以半導體銻化銦研究光學負折射現象

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(1)國立台灣師範大學光電科技研究所碩士論文 Institute of Electro-Optical Science and Technology National Taiwan Normal University. 以半導體銻化銦研究光學負折射現象 Study of Negative Refraction Phenomenon in Semiconductor of InSb. 指導教授：李敏鴻. 博士. 研究生：曾義閔. 中華民國. 一○三. 年六月.

(2) Abstract. This thesis studies the phenomenon of negative refraction (NR) in semiconductor (InSb)-dielectric layered structures. Using the complex wave vector, we analyze the propagation direction of light energy in semiconductor-dielectric interface, and show that the direction of P-polarized light is on the same side of the incident light. In semiconductor material, propagation of an electromagnetic wave is inhomogeneous described in Chapter 3. Negative refraction can happen in semiconductor-dielectric interface under certain appropriate conditions, which will be discussed in detail in Chapter 4. In second part, we have theoretically explored the NR in one-dimensional semiconductor-dielectric photonic crystals (SDPC) consisting of n-type InSb and dielectric materials. By using a theoretical analysis in group velocity, we can investigate phenomenon of NR in SDPC. It is also shown that the NR is closely related to the thicknesses of constituents of SDPC. In addition, we also investigate the tunable feature in NR by varying the temperature and the doping concentration. This study will be presented in Chapter 5.. Keywords: Negative Refraction, Semiconductor, Photonic Crystals, Group Velocity, Inhomogeneous Waves.. I.

(3) 摘要. 負折射現象最早於 1958 年由蘇聯物理學家 Veselago 提出。Veselago 提出了左手材料的概念，顛覆了物理學的傳統知識。左手材料從此成為近十餘年來物理學界熱門的研究話題。最近(2013 年)，Fedorov 和 Nakajima 研究得出使用非左手材料如金屬材質也可得到負折射現象，這篇研究對於不均勻波的敘述以及材料結構有更深一層的探討。本篇論文將金屬取代為半導體，使用 InSb 作為半導體材料。我們參考 Sánchez 和 Halevi 於 2003 年發表的研究報告，當中對於 InSb 材料參數講述詳細。基於先前的研究成果，我們根據真實實驗數據進行理論數據模擬，成功找出發生負折射現象的最佳條件。並且，對於參數間的相互影響也進行了詳盡的分析。半導體性質受三種參數影響：溫度、參雜濃度、入射波頻率。在此，利用 Snell's law 進行相關推導，找出折射角與材料參數之間的關係，此關係式讓我們判斷負折射現象的發生。接著，我們將半導體材料以及介電材料進行週期性排列，形成一維光子晶體。光子晶體有獨特的特性，除了半導體參數影響外，厚度比例也是影響的因素。我們設定光波沿 x-z 正向傳播，使用群速度作為判斷負折射現象發生條件。當 x 方向的群速度沿相反方向行進，可判斷負折射現象發生。本論文架構如下：第一章講述 InSb 基本參數、不均勻波理論以及光子晶體概論等基本介紹；第二章講述本論文重點理論-負折射現象的基本概念；第三章推論出在不均勻介質中，負折射理論的關係式；第四章，進入本篇論文主要研究，分別闡述理論以及展現數值分析結果，詳盡的描述材料參數的相互關係；最後，在第五章，我們從半導體光子晶體基本理論出發，完整推導在光子晶體中，群速度的表達式，並且改變模擬的操作變因，多面向地分析負折射發生條件以及負折射發生之明顯程度。關鍵字：負折射現象、半導體、光子晶體、群速度、不均勻波 II.

(4) 致謝. 研究接近尾聲，本篇論文能夠順利完成，首先要感謝我的指導教授吳謙讓博士的悉心指導，給予論文上的指導以及生活上的關心及勉勵。以及，指導教授李敏鴻博士於半導體專業領域的指導，其專業廣博的學術令學生於求學期間受益良多，師恩浩瀚，永銘於心。口試期間，承蒙長庚大學光電研究所張宗文博士於百忙中撥冗費心審閱，並提供許多精闢的見解，使本論文更加完備，惠我良多，僅申謝忱。研究期間，感謝學長家瑋學長、昱志學長、岳龍學長以及同窗好友冠甫、為頡，給予我研究上的建議及協助，使得論文能順利完成。同時，也要感謝十年好友渝筠、孟伶、秉軒、幸嚴、徹峰、仕倫、庭姍…等數十位高中朋友以及高中教師源隆老師，謝謝你們在我面臨情感相關問題以及在人生路途上迷茫時給予我關懷以及支持。感謝鈺屏學姊、淑慧學姊、良佑學長、勝勳學長在我尋找研發替代役職缺期間給予的建議以及幫助，令我獲益良多。同時，感謝逢甲大學林立謙老師及研究室朋友海峰、彥翔、振添以及就讀中正大學的朋友准誠，在研究期間給予我許多建言及鼓勵。除此之外，感謝我的女友佩珊，謝謝妳陪伴我度過研究這些日子，給我繼續前進的力量。最後，謝謝我的家人，感謝你們給予我生活上的支持並且深信著我能夠在研究上做出成果，你們總是在背後默默的支持我，長久以來辛苦你們了，謝謝你們。. 僅以此篇致謝，送給我在我求學期間幫過我的所有師長以及朋友. III.

(5) Contents. Abstract. I. Chinese Abstract. II. Acknowledgements. III. Contents. IV. Chapter 1 Introduction 1-1 Negative refraction in optics. 1. 1-2 General properties of inhomogeneous waves. 2. 1-3 Electromagnetic model of InSb. 4. 1-4 Photonic crystals. 6. 1-5 Format of thesis. 9. Chapter 2 Negative refraction in double negative media 2-1 Introduction. 10. 2-2 Electromagnetic wave propagation in DNG media. 12. 2-3 Negative refraction in lossy materials. 14. Chapter 3 Negative refraction in inhomogeneous waves 3-1 Introduction. 16. Inhomogeneous wave in a single interface of lossy 3-2. 17 metamaterial. 3-3 Generalized Laws of Reflection and Refraction. 23. 3-4 Transmission angle in inhomogeneous medium. 27. IV.

(6) Chapter 4 Negative refraction in air/InSb interface 4-1 Introduction. 30. 4-2 Basic equations. 30. 4-3 Two possible polarizations for the incident wave. 32. 4-4 Numerical illustration of negative refraction. 35. 4-5 Tunable NR in air/InSb. 37. 4-6 Frequency-dependent negative refraction. 42. 4-7 Temperature-dependent negative refraction. 45. 4-8 Doping concentration dependence of negative refraction. 47. Chapter 5 Negative refraction in an InSb-based photonic crystal 5-1 Theoretical analysis. 49. 5-2 Group velocity and negative refraction. 53. 5-3 Negative refraction in an infinite semiconductor photonic 58 crystals 5-4 Summary. 64. Chapter 6 Conclusions. References. 66. V.

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