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UC San Diego Electronic Theses and Dissertations UC San Diego UC San Diego Electronic Theses and Dissertations Title Metallo-dielectric Nanolasers for Dense Chip-scale Integration Permalink https://escholarship.org/uc/item/796020f2 Author Gu, Qing Publication Date 2014 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA, SAN DIEGO Metallo-dielectric Nanolasers for Dense Chip-scale Integration A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Electrical Engineering (Photonics) by Qing Gu Committee in charge: Professor Yeshaiahu Fainman, Chair Professor Vitaliy Lomakin Professor Shirley Meng Professor Lu Sham Professor Charles Tu 2014 Copyright Qing Gu, 2014 All rights reserved. SIGNATURE PAGE The dissertation of Qing Gu is approved, and it is acceptable in quality and form for publication on microfilm and electronically: Chair University of California, San Diego 2014 iii DEDICATION To my family 。 iv EPIGRAPH Weakness of attitude becomes weakness of character. − Albert Einstein v TABLE OF CONTENTS Signature Page ................................................................................................................... iii Dedication .......................................................................................................................... iv Epigraph .............................................................................................................................. v Table of Contents ............................................................................................................... vi List of Figures .................................................................................................................. viii List of Tables ...................................................................................................................... x Abbreviations ..................................................................................................................... xi Acknowledgments............................................................................................................. xii Vita ................................................................................................................................... xiv Abstract of the Dissertation ............................................................................................. xvi Chapter 1 Introduction ........................................................................................................ 1 1.1 The history of laser miniaturization .................................................................... 2 1.2 Fundamental scale limits of lasers ...................................................................... 4 1.3 The metal-clad nanolaser .................................................................................... 9 Chapter 2 Purcell Effect and the Evaluation of Purcell factor and Spontaneous Emission Factors ............................................................................................................................... 20 2.1 Formulation of Purcell effect for semiconductor nanolasers at room temperature ................................................................................................................... 22 2.2 Evaluation of Purcell effect in a metallo-dielectric nanolaser .......................... 30 2.3 Dependence of spontaneous emission factor on temperature ........................... 36 2.4 Discussion ......................................................................................................... 40 Chapter 3 Active Medium for Semiconductor Nanolasers: MQW vs. Bulk Gain ............ 41 3.1 Current injection in semiconductor nanolasers ................................................. 43 3.2 Optical cavity and material gain optimization .................................................. 46 3.3 Reservoir model for semiconductor lasers ........................................................ 51 3.4 Laser rate equation analysis with the reservoir model ...................................... 55 3.5 Discussion ......................................................................................................... 61 Chapter 4 Electrically Pumped Metallo-dielectric Nanolasers ......................................... 64 4.1 Initial electromagnetic cavity mode design and experimental validation ......... 65 4.2 Thermal management and design co-optimization of electrically pumped metallo-dielectric nanolasers ........................................................................................ 72 4.2.1 Simulation of nanolaser’s temperature performance ................................................ 73 4.2.2 Choice of dielectric material and fabrication techniques for thermal management .. 76 4.2.3 Preliminary experimental validation ......................................................................... 81 4.2.4 Nanolaser’s electrical and thermal analysis .............................................................. 86 4.3 Integrated nanolaser design for room temperature operation ........................... 91 4.4 Discussion ......................................................................................................... 96 vi Chapter 5 Conclusion and Future Directions .................................................................. 100 5.1 Coupling between nanolasers and optical waveguides ................................... 102 5.2 Integration with silicon platform .................................................................... 103 5.3 Ultra-dense arrays of individually-addressable metal-clad nanolasers ........... 105 Appendix A ..................................................................................................................... 108 A.1 Non-relativistic QED in free space and in a resonant cavity .......................... 108 A.2 Spontaneous Emission probability in free space and in a resonant cavity ..... 113 A.3 Discussions ..................................................................................................... 115 References ....................................................................................................................... 117 vii LIST OF FIGURES Figure 1.1: Schematic of a conventional Fabry-Perot cavity. The cavity length, L, is along the z-direction in which the wave propagates. The two end-facets have reflection coefficient r 1 and r 2, respectively. ................................................... 6 Figure 1.2: The M=4 whispering gallery resonance for a thick semiconductor disk. ...... 13 Figure 1.3: (a) Cross section of the metal-coated composite gain waveguide. (b) Cylindrical closed 3D resonator. (c) Cylindrical open 3D resonator. ........... 15 Figure 1.4: (a) A metal-clad cylindrical nanocavity with a subwavelength gain medium cross section, acting as a Fabry-Perot nanolaser, and (b) A metal-clad nanocavity whose size is subwavelength in all three dimensions. ................ 16 Figure 1.5: Cross-sections of |E| for the TE 012 mode of the cavity. .................................. 17 Figure 1.6: (a) Light−light curve for a nanolaser with major and minor core diameters of 490 nm and 420 nm (dotted curve). (b) Evolution of the emission spectra from PL to lasing. .......................................................................................... 18 Figure 2.1: (a) The lasing mode’s electric field profile and the three spectra in the evaluation of the Purcell factor: (b) cavity lineshape, (c) homogeneous broadening lineshape and (d) PL spectra. Dashed red: measured at low pump powers, and solid blue: datasheet provided by OEpic Inc. ........................... 33 Figure 2.2: Simulated mode distribution of all modes that falls within the spectral window of PL and have cavity Q>20. Also shown are Purcell factors for each mode, F cav , calculated using two different sources of PL spectra. ................ 36 Figure 2.3: (a) Transparent wavelength versus carrier density and (b) Spontaneous emission factor versus temperature for a 10 nm MQW-InGaAsP-metal-clad nanolaser similar to that of Section 2, but with 250 nm and 350 nm core and total radii, respectively. ................................................................................. 38 Figure 3.1: Simulated band diagrams with the electrons and holes quasi-Fermi levels (E fc and E fv ) of a (a) unbiased MQW heterostructure; (b) forward biased MQW heterostructure; (c) unbiased bulk heterostructure and (d) forward biased bulk heterostructure. .............................................................................................. 45 Figure 3.2: Schematics of a nanopatch laser resonator. .................................................... 47 Figure 3.3: Material gain dependence with wavelength for (a) an InGaAsP MQW structure (red) and an InGaAsP barrier (blue) at the threshold carrier density for the first order mode and (b) an InGaAsP bulk material for two different carrier densities.. ............................................................................................ 49 Figure 3.4: Reservoir schematics to illustrate the interchange of carriers between the well and barrier... ................................................................................................... 54 Figure 3.5: Log-log curves of the light output power versus injection current for (a) MQW gain media and (b) bulk gain media with several β’s. (c) and (d) are viii the carrier density versus injection
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