臺灣博碩士論文加值系統

本論文主要是針對幾種二維光子晶體波導的延遲線做設計及分析，包括六種延遲線結構的作法：一是改變線缺陷波導兩旁的空氣孔半徑，二是改變線缺陷波導兩旁的空氣孔位置，三是線缺陷波導兩旁使用空氣環結構，四是膠囊形空氣孔的光子晶體波導，五是使用W2型波導，六是使用耦合共振腔波導。在數值方法方面，我們使用平面波展開法來計算光子能隙和色散曲線，藉以分析各種延遲線結構的群速度和群折射率，並且計算出其延遲頻寬乘積。我們發現，適當調整線缺陷波導兩旁的空氣孔結構，可以有效提高延遲線的群折射率和延遲頻寬乘積。其中藉由改變空氣孔的半徑或位置，可使延遲頻寬乘積提升到0.1以上，或是使用空氣環的方式，可使延遲頻寬乘積提昇到0.33；至於使用膠囊形空氣孔的方式，也可以使延遲頻寬乘積提昇到接近0.25。相較於一個未經設計的線缺陷波導而言(延遲頻寬乘積為0.03)，以上幾種結構確實可大幅改善光子晶體延遲線的效能。

This work is focused on the design and analysis of optical delay lines in two-dimensional photonic crystals. Six delay line structures are discussed in this work. The first one is by adjusting the radii of air holes adjacent to a line-defect waveguide. The second one is by adjusting the positions of air holes adjacent to a line-defect waveguide. The third one is by employing air rings adjacent to a line-defect waveguide. The fourth one is a photonic crystal waveguide with capsule-shaped air holes. The fifth one is a W2 waveguide. And the sixth one is a coupled-cavity waveguide. As for the numerical method, the plane wave expansion method is employed to calculate photonic bandgaps and dispersion curves. Group velocity, group index, and delay-bandwidth product (DBP) can therefore be obtained. By adjusting the structure of air holes adjacent to the line-defect waveguide, both group index and DBP can be enhanced. The DBP can be made larger than 0.1 by adjusting the radii or positions of air hole. By employing air rings, a DBP of about 0.33 can also be obtained. By using capsule-shaped air holes, a DBP of about 0.25 can also be obtained. Compared to a primitive line-defect waveguide (with a DBP = 0.03), the six structures studied in this work can really be used to improve the performance of photonic crystal delay lines.

中文摘要 i
ABSTRACT ii
誌謝 iv
目錄 v
表目錄 vii
圖目錄 viii
第一章 導論 1
1.1 光子晶體簡介 1
1.2 研究動機 3
1.3 文獻回顧 4
1.3.1 改變波導兩側的空氣孔大小 4
1.3.2 改變波導兩側的空氣孔位置 4
1.3.3 在波導兩側使用空氣環結構 5
1.3.4 膠囊形空氣孔的光子晶體 5
1.3.5 W2型波導 5
1.3.6 耦合共振腔波導 6
1.4 論文架構 8
第二章 數值方法 9
2.1 馬克斯威爾方程式 9
2.2 平面波展開法 11
2.3 時域有限差分法 14
2.3.1 Yee演算法及Yee晶格 14
2.3.2 中央差分展開馬克斯威爾方程式 16
2.4 色散曲線、群速度和延遲頻寬乘積 17
第三章 延遲線波導的分析 21
3.1 基本的W1線缺陷波導 21
3.2 改變波導兩側的空氣孔大小 25
3.3 改變波導兩側的空氣孔的位置 35
3.4 在波導兩側使用空氣環結構 44
3.5 膠囊形空氣孔的光子晶體 49
3.6 W2型波導 56
3.7 耦合共振腔波導 60
3.8 延遲頻寬乘積的整理 67
第四章 結論 69
參考文獻 70

[1] A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett., 24, no.11, pp. 711-713, 1999.
[2] A. Taflove, Computational Electromagnetics: The Finite-difference Time-Domain Method (Artech House, Norwood, Ma, 1995)
[3] A. Saynatjoki, “Dispersion engineering of photonic crystal waveguides with ring-shaped holes,” Opt. Express, vol.15, no. 13, pp. 8323-8328, June, 2007.
[4] A. Chutinan, “Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. vol. 80, no. 10, pp. 1698-1700, Mar. 2002.
[5] A. Chutinan, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B, vol. 62, no. 7, pp. 4488-4492, Aug. 2000.
[6] Daisuke Mori, “Dispersion-controlled optical group delay device by chirped photonic crystal waveguides,” Appl. Phys. Lett., vol. 85, no. 7, pp.1101-1102, Aug. 2004.
[7] D. Mori and T. Baba, “Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide,” Opt. Express, vol. 13, pp. 9398–9408, Nov. 2005.
[8] E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett., vol. 58, pp. 2059-2062, 1987.
[9] E. Yablonovitch, “Photonic crystals: semiconductor of light,” Scientific American, vol. 285, no. 6, pp. 47-55, 2001.
[10] G. Lenz, “Optical delay lines based on optical filters,” IEEE Journal of Quantum Electronics, vol. 37, no. 4, pp.525-532, Apr. 2001.
[11] Joyce K. S. Poon, “Designing coupled-resonator optical waveguide delay lines,” Opt. Soc. Am. B, vol. 21, no. 9, pp.1665 -1673, Sep. 2004.
[12] J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express, vol. 16, pp. 6227–6232, Apr. 2008.
[13] J. Grgic, “Group index limitations in slow-light photonic crystals,” Photonic and Nanostructures – Fundamentals and Applications, vol. 8, pp. 56-61, 2010.
[14] J.-M. Brosi, J. Leuthold, and W. Freude, “Microwave-frequency experiments validate optical simulation tools and demonstrate novel dispersion-tailored photonic crystal waveguides,” vol. 25, no. 9, pp. 2502-2510, Sep. 2007.
[15] J. He, “Slow light in a dielectric waveguide with negative-refractive-index photonic crystal cladding,” Opt. Express, vol. 16, no. 15, pp. 11077-11082, July 2008.
[16] L. H. Frandsen, A. V. Lavrinenko, J. Fage-Pedersen, and P. I. Borel, “Photonic crystal waveguides with semi-slow light and tailored dispersion properties,” Opt. Express, vol. 14, pp. 9444–9450, Oct. 2006.
[17] L. Dai, “Photonic crystal slow light waveguides with large delay-bandwidth product,” Appl. Phys. B, vol. 95, pp.105-111, Apr. 2009.
[18] Min Qiu, “Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals,” Appl. Phys. Lett., vol. 81, no.7, pp. 1163-1165, Aug. 2002.
[19] M. S. Moreolo and G. Cincotti, “Performance enhancement of photonic crystal slow-light devices,” ICTON, pp. 34-37, 2008.
[20] M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth,” Opt. Express, vol. 15, pp. 219–226, Jan. 2007.
[21] R. S. Tucker, P.-C. Ku, and C. J. Chang-Hasnain, “Slow-light optical buffers: capabilities and fundamental limitations,” J. Lightwave Technol., vol. 23, no.12, pp. 4046-4066, Dec. 2005.
[22] S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett., vol. 58, pp. 2486-2489, 1987.
[23] S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express, vol. 8, pp. 173-190, 2001.
[24] Steven G. Johnson, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B, vol. 62, no. 12, pp. 8212-8222, Sep. 2000.
[25] Steven G. Johnson, “Guide modes in photonic crystal slabs,” Phys. Rev. B, vol. 60, no. 8, pp. 5751-5758, Aug. 1999.
[26] T. F. Krauss, “Slow light in photonic crystal waveguides,” J. Phys. D: Appl. Phys., vol. 40, pp. 2666-2670, 2007.
[27] Yun-Sheng Chen, “Delay-time-enhanced flat-band photonic crystal waveguide with capsule-shaped holes on silicon nanomembrane,” IEEE J. Sel. Topics in Quantum Electron., vol. 15, no. 5, pp. 1510-1514, Sep./Oct. 2009.