Sub-Wavelength Resonant Structures at Microwave and Optical Frequencies
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UC San Diego UC San Diego Electronic Theses and Dissertations Title Sub-wavelength resonant structures at microwave and optical frequencies Permalink https://escholarship.org/uc/item/3th147ss Author Simić, Aleksandar Publication Date 2011 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA, SAN DIEGO Sub-Wavelength Resonant Structures at Microwave and Optical Frequencies A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Physics by Aleksandar Simi´c Committee in charge: Professor Yeshaiahu Fainman, Chair Professor Sheldon Schultz, Co-Chair Professor Leonid V. Butov Professor Vitaliy Lomakin Professor Clifford M. Surko 2011 Copyright Aleksandar Simi´c,2011 All rights reserved. The dissertation of Aleksandar Simi´cis approved, and it is acceptable in quality and form for publication on microfilm and electronically: Co-Chair Chair University of California, San Diego 2011 iii DEDICATION To my children Ekatarina and Nikola, and my wife Blaˇzenka. I am so happy to have you. iv EPIGRAPH The important thing is not to stop questioning. — Albert Einstein v TABLE OF CONTENTS Signature Page.................................. iii Dedication..................................... iv Epigraph.....................................v Table of Contents................................. vi List of Figures.................................. ix List of Tables................................... xi Acknowledgements................................ xii Vita and Publications.............................. xiv Abstract of the Dissertation........................... xv Chapter 1 Introduction............................1 1.1 Sub-wavelength scale resonators..............1 1.1.1 Passive sub-wavelength resonators.........1 1.1.2 Active sub-wavelength resonators.........3 1.2 Dissertation organization..................4 Chapter 2 Experimental confirmation of negative phase change in planar negative index material samples.................6 2.1 Introduction.........................6 2.2 Characterization.......................7 2.2.1 Methods of confirming the negative index.....7 2.2.2 Experimental setup and calibration........9 2.2.3 Experimental results and discussion........ 11 2.3 Conclusion.......................... 14 Chapter 3 Room-temperature sub-wavelength metallo-dielectric lasers.. 16 3.1 Introduction......................... 16 3.2 Design............................ 17 3.3 Design and Simulation................... 20 3.4 Fabrication......................... 22 3.5 Characterization....................... 23 3.6 Conclusion.......................... 27 3.7 Methods and additional material.............. 28 3.7.1 Simulations..................... 28 vi 3.7.2 Purcell factor estimation.............. 31 3.7.3 Fabrication..................... 31 3.7.4 Characterization results.............. 32 Chapter 4 Cryogenic operation of nanolaser structures........... 35 4.1 Introduction......................... 35 4.2 Advantages of cryogenic operation............. 36 4.3 Experimental results of cryogenic operation........ 38 4.3.1 Temperature vs. size tradeoff........... 38 4.3.2 Lasing results at 77 K................ 41 4.4 Discussion and conclusion................. 44 4.4.1 Degradation of nanolaser performance with time. 44 4.4.2 Lasing at different modes at 77 K......... 46 4.4.3 Conclusion...................... 47 Chapter 5 Wafer bonded sub-wavelength metallo-dielectric laser..... 49 5.1 Introduction......................... 49 5.2 Design and Simulations................... 51 5.3 Fabrication......................... 53 5.4 Measurements........................ 56 5.5 Conclusion.......................... 60 Chapter 6 Thresholdless nanoscale coaxial lasers.............. 62 6.1 Introduction......................... 62 6.2 Design, simulation and fabrication............. 63 6.3 Characterization and analysis............... 66 6.4 Conclusion.......................... 69 6.5 Methods and additional materials............. 70 6.5.1 Fabrication..................... 70 6.5.2 Measurements.................... 71 6.5.3 Rate equation model................ 72 Chapter 7 Future directions and conclusion................. 74 7.1 Future directions...................... 74 7.1.1 Direct current injection nanolasers......... 74 7.1.2 Measuring coherence................ 79 7.1.3 Comparing optical losses of different metals... 80 7.2 Conclusions......................... 82 Appendix A Meta-material inspired sub-wavelength antenna........ 84 A.1 Introduction......................... 84 A.2 Design and simulation of a magnetic dipole antenna... 85 A.3 Fabrication and measurements............... 88 A.4 Conclusions and future directions............. 89 vii Appendix B Permittivity () and permeability (µ) retrieval from S-matrix parameters............................. 90 B.1 Explanation of S–Matrix and S–parameters........ 90 B.2 Retrieval of and µ from S-parameters.......... 91 Appendix C Optical setup for characterization of nanolasers........ 94 C.1 Setup design......................... 94 C.2 Cryostat implementation.................. 97 C.2.1 Modifications for electrically pumped nanolasers. 97 C.3 Summary.......................... 100 Appendix D Analytical solution of electromagnetic modes in coaxial waveg- uide................................ 101 D.1 Introduction......................... 101 D.2 Solution of wave equation in cylindrical coordinates... 102 D.3 Applying the boundary conditions............. 105 D.3.1 Special cases..................... 108 D.4 Numerical solver, results and discussion.......... 108 Appendix E Explanation of the Purcell effect................. 111 Appendix F Second order coherence g(2) ................... 114 F.1 Background information on coherence........... 114 F.2 Quantum (QED) treatment of coherence......... 115 F.3 Young’s double slit experiment and g(1) .......... 116 F.4 Second order coherence function — g(2) .......... 118 F.5 Measuring second order coherence — g(2)(0)....... 119 F.5.1 Hanbury Brown and Twiss experiment...... 119 F.5.2 Streak camera approach.............. 121 Bibliography................................... 123 viii LIST OF FIGURES Figure 1.1: Split ring resonator.........................2 Figure 2.1: Schematic representation of various experimental approaches for verification of negative index...................9 Figure 2.2: Free-space transmitted phase measurement system....... 10 Figure 2.3: Setup calibration using Teflon sheets............... 11 Figure 2.4: Experimental and simulation data for |S21| vs. frequency.... 12 Figure 2.5: Experimental and simulation data for phase change of |S21| vs. frequency.............................. 13 Figure 2.6: Refractive index n vs frequency calculated from experimental data and numerical simulation.................. 14 Figure 3.1: Geometry and mode shape for a thick semiconductor disk (a,b), and the same disk covered by optically thick layer of gold(c – e). 18 Figure 3.2: Optical design of optimized nanolaser geometry and simulation of electromagnetic mode profile................... 21 Figure 3.3: Various stages of the nanolaser fabrication process........ 23 Figure 3.4: Light–light curve for the nanolaser at room temperature..... 24 Figure 3.5: Evolution of the emission spectrum from PL to lasing...... 25 Figure 3.6: Estimation of the effective refractive index of the MQW gain medium................................ 26 Figure 3.7: Pump absorbtion in the gain core (3D FEM simulation).... 30 Figure 4.1: Photoluminescence (PL) of bulk InGaAsP as a function of tem- perature............................... 37 Figure 4.2: Photoluminescence (PL) peak of bulk InGaAsP as a function of temperature............................. 37 Figure 4.3: Lasing threshold as a function of temperature.......... 39 Figure 4.4: Size map of a typical nanolaser sample array........... 40 Figure 4.5: Size vs. temperature — laser performance at 295 K and 77 K.. 41 Figure 4.6: Emission spectra for Dcore = 604 nm laser at 295 K and 77 K.. 42 Figure 4.7: Lasing characteristics for Dcore = 284 nm laser at 77 K..... 43 Figure 4.8: Comparison of nominally identical nanolasers.......... 45 Figure 4.9: Nanolaser lasing at different modes 295 K and 77 K....... 47 Figure 4.10: Nanolaser lasing at multiple modes simultaneously 77 K.... 48 Figure 5.1: Scheme of the original, and wafer-bonded sub-wavelength me- tallo-dielectric laser......................... 50 Figure 5.2: Schematic drawing and FEM simulation of the wafer bonded metallo-dielectric resonator design................ 53 Figure 5.3: Fabrication steps of a wafer bonded metallo-dielectric laser... 54 Figure 5.4: SEM micrographs after two steps in the fabrication process.. 55 ix Figure 5.5: Room temperature lasing results for a nanolaser with gain core radius of Rcore = 450 nm...................... 58 Figure 5.6: 77 K lasing results for a nanolaser with gain core radius of Rcore = 450 nm........................... 59 Figure 5.7: 77 K lasing results for a nanolaser with gain core radius of Rcore ≈ 250 nm........................... 60 Figure 6.1: Schematic representation of coaxial nanolaser and SEM micro- graphs of fabricated samples.................... 64 Figure 6.2: Modal spectra of cavities of Structure A and Structure B.... 66 Figure 6.3: Lasing results in Structure A ................... 68 Figure 6.4: Thresholdless lasing in Structure B ................ 69 Figure 7.1: Schematic representation of electrically pumped nanolaser de- sign, and SEM micrographs of