material is mounted in the growth chamber. This design will maximize the number of grating periods produced in the range obtained from our tuning curves in Figure 15, and will help cushion us from any errors in our Λ calculations.

46

Figure 17: Detail of OPGaAs grating mask design showing how the spacing between waveguide ridges will be varied in order to allow for easy identification of grating period. One potential issue with the design shown in Figure 16 is that a grating period difference of 0.2 μm is nearly impossible for us to measure with our available microscopy equipment. Therefore we needed to incorporate something into our design that will allow for easy identification of grating period. We decided it would be easiest to incorporate this feature into the waveguide template itself since this will be the last stage of growth. The mask design we created is shown in Figure 17. As mentioned previously each grating period will have an 8 and 10 μm ridge waveguide fabricated on it. Our solution to the issue of identifying the grating period Λ was to have the distance between these two ridges vary for each grating period. Each adjacent grating period in our design will have an additional 4 μm of space between the two ridges, starting at d = 300 μm for the 33 μm grating. Since a difference of 4 μm is measureable with an optical microscope this design gave us a simple way to determine the grating period of the waveguides once the wafer is diced up, all we have to do is measure the distance between the two ridges.

47

This mask design was printed on glass using E-beam lithography, and was sent to the

University of Wisconsin Madison to use in their photolithographic etch process (the final step where they make the ridges). This mask was used for all of the template runs that were made, as discussed in Chapter 4.

3.4 Other design considerations

Al0.25Ga0.75As cladding (n2)

θmax2 θc1 θc2 θc1 > θc2 GaAs core (n1) θ θ < θ max1 c2 c1 n1 > n2 > n3

θ > θ Al0.3Ga0.7As cladding (n3) max2 max1

Figure 18: Diagram illustrating the concept of numerical aperture in a waveguide with an asymmetric cladding. Because of the cladding asymmetry, the critical angles (θc1 and θc2) are different at the two interfaces. The acceptance cone (numerical aperture) is determined solely by the interface with the largest critical angle (index closest to the core).

When designing a waveguide, there are considerations that must be made in addition to the choice of materials and device geometry. One major consideration is what is known as the numerical aperture or acceptance cone of a waveguide. The numerical aperture is a dimensionless number that characterizes the range of angles over which a system can accept or emit light. The solution of this problem is routinely covered in optics textbooks39 and is described by the equations:

√ √

where n is the refractive index of the coupling medium (in our case air, n ≈ 1), n1 is the refractive index of the core, and n2 is the refractive index of the cladding.

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Equations (3.7) and (3.8) assume that the cladding is symmetric on both sides of the waveguide, but this is not the case for our design. As illustrated in Figure 18, since our waveguide has an asymmetric cladding we require that the ray enter at an angle such that it strickes both surfaces at an angle greater than the critical angle for both claddings

(θc1 and θc2) in order to experience total internal reflection (TIR). Thus, it is the cladding with the largest critical angle (or whose index is closest to the core) that will determine the acceptance cone in an asymmetric waveguide. In our case, this is the Al0.25Ga0.75As cladding, whose refractive index is 3.201209595 at 2.05 µm based on the UW model, combined with the refractive index of the core (3.336295235) based on48 we have:

√

This is a much larger numerical aperture than any of the coupling optics we will use in our experimental setup (typical NA for a microscope objective is 0.2), thus we will not have to concern ourselves with NA matching for our experiments. Virtually any optic used normally incident to the waveguide will couple into it, although if the numerical aperture of the optic is too small mode overlap can become an issue.

The last consideration we must make about our waveguide design is how robust it is to changes in the structure. Fabrication of microstructures is not an exact science and it is quite possible that there could be defects in our finished samples. Changes in the alloy concentration, layer thicknesses, QPM period, and ridge dimensions can all impact the effective index of the waveguide modes and ultimately the performance of the device.

We ran a series of simulations to determine what the effects of these changes would be and found that our design is quite resistant to design defects. A change of alloy

49 concerntration for both claddings of +5%, for example, only results in a 1 µm change in the needed grating period for phasematching. Similar results were found for layer thicknesses and ridge dimensions as well. Our choice of model for the refractive index of

AlxGa1-xAs is more significant than any flaws caused by the manufacture of the devices, and so we can be confident that our devices are resilent to any errors that could (and as we shall see -- did) occur.

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CHAPTER 4

WAVEGUIDE FABRICATION, PREPARATION, AND ANALYSIS

As mentioned previously, our orientation templates were fabricated by BAE systems and then sent to the University of Wisconsin Madison to have waveguides fabricated on top of them. While we were not directly involved in either of these fabrication processes they are an important part of waveguide device development and deserve mention. Rather than cover all of the details of the fabrication processes this chapter will focus on our involvement, including analysis of the finished samples and preparation of the materials to be used in our experiments.

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4.1 Waveguide MOCVD growth

Figure 19: Illustration of our OPGaAs waveguide structure (left) and a picture of the MOCVD chamber used at UW to fabricate it (right). As mentioned previously our waveguide structures were fabricated using

MOCVD, a gas-phase growth process that does not require a clean room or a vacuum chamber making it ideal for the growth of metastable alloys such as AlGaAs. The orientation-patterned template is mounted in the chamber shown in Figure 19 and acts as the seed crystal. Gases are then flowed over the templates, reacting on the surface to form new layers. Because the growth will follow the orientation of the surface of the wafer, the nonlinear domains will propagate through the whole structure as shown in the illustration in Figure 19.GaAs is grown through the mixture of tetramethylgallium (TMG) and arsine in the following chemical reaction:

Ga(CH3)3 + AsH3 = GaAs + 3CH4

Similarly AlGaAs is grown through the addition of tetramethylaluminum (TMA) to the reaction given in equation (4.1). To determine the aluminum concentration of the alloy layers x-ray diffraction is used in combination with Vergard’s law, which gives a linear

52 relationship between the lattice constant and the unit cell volume55. On a visit to the UW campus we questioned the accuracy of this assumption because of the importance of the refractive index of the AlxGa1-xAs layers to our grating period calculations. The crystal growers made a literature search and found a correction to Vergard’s law56, written by the same group whose work was the basis for our AlxGa1-xAs refractive index model. The relationships from this paper were used for all of the growth processes for templates discussed in this work.

Figure 20: Diagram and photographs depicting the chemical mechanical polishing (CMP) system employed by UW. By polishing the template after each layer of growth we were able to overcome the corrugation issues seen in previous attempts to manufacture OPGaAs OPOs. One of the major difficulties associated with growing structures in orientation patterned materials is that the different crystal orientations grow at different rates and with different morphologies, which causes an uneven top surface after growth. A number of previous efforts to achieve OPO in OPGaAs waveguides have failed due to the relatively high losses associated with these corrugated layers57,58,59,60, so this was a major problem we needed to address for our devices. To counteract these problems the group at

UW utilized a technique known as chemical mechanical planarization/polishing (CMP),

53 an advanced polishing technique that can yield surfaces with rms roughnesses lower than

1 nm. The process is depicted in Figure 20. The wafer to be polished is held in a chuck above a spinning polishing pad that is continuously bathed in a chemical slurry solution.

The chuck is then lowered onto the polishing pad with a very low contact pressure (1-2 psi) so that the wafer does not actually contact the pad but instead hydroplanes on the slurry surface. The centrifugal force of the spinning pad spreads the slurry evenly over the wafer, resulting in a very flat contact surface. The material removal rate depends on many factors, and has to be determined experimentally, but is typically on the order of

Figure 21: Photos of the cleanrooms at UW where our waveguide etching was performed. The etch process must be performed in a clean facility to prevent dirt from contaminating the polished surfaces and photoresists. 1 µm of material per hour. Once the layer was polished down to the appropriate thickness for our design, the wafer was placed back into the chamber for another layer of growth.

The resulting process takes about a week to complete, with each layer of growth (4 total) taking about a day. Unfortunately UW did not possesses any equipment capable of measuring the surface quality of their wafers after polishing, so we had to provide this feedback for them as discussed in section 4.3.

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Figure 22: Scanning Electron Microscope (SEM) images of waveguide ridges made with ECR etching (left) and ICP etching (right). The ridge fabricated through ICP has much more rectangular sidewalls, and does not exhibit the detritus found in the ECR etched sample. Once all the layers were grown, the final step of the process was to etch the ridges out of the top layer of GaAs using photolithography. These processes were carried out in a class 100 clean room as shown in the pictures in Figure 21, and initially consisted of a combination of dry etching through electron cyclotron resonance (ECR) and wet etching with boron trichloride (BCl3). While this process works well for bulk GaAs, we found that it resulted in waveguide ridges that were trapezoidal rather than rectangular, and also left a residue on the surface of the wafer. This detritus was found to be methane building up in the etcher’s solenoid valve, so UW switched to using an inductively coupled plasma

(ICP) etch process for the subsequent templates, which resulted in much improved ridge quality as shown in Figure 22. Once the ridges were formed, the completed wafers were packaged and sent to our labs at Wright Patterson Air Force Base (WPAFB), where we analyzed the samples to provide UW feedback on their growth process.

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4.2 Template results and analysis

Figure 23: Photo of the first delivered waveguide template (left) and an SEM image of one of its ridges (right). The first template had a number of issues, including a contaminated surface and trapezoidal ridges. The first template we received from UW had a number of issues and was unfortunately not useable for our experiments. The wafer, shown in Figure 23, was covered with a large amount of methane emulsion and also exhibited a large number of pits at the domain boundaries. In addition, there were errors with the etching process resulting in trapezoidal ridges, also shown in the Figure, which were not the proper dimensions or shape. Although our computational models show that this will not have a significant effect on the effective index, the other issues with the template will, particularly the pits which we found were more than 3 µm deep, penetrating the waveguide core. Since the template was useless for frequency conversion, we decided to use it to test our metrology and wafer dicing equipment, discussed in the next section.

After receiving feedback on the first template, the growers at UW changed over to

ICP etching as discussed previously. The resulting second template, shown in Figure 24, while free of the contamination seen in the first template exhibited many more pits than

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Figure 24: Microscope image of the second template, showing a very large defect cluster. The pit defects seen in the previous sample were significantly more prominent in this growth run. before. In addition, there were very large defect clusters formed on the template that rendered much of the wafer unusable. While it did not look like this template would yield any usable devices either, we decided to have it diced up and try to see guidance nonetheless. Unfortunately an accident in the lab resulted in the whole wafer being broken before we could have it cut into smaller pieces, and the entire template was lost.

We were able to use fragments of the wafer for testing dicing and polishing equipment, which combined with scraps from the first wafer helped us avoid damaging anything from our third and fourth delivered templates.

Figure 25: Nomarski micrographs of an OPGaAs orientation-patterned template (left) before and (right) after HVPE growth showing how this process seems to ‘heal’ over the defects in the template.

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The source of the pit defects at the domain boundaries remains a bit of a mystery.

BAE Systems claims they have never seen these defects in any of the growth runs they have performed using MBE, and therefore the problem must be with UW’s MOCVD process. UW on the other hand claims that inherent defects in the templates supplied by

BAE Systems are the source of the defects. To support this claim UW did an in-depth analysis of the orientation patterned templates (before growth) using Nomarski microscopy. They found that small defects (about 1 µm in diameter) were present at the domain boundaries in the templates, as shown in Figure 25. Since these defects are localized on the domain boundaries much like the pit defects seen in the finished samples, it would appear that they are the cause of the pits. To confirm this theory a layer of HVPE growth was performed on the template, since HVPE is known to ‘heal’ over defects much better than MOCVD. The results, also in Figure 25, show almost no defects present after 20 μm of growth. This confirms that the pits present in our current samples are most likely caused by the small defects present in the templates and are not a result of any problemswith the growth process itself, other than the fact thatMOCVD is much more sensitive to defects (the mechanism behind this drawback is not well understood64).

Unfortunately UW is unable to perform HVPE growth on 1’’ wafers, but this does indicate a method we could use in future waveguide development to avoid the pitting problem. BAE has also been contacted about these defects, and they have begun their own investigation into the cause.

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Figure 26: Microscope images of the (left) third and (right) forth delivered waveguide templates. While the third template still exhibited a significant amount of pitting, it did not have the defect clusters seen in the second wafer. The forth wafer is nearly defect free.

The method that UW finally settled upon to minimize these pit defects in the next deliverable template was to perform an excessive amount of growth and then CMP the top 10 µm or so of material, with the hopes that the defects would not propagate very far below this sacrifical layer. The subsequent third and fourth delivered templates, shown in

Figure 26, showed significant improvements in terms of surface quality and defect density. While the third template still showed a significant amount of pitting, the pits were found to be much shallower (about 1.0 µm deep), and they did not cluster around the waveguide ridges themselves. This template was diced up and used in our early OPA experiments (discussed in the next chapter), although we were not successful in witnessing guiding in these samples.

The fourth template that was delivered to us was nearly defect free, and had a surface rms roughness of 1 nm. This template was substantially better than the third, and thus was used for nearly all of our subsequent experiments. The only flaw with the fourth delivered template was that there was a slight error in the final polishing step, such that

59 the ridges were only 0.5 µm tall instead of 1.5 µm. However the sidwalls were very rectangular (about a 75° sidewall angle), so the effects on the mode shape and effective index were not significant. While this template was not perfect, it came closest to our design specifications.

4.3 Sample preparation and surface metrology

Figure 27: Photograph of the AFM used at UC (left) and an AFM image of a sample from the third wafer (right). Metrology measurements like these were crucial for providing UW feedback on their growth processes.

When each waveguide wafer was delivered to us, we performed a series of metrological scans to determine a number of features such as the rms surface roughness, ridge dimensions, grating period, and pit depth in order to provide UW with feedback on how each growth run came out. As mentioned previously UW lacked the equipment necessary to make these measurements on a 2’’ wafer, so our contributions on this front were crucial to the success of subsequent growth runs, especially the fourth wafer.

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Figure 28: SEM images taken at UC of waveguide ridges from the fourth template. These images were used to determine the sidewall angle and the depth of some of the pit defects. We used a number of devices to measure surface quality including atomic force microcopy (AFM), as shown in Figure 27; scanning electron microcopy (SEM); and white light interferometry. Because of the amount of time involved with AFM and SEM measurements, many of these data were collected by B. Reynolds, an undergraduate at the University of Cincinnati who made the measurements as part of his senior project. A large amount of AFM data were collected on all four templates, from which we were able to determine that the pits in the third and fourth templates were not nearly as deep as the previous defects seen, confirming that UW’s efforts to eliminate the pits were successful.

These measurements also provided accurate values for the ridge sidewall angles, as shown in Figure 28, which was useful feedback on the changes UW made to their ridge etch process.

In addition to the AFM and SEM measurements made at UC, we utilized a Zygo

NewView 7300 white light interferometer at WPAFB. The interferometer, shown in

Figure 29, operates in a manner similar to a normal white light microscope. The only difference is that the microscope objective contains a Michelson interferometer, which

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Figure 29: Photo of the Zygo white light interferometer (left) and an example 3D plot obtained from the scan of a waveguide ridge. The spikes seen in the 3D image are specks of GaAs left on the surface after dicing. causes interference fringes to appear when the surface of the sample is exactly one focal length away from the objective. Because these fringes are very sensitive to position, by scanning the objective up and down and taking a series of images a map of the surface topography can be produced. This near-field method of measurement has extremely high resolution in the height dimension (0.1 Å), while being limited to normal optical microscope resolution in the other two dimensions. The main advantage of the Zygo over other measurement techniques is that it is extremely fast, taking only a few seconds to create a complete scan, such that many scans across the surface of a sample can be made.

This device allowed us to make a series of rms roughness measurements before and after we diced up our samples, from which we found that the rms roughness of the diced samples from the fourth template was only 5 nm (increased from 1 nm before the wafer was cut, see Figure 29), well within our goal of 10 nm rms roughness. With these measurements finalized and the wafer diced into usable pieces, the next step was to prepare the sample surfaces.

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4.4 Polishing and cleaving

Figure 30: Microscope image of an OPGaAs waveguide sample after being diced. The obviously rough surface will result in significantly increased scattering and a reduction in damage threshold. Completed waveguide samples were delivered by the University of Wisconsin as whole wafers. It was then necessary to turn the wafers into samples suitable for optical experiments. Since OPGaAs is not monocrystalline, it cannot be cleaved as easily as bulk

(unpatterned) GaAs so a diamond dicing saw was used to cut up the wafer into small rectangular pieces about 2 cm x 1 cm in size. While dicing the wafer into small pieces proved to be relatively simple, the resulting end surfaces left much to be desired, as shown in Figure 30. Such a rough surface would introduce large scattering losses on top of GaAs’ already large Fresnel reflection, as well as reducing the damage threshold, making it necessary to polish the entrance and exit faces of the waveguides. To determine exactly how much of an effect polishing has on a sample, we performed a small experiment where we compared the transmission through a bulk OPGaAs sample before and after polishing. The results, shown in Figure 31, indicated that a polished sample exhibited almost exclusively Fresnel losses, while an unpolished sample transmitted

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Figure 31: Plot showing input vs. transmitted power for a bulk OPGaAs sample before and after polishing. We found that polishing triples the transmission and doubles the damage threshold. only a third as much power. In addition, we found that the damage threshold of an unpolished sample was half that listed in Table 1, confirming the importance of good surface quality for power handling as well.

The problem with having OPGaAs polished, whether bulk or waveguide, is that a majority of vendors refuse to work with the material at all due to potential health risks.

When GaAs is polished the removed grains of material are small enough that the bonds can be broken apart by a polar liquid such as water. This leaves any polishing runoff contaminated with arsenic (As), which is known to be very hazardous to human health and the environment. These risks can be mitigated by using protective equipment and proper waste disposal methods, however many third party vendors still eschew polishing any samples that can break down into hazardous materials (such as GaAs and ZnSe).

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Figure 32: Microscope images comparing the bulk OPGaAs polishing results from a commercial vendor (left) and our own in-house efforts (right). Only one vendor could be found who was willing to polish the end facets of our OPGaAs samples and the results they obtained are far from adequate as shown in Figure 32. This led us to develop our own in-house method of polishing in order to obtain bulk and waveguide samples suitable for our experiments. We tried a series of different methods like CMP, hand polishing, and lapping, and we were finally able to create a working recipe using an Allied Multi-Prep polishing machine, shown in Figure 33. This device allowed us to polish bulk waveguide samples to surface rms roughnesses less than 10 nm, as indicated by the picture in Figure 32, which is well within the 10-2 scratch/dig specification normally used for samples pumped by high power lasers. We were not able to successfully polish any waveguide samples, however, due to how thin and fragile they are compared to bulk samples. Every method we tried just resulted in more broken samples, eating up much of the leftovers from our first and second templates.

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Figure 33:(left) Allied Multi-Prep polishing machine. (right) A bulk OPGaAs sample mounted with the machine running. This machine uses a series of progressively finer grits to polish a surface flat. Because of our inability to polish the waveguide samples, much of our initial experimental work was carried out with the raw, diced surfaces. Results with these samples were unsatisfactory, so we began investigating ways to cleave the samples. We tried a number of different techniques and were finally successful thanks to the help of another research group at WPAFB. They allowed us to use their Loomis automated cleaving machine, shown in Figure 34. This device allows very precise control of the scribe, allowing us to cleave around our waveguide ridges. We found that

Figure 34: Loomis automated cleaver. The sample is placed on a sticky matt (right) and a diamond scribe is used to make a very small incision (10 µm) in the crystal surface at a set pressure. A roller is then moved over the sample at a user-specified pressure to propagate this incision across a crystal plane.

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Figure 35: (left)Cleaved waveguide sample showing how well the cleave propagates along the sample.(right) Microscope image of the cleaved sample surface. backside polishing the waveguide substrate down to a thickness of 100 µm combined with a 1.1 psi pressure setting on the roller resulted in very clean, repeatable cleaves, as shown in Figure 35. With this method in hand we had recipes for preparing the end facets of both bulk and waveguide samples, and preparations for our waveguide experiments were complete.

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CHAPTER 5

EXPERIMENTAL PROCEDURE AND RESULTS

In this final chapter we discuss the waveguide experiments. The goal is to demonstrate nonlinear gain in a waveguide structure and to measure its propagation losses, validating our design. To this end, we constructed a tunable bulk OPGaAs OPO seed source, so we can tune the input signal wavelength if necessary to phasematch to the gratings on the waveguide sample.

5.1 Experimental setup

Tm:Ho:YLF pump laser Bulk OPGaAs OPO

3-4 μm band-pass filter

2.05 μm

3.58 μm Power meter

4.80 μm Spectrometer Waveguide positioner and focusing objectives

Power meter/IR camera

Figure 36: Waveguide OPA experiment. A Tm:Ho:YLF laser is used to pump a tunable OPGaAs OPO which is then used to seed the waveguides.

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Figure 37: Photos of our Tm:Ho:YLF pump laser. The crystal is housed in the cold finger of a Dewar (left) and suspended between two turning mirrors inside (right). The design of the waveguide OPA experiment is shown in Figure 36. A yttrium lithium fluoride crystal doped with 5% thulium and 1% holmium (Tm:Ho:YLF) pumped by a fiber-coupled diode laser array is used as the pump source65. This crystal is mounted in a cryogenic housing and operated at a temperature of -143°C (130 K) in order to achieve efficient population inversion as a quasi-three-level system. This housing is shown in Figure 37, where the crystal can be seen suspended in the copper cold finger of the mount. When assembled, the mounted crystal hangs between two dichroic turning mirrors, which transmit the diode laser input into the crystal (λ = 792 nm), while reflecting the laser wavelength to form a resonator. The backside of the crystal is coated to transmit this input but reflect the fluorescence wavelength (λ = 2.05 µm), acting as the laser incoupler. The housing includes two identical dichroic mirrors to permit pumping from either or both sides of the crystal, and the use of a discrete HR mirror placed outside

69 of the housing. The outcoupler mirror of the laser cavity is placed outside the Dewar for ease of alignment and to allow for an acousto-optic Q-switch.

Figure 38: Output spectrum of our Tm:Ho:YLF laser. A single lasing mode is observed at 2051.46 nm, with a spectral width of 0.96 nm. The spectrum of the pump laser, shown in Figure 38, is single mode with a fairly narrow linewidth, making it an ideal pump source for materials with a moderate phasematching bandwidth like OPGaAs (approximately 3-4 nm).When pumped from both ends at full power this laser can produce 15 W of CW output power. With the Q- switch turned on, it operates with a pulsewidth of 70 ns at a 1 kHz rep-rate, yielding peak intensities more than strong enough to initiate frequency conversion in OPGaAs.

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Downstream of the pump laser is a variable attenuator consisting of a waveplate followed by a polarizer, which allows us to control the pump power to the OPGaAs OPO to prevent damage. The remainder of the pump beam is split off down a second path where it can be directed into the waveguide samples. The OPGaAs OPO cavity consists of two 10 cm focal length CaF2 mirrors, one is coated to be transmissive at the pump

(incoupler) and the other is highly reflective at the signal and idler wavelengths (λ = 3-5

µm), as discussed in the theory section. At maximum pump power this OPO can produce

30 mW of power (approximately 20 mW of signal), with a pulse width of 65 ns, a bit shorter than the pulse width of the pump (70 ns). This output is then passed through a filter which blocks the idler, and the remaining signal is steered into the waveguide,

Figure 39: Photos of the waveguide arm of our experiment. Our waveguide chip is placed between two microscope objectives. The first focuses the input beams down to a very small spot size, and the second collimates the output. collinear with the pump beam. The waveguide sample is placed between two microscope objectives, which focus the pump and signal beams down to a very small spot size (30

µm), as shown in Figure 39 in order to couple to the mode of the waveguide. The output

71 is then collimated by the second objective, and steered into a Horiba i550 imaging monochromator in order to measure spectral profile and intensity. It should be noted that alignment of this system required considerable care due to the number of optical elements, as shown in Figure 40. The co-alignment of the pump and signal beams into the waveguide was particularly difficult, and required several design iterations before we could observe guidance and measure waveguide loss.

Figure 40: Final experimental setup, showing the number of optical elements involved. Not shown are the waveguide stages seen in Figure 40 and the monochromator. 5.2 Waveguide loss measurements

Figure 41: Streak-imaging experiment. An IR camera is positioned above the waveguide (left) and images the propagating mode through the waveguide (right). Note that the GaAs appears transparent in the IR.

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One of the main goals of this experiment was to fabricate OPGaAs waveguides with lower propagation losses than any of the previously reported efforts. There are many different ways to measure propagation loss62,63, but most of these are not well suited to our experiment. For example, the cutback method is impractical since it requires the destruction of the sample. The Fabry-Perot resonance technique requires a tunable laser source with a stable output power which we do not possess.

Instead, we have decided to utilize the streak imaging technique, in which light scattered by the waveguide is measured with a digital camera. Since the scattered light is proportional to the incident light it should decrease at the same rate. One can thus plot the scattered intensity as a function of position across the waveguide and fit it to an exponential decay, extracting the loss using Beer’s Law:

(5.1)

where Ioin equation (5.1) is the incident intensity and α is the absorption coefficient, given in units of inverse length (cm-1). This method is not very accurate, but since we expect the losses of our waveguides will be high it should give us a reasonable estimate.

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Figure 42: The IR photo shown in Figure 42 with the contrast turned down (left), showing how the scattered light decays as it propagates through the waveguide. Also shown is a plot of the total pixel count (intensity) versus position, showing the exponential decay.

To calculate the loss of our waveguides, we first aligned the system to ensure we were guiding. We then placed an infrared camera above the waveguide and pointed it at a mirror which allowed it to view the propagating mode, as shown in Figure 41. This camera was a Santa Barbara Focal Plane (SBFP) Aura SR 1024 x 1024 indium antimonide (InSb) pixel camera, which is sensitive from 3.3 – 4.8 µm (covering our signal wavelengths). The resulting image, shown in Figure 42, clearly shows the propagation loss as the beam travels through the waveguide. Plotting the camera counts vs. pixel position as shown in Figure 42, we do see an exponential decay, albeit a noisy one. By fitting Beer’s law to this distribution (line in Figure 42) we obtain a loss in inverse pixels (pixel-1), which we can then convert to cm-1 using an object of known length. In our case this object was the waveguide sample itself, which was 180 pixels long in the image and measured to be 2.2 cm long. With this conversion factor, we obtain

74 a loss values ranging from 0.23 to 0.89 cm-1. In general losses for waveguides are expressed in units of decibel per cm (dB/cm), which is defined by the equation:

(5.2)

The relationship between dB/cm given by equation (5.2) and cm-1 can be found by manipulation of equation (5.1) to yield:

(5.3)

Dividing equation (5.2) by (5.3) yields:

(5.4)

Thus our lowest measured losses expressed in this form are 1.0 dB/cm. This represents a record low loss, as the lowest losses ever recorded in an OPGaAs waveguide were 1.5 dB/cm52, signifying the achievement of one of our project goals.

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5.3 Temperature tuning

Figure 43: Schematic of our OPGaAs oven (left), and a photo of the OPGaAs sample with oven mounted in the OPO. By changing the temperature of the GaAs crystal, we can tune the output of our OPO. In order to maximize our chances of seeing OPA gain, we desire a tunable signal output to mix with the pump. Luckily, GaAs has very favorable thermal properties and a sufficiently temperature dependent refractive index (dn/dT = 5 * 10-6 K-1) that by changing the temperature of an OPGaAs sample we can change the phasematching conditions and by extension the signal and idler wavelengths. To accomplish this we constructed an oven for heating the bulk OPO sample, shown in Figure 43. The oven is a copper block with a piece hollowed out of the top for the OPGaAs to sit in. Two holes are also milled into the block, and we place a cartridge heater and a thermocouple into these.

The wires from these two devices are connected to an Omega temperature controller, which allows us to set the temperature of the oven.

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Figure 44: Spectra of OPGaAs OPO signal output as a function of temperature. As temperature increases the signal wavelength decreases (similarly the idler wavelength increases). The signal output as a function of temperature is shown in Figure 44, where we see that as temperature increases the signal wavelength decreases, and by energy conservation, the idler wavelength similarly increases. Also from Figure 44 one can see the wide range of tunability achievable with this technique, a tuning bandwidth of 400 nm (the bandwidth of the entire visible spectrum) is achievable with only a 60°C change in temperature. Comparing these results to the theoretical temperature dependent refractive index model given in48, we see fairly good agreement with theory. A plot comparing the two is shown in Figure 45. While there is slight deviation from theory it is not too surprising given the output wavelengths significant dependence on the refractive index. In addition, the temperature controller was not the most stable, allowing for fluctuations in temperature on the order of +- 2°C, which certainly could account for

77 some of the error. Regardless, we have demonstrated a tunable seed source for our waveguide OPA, now all that remains is trying to observe gain in our waveguides.

Figure 45: Plot comparing measured and calculated peak signal wavelengths as a function of temperature. 5.4 OPA results

Figure 46: IR camera image of the output of a waveguide (left) compared with the calculated mode profile for a waveguide with a 0.5 µm tall ridge.

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While we were successful in demonstrating guidance in our waveguide samples, as shown in Figure 46, and measuring record low propagation losses, we were unable to demonstrate gain. The procedure to measure gain was as follows: measure the output spectrum of the OPO signal transmitted through the waveguide with the pump arm blocked; then unblock the pump beam and collect a second spectrum and see if the signal increases. If no gain is observed, the output of the OPO is changed by adjusting the temperature of the OPGaAs and the process is repeated. Since our theoretical gain is over

300 (see section 2.6), we expect to be able to measure the amplification of the signal even considering the losses at the waveguide surfaces and all of the steering optics between the waveguide and the monochromator. We were unable to observe any gain in the waveguides, even with heating the OPGaAs oven to a temperature of 100°C.

There are several possible reasons for the lack of observed nonlinear gain. First, there could be an issue with the coupling optics. Since the focal length of the coupling objectives is a function of wavelength (due to dispersion), it is possible that we are not coupling enough pump light into the waveguide to get observable conversion. Since the camera used for alignment is sensitive only to the signal wavelength, we have no independent way of confirming that the pump is co-linear with the signal, other than the alignment procedure. Second, there could be an error in our calculations for the grating period. During the course of our experiment, we realized that both the pump and signal were both polarized vertically (perpendicular to the surface of the table). As discussed in the theory section, if the signal and pump have parallel polarizations the deff is zero (i.e.

79 no gain is observed). Even after rotating the polarization of our pump beam, however we were still unable to observe gain. One possible reason is that this change in polarization will have an effect on the effective index of the waveguide and subsequently the grating period needed for phasematching. The theoretical results shown in Figure 15 assumed that all of the interacting waves (pump, signal, and idler) were propagating as TE modes, when in reality one of these three must be a TM mode in order to observe gain.

Figure 47: Plot comparing the tuning curves for the case where all three wavelength s propagate as TE modes (red), or the pump is TM polarized and the signal and idler are TE polarized (blue). The tuning curve is shifted by 2 µm, which combined with other uncertainties in our model could explain why we were unable to see gain (the red plot here corresponds to the purple plot in Figure 16). We went back and calculated what impact this would have on the grating period, and these results are shown in Figure 47. We see that the needed grating period is shifted

80 by 2 µm. Combined with all of the other sources of uncertainty in calculating Λ this could account for our lack of gain: we simply don’t have the proper grating period.

Finally, there could still be issues with the quality of the material itself. Given all of the issues with have had with waveguide growth this would not be surprising, and something as simple as an AlxGa1-xAs layer that contained 20% more aluminum than specs could account for this discrepancy.

5.5 Future Work

In conclusion, while our inability to observe gain is disappointing we have made several significant strides towards the creation of an OPGaAs waveguide device. We have established a working recipe for manufacturing OPGaAs waveguides with high surface quality and low losses, and empirically demonstrated these qualities. We have developed a system for in-house polishing and cleaving of OPGaAs samples, which is crucial to the success of any future project based on this material system. We have developed a theoretical model to predict the needed grating period Λ for phasematching, and identified several areas (AlGaAs Sellimeier equations, polarization effects) where further study is needed. Finally, we have constructed an experimental setup with a tunable OPGaAs OPO source that can be used for future studies of nonlinear devices, both waveguide and bulk, and demonstrated the wide range of tunability achievable with

OPGaAs.

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Options for future efforts include using a different growth technique for the waveguide, as discussed in Chapter 4, to overcome the pitting issues seen with MOCVD growth. In addition, because of the complexity involved in achieving OPA in these samples, it may be a better idea to try and obtain OPO instead. If the end facets of our waveguide samples were coated with the appropriate reflectivities, then OPO will occur for our given pump wavelength so long as the grating period is not too far from the degeneracy point. We could then measure these output wavelengths, and use them to find what corrections are needed to our model, similar to the efforts carried out by Soreq.

Finally, alternate waveguide designs could be investigated which are not as dependent on the indicies of the AlxGa1-xAs layers, such as a photonic crystal waveguides. While the future of OPGaAs integrated optical devices remains uncertain, we are confident that the findings of this dissertation will contribute to the future direction of this research.

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