本論文藉助表面電漿波可強力侷限電磁波於垂直金屬-介電材料介面之特性，設計出幾不受極化影響「金屬-多層介電質」組態之90度波導轉折結構。文中闡述波導結構設計之概念，並對波導結構參數依序由輸入端至輸出端逐步進行最佳化設計。模擬時以內建有限時域差分法之Rsoft商用軟體進行，網格大小不大於5 nm，並以採用有限元素分析法之商用軟體COMSOL Multiphysics相互驗證。此二維波導轉折結構透過歸一化後發現橫向電場與橫向磁場模態於轉折處之轉折效率皆可達近0.99，表示波導結構之損耗主要是由光波通過模態轉換器後能量散失至空氣所造成。又橫向電場與橫向磁場模態之插入損耗分別為-0.0846與-0.2287 dB。整體波導轉折結構所佔面積僅有3.773 μm2。轉折處長度透過最佳化設計可縮減至450 nm，小於三分之ㄧ操作波長(1550 nm)，尺寸在次波長範圍下。不同極化模態之傳輸效率在波長1414 nm 到 1605 nm 間皆可達0.90以上。
在決定最佳化之參數後再對能量於波導結構內轉移情況進行分析，細部探討在不同極化下波導結構幾何形狀改變對於能量轉移之影響，描繪最佳化波導轉折結構傳輸效率對波長之變化。最終將此金屬-多層介電質組態之90度波導轉折結構與目前文獻結果比較，分析此轉折波導之優劣。對比他人文獻結果，本論文所描述之「金屬-多層介電質」組態之90度波導轉折結構具有幾不受極化影響與狹小轉折區域之優點，期望可對奈米積體光路帶來相當助益。

With the aid of surface plasmon polaritons featuring strong lateral confinement of electromagnetic energy in the direction perpendicular to the metal-insulator interface, a polarization-insensitive 90o waveguide bend in the metal/multi-insulator configuration is described in this thesis. The design and optimizations are conducted using Finite-Difference-Time-Domain-based software package, RSOFT Design Group, with the grid size no larger than 5 nm and are cross-checked by COMSOL Multiphysics, a software based on Finite Element Method. The bending efficiency associated with the metal/multi-insulator structure, excluding the input/output tapers, can achieve approximately 0.99 for transverse electric (TE) and transverse magnetic (TM) polarizations, indicating the loss primarily results from the input/output tapers. The insertion losses for modes are -0.0846 and -0.2287 dB, respectively. The area occupied by the plasmonics-assisted region is only 3.773 μm2 and the length of waveguide bending section is shorter than one-third of the operating wavelength at 1550 nm. The transmission is above 0.90 in the wavelength window ranging from 1414 nm to 1605 nm for both polarizations.
In addition to the design optimizations, power transfer between silicon and silica regions along the bend and the transmission spectra are presented for both polarizations. Comparing with other literature, the present 90o waveguide bend in metal/multi-insulator configuration is polarization-insensitive and has an ultra-small footprint. This research may thus be of real value in integrated photonics.

[1] W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature, vol. 424, no.14, pp. 824-830, Aug. 2003.
[2] E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science, vol. 311, no. 5758, pp. 189-193, Jan. 2006.
[3] R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, ”Plasmonics: The next chip-scale technology,” Mater. Today, vol. 9, no. 7, pp. 20-27, Jul. 2006.
[4] R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. Physical Soc., vol.18, pp. 269-275, Jun. 1902.
[5] R. H. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Review, vol. 106, no. 5, pp. 874-881, Jun. 1957.
[6] H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, New York: Springer, 1988.
[7] J. Vuckovic, M. Loncar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quantum Electron., vol. 36, no. 10, pp. 1131-1144, Oct. 2000.
[8] S. Wedge, J. A. E. Wasey, and W. L. Barnes, “Coupled surface plasmon-polariton mediated photoluminescence from a top-emitting organic light-emitting structure,” Appl. Phys. Lett., vol. 85, no. 2, pp. 182-184, Jul. 2004.
[9] J. Hashizume and F. Koyama, “Plasmon enhanced optical near-field probing of metal nanoaperture surface emitting laser,” Opt. Express, vol. 12, no. 25, pp. 6391-6396, Dec. 2004.
[10] N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub–Diffraction-Limited Optical Imaging with a Silver Superlens,” Science, vol.308, pp. 534-537, Apr. 2005.
[11] M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, L. Martin-Moreno, J. Bravo-Abad, and F. J. Garcia-Vidal, “Enhanced millimeter-wave transmission through subwavelength hole arrays,” Opt. Lett., vol. 29, no. 21, pp. 2500-2502, Nov. 2004.
[12] B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2d ed. Hoboken: Wiley, 2007.
[13] J. Yakahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett., vol. 22, no. 7, pp. 475-477, Apr. 1997.
[14] R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Amer. A, vol. 21, no. 12, pp. 2442-2446, Dec. 2004.
[15] Z. Yu, G. Veronis, and S. Fan, “Gain-induced switching in metal-dielectric-metal plasmonic waveguide,” Appl. Phys. Lett., vol. 92, pp. 041117, Jan. 2008.
[16] T. Miya, “Silica-based planar lightwave circuits: passive and thermally active devices,” IEEE J. Sel. Topics Quantum Electron., vol. 6, no. 1, pp. 38-45, Jan. 2000.
[17] Z. Sheng, D. Dai, and S. He, “Comparative study of losses in ultrasharp silicon-on-insulator nanowires bends,” IEEE J. Sel. Topics Quantum Electron., vol. 15, no.5, pp.1406-1412, Sep. 2009.
[18] G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett., vol. 87, pp. 131102, Sep. 2005.
[19] Y. A. Vlasov and S. J. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express, vol. 12, no. 8, pp.1622-1631, Feb. 2004.
[20] V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Bend loss for channel plasmon polaritons,” Appl. Phys. Lett., vol. 89, pp. 143108, Aug. 2006.
[21] C. Seo and J. C. Chen, “Low transition losses in bent rib waveguides,” J. Lightw. Technol., vol. 14, no. 10, pp. 2255-2259, Oct. 1996.
[22] S. Akiyama, M. A. Popovic, P. T. Rakich, K. Wada, J. Michel, H. A. Haus, E. P. Ippen, and L. C. Kimerling, “Air trench bends and splitters for dense optical integration in low index contrast,” J. Lightw. Technol., vol. 23, no. 3, pp. 2271-2277, Jul. 2005.
[23] A. Himeno, H. Terui, and M. Kobayashi, “Loss measurement analysis of high-silica reflection bending optical waveguides,” J. Lightw. Technol., vol. 6, no. 1, pp. 2271-2277, Jan. 1988.
[24] L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, “Ultrasmall waveguide bends：the corner mirrors of the future,” IEE Proc.-Optoelectron., vol. 142, no. 1, pp.61-65, Feb. 1995.
[25] L. Li, G. P. Nordin, H. M. English, and J. Jiang, “Small-area bends and beamsplitters for low-index-contrast waveguides,” Opt. Express, vol. 11, no. 3, pp.282-290, Feb. 2003.
[26] M. Popovic, K. Wada, S. Akiyama, H. A. Haus, and J. Michel, “Air trenches for sharp silica waveguide bends,” J. Lightw. Technol., vol. 20, no. 9, pp. 1762-1772, Sep. 2002.
[27] V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett., vol. 29, no. 11, pp. 1209-1211, Jan. 2004.
[28] Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett., vol. 29, no. 14, pp. 1626-1628, Jul. 2004.
[29] P. A. Anderson, B. S. Schmidt, and M. Lipson, “High confinement in silicon slot waveguides with sharp bends,” Opt. Express, vol. 14, no. 20, pp.9197-9202, Oct. 2006.
[30] C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High-density integrated optics,” J. Lightw. Technol., vol. 17, no. 9, pp. 1682, Sep. 1999.
[31] G.. P. Nordin, S. Kim, J. Cai, and J. Jiang, “Hybrid integration of conventional waveguide and photonic crystal structures,” Opt. Express, vol. 10, no. 23, pp.1334-1341, Nov. 2002.
[32] C. Ma, Q. Zhang, and E. V. Keuren, “Right-angle slot waveguide bends with high bending efficiency,” Opt. Express, vol. 16, no. 19, pp. 14330-14334, Sep. 2008.
[33] A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett., vol. 77, no. 18, pp. 3787-3790, Oct. 1996.
[34] D. F. P. Pile and D. K. Gramotnev, “Plasmonics subwavelength waveguides: next to zero losses at sharp bends,” Opt. Lett., vol. 30, no. 10, pp.1186-1188, Aug. 2005.
[35] J.-C. Weeber, M. U. Gonzalez, A.L. Baudrion, and A. Dereux, “Surface plasmon routing along right angle bent metal strips,” Appl. Phys. Lett., vol. 87, pp. 221101-1, Nov. 2005.
[36] V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Compact gradual bends for channel plasmon polaritons,” Opt. Express, vol. 14, no. 10, pp. 4494-4503, Mar. 2006.
[37] N. N. Feng and L. D. Negro, “Plasmon mode transformation in modulated-index metal-dielectric slot waveguides,” Opt. Lett., vol. 32, no. 21, pp. 3086-3088, Nov. 2007.
[38] S. A. Maier, Plasmonics: Fundamentals and Applications, New York: Springer, 2007.
[39] N. N. Feng, M. L. Brongersma, and L. D. Negro, “Metal-dielectric slot-waveguide structures for the propagation of surface plasmon polaritons at 1.55μm,” J. Lightw. Technol., vol. 43, no. 6, pp. 479-485, Jun. 2007.
[40] P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B, vol. 6, no. 12, pp. 4370-4379, Dec. 1972.
[41] K. S. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag., vol. ap-14, no.3, pp. 302-307, May 1966.
[42] A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2d ed. Boston: Artech House, 2000.
[43] J. P. Berenger, “A perfectly matched layer of the absorption of electromagnetic waves,” J. Comput. Phys., vol. 114, pp. 185-200, 1994.
[44] Y.-J. Chang and Y.-C. Liu, “A Plasmonic-Mode-Assisted Sharp Waveguide Bend for Silicon Optical Nanocircuitry,” IEEE Photon. Technol. Lett., vol. 23, no. 2, pp. 121-123, Jan. 2011.