具增強耳語廊模態之光子晶體共振腔拓樸優化及光耦合類分子之研究

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(1)國立交通大學光電工程研究所碩士論文. 具增強耳語廊模態之光子晶體共振腔拓樸優化及光耦合類分子之研究 Topological Optimization and Photonic Molecule by Photonic Crystal Microcavity with Enhanced Whispering-Gallery Mode. 研究生：林孟穎指導教授：李柏璁教授. 中華民國九十七年七月.

(2) 具增強耳語廊模態之光子晶體共振腔拓樸優化及光耦合類分子之研究. 研究生：林孟穎指導老師：李柏璁. 教授. 國立交通大學光電工程研究所碩士班. 摘要. 本論文可分為兩大部分，在第一部分中，基於拓樸原理我們先模擬了微碟型 (Microdisk)與微齒輪型(Microgear)共振腔中耳語廊模態(Whispering-Gallery Mode) 的Q值最佳化過程，接著我們進一步設計出微花型(Microflower)共振腔，並討論這三者共振腔邊界對於Q值的影響。由於微碟型共振腔在優化會有體積上的限制，故我們在這部分也提出一具有耳語廊模態之光子晶體修正共振腔，我們以相同的討論結果作基礎，將Q值最佳化的對象換成在小體積時也能有良好Q值表現的光子晶體，成為花型拓樸光子晶體共振腔(Photonic Crystal Micro-Flower CD 2 Microcavity, PC MFCD 2 )，接著藉由製程方法實現該設計，並討論其量測結果。在第二部分，我們會介紹另一種會應用在微碟型共振腔上的設計，也就是光子分子。而針對光子分子的概念應用在光子晶體上時，我們也提出一個全新的結構：基於光子晶體共振腔的雙層光子分子(Double Layer Photonic Molecules, DLPM)。同樣的我們會先介紹光子晶體共振腔光子分子在模擬上的結果，包括了光子分子模態以及其可調變的模態特性。接下來的章節中，我們主要會著重在製程方法的研究。利用設計的砷化鎵雙層磊晶結構，我們改變了樣本的設計，包括周期數與樣本旁蝕刻窗的大小，調變乾式與濕式蝕刻的時間，還有光子晶體洞本身的直徑，以完成雙層光子分子的製程結構。. ii.

(3) Topological Optimization and Photonic Molecule by Photonic Crystal Microcavity with Enhanced Whispering-Gallery Mode Student: Meng-Ying Lin Advisor: Prof. Po-Tsung Lee. National Chiao Tung University Department of Photonics & Institute of Electro-Optical Engineering. Abstract This thesis can be divided into two parts. In the first part, based on topology rule, we will investigate microdisk and microgear with whispering-gallery (WG) mode with azimuthal number six and optimize their quality (Q) factors. And we will also investigate microflower topology by further modifying the edge of the grating in microgear. From these simulation results, we analyze and discuss the influence of cavity boundary on Q factors of WG modes. Since there is scale size limitation due to diffraction limitation in microdisk, we also propose a novel design of photonic crystal circular-shaped (CD 2 ) microcavity with well-sustained WG mode. We will apply the same optimization method on this microcavity named photonic crystal microflower CD 2 (MFCD 2 ) microcavity. And then this design is realized by a series fabrication processes and the measurement results will be analyzed and discussed.. In part two, we will introduce the photonic molecules composed by microdisk and photonic crystal microcavity. We also propose a brand new photonic molecule (PM) design composed by two identical photonic crystal CD 2 microcavity membranes in vertical direction named double-layer PM (DLPM). We will investigate and discuss the basic tunable PM states modal properties by 3D FDTD simulations, including Q factor and wavelength. And then we will develop the related fabrication process based on designed GaAs epitaxial structure. This will include the process by changing patterns design, periods of the pattern, the windows and holes size, and dry / wet etching time. iii.

(4) Acknowledgements 這段日子最需要感謝的就是我的家人，他們所給我的在物質與精神上的支持，是支持我完成學業的最大助力，父母親與其他家人的關心與體諒讓我在這兩年之中能安心完成我的學業與實驗。在求學的路上我想我還是要將最高的感謝送給我的指導老師李柏璁老師，老師就像一個和藹的母親，在我還是新生的時候，一步步的引導我成為合格的研究生，在我研究階段溫和而切中要點的指出每一個需要改進的地方跟需要深思的問題，讓我受益良多。還要謝謝盧讚文學長，在研究上給我莫大的幫助，另外也要感謝跟我一起努力的同學們，蔡宜育、施均融、王明璽跟宋和璁，常常在研究室中創造許多歡樂，特別是常常幫助我的蔡宜育，要是沒有你我不可能完成論文。另外還有跟我一起做實驗後來也幫我很多的蕭逸華學弟，謝謝所有人在這段日子的共同勉勵與成長。. 2008/09/04 于新竹國立交通大學交映樓 401 室. iv.

(5) Content Abstract (In Chinese)……………………………………………………………ii Abstract (In English)……………………………………………………………iii Acknowledgements……………………………………………………………..iv Content……………………………………………….………………………….v List of Tables..……………………………………………………………….…vii List of Figures…………………………………………………………………viii. Chapter 1 Introduction 1.1.. Microdisk, Microgear, and Microflower…………………………….……1. 1.2.. Photonic Crystal Microcavity…………………………………………….4. 1.3.. Photonic Molecules (PM)………………………………………..……….8. 1.4.. An Overview of This Thesis…………..……………………………...…10. Chapter 2 From Microdisk, Microgear, to Microflower: Design and Optimization 2.1.. Introduction………………………………………………..………...…..11. 2.2.. Finite-Difference Time - Domain (FDTD) Method……………..………11. 2.3.. The Basic Simulation of Microdisk and Microgear………………..……14. 2.4.. Microflower…………………………………………………………..….20. 2.5.. Conclusion…………………………………………………………….…22. Chapter 3 Photonic Crystal Circular-Shaped D 2 (CD2 ) Microcavity 3.1.. Introduction and Motivation………………………..……………….…..23. 3.2.. Fabrication of Photonic Crystal Membrane Microcavity …………...….23 v.

(6) 3.3.. The Basic Design and Simulation of Photonic Crystal CD2……………26. 3.4.. Microflower Topology on Photonic Crystal CD2 Microcavity………..29 3.4.1. FDTD Simulation………….…………………………………....…29 3.4.2. Device Fabrication ……..…………………………………….....…33. 3.5.. Measurements……………..……...………….…………….……………35 3.5.1 Measurement System Setup…………………………………...……..35 3.5.2 The Lasing Characteristic of WGM Mode in Microflower………....36. 3.6.. Conclusion……………………………………………………………….39. Chapter 4. Double-Layer Photonic Molecules Composed by Photonic Crystal Microcavities. 4.1.. Introduction……………………………………………………………...40. 4.2.. Design of Double-Layer Photonic Molecule…………….…...……….40 4.2.1. Design Background & Motivation…….….…………………..…..40 4.2.2. Design Scheme……………………………………………………42 4.2.3. Simulations……………………………………………………….43. 4.3.. Fabrication.…………………………………..…………….…...……….46 4.3.1. Designed Epitaxial Structure…….….………………………..…..47 4.3.2. Dielectric Deposition & Pattern Definition………………………48 4.3.3. Patterns Transfer………………..………………...………………48 4.3.4. Substrate Undercut……………………………………………..…51. 4.4.. Conclusion……………...………………………………….…………….53. Chapter 5. Conclusions……………...………..…………….……….54. References……………………………………………….…………………56 Vita……………………………………………………………………………57. vi.

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(8) List of Tables Table I: The simulated wavelength and Q factor of WG mode with different azimuthal numbers……………………………………………………………..…16 Table II: The relationship of wavelength, Q factor and radius …………………………17 Table III: The simulated Q factor from WG 6, 1 mode in microgear with different grating height (H) and width (W)………………………………………………….19 Table IV: The relation of Q and curvature…………………………………………...22 Table V: The table of simulated WG 6, 1 vertical Q factor and air-hole curvature R…….…32. viii.

(9) List of Figures Figure 1.1: (a) The scheme of microdisk composed by thin semiconductor disk. (b) The scheme of total internal reflection in microdisk………………………..……2 Figure 1.2: The WG mode formed in circumference of microdisk by TIR effect and its mode profile. with. azimuthal. number. six,. denoted. as. WG 6,. 1. mode ……………….…2 Figure 1.3: (a) Scheme and (b) its SEM picture of microdisk laser with microgear proposed by M. Fujita and T. Baba. (Adopted from Masayuki Fujita and Toshihiko BaBa) (c) The scheme of micro-flower with radius of 0.9 μm....……………………3 Figure 1.4: The scheme of (a) 1D, (b) 2D, and (c) 3D photonic crystal…………………..4 Figure 1.5: (a) The scheme of triangular photonic crystal and its Brillioun Zone. (b) The calculated triangular photonic crystal TE mode band structure with r/a = 0.25 and a = 1000 nm……………………………………………………….6 Figure 1.6: The scheme of photonic crystal membrane microcavity……………………...7 Figure 1.7: A simple PMs constructed by two fabricated identical microdisks side by side...8 Figure 1.8: The scheme of DLPM composed by two identical photonic crystal microcavity membranes sustaining enhanced WG 6, 1 mode ……………………………...9 Figure 2.1: (a) Scheme of microdisk and its simulation setup by approximated FDTD method. (b) The typical simulated WG 8,. 1. mode. in microdisk in magnetic. field……….15 Figure 2.2: The relationship between simulated wavelength and Q factor of WG mode with different azimuthal numbers from 5 to 8………………………………….15 Figure 2.3: The relationship of wavelength, Q factor and radius……………………….17 Figure 2.4: The scheme of micro-gear and the definition of grating width and height…….18 Figure 2.5: (a) The simulated Q factor mapping of grating height (H) and grating width (W) from WG 6, 1 mode. (b) The simulated WG 6, 1 mode profile in magnetic field when. H. =. μm. 0.125. and. μm………………………………………..18 ix. W. =. 0.175.

(10) Figure 2.6: (a) The simulated Q factor of WG mode with azimuthal number 4 to 10 in micro-gear with M = 6. (b) The simulated WG mode spectra of microdisk (Top) and micro-gear with M = 6 (bottom)……………………………………..20 Figure 2.7: The scheme and the parameter R definition of micro-flower………………..21 Figure 2.8: (a) The simulated WG 6, 1 Q factor mapping in micro-flower with different height (H) and curvature (R). (b) The simulated WG 6, 1 mode profile in magnetic field in micro-flower…………………………………………………………..21 Figure 3.1: The epitaxial of the structure…………………………………………….24 Figure 3.2: The scheme of the membrane structure…………………………………...25 Figure 3.3: The fabrication processes of 2D photonic crystal membrane structure……….26 Figure 3.4: Scheme and cavity design of PCCD2 microcavity…………………………28 Figure 3.5: (a) Electric-field distribution in x-y plane. (b) Magnetic-field distribution in the x-z plane ……………………………………………………………...29 Figure 3.6: Different resonance mode including K=1, 3, 5, 6, 7………………………..30 Figure 3.7: The designing rule of microflower in PCCD2……………………………..31 Figure 3.8: The resonance of WGM in microflower PCCD2………………………………..33 Figure 3.9: The relation of Q and curvature…………………………………………………34 Figure 3.10: The scheme painted in AutoCAD …………………………………………..35 Figure 3.11: The fabrication result of microflower. (a) top view (b) side view (c) full view (d) flower shape. …………………………………………………………………..36 Figure 3.12: The configuration of micro-PL system………………………………………...37 Figure 3.13: (a) The relationship of normalize frequency (r/a) to lattice (a) and (b) The lasing spectrum of PCCD2……………………………………………………………38 Figure 4.1: Various PMs composed by microspheres, micro-cylinders, and micro-disks. …41 Figure 4.2: Various PMs composed by photonic crystal microcavity single membrane. …..41 Figure 4.3: The scheme of DLPM composed by two identical photonic crystal CD 2 microcavity membranes. ………………………………………………………..43 Figure 4.4: The simulated electrical-field profiles of (a) bonding and (b) anti-bonding states in x-z plane. (c) The relationship between wavelengths and air-gap distance of bonding and anti-bonding states, which can be easily analog to electronic states x.

(11) in molecules. ……………………………………………………………………44 Figure 4.5: The relationship between Q bonding and air-gap distance d that is varied from 110 to 1430 nm. ………………………………………………………………………...45 Figure 4.6: The designed GaAs based epitaxial structure for DLPM. ………………………47 Figure 4.7: The designed photonic crystal CD 2 microcavity pattern with windows. ……….48 Figure 4.8: The fabricated patterns with different etching time of (a) 180, (b) 220, (c) 280, and (d) 290 seconds. The fabricated hole radius is 122.5 nm in diameter. …….50 Figure 4.9: The patterns with air-holes radius 109 nm in diameter with the dry-etching time of (a) 220 and (b) 290 seconds. …………………………………………………51 Figure 4.10: The photonic crystal CD 2 microcavity patterns (a) with and (b) without windows. ………………………………………………………………………51 Figure 4.11: The photonic crystal etched patterns with wet etching time and period of (a) 30 seconds and eight periods, (b) 50 seconds and eight periods, (c) 80 seconds and eight periods, and (d) 80 seconds and ten periods. ……………………………52 Figure 4.12: The tilted-view SEM pictures of fabricated DLPM. …………………………..53. xi.

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