UNIVERSITY OF OTTAWA MASTERS THESIS Exploring Optical Nonlinearity in III-V Semiconductors Author: Mfon ODUNGIDE Supervisor: Prof. Ksenia DOLGALEVA A thesis submitted in partial fulfillment of the requirements for the degree of Masters of Applied Science Ottawa-Carleton Institute for Electrical and Computer Engineering University of Ottawa c Mfon Odungide, Ottawa, Canada, 2019 ii Declaration of Authorship I, Mfon ODUNGIDE, declare that this thesis, titled “Exploring Optical Non- linearity in III-V Semiconductors”, and the work presented in it are my own. I confirm that except where specific reference is made to the work of others, the contents of this dissertation are original and have not been submitted in whole or in part for consideration for any other degree or qualification in this, or any other university. This dissertation is my own work and contains nothing which is the outcome of work done in collaboration with others, ex- cept as specified in the text and Acknowledgements. Mfon Odungide November, 2019 Ottawa, Canada iii UNIVERSITY OF OTTAWA Abstract School of Electrical Engineering and Computer Science Ottawa-Carleton Institute for Electrical and Computer Engineering Masters of Applied Science Exploring Optical Nonlinearity in III-V Semiconductors by Mfon ODUNGIDE iv This Master’s dissertation focuses on exploring optical nonlinearities in III- V semiconductors. This work covers a range of III-V materials and a few devices. To begin with, optical characterization of Aluminium Gallium Ar- senide (AlGaAs) waveguides with enhanced nonlinear optical interactions was carried out. We have experimentally demonstrated wide conversion ranges and high conversion efficiencies for four-wave mixing in AlGaAs waveg- uides with three different geometries. In addition to that, both linear and nonlinear losses in each of these geometries were explored. AlGaAs represents only one compound of the large group of III-V semicon- ductors. To explore the potentials of other semiconductors compounds of this group for nonlinear optics, it is imperative to have information about refrac- tive indices of different III-V compounds. This refractive index information is only available for some binary compounds in isolated spectral windows. In this thesis, we developed a model capable of predicting the values of the refractive indices of binary, ternary and quaternary III-V semiconductor com- pounds from the values of their band-gap energies. We compared the value predicted by our proposed model with existing ex- perimental data and it was found not only is the predicted values in good agreement with the known values, but also has a lower error margin when compared to previously reported models. Finally, in quest for more suitable material platform for nonlinear photonic integration at different wavelength ranges, a detailed analysis of other potential III-V compounds not previously explored for photonic integration is presented. v Acknowledgements I would like to express my profound gratitude and deepest appreciation to my supervisor, Prof. Ksenia Dolgaleva for her support, guidance, and wise supervision. Her deep insights and invaluable lessons helped me at many stages of my research and in my overall growth as a researcher. She is a great teacher and an amazing mentor. I feel very fortunate and honored having her as my supervisor and being a part of her research team. I am particularly thankful to our post doctoral fellow, Daniel H. G. Espinosa for his immense contributions in all the projects outlined here, from the set- ting up of the Four-Wave Mixing experiment in AlGaAs, as detailed in Chap- ter2, to validating results and data for the generalized refractive index model detailed in Chapter3. Through his vast experience, these projects were com- pleted with less complications and success. Special thanks to our recently graduated Doctoral student, Kashif Awan, who performed the design and fabrication of AlGaAs waveguide structures de- tailed in Chapter2, and provided input in the development of the general- ized refractive index model, detailed in Chapter3. His experience in fab- rication was of great importance in the quest for new materials detailed in Chapter4. Many thanks to my fellow graduate and undergraduate students from Prof. Dolgaleva’s research group and the much larger group, the CERC uOttawa group, who in diverse ways have contributed to these projects and also as a source of inspiration in my journey as a researcher. Finally, I would like to express my profound gratitude to my mother Patricia, sister Madis, and my brother Etuks for their endless support and encourage- ment in every steps of my life. This accomplishment would not have been possible without them. vi Contents Declaration of Authorship ii Abstract iv Acknowledgementsv 1 Introduction1 1.1 Motivation..............................1 1.2 Integrated Photonics........................3 1.3 Nonlinear Optics..........................4 1.3.1 Nonlinear optical phenomena...............6 1.3.2 Four-wave mixing.....................7 1.3.3 All-optical wavelength conversion using FWM.....9 1.3.4 Optical Time Division Multiplexing........... 10 1.4 Waveguide Optics.......................... 11 1.4.1 Ray Optics Representation................ 12 1.4.2 Critical Angle and Guidance............... 13 1.4.3 Wave Optics Representation................ 14 1.4.4 Electromagnetic field polarization............ 17 1.4.5 Waveguide Modes..................... 17 1.4.6 Mode propagation constants............... 20 1.4.7 Number of modes..................... 21 1.4.8 Mode field distribution.................. 22 1.4.9 Superposition of Modes.................. 23 1.4.10 Waveguides with 2D Confinement............ 24 1.5 III-V Semiconductors........................ 26 1.5.1 Ternary and Quaternary III-V Semiconductors..... 27 1.5.2 Energy Gap and Lattice Constant............. 29 1.5.3 Direct Band-Gap and Indirect Band-Gap III-V Semicon- ductors............................ 29 1.5.4 Operation Wavelengths of Different Devices...... 31 1.5.5 Integrated Photonics in III-V Semiconductors...... 33 vii 1.6 Thesis Layout............................ 35 2 Experimental Demonstration of Four-Wave Mixing in AlGaAs Waveg- uide 36 2.1 Introduction............................. 36 2.2 AlGaAs waveguide design..................... 37 2.2.1 Designing Waveguide Geometry............. 38 Strip-loaded optimization................. 39 Nanowire optimization.................. 40 Half-core optimization................... 41 2.2.2 AlGaAs Waveguide layout................ 42 2.3 Linear Characterization...................... 44 2.3.1 Linear Characterization Experimental Setup...... 44 2.3.2 Propagation Losses..................... 45 2.3.3 Coupling Losses...................... 46 2.3.4 Taper Loss.......................... 46 2.3.5 Nanosection Loss...................... 47 2.4 Nonlinear Characterization.................... 48 2.4.1 Four-wave mixing experimental setup.......... 48 2.4.2 Four-Wave Mixing Experiment.............. 49 2.4.3 Nonlinear Absorption................... 56 2.4.4 Absorption experimental setup.............. 57 2.4.5 Two-photon Absorption.................. 58 2.5 Conclusions............................. 59 3 Generalized model for Refractive index of III-V Semiconductors 62 3.1 Introduction............................. 62 3.2 Refractive index as function.................... 63 3.2.1 Refractive Index as a function of density of a material. 64 Gladstone–Dale Relationship............... 64 3.2.2 Refractive index as a function of Wavelength of light. 64 Cauchy Dispersion Equation............... 65 Sellmeier Dispersion Equation.............. 65 3.2.3 Refractive index as a function of band-gap energy... 66 The Moss Model...................... 66 Ravindra Model....................... 67 Herve and Vandamme Model............... 67 Reddy, et al. Model..................... 68 Kumar and Singh Model.................. 68 viii Tripathy Model....................... 68 Other Fitted Models.................... 69 3.2.4 Analysis of examined models............... 69 3.2.5 Proposed Model...................... 70 3.3 Conclusion.............................. 80 4 Nonlinear Photonic Integration: Quest for new materials 82 4.1 Introduction............................. 82 4.2 Material Selection Criteria..................... 83 4.2.1 Material composition selection.............. 83 4.2.2 Lattice Matching...................... 84 4.2.3 Epitaxial Growth: MOCVD and MBE.......... 85 4.2.4 Refractive index contrast................. 86 4.3 Potential Material Candidates................... 86 4.3.1 Indium Gallium Phosphide Nitride........... 86 Common Use........................ 87 Substrates.......................... 87 Lattice Matching...................... 88 Energy gap......................... 88 Refractive Index/Dispersion............... 88 InxGa1−xPyN1−y Summary................ 89 4.3.2 Aluminium Gallium Indium Phosphide......... 90 Common Use........................ 90 Substrates.......................... 91 Lattice Matching...................... 91 Energy gap......................... 92 Refractive Index/Dispersion............... 92 AlxGayIn1−x−yP Summary................ 93 4.3.3 Aluminium Gallium Nitride............... 94 Common Use........................ 94 Substrates.......................... 95 Lattice Matching...................... 95 Energy gap......................... 96 Refractive Index/Dispersion............... 97 AlxGa1−xN Summary................... 98 4.4 Conclusions............................. 100 5 Conclusion 103 5.1 Conclusion.............................