矽線波導馬赫詹德延遲干涉儀(Delayed Mach-Zehnder Interferometer, DMZI)，不僅可運用於色散(Chromatic Dispersion, CD)與光訊雜比(Optical Signal-to-noise Ratio, OSNR)監測，也可以應用在相位偏移鍵控(Phase Shift Keying, PSK)調變技術。非理想型馬赫詹德延遲干涉儀在相位解調變時，會使得光隔離度下降，導致消光比變小及誤碼率表現不佳，同時也使得系統監測之靈敏度下降。此原因在於干涉儀分光率不均，且DMZI的頻率位移(Frequency Offset)現象會造成OSNR的下降，這顯示出在DMZI延遲長度群折射率ng (Group Index)的重要性。吾人利用低同調干涉系統搭配絕緣層上覆矽之環形共振器，量測出波導群折射率在TM模態下為4.62，波導製程線寬誤差使得其與理論模擬值4.17有所偏離，此SMF-28光纖組成之低同調干涉系統精準度可以量測到0.01誤差率，將來在極化保持光纖改進系統中，0.00002精準度是可以預期的。
在干涉儀分光率方面，為了同時展現建設性輸出端(Constructive Port)與破壞性輸出端(Destructive Port)最大光隔離度，延遲干涉儀前端使用分光率為50：50，而後端則使用因延遲路徑光損耗有關的分光率，同時為了能應用分波多工(Wavelength Division Multiplexing)光通訊系統，吾人提出了兩種與波長不敏感分光器元件 - 馬赫-詹德方向耦合器(Mach-Zehnder Directional Coupler, MZDC)與混合式電漿波導(Hybrid Plasmon Waveguide, HPW)分光器。
本論文以RSoft與Photo Design套裝商用軟體進行數值模擬分析並以理論基礎設計出矽線波導馬赫詹德方向耦合器，本元件比較傳統的光功率分光器Direction Coupler (DC)與Multimode Interferometer (MMI)，具有波長不敏感以及可任意分光率的特性，而混合式電漿波導分光器則使用矽線波導上覆蓋金屬來展示分光功能，以上兩種分光器均是運用非耦合區相位延遲造成的光程差，進而設計出一個更寬工作光波段且與波長不敏感及可任意分光比之光功率分光器元件。
矽線波導光功率分光器尺寸為次微米，在元件外彎曲結構會影響原先分光率，所以吾人設計元件時特別考慮到彎曲結構帶來的耦合影響，模擬出波長範圍C-Band間，分光率50：50之矽線波導馬赫詹德方向耦合器，其分光率變動量為0.02。由於製程誤差，波導寬度從0.35 µm變為0.4 µm，且波導間距由0.35 µm變為0.32 µm，量測結果分光率為47：53且分光率變動量為0.08，這與吾人所模擬因製程誤差所造成的結果吻合，在相同製程誤差下分光率50：50 之DC，分光率變為39：61且分光率變動量為0.16由此可得知馬赫詹德方向耦合器之製程誤差容忍度要比方向耦合器來的優越。混合表面電漿之馬赫詹德方向耦合器在波長範圍S至L-Band間，設計分光率50：50時，其分光率變動量為0.068，以上元件應用於DMZI可讓DMZI有較佳光隔離度。

The delayed Mach-Zehnder interferometer (DMZI) can be applied to the chromatic dispersion (CD) monitoring, optical signal-to-noise ratio (OSNR), and differential phase shift keying (DPSK) modulator/demodulator. The optical isolation of a non-ideal DMZI is reduced in the phase modulation. Then less extinction ratio and worse bit error rate would be followed besides less sensitive system monitoring. The above is coming from the uneven interferometer splitting ratios and the DMZI frequency offset, which will cause a declined OSNR, which implies the importance of the group index, ng, in the delayed arm. The optical low coherence interferometer (OLCI) was utilized to characterize the group index of 4.62 in the TM polarization using silicon-on-insulator based microring resonator, which deviated from the theoretical value of 4.17 due to the process variation of the waveguide width. The OLCI, constructed by the SMF-28 fibers, could demonstrate 0.01 accuracy on group index and further improvement up to 0.00002 index accuracy could be achieved by the polarization maintained fiber based OLCI.
In the interferometer splitting ratio, the first optical power divider should be 50:50 in order to demonstrate the output maximum optical isolation simultaneously on constructive and destructive output ports. The second optical divider ratio will depend on the additional optical loss on the delalyed arm of the decoupled region. For wavelength division multiplexing (WDM) system applications, two wavelength-insensitive optical power dividers were proposed, Mach-Zehnder directional coupler (MZDC) and hybrid plasmon waveguide (HPW).
In this paper, the commercial software of Photo Design and RSoft were taken for numerical simulation on the design of the silicon-wire based MZDC. Compared with the traditional direction coupler (DC) and multimode interferometer (MMI), the optical power splitter from MZDC owns the wavelength independence and arbitrary splitting ratios. On the other hands, the HPW optical power splitter is take advantage of the metal on top of silicon-wire. The decoupled region in the above two types of power dividers was using delayed arm to couple two DC spectrum for insensitive wavelength response and flexible optical power splitter splitting ratios.
Silicon-wire based optical power splitter is sub-micron size, the curved structure will significantly affect the spectral response and need to be takn into account in the coupling regions of MZDC. The simulation showed that the splitting ratio of 50:50 and 0.02 variation demonstrated on the silicon-wire based MZDC in the C-Band. The manufacture errors caused the waveguide width varied from 0.35 m to 0.4 m and the waveguide spacing from 0.35 m to 0.32 m. The spectral results experimentally showed the splitting ratio of 47:53 with the variation of 0.08, which is the same as the simulation results corrected form the processing variation. Under the same manufacture error, the 50:50 splitting from DC could be theoretically derived as 47:53 and the power divider variation is up to 0.16. It could be concluded that the processing tolerance in MZDC is better than DC. The splitting ratio and its variation of HPW based MZDC were 50:50 and 0.068 from the S to L bands, respectively. The technologies we were demonstrating will allow DMZI for better optical isolation.

[1] John Senior and M. Yousif Jamro, Optical Fiber Communications: Principles and Practice, 3rd ed, Financial Times/Prentice Hall, 2009.
[2] Richard A. Soref, Joachim Schmidtchen, and Klaus Petermann, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” IEEE Journal of Quantum Electronics, Vol. 27, No. 8, pp. 1971-1974 , 1991.
[3] S. P. Chan, C. E. Png, S. T. Lim, G. T. Reed, and V. M. N. Passaro, “Single-mode and polarization-independent Silicon-on-Insulator waveguides with small cross section,” Journal of Lightwave Technology, Vol. 23, No. 6, pp. 2103-2111, 2005.
[4] T. Aalto, Microphotonic silicon waveguide components: VTT Technical Research Centre of Finland, 2004.
[5] Kah-Wee Ang, Guo-Qiang Lo Patrick, “Avalanche photodiodes: Si charge avalanche enhances APD sensitivity beyond 100 GHz,” Laser Focus World, Vol. 46, No. 8, pp. 41, 2010.
[6] Pieter Dumon, Wim Bogaerts, Vincent Wiaux, Johan Wouters, Stephan Beckx, Joris Van Campenhout, Dirk Taillaert, Bert Luyssaert, Peter Bienstman, Dries Van Thourhout, Roel Baets, “Low-loss SOI photonic wires and ring resonators fabricated with deep UV lithography,” IEEE Photonics Technology Letters, Vol. 16, No. 5, pp. 1328-1330, 2004.
[7] Yoshinori Hibino, “Recent advances in high-density and large-scale AWG multi/demultiplexers with higher index-contrast silica-based PLCs,” IEEE Journal of Selected Topics in Quantum Electronics, Vol. 8, No. 6, pp. 1090-1101, 2002.
[8] Atsushi Sakai, Go Hara, and Toshihiko Baba, “Sharply bent optical waveguide on silicon-on-insulator substrate,” Proceedings of SPIE, Vol. 4283, pp. 610-618, 2001.
[9] E. A. J. Marcatili, “Bends in optical dielectric guides,” The Bell System Technical Journal, pp. 2103-2132, 1969.
[10] Mordehai Heiblum, and Jay H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE Journal of Quantum Electronics, Vol. QE-11, No. 2, pp. 75-83, 1975.
[11] Yurii A. Vlasov, and Sharee J. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Optics Express, Vol. 12, No. 8, pp. 1622-1631, 2004.
[12] Vijaya Subramaniam, Gregory N. De Brabander, David H. Naghski, and Joseph T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” Journal of Lightwave Technology, Vol. 15, No. 6, pp. 990-997, 1997.
[13] Kevin K. Lee, Desmond R. Lim, Hsin-Chiao Luan, Anuradha Agarwal, James Foresi, and Lionel C. Kimerling, “Effect of size and roughness on light transmission in a Si/SiO2 waveguide: experiments and model,” Applied Physics Letters, Vol. 77, No. 11, pp. 1617-1619, 2000.
[14] Marcuse D., “Mode conversion caused by surface imperfections of a dielectric slab waveguide,” Bell System Technical Journal, Vol. 48, No. 10, pp. 3187-3215, 1969.
[15] F. P. Payne, J. P. R. Lacey, “A theoretical analysis of scattering loss from planar optical waveguides,” Optical and Quantum Electronics, Vol. 26, pp. 977-986, 1994.
[16] Mordehai Heiblum, and Jay H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE Journal of Quantum Electronics, Vol. QE-11, No. 2, pp. 75-83, 1975.

[17] F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, "Size influence on the propagation loss induced by sidewall roughness in ultrasmall SOI waveguides," IEEE Photonics Technology Letters, Vol. 16, pp. 1661-1663, 2004.
[18] Amnon Yariv and Pochi Yeh, Photonics: Optical Electronics in Modern Communications (The Oxford Series in Electrical and Computer Engineering), Oxford, 2006.
[19] Jia-Ming Liu, Photonic devices, Cambridge University Press, pp. 206-209, 2005.
[20] Hirohito Yamada, Tao Chu, Satomi Ishida, and Yasuhiko Arakawa, “Optical Directional Coupler Based on Si-Wire Waveguides,” IEEE Photonics Technology Letters, Vol. 17, No. 3, pp. 1041-1135, 2005.
[21] Shih-Hsiang Hsu, “Signal power tapped with low polarization dependence and insensitive wavelength on silicon-on-insulator platforms,” Journal of the Optical Society America B, Vol. 27, No. 5, pp. 941-947, 2010.
[22] Brent E. Little, and Tom Murphy, “Design rules for maximally flat wavelength-insensitive optical power dividers using mach-zehnder structures,” IEEE Photonics Technology Letters, Vol. 9, No. 12, pp. 1607-1609, 1997.
[23] S. H. Hsu, “Optical waveguide tap with low polarization dependence and flattened wavelength using a Mach-Zehnder directional coupler,” Applied Optics, Vol. 49, No.13, pp. 2434-2440, 2010.
[24] R. F. Oulton1, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation’’, Nature Photonics, 2, pp. 496 – 500, 2008.
[25] Ivan Avrutsky, Richard Soref, and Walter Buchwald, “Sub-wavelength plasmonic modes in a conductor-gap-dielectric system with a nanoscale gap’’, Optical Express, 18(1), pp. 348-363, 2010.
[26] 廖高崧，金屬-介質-金屬波導結構的表面電漿分光器之研究，碩士論文，國立交通大學光電工程學系碩士班(2013)
[27] 郭建銘，效能增強混合式表面電漿子波導管之設計與分析，碩士論文，國立清華大學工程系統科學系(2013)
[28] 林君豪，以全向量虛軸有限元素波束傳播法分析數種表面電漿波導結構的模態特性，碩士論文，國立臺灣大學電機資訊學院光電工程學(2014)
[29] 洪仕熹，發展高階有限差分法與邊界匹配條件分析介電質與金屬光波導結構，碩士論文，國立高雄應用科技大學電子工程系(2012)
[30] S. H. Hsu, J.-C. Hsu, and S.-C. Chen, “Interferometric fiber strain sensor using fiber Bragg grating based optical ruler,” 2013/June, CLEO, p. JW2A.72, San Jose, California, USA, 2013.
[31] M. Z. Alam, J. Niklas Caspers, J. S. Aitchison, and M. Mojahedi , “Compact low loss and broadband hybrid plasmonic directional coupler”, Optics Express, 21(13), pp. 16029-16034, 2013.
[32] 吳民耀,劉威志,"表面電漿子理論與模擬",物理雙月刊,廿八卷二期, pp. 486-496, 2006.
[33] 邱國斌,蔡定平,"金屬表面電漿簡介",物理雙月刊,廿八卷二期, pp. 472-485, 2006.
[34] T. A. Carriere, et al, “Measurement of waveguide birefringence using ring resonator, ” IEEE of Photonics Technology Letters, vol.16, no.4, 2004.
[35] 蘇昱豪，光環型共振腔之干涉式生醫感測，國立台灣科技大學，台北，2012.
[36] G. T. Reed and A. P. Knights, ”Silicon Photonics an Introduction, ” John Wiley and Sons, Ltd, 2004.
[37] G. Ducournau, O. Latry, M. Ketata,“The All-fiber MZI structure for optical DPSK demodulation and optical PSBT encoding,”Systemics, Cybernetics and Informatics, Vol. 4, No. 4, pp. 78-89, 2006.
[38] 葉子豪，微環形共振腔於生醫感測之應用，國立台灣科技大學，台北，2011.
[39] Lucas B. Soldano and Erik C. M. Pennings, Member, “Optical Multi-Mode Interference Devices Based on Self-Imaging : Principles and Applications,” Journal of Lightwave Technology, Vol. 13,No. 4, pp. 615-627, 1995.
[40] Dan-Xia Xu, Adam Densmore, Philip Waldron, Jean Lapointe, Edith Post, André Delâge, Siegfried Janz, Pavel Cheben, Jens H. Schmid, and Boris Lamontagne, “High bandwidth SOI photonic wire ring resonators using MMI couplers,” Optical Society of America, 2007.
[41] D. J. Thomson, Y. Hu, G. T. Reed, and Jean-Marc Fedeli, “Low Loss MMI Couplers for High Performance MZI Modulators,” IEEE Photonics Technology Letters, Vol. 22, No. 20, pp. 1485 – 1487, 2010
[42] Daoxin Dai, Yaocheng Shi, Sailing He, Lech Wosinski, and Lars Thylen, “Silicon hybrid plasmonic submicron-donut resonator with pure dielectric access waveguides,” Optics Express, Vol. 19, No. 24, pp. 23671-23682, 2011.
[43] Fei Lou, Zhechao Wang, Daoxin Dai, Lars Thylen, and Lech Wosinski, “Experimental demonstration of ultra-compact directional couplers based on silicon hybrid plasmonic waveguides,” Appl. Phys. Lett., Vol. 100, pp. 241105, 2012.
[44] Daoxin Dai and Sailing He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Optics Express, Vol. 17, No. 19, pp. 16646-6653, 2009.
[45] Daoxin Dai and Sailing He, “Low-loss hybrid plasmonic waveguide with double low-index nano-slots,” Optics Express, Vol. 18, No. 17, pp. 17958-17966, 2010.
[46] Adam Densmore , Dan-Xia Xu, Philip Waldron, Siegfried Janz, André Delâge, Pavel Cheben, Jean Lapointe, “Thin silicon waveguides for biological and chemical sensing,” SPIE, 6477, pp. 647718, 2007.
[47] Peter Debackere, Stijn Scheerlinck, Peter Bienstman, and Roel Baets, “Surface plasmon interferometer in silicon-on-insulator: novel concept for an integrated biosensor,” Optics Express, Vol. 14, No. 16, pp. 7063-7072, 2006.
[48] Qiang Li, Yi Song, Gan Zhou, Yikai Su, and Min Qiu, “Asymmetric plasmonic-dielectric coupler with short coupling length, high extinction ratio, and low insertion loss,” Optics Letters, Vol. 35, No. 19, pp. 3153-3155, 2010.
[49] Hirohito Yamada, Tao Chu, Satomi Ishida, and Yasuhiko Arakawa, “Optical Directional Coupler Based on Si-Wire Waveguides,” IEEE Photonics Technology Letters, Vol. 17, No. 3, pp. 1041-1135, 2005.
[50] M. Z. Alam, J. S. Aitchison, and M. Mojahedi, “Polarization-independent hybrid plasmonic coupler for a silicon on insulator platform,” Optics Letters, Vol. 37,No. 16, pp. 3417-3419, 2012.
[51] Ilya Goykhman, Boris Desiatov and Uriel Levy, “Experimental demonstration of locally oxidized hybrid silicon-plasmonic waveguide,” Applied Physics Letters , Vol. 97, pp. 141106, 2010.
[52] Daoxin Dai and Zhen Sheng, “Numerical analysis of silicon-on-insulator ridge nanowires by using a full-vectorial finite-difference method mode solver,” Journal of the Optical Society of America B, Vol. 24, No. 11, pp. 2853-2859, 2007.
[53] William L. Barnes, Alain Dereux, and Thomas W. Ebbesen, “Surface Plasmon subwavelength optics," Nature, Vol. 424, No. 6950, pp. 824-830, 2003.
[54] Nemanya Sedoglavich, John C. Sharpe, Rainer Künnemeyer, and Sergey Rubanov, “Polarisation and wavelength selective transmission through nanohole structures with multiple grating geometry,’’ Optical Express, Vol. 16, No. 8, pp. 5832-5837, 2008.
[55] Alexandra Boltasseva, Thomas Nikolajsen, Kristjan Leosson, Kasper Kjaer, Morten S. Larsen, and Sergey I. Bozhevolnyi, “Integrated Optical Components Utilizing Long—Range Surface Plasmon Polari tons,’’ Journal of Lightwave Technology, Vol. 23, No. 1, pp. 43-45, 2005.
[56] M. K. Chin and S. T. Ho, “Design and modeling of waveguide coupled single-mode microring resonators,’’ Journal of Lightwave Technology, Vol. 16, No. 8, pp. 1433, 1998.
[57] Kretschmann E , and Raether H, ‘'Radiative decay of nonradiative surface plasmons excited by light,” Z. Natureforsch, Vol. 23, pp.2135-2136, 1968.
[58] Koji Matsubara,Satoshi Kawata, and Shigeo Minami,“Optical chemical sensor based on surface plasmon measurement,” Applied Optics, Vol. 27, No. 6, pp. 1160-1163 , 1988.
[59] B.Liedberga,I.Lundstr6ma, and E.Stenbergb, “ Principles of biosensing with an extended coupling matrix and surface plasmon resonance,” Sensors and Actuators B：Chemical, Vol. 11, No. 1-3, pp. 63-72, 1993.
[60] Reinhard März,“Integrated Optics, Design and Modelling, ”Artech House Publishers, Boston-London, 1995.
[61] A. H. Gnauck, P. J. Winzer,“Optical phase-shift-keyed transmission,” Journal of Lightwave Technology, Vol. 23, No. 1, pp. 115-130, 2005.
[62] C. Wu, X. Liu, X. Wei,“Differential phase-shift keying for high spectral efficiency optical transmissions,”IEEE Selected Topics in Quantum Electronics, Vol. 10, No. 2, pp. 281- 293, 2004.
[63] Eric Dulkeith, Fengnian Xia, Laurent Schares, William M. J. Green, and Yurii A. Vlasov, “Group index and group velocity dispersion in silicon-on-insulator photonic wires,” Optics Express, Vol. 14, No. 9, pp. 3853-3863, 2006.
[64] A. L. Campillo, "Chromatic dispersion-monitoring technique based on phase sensitive detection," IEEE Photonics Technology Letters, vol. 17, no. 6, pp. 1241-1243, 2005