View of the Algorithm Will Be Discussed Below to Summarize the Key Points of the Algorithm

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View of the Algorithm Will Be Discussed Below to Summarize the Key Points of the Algorithm EFFECTIVE NONLINEAR SUSCEPTIBILITIES OF METAL-INSULATOR AND METAL-INSULATOR-METAL NANOLAYERED STRUCTURES 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 Electro-Optics By Mallik Mohd Raihan Hussain Dayton, Ohio May, 4242 EFFECTIVE NONLINEAR SUSCEPTIBILITIES OF METAL-INSULATOR AND METAL-INSULATOR-METAL NANOLAYERED STRUCTURES Name: Hussain, Mallik Mohd Raihan APPROVED BY: Imad Agha, Ph.D. Andrew Sarangan, Ph.D. Advisory Committee Chairman Committee Member Associate Professor, Department of Professor, Department of Physics, and, Department of Electro- Electro-Optics and Photonics Optics and Photonics Partha Banerjee, Ph.D. Michael Scalora, Ph.D. Committee Member Committee Member Professor and Department Chair, Research Physicist, Charles M. Department of Electro-Optics and Bowden Research Facility, Photonics AMRDEC, US Army RDECOM Robert J. Wilkens, Ph.D., P.E. Eddy M. Rojas, Ph.D., M.A., P.E. Associate Dean for Research Dean, School of Engineering and Innovation Professor, School of Engineering ii © Copyright by Mallik Mohd Raihan Hussain All rights reserved 4242 ABSTRACT EFFECTIVE NONLINEAR SUSCEPTIBILITIES OF METAL-INSULATOR AND METAL-INSULATOR-METAL NANOLAYERED STRUCTURES Name: Hussain, Mallik Mohd Raihan University of Dayton Advisor: Dr. Imad Agha Nonlinear electromagnetic radiation (second and third harmonic) from the metal-insulator and metal-insulator-metal structures were measured and compared against predictions from the hydrodynamic models of plasmonics. This model incorporated higher order terms stem- ming from electron tunneling and nonlocality. This study shows that, besides the linear optical parameter like permittivity, conductivity etc, changes in the nonlinear optical pa- rameters, namely, second and third order susceptibilities (χ(2) and χ(3), respectively) can also be used to probe and compare the higher-order terms of the hydrodynamic model of plasmonics. Two insulator materials (ZnO and Al2O3) were used in two separate sets of experiments, and atomic layer deposition was used to cover the gold substrate with variable thicknesses of these insulator films (nanometer to sub-nanometer range). Large reduction in second and third harmonic signals was measured after the insulator film was deposited over the gold substrate revealing the spilled-out electronic states in the insulator region at the vicinity of the metal-insulator interface, which are dubbed metal insulator gap states. Then, the metal-insulator samples were spin-coated with Au-nanoparticle solution to pre- pare a metal-insulator-metal structures. For these structures, saturation and quenching of the third harmonic efficiencies were observed which were indicative of the capping of E-field enhancement due to the existence of higher order terms in the hydrodynamic model that accounts for nonlocality and quantum tunneling of electrons. A generalized 4 × 4 matrix iii method was utilized to calculate the effective χ(2) and χ(3) parameters that confirm the changes of effective material properties for ultra-thin films. These nonlinear coefficients, besides the linear permittivity and conductivity σ, can be a useful material parameter to study the effects of higher-order terms of hydrodynamic model. iv To my mentor, Dr. Joseph W. Haus, my parents, Nasima Khatun & Mohd Shakhawat Hussain Mallik. v ACKNOWLEDGMENTS A lot has changed since I started my journey as a Ph.D. student. My ex-advisor, Dr. Joseph Haus suddenly passed away on January 33, 423;. I would not have come this far without him. He used to challenge me with hard problems and give me the space to work on novel ideas. I always admired his openness and humble, close-to-earth demeanor during technical/nontechnical discussions. After Dr. Haus’s death, I was kindly picked up by my current advisor Dr. Imad Agha. I would like to thank him from the deepest of my heart for supporting me till the end. I appreciate his patience and encouragements during every meeting. I have truly found a friend in him and I am looking forward to grow this friendship into a life-long research collaboration tackling the frontiers of optics. I would like to extend my sincere gratitude towards Dr. Andrew Sarangan. His support through the Laser-assisted Si wet etch project has helped me immensely. I have learned a lot from his teaching style and attitude towards solving a problem. In October 423;, Dr. Partha Banerjee suggested me to work with Dr. Behzad Bordbar on the ONR project and he finally offered me a position as a ’Research Engineer’. That opportunity has been a blessing to me and I can never thank Dr. Banerjee enough for trusting in me. I will keep working hard. I would like to thank Drs. Michael Scalora, Domenico de Ceglia, Maria Vincenti, Parag Banerjee and Zhengning Gao for making me a part of a wonderful collaboration. I look forward to contribute more to this collaboration in future. I would like to thank Dr. Shekhar Guha for promptly replying to my emails and queries. I found his book titled “Laser Beam Propagation in Nonlinear Optical Media” to be very rigorous and detailed. The book helped me with many concepts. I would also like to thank Dr. Qiwen Zhan for his insightful suggestions on how to incorporate evanescent/inhomogeneous waves in TMM. I have had many friends in the department over the years. I would like to thank all of them for being my well-wishers. I would like to thank the University of Dayton for creating such vi a warm sense of community and being my home away from home. Lastly, I would like to thank my dear wife Syeda Prem Ara Bahar for supporting me through thick and thin. The world is going through a pandemic. In such situation, I can not defend my dissertation in person and thank and shake hands with everyone who congratulates me. Yet, I feel everyone’s blessings are with me. vii TABLE OF CONTENTS ABSTRACT . iii DEDICATION . v ACKNOWLEDGMENTS . vi LIST OF FIGURES . x LIST OF TABLES . xv CHAPTER I. INTRODUCTION . 3 3.3 Problem statement and novel contributions . 5 3.4 Organization of ideas . 7 CHAPTER II. LIGHT PROPAGATION IN STRATIFIED MEDIA . 9 4.3 Notation convention . 32 4.3.3 Subscripts and superscripts . 32 4.3.4 Vectors and scalars . 33 4.3.5 Tensors . 34 4.3.6 Matrices . 34 4.4 Material birefringence and layer geometry . 35 4.5 Maxwell’s equations . 37 4.6 Free mode calculation . 43 4.6.3 Free K-mode calculation . 44 4.6.4 Free E-mode calculation . 46 4.6.5 Boundary conditions for free modes . 4; 4.6.6 Reflectance and transmittance . 56 4.7 Bound mode calculation . 64 4.7.3 Bound K-mode calculation . 64 4.7.4 Bound E-mode calculation . 66 4.7.5 Boundary conditions with free and bound modes . 67 4.8 A interim summary of the TMM algorithm . 74 4.9 What is effective susceptibility? . 76 (2),2ω 4.9.3 deff calculation . 77 (3),3ω 4.9.4 deff calculation . 78 4.: Theoretical models of susceptibility . 79 4.:.3 Herman-Hayden model . 79 4.:.4 Effective medium model . 79 4.:.5 Nonlocality and tunneling . 82 CHAPTER III. EXPERIMENTS AND RESULTS . 83 5.3 Experimental setup . 83 5.4 Results . 86 5.4.3 Effective d(2),2ω calculation . 87 5.4.4 Effective d(3),3ω calculation . 8: 5.5 Electron density in metal-induced-gap-states . 92 viii 5.6 Effects of nonlocality and quantum tunneling . 95 5.7 Summary of findings . 96 CHAPTER IV. CONCLUSION . 98 BIBLIOGRAPHY . 9: APPENDICES A. Surface Characterization . :8 A.3 Thickness and growth rate . :8 A.4 Surface roughness . :9 A.5 Surface coverage . :; A.6 Chemical composition . :; A.7 Au nanoparticle distribution . ;2 B. Singular Value Decomposition . ;4 C. MATLAB Codes . ;5 ix LIST OF FIGURES 3.3 Miniaturization of electronics has opened a new paradigm of nanoplasmonics that can serve as an interface between electronics and photonics [38]. 4 4.3 A stratified layered structure with arbitrary numbers of layers and layer thick- nesses. 9 4.4 (a)Resonant metamaterial structures (e.g. split-ring resonators show resonance in dispersion relation) are used to design left-handed-materials, whereas, (b) a non-resonant metamaterial structure is designed to engineer exotic anisotropic behaviour. : 4.5 The transformation between the laboratory axes system and the principle axes system of the crystal. The symbols of Euler angles (Φ, Θ, Ψ) are uppercase and color coded to green, red and green respectively. Symbols for angle of incidence and azimuthal angle (θ, φ) are lowercase. 36 4.6 Vector diagram of EM fields (not to scale and color coded for easy correspondence). 38 4.7 An example case of the normal surface of a positive uniaxial medium with an arbitrary direction of o^ with respect to the laboratory axes system (x^y^z^). Four (1),Ω (1),Ω free K-modes (Kl ) along with their angles (θl ) with respect to z^ is marked. 44 4.8 Index ellipsoid indicating the directions of free K-modes and free E-modes (scaled for easy visualization) of an isotropic material for 0◦ ≤ θ < 90◦ and 0◦ ≤ φ < 360◦.......................................... 47 4.9 Index ellipsoid indicating the directions of free K-modes and free E-modes (scaled for easy visualization) of a positive uniaxial material (arbitrary orientation of optic axis, oˆ) for 0◦ ≤ θ < 90◦ and 0◦ ≤ φ < 360◦.................. 47 4.: Index ellipsoid indicating the directions of free K-modes and free E-modes (scaled for easy visualization) of a negative uniaxial material (arbitrary orientation of optic axis, oˆ) for 0◦ ≤ θ < 90◦ and 0◦ ≤ φ < 360◦.................. 48 4.; Index ellipsoid indicating the directions of free K-modes and free E-modes (scaled for easy visualization) of a type-3 hyperbolic uniaxial material (for optic axis, oˆ k zˆ) for 0◦ ≤ θ < 90◦ and 0◦ ≤ φ < 360◦.....................
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