臺灣博碩士論文加值系統

摘要

隨著科技的日新月異人類的的生活水準也日益提升，傳統的基體電路已不能滿足現今人們的需求，因此研發更新型、更具功能性的光電元件來因應人類的需求是刻不容緩的課題。本論文提出以光子晶體的基本物理特性及常用的數值演算法，並藉由數值計算及模擬，將光子取代電子作為訊號的傳遞，實現奈米積體光學檢測元件之光子晶體同位元訊號檢測器設計。
研究中，將平面波展開法(Plane Wave Expansion Method)及時域有限差分法(Finite-Difference Time-Domain Method, FDTD Method)，加以分析光子晶體波導物理特性，搭配傳統光學的波導設計以及介電質材料的選擇，得以找到最佳化參數來實現奈米積體光學檢測元件之光子晶體同位元訊號檢測器，其具有良好導光效率、體積小、不易受電磁波的干擾及不易受溫度變化影響等優點。另外，我們也設計了一種新型波導結構-狹縫式波導(slot-waveguide)，期待此種型式的波導結構會在光電元件及積體光學中扮演重要角色。

Abstract

As the technology as well as the living standard of human being are improving day by day, the traditional circuit matrix is no longer meet the demand. Thus, the development of novel optical components with more functions is a very urgent issue. Development of novel optical components with more functions is a very urgent issue. In this thesis, a fundamental physical property of photonic crystal and numerical algorithms via calculation and simulation were used. The signal transmission by electrons will be replaced by photon as a signal transmission medium in order to achieve the detection of nano-optical components integrated.

In this study, the plane wave expansion method (Plane Wave Expansion Method), FDTD (Finite-Difference Time-Domain Method, FDTD Method) are used. The analysis of photonic crystal waveguide physical characteristics, design of conventional optical, and selection of material of dielectric medium help us to optimize the parameters to achieve the detection of nanometer integrated optical components. The advantage of this method is that it has good optical efficiency, smaller size, less susceptible to both electromagnetic interference and temperature change, and so on. In addition, we also design a new type of waveguide structure - slit-type waveguide (slot-waveguide), and it is expected to play an important role in optoelectronic integrated optical components.

目錄

中文摘要 i
英文摘要 ii
目錄 iv
圖目錄 vi

第一章 導論 1
1-1 緒論 1
1-2 研究目的及方法 2
1-3 論文架構 3

第二章 數值分析與基本概念 4
2-1 光子晶體的基本原理 4
2-2 晶格、倒晶格與週期函數 8
2-3 波動方程式 9
2-4 數值分析方法 11
2-4-1 平面波展開法(Plane wave expansion method) 12
2-4-2 有限時域差分法(FDTD method) 13
2-4-3 二維FDTD形式 15
2-5 入射波源 18
2-6 布里淵區 19
2-7 光子能帶成因 21
2-8 能帶結構 22

第三章 光子晶體奈米元件之設計與分析 23
3-1 週期性陣列排列光子晶體 24
3-2 光子晶體設計奈米級光學檢測器 25
3-2-1 光子晶體互斥或閘(XOR Gate) 25
3-2-2 光子晶體同位元訊號檢測器 27
3-3 狹縫式波導(Slot-Waveguide) 41
3-4 總結 44

第四章 結論 45

第五章 參考文獻 46



圖目錄

圖2-1 材料折射率週期性變化的結構示意圖。 6
圖2-2 典型的二維光子晶體能帶結構圖。 7
圖2-3 Yee’s晶格圖，電場及磁場在空間上的分割表示。 15
圖2-4 二維Yee’s晶格圖，電場及磁場在分空間上的分割。 17
圖2-5 三角晶格結構。 20
圖2-6 三角晶格的第一布里淵區，灰色區域為最簡布里淵區。 20
圖2-7 正方晶格光子晶體的頻帶結構圖。 22
圖3-1 二維光子晶體結構示意圖。 25
圖3-2 互斥或閘(XOR Gate)光子晶體波導設計圖。 26
圖3-3 四位元同位元檢測器電路圖。 28
圖3-4 同位元檢測器電子動作真值表。 29
圖3-5 同位元檢測器之光子晶體波導設計圖。 32
圖3-6 同位元檢測器，A0輸入端輸入光源的FDTD光場圖。 33
圖3-7 同位元檢測器，A0輸入端輸入光源的電場能量圖俯視圖。 33
圖3-8 同位元檢測器，A2、A3輸入端輸入光源的FDTD光場圖。 34
圖3-9 同位元檢測器，A2、A3輸入端輸入光源的電場能量圖俯視圖。 34
圖3-10 同位元檢測器，A1、A3輸入端輸入光源的FDTD光場圖。 35
圖3-11 同位元檢測器，A1、A3輸入端輸入光源的電場能量圖俯視圖。 35
圖3-12 同位元檢測器，A1、A2、A3輸入端輸入光源的FDTD光場圖。 36
圖3-13 同位元檢測器，A1、A2、A3輸入端輸入光源的電場能量圖俯視圖。 36
圖3-14 同位元檢測器，A0、A2輸入端輸入光源的FDTD光場圖。 37
圖3-15 同位元檢測器，A0、A2輸入端輸入光源的電場能量圖俯視圖。 37
圖3-16 同位元檢測器，A0、A1輸入端輸入光源的FDTD光場圖。 38
圖3-17 同位元檢測器，A0、A1輸入端輸入光源的電場能量圖俯視圖。 38
圖3-18 同位元檢測器，A0、A1、A2輸入端輸入光源的FDTD光場圖。 39
圖3-19 同位元檢測器，A0、A1、A2輸入端輸入光源的電場能量圖俯視圖。 39
圖3-20 同位元檢測器，A0、A1、A2、A3輸入端輸入光源的FDTD光場圖。 40
圖3-21 同位元檢測器，A0、A1、A2、A3輸入端輸入光源的電場能量圖俯視圖。 40
圖3-22 狹縫波導結構設計示意圖。 41
圖3-23 狹縫波導立體剖面圖，覆蓋層波導與傳導層波導。42
圖3-24 狹縫波導，輸入端輸入光源的FDTD光場圖。 43
圖3-25 狹縫波導，輸入端輸入光源的電場能量圖俯視圖。 43
圖3-26 狹縫波導，輸入端輸入光源的截取單一波峰電場能量圖。 44

參考文獻

[1] Yaw-Dong Wu, All-Optical Logic Gates by Using Multibranch Waveguide Structure With Localized Optical Nonlinearity, IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 11, NO. 2, MARCH/APRIL 2005.
[2] S. Kumar, D. Gurkao, A. E. Willner, and K. Parameswaran, M. Fejer, All-optical half adder using a PPLN waveguide and an SOA, 02004 Optical Society of America, (060.2330) Fiber optics wmmunicalions, (070.4560) Optical data processing.
[3] Tetsuro Yabu, Masahiro Geshiro, Toshiaki Kitamura, Kazuhiro Nishida, and Shinnosuke Sawa, All-Optical Logic Gates Containing a Two-Mode Nonlinear Waveguide, IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 38, NO. 1, JANUARY 2002.
[4] Katsumi Nakatsuhara, Seok-Hwan Jeong, Yukio Tsukishima and Tetsuya Mizumoto, Demonstration of all-optical AND gate operation in a GaInAsP waveguide, 0-7803-5661-I69 9 / 1999 IEEE.
[5] K. Nakatsuhara, S. H. Jeong, Y. Tsukishirna, T. Mizumoto B. J. Mat and Y. Nakanot, Demonstration of all-optical threshold operation in GaInAsP distribnted feedback waveguides and its application to AND gate, IEEE.
[6] E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and
electronics,” Physical Review Letters, Vol.58, pp.2059-2062 (1987).
[7] S. John, “Strong localization of photons in certain disordered dielectric
superlattices,” Physical Review Letters, Vol.58, pp.2486-2489 (1987).
[8] E. Yablonovitch, “ Photonic Band-gap structures,” J. Opc. Amer. B, vol. 10, pp. 283-295, Feb. 1993.
[9] http://ab-initio.mit.edu/photons/tutorial
[10] J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals—Molding the Flow of Light, Princeton University Press (1995).
[11] K. Sakoda, Optical Properties of Photonic Crystals, Springer, Berlin (2001).
[12] Bikash C. Gupta, Chao-Hsien Kuo, and Zhen Ye, “Propagation inhibition and
localization of electromagnetic waves in two- dimensional random dielectric
systems,” Phys. Rev. E 69, 066615 (2004).
[13] A. Taflove, Computational Electrodynamics, Artech House, Boston, (1995).
[14] J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
[15] J. D. Jackson, Classical electrodynamics 3rd, John Wiley&Sons, New York, (1999).
[16] K. M. Ho, C. T. Chan and C. M. Soukoulis, “Existence of photonic gap in periodic dielectric structures,” Physical Review Letters, Vol.65, pp.3152-3155 (1990).
[17] K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Physical Review Letters, Vol.65, pp.2646-2649 (1990).
[18] Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Physical Review Letters, Vol.65, pp.2650-2653 (1990).
[19] J. Yonekura, M. Ikeda and T. Baba, “Analysis of finite 2-D photonic crystals of columns and lightwave devices using the scattering matrix method,” Journal of Lightwave Technology, Vol.17, pp.1500-1508 (1999).
[20]A. Taflove, Computational Electrodynamics, Artech House, Boston, (1995).
[21] S.-T. Chu and S. K. Chaudhuri, “A finite-difference time-domain method for the design and analysis of guided-wave optical structures,” Journal of Lightwave Technology, Vol.7, pp.2033-2038 (1989).
[22] C. T. Chan, Q. L. Yu and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Physical Review B, Vol.51, pp.16635-16642 (1995).
[23] L. Shen, S. He and S. Xiao, “A finite-difference eigenvalue algorithm for calculating the band structure of a photonic crystal,” Computer Physics Communications, Vol.143, pp.213-221 (2002).
[24] S. Yamada, Y. Watanable, Y. Katayama and J. B. Cole, “Simulation of optical pulse propagation in a two-dimensional photonic crystal waveguide using a high accuracy finite-difference time-domain algorithm,” Journal of Applied Physics, Vol.93, pp.1859-1864 (2003).