臺灣博碩士論文加值系統

摘要

　　本論文中，以有限元素法模擬一維光子晶體，討論其能隙和晶體結構之間的關係。如適當地破壞光子晶體之週期性，製造出缺陷，則能在光子晶體能隙之中開闢出缺陷模態( defect mode )，在光波無法穿透的波段之開出可通過的波長。利用缺陷模態的概念，我們可設計出可取出一個或多個所需波長之光子晶體濾波器。

　　利用三個缺陷之間微弱的耦合，使其缺陷模態重疊，製造出平坦可通過之波段( pass band )。如此，耦合缺陷模態外形更接近長方形，藉此優化濾波器。此外，亦設計含四個耦合缺陷來優化雙缺陷之光子晶體濾波器。

　　將向列型液晶( nematic liquid crystal )當成缺陷引入一維光子晶體結構，如此，可以外加電場改變其光學性質，使其缺陷模態發生變化。利用此可控制的缺陷模態，進一步設計出光開關。

Abstract
In this dissertation, we present the finite element method to simulate the optical response of a finite one-dimensional (1D) photonic crystal (PhC). We discussed the relation between the photonic bandgap and the parameters of the photonic crystal structure. We can find a defect mode that let the light wave with specific wavelength pass through the structure by introducing a defect into a periodic PhC. Utilizing the concept of defect mode, we can design a photonic crystal filter which can take out the light wave with one or more wavelength.

We can create a flat pass band by utilizing the three coupled defects to make their defect modes overlapping, therefore, the shape of the coupled defect mode can be much closer to a rectangle. In addition, we optimized the two-wavelength filter with four coupled defect modes.

A nematic liquid crystal defect layer is introduced into a 1D PhC and the refractive index of the liquid crystal can be controlled by an external electric field. Thus, the defect mode can be tuned. By making use of the tunable defect mode, we can design an optical switch further.

目 錄

摘要 Ⅰ
Abstract Ⅱ
目錄 Ⅲ
圖目錄 Ⅴ
符號說明 Ⅸ
第一章 緒論 1
1-1 前言 1
1-2 文獻回顧 2
1-3 本文架構 4
第二章 光子晶體能隙與群速度 7
2-1 前言 7
2-2 有限元素法 7
2-3 群速度 15
第三章 光子晶體與帶有缺陷之光子晶體結構 22
3-1一維光子晶體結構 22
3-2含單一缺陷之一維光子晶體結構 23
3-3含多缺陷之一維光子晶體結構 26
第四章 含向列型液晶之光子晶體及其應用 45
4-1 液晶簡介 45
4-1-1 概述 45
4-1-2 液晶之分類 46
4-1-3 液晶分子之秩序參數 47
4-1-4 液晶之複折射性 47
4-2 利用液晶材料為缺陷之一維光子晶體結構 48
4-3 光開關之應用 49
第五章 綜合結論 56
參考文獻 57

參考文獻

1.E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
2.S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987).
3.K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: New layer-by-layer periodic structures,” Solid State Commun. 89, 413-416 (1994).
4.S. Y. Lin and J. G. Fleming, “A Threee-Dimensional Optical Photonic Crystal,” J. Lightwave Technol. 17, 1944-1947 (1999).
5.S. Noda, N. Yamamoto, M. Imada, H. Kobayashi, and M. Okano, “Alignment and Stacking of Semiconductor Photonic Bandaps by Wafer-Fusion,” J. Lightwave Technol. 17 1948-1955 (1999).
6.K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152-3155 (1990).
7.E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: The face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295-2298 (1991).
8.P. M. Bell, J. B. Pendry, L. M. Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306-322 (1995).
9.C. T. Chan, Q. L. Yu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B 51, 16635–16642 (1995).
10.X. Wang, X. G. Zhang, Q. Yu, B. N. Harmon, “Multiple scattering theory for electromagnetic waves,” Phys. Rev. B 47, 4161–4167(1993).
11.J. Jin, The Finite Element Method in Electromagnetics. 2nd, (IEEE, 2002)
12.A. Suryanto, E. Vangroesen, M. Hammer and H. J. W. M. Hoekstra, “A finite element scheme to study the nonlinear optical response of a finite grating without and with defect”Optical and Quantum Electronics 35 313-332(2003)
13.A. Suranto, E. Vangroesen, and M. Hammer, “Finite element analysis of optical bistability in one dimensional nonlinear photonic band gap structures with a defect” Journal of Nonlinear Optical Physics & Materials 12 187-204(2004)
14.Q. Hong and T. X. Wu, “Optical wave propagation in a cholesteric liquid crystal using the finite element method” Liquid Crystal 30 367-375
15.B. P. Hiett, J. M. Generowicz, S. J. Cox, M. Molinari, D. H. Beckett and K. S. Thomas, “Application of finite element methods to photonic crystal modelling” IEE Proc. Sei. Meas. Technol. 149 293-296(2002)
16.J. Y. Chen and L. W. Chen, “Photonic defect modes of cholesteric liquid crystal with spatially varying pitch” Physica B 357 282-289(2005)
17.A. Mekis, J. C. Chen, I. Kurland, S. Fan, Pierre R. Villeneuve, and J. D. Joannopoulos, ” High Transmission through Sharp Bends in Photonic Crystal Waveguides.” Phys. Rev. Lett. 77 3787-3790(1996)
18.J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N. J., 1995).
19.S. Fan, P.R. Villeneuve, J.D. Joannopoulos, H.A. Haus, “Channel Drop Tunneling through Localized States” Phys.Rev. Lett. 80, 960-963 (1998)
20.M. Qiu, B. Jaskorzynska, “Design of a channel drop filter in a two-dimensional triangular photonic crystal” Appl. Phys. Lett. 83, 1074 (2003)
21.J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, Henry I. Smith, E. P. Ippen,”Photonic bandgap microcavities in optical waveguides.”Nature 390, 143-145 (1997)
22.A. S. Jugessur, P. Pottier, and R. M. De La Rue, ,” Engineering the filter response of photonic crystal microcavity filters”Optics Express 12, 1304-1312 (2004)
23.S. Noda, A. Chutinan, M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure.”Nature 407, 608-610 (2000)
24.M.Bayindir, B. Temelkuran, E. Ozbay, “Photonic crystal based beam splitters”App. Phys. Lett. 77 3902-3904 (2000)
25.M. Bayindir and E. Ozbay, “Heavy photons at coupled cavvity waveguide band edges in a three-dimensional photonic crystal”, Phys. Rev. B 62 R2247-R2250(2000)
26.A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single photon tunneling time” Phys. Rev. Lett. 71, 708-711(1993)
27.J. M. Bendickson, and J. P. Dowling, “Analytic expressions for the electromagnetic mode density in finite, one dimensional, photonic band-gap structures” Phys. Rev. E 53 ,4107-4121(1996)
28.S. Lan, S. Nishikawa, and H. Ishikawa“Design of imprity band-based photonic crystal waveguides and delay lines for ultrashort optical pulses” J. App. Phys. 90 4321 - 4327(2001)
29.S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, “Analysis of defect coupling in one- and two-dimensional photonic crystals” Phys. Rev. B 65 165208-1(2002)
30.T. Fukamachi, K. Hosomi, T. Katsuyama, and Y. Arakawa, “Group delay properties of coupled-defect structures in photonic crystals” J. Appl. Phys. 43 L449-L452(2004)
31.I. D. Villar, I. R. Matias, and F. J. Arregui, “Fiber-optic multiple-wavelength filter based on one-dimensional photonic bandgap structure with defects” J. Lightwave Technol. 22 1615-1621 (2004)
32.Young-Ki Ha, Y.-C. Yang, J.-E. Kim, and H. Y. Park, “Tunable omnidirectional reflection bands and defect modes of a one dimensional photonic band gap structure with liquid crystals” Appl. Phys. Lett. 79 15-17(2001)
33.R. Ozaki, T. Matsui, M. Ozaki, and K. Yoshino, “Electrically wavelength tunable laser based on one dimensional structure with liquid crystal defect layer” Electronics and Communications in Japan, Part 2, 87,1-8(2004)
34.R. Ozaki, T. Matsui, M. Ozaki, and K. Yoshino,” Optical property of electro-tunable defect mode in 1D periodic structure with light crystal defect layer” Electronics and Communications in Japan, Part 2, 87, 24-31(2004)
35.Chen-Yang Liu, and Lien-Wen Chen,“Tunable Photonic Crystal Waveguide Mach-Zehnder Interferometer Achieved by Nematic Liquid-Crystal Phase Modulation,” Optics Express, Vol. 12, No. 12, pp. 2616-2624(2004)
36.M. Faith, S. Fan, “High contrast all-optical bistable switching in photonic crystal microcavities.” App. Phys. Lett. 83 2739-2741 (2003)
37.M. Solia i , M. Ibanescu, S. G. Johnson, Y. Fink, J. D. Joannopoulos,”Optimal bistable switching in nonlinear photonic crystals.”Phys. Rev. E 66 055601(R)
38.K. Busch, “Photonic band structure theory : assessment and perspectives,” C. R. Physique 3, 53-66 (2002).
39.V. Yu. Pervak and Yu. A. Pervak,” Suppression of Background Transmission of Interference Filters”Optics and Spectroscopy 88 507-511(2000)
40.A. Yariv, and P. Yeh Optical waves in crystals. New York 1984
41.松本正一, 角田市良, “液晶之基礎與應用”國立編譯館出版, 1996