相學調變器為積體光學上一項重要的基本元件，而利用Silicon-on-insulator (SOI) wafer 的製程方式普遍被大家所採用，原因在於SOI wafer具有高的折射率對比(High Index Ratio)可以有效率的侷限(Confinement)光場並可以降低每單位元件的價格。
本論文的研究方向系採用SOI wafer基板，利用簡單的蝕刻方式在SOI wafer上定義出可撓式矽波導(Deformable Waveguides)結構與電極區域並且使用Mack-Zehnder Interferometer設計在收光端觀察干涉現象，而兩端則採用多模干涉耦合器(Multimode Interference Coupler)進行光的分離與結合，不僅在製作上有較大的可接受誤差亦可達到約20nm的操做頻寬與光偏極化(Polarization)的不敏感性。
量測上，利用串連6個長度為150□m可撓式矽波導在靜電力的吸引下使得矽波導整體長度上出現變化達到相位調變的目的。當外加偏壓200V且為TM偏振情況下大約可以達到0.35□□的相位變化，而元件的反應時間(Response time)約為103□s。

An optical phase shifter for integrated optics is proposed and demonstrated in a single SOI chip. By monolithic integration of deformable silicon wire waveguides and micro-electro-mechanical- system (MEMS) actuators, the optical phase shifter for a guided wave can be realized by mechanically stretching the waveguide length using the electrostatic force. Besides, in order to realize highly compact photonic integrated circuits based on silicon photonic wires, multimode interference (MMI) couplers were introduced for performing light splitting and combing due to the advantages of wide optical bandwidth(about 20nm), polarization independence and large fabrication tolerance. In experimental measurement, the maximum phase shift of 0.35□ is attained at 200V around the wavelength 1550nm for the TM-polarized light. The dynamic actuation speed is also verified to be near 103□s for the proposed device.

[1]K. E. Petersen, “Silicon as a mechanical material,” Proc. IEEE, vol.70, no.5,pp.420-457, 1982.
[2]R. T. Howe and R. S. Muller, “Polycrystalline silicon micromechanical beams,”Proc. Electrochemical Society Spring Meeting, pp.184-185, 1982.
[3]Long-Shen Fan, Yu-Chong Tai and Richard S. Muller, “IC-processed electrostatic micromotors,” Sensors and Actuators, vol.20, no.1-2, pp41-47, 1989.
[4]M. Sasaki, T. Hosono, S. Kumagai, “Liquid immersion angled exposure for 3D photoligthography,” Proc. of IEEE/LEOS Int. Conf. Optical MEMS and Nanophotonics, pp75-76, 2009.
[5]R. R. A. Syms, H. Zou, J. Stagg, and H. Veladi, “Sliding-blade MEMS iris and variable optical attenuator,” Journal of Micromechanics and Microengineering, 14,pp1700-1710, 2004.
[6]S. Chung, and Y. Kim, “Design and Fabrication of a 10x10 micro-spatial Light Modulator Array for phase and Amplitude Modulation,” Sensor and Actuators, vol78, pp.63-70, 1999.
[7] A. Higo, H. Fujita, Y. Nakano, H. Toshiyoshi, “Design and fabrication photonic MEMS waveguide modulator,” Proc. of IEEE/LEOS Int. Conf. Optical MEMS and Nanophotonics, pp173-174, 2007.
[8]Hornbeck, L J, ”DMD projection display chip: A MEMS-based technology,” MRS Bulletin, vol.26, no.4, pp.325-327, 2001.
[9]M. T. Tinker, J. B. Lee, “Thermo-optical photonic crystal light modulator,” Applied Physics Letters, 86, 221111, 2005.
[10]R. A. Soref, B. R. Bennett, “Electrooptical effects in silicon,” IEEE Journal of Quantum Electronics, vol.23, pp.123-129, 1987.
[11]D. T. Fuchs, H. B. Chan, H. R. Stuart, F. Baumann, D. Greywall, M.E. Simon and A. Wong-Foy, “Monolithic integration of MEMS-based phase shifters and optical waveguides in silicon-on-insulator,” Electronics Letters, 40, pp.142-143, 2004.
[12] T. Ikeda, Kazunori Takahashi, Yoshiaki Kanamori and Kazuhiro Hane, “Phase-shifter using submicron silicon waveguide couplers with ultra-small electro-mechanical actuator,” Optics Express, 18, 7035, 2010.
[13]T. Ma, W. Zhao and J. Liu, “ A MEMS vibration sensor based on Mach Zehnder interferometers,” Proc. SPIE, 6529:2C-1, 2007.
[14]U. Fischer, T. Zinke, J. R. Kropp, F. Arndt and K. Petermann, “0.1 dB/cm waveguide losses in single-mode SOI rib waveguides,” IEEE Photonics Technology Letters, vol.8, pp.647-648, 1996.
[15]P. D. Trinh, S. Yegnanarayanan, and B. Jalali, “Guided-wave optics circuits in silicon-on-insulator technology,” IEEE Proceedings-Optoelectronics, vol.143, pp.307-311, 1996.
[16]S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtx, and Jim Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature, vol.394, pp.251-253, 1998.
[17]S. McNab, N. Moll, and Y. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Optics Express, vol.11, pp. 2927-2939, 2003.
[18]V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Optics Letters, vol.29, pp.1209-1211, 2004.
[19] Okamoto K.”Fundamentals of Optical Waveguides 2/E,” Academic Press. 2006
[20] 0. Bryngdahl, “Image formation using self-imaging techniques,” Journal of the Optical Society of America , vol.63, no.4, pp.41-19, 1973.
[21]L.B. Soldano, and E. C. M. Pennings, “Optical multimode interference devices based on self-image principles and applications”, Journal of Lightwave
Technology, vol.13, pp.615-627, 1995.
[22] M. Bachmann, P. A. Besse, and H. Melchior, “General self-imaging properties in N x N multi-mode interference couplers including phase relations,” Applied Optics, vol.33, no.17, pp.3905-3911, 1994.
[23] W. N. Ye, D. X. Xu, S. Janz, P. Cheben, A. Delage, M. J. Picard, B. Lamontagne, and N. G. Tarr, “ Stress-induced birefringence in silicon-on-insulator (SOI) waveguides”, Proc. SPIE, vol.5357, pp.57-66, 2004.
[24] W. N. Ye, D. X. Xu, S. Janz, P. Cheben, M. J. Picard, B. Lamontagne and N. G. Tarr, ” Birefringence control using stress engineering in silicon-on-insulator (SOI)
Waveguides,” Journal of Lightwave Technology, vol. 23, pp.1308-1318, 2005.
[25]M. Huang, “ The influence of light propagation direction on the stress-induced polarization dependence of silicon waveguides,” IEEE Photonics Technology Letters, vol.18, pp.1314-1316, 2006.
[26]Yoshitery Amemiya, Yuichiro Tanushi, Tomohiro Tokunaga and Shin Yokoyama, ”Photoelastic effect in silicon ring resonators,” Japanses Journal of Applied Physics, vol.47, no.4, pp.2910-2914, 2008.
[27] R. K. Gupta, “Electrostatic pull-in test structure design for in-situ mechanical property measurements of microelectromechanical systems (MEMS)”, Ph.D.dissertation, MIT, Cambridge, pp.10–27, 1997.
[28]S. Pamidighantam, R. Puers, K. Baert, and A. C. Tilmans, “ Pull-in voltage analysis of electrostatically actuated beam structures with fixed-fixed and fixed-free end conditions,” Journal of Micromechanics and Microengineering , vol.12, pp.458-464, 2002.
[29] S. K. De and N. R. Aluru, “Full-Lagrangian schemes for dynamic analysis of electrostatic MEMS”, Journal of Microelectronic Systems, vol.13, no.5, pp.737 - 758, 2004.
[30]H. Sadeghian and G. Rezazade, “The influence of stress gradient on the pull-in phenomena of microelectromechanical switches,” Journal of Physics: Conference Series, vol.34, pp.1117-1122, 2006.