跳到主要內容

臺灣博碩士論文加值系統

(3.90.139.113) 您好!臺灣時間:2022/01/16 17:59
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

: 
twitterline
研究生:陳科遠
研究生(外文):Ke-Yuan Chen
論文名稱:一維與二維光子晶體之分析與模擬
論文名稱(外文):Analysis and Simulation of 1-D and 2-D Periodical Photonic Crystal
指導教授:謝太炯
指導教授(外文):Tai-Chiung Hsieh
學位類別:碩士
校院名稱:國立交通大學
系所名稱:電子物理系
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:104
中文關鍵詞:光子晶體模擬MathCADC語言
外文關鍵詞:photonic crystalsimulationMathCADlanguage C
相關次數:
  • 被引用被引用:3
  • 點閱點閱:375
  • 評分評分:
  • 下載下載:74
  • 收藏至我的研究室書目清單書目收藏:3
當兩種不同介電常數的材質在空間中成週期性的排列,則某些特定波長的光波或電磁波會被排斥,亦即在該頻率電磁波不能存在其間。材料的結構具備這種光子能隙的性質者,稱為光子晶體。
本論文從一個平面波展開法的數學通式出發,探討光子晶體的TE及TM的波動行為。在一維光子晶體的分析,實際的情形是有限週期的結構及材質具有耗損(σ≠0)性質,因為偏離平面波展開法所能處理之範圍,改採傳輸矩陣法,其結果和平面波展開法在零損耗的的結果大致符合。從一維光子晶體的分析嘗試設計工作波長為1500nm的光濾波器的設計,其通帶的寬度約為130nm;以矽及砷化鎵為例,光晶的空間週期長度約為1μm,所設計的濾波器允許入射角的範圍約為15°,在此角度範圍內的光子能隙相當完整。同樣使用平面波展開法應用到二維光子晶體的計算,其結果和已知文獻之結果大致符合。本論文主要以建立光子晶體之模擬方法為主,數學的計算包括MathCAD及C語言的程式編寫,但尚未進行光子晶體的實驗驗證。
Materials with periodic dielectric structure have the property to suppress or allow the propagation of the electromagnetic waves in them for only some specific wavelengths. It means that light with specific wavelength can not subsist in such a material structure. Materials with this property is named as photonic crystal.
This study aims at the development of simulation technique to investigate the photonic crystal or photonic bandgap structure. We use MathCAD and C++ -Language in calculations.
We formulate the photonic crystal equations mainly with the Plane Wave Method Expansion Method. This method is efficient in investigating the behavior of transverse-electric modes and transverse—magnetic modes of electromagnetic waves in photonic crystal. However, for the analysis of 1-dimensional (1-D) photonic crystal where the material is lossy (σ≠0) and the dielectric distribution has finite periodicity, we adopt the Transfer Method for the reason that the Plane Wave Expansion Method is not appropriate in dealing with those problems. The solutions for the lossless material obtained by the Transfer Method agree basically with that of the Plane Wave Method Expansion Method. From the analysis for 1-D photonic crystal, we also propose the implementing structures of an optical filter which has a center wavelength 1500nm with a bandwidth of nearly 130nm. Taking Si and GaAs as base materials, according to the simulations, the proposed 1-D structure has period around 1μm in space. This filter possesses still wide frequency bandgap for an oblique incidence of light at angle within ±30°.
We also apply the Plane Wave Expansion Method to deal with the 2- dimensional (2-D) photonic crystal. Since at this stage of study no experimental work is conducted to verify our simulations, the numerical results of 1-D and 2-D simulations can only be compared with the published data found in the literature. The fair agreement of our results with that of the literature would suggest that the so far self-developed simulation technique is acceptable, although it needs surely further work of improvement.
第一章 導論─光子晶體的基本分析法
第二章 一維光子晶體之平面波展開法
2.1. 平面波展開法
2.1.1 垂直入射
2.1.2 斜向入射
2.1.3 斜向入射模擬結果分析
2.2. 電磁波在光晶中的狀態
2.3. 討論
第三章 傳輸矩陣計算法─模擬有限尺度的一維光晶
3.1. 損耗介質的穿透率
3.2. 傳輸矩陣法與平面波展開法結果比較
3.3. 縮減光晶的週期數
3.4. 複合式光子晶體
3.5. 討論
第四章 二維光子晶體理論與分析
4.1. 平面波展開法
4.1.1 TE波
4.1.2 TM波
4.2. 模擬平面波展開法
4.3. 非平面傳播 (Out-of-Plane Propagation)
4.4. 電磁波在光晶中的分佈
4.5. 討論
第五章 結論
參考文獻
附錄
附錄A 一維光晶之平面波展開法程式
附錄A-1 一維光晶垂直入射
附錄A-2 一維光晶斜向入射 (E垂直極化)
附錄A-3 一維光晶斜向入射 (E平行極化)
附錄A-4 一維光晶 : 以H展開求E、H
附錄B 一維光晶之傳輸矩陣法程式
附錄B-1 一維光晶 : 傳輸矩陣法
附錄B-2 一維光晶 : 波在帶拒區的衰減
附錄C 二維光晶之平面波展開法程式
附錄C-1 二維光晶─方形陣列
附錄C-2 二維光晶─圓柱六角陣列
附錄C-3 二維光晶- TE wave電場分佈
1. E. Yablonovitch : Phys. Rev. Lett., Vol.58, p2059 (1987)
2. S. John and R. Rangarjan : Phys. Rev. Lett. B, Vol 38, 10101 (1988)
3. M. Plihal and A. A. Maradudin : Phys. Rev. B, Vol 44, 8569 (Oct, 1991)
4. Karlheinz Bierwirth : IEEE Trans. Microwave Theory and Tech., Vol 34,
p1104 (Nov, 1986)
5. Dennis M. Sullivan : Electromagnetic Simulation Using The FDTD Method.
IEEE press, New York, 2001
6. S.T. Peng(彭松村) and C.K. Tzuang(莊晴光): The lecture on Photonic Bandgap Structure at Chiao Tung University, Aug 20, 2001
7. Russel et al. : J. Lightwave Technol. 17, p1982 (1999)
8. W.F. Hsieh(謝文峰) : 台灣光電科技研究所會, p459 ~ p467, 2001.
9. Giuseppe Grosso : Solid State Physics.
10. Robert D. Meade, John D. Joannopoulos, et al :
Appl. Phys. Lett., Vol 61, p495~497 (July, 1992)
11. John D. Joannopoulos : Photonic Crystals, Princeton University Press,1995.
12. K. M. Leung : Physical Review Letter, Vol 65, p2646, Nov, 1990 .
13. Ze Zhang : Physical Review Letter, Vol 65, p2650, Nov, 1990 .
14. A.A. Maradudin : Journal of Modern Optics, Vol 41, p275~284, 1994.
15. Shandon D.Hart, Garry R. Maskaly and Joannopoulos :
SCIENCE, Vol 296, p510~513 (April, 2002)
16. V. Lehmann : The Electrochemical Society, Vol.140, No.10 (Oct, 1993)
17. Lightwave Devices Group MESA, University of Twente,
http://www.el.utwente.nl/tdm/ldg/research/pc_dev/PosterPrague2000.pdf
18. D. Cassagne, C. Jouanin, and D. Bertho:
Physical Review B, Vol 53, No. 11, p7134~7142 (Mar 1996)
19. Roberto Coccioli, Tatsuoh Itoh (UCLA):
Photonic Band Engineering MURI Annual Review Meeting, Nov. 18, 1999
http://www.ee.ucla.edu/~pbmuri/index.html
20. Ramòn Gonzalo : Microwave & Opt. Tech. Letters. Vol. 23, No. 2 (Oct 20, 1999)
21. M. Plihal and A. A. Maradudin : Physical Review B. Vol. 44, No. 16, p8586~8570, (Oct 15, 1991)
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top