本論文所研究的液晶波導，主要是將液晶注入以二氧化矽為包覆層之中空波導核心，藉由液晶的介電特性，期望此液晶波導變成電調變的光學元件。
由於液晶波導的包覆層為二氧化矽，其光運用全反射原理傳播，操作波段為1550 nm。首先利用單層介面反射與穿透原理與光束傳播法（Beam Propagation Method）來模擬計算，以決定製程上所需要的二氧化矽膜層厚度為4 ?m，而不論波導核心為no、ne或n ̅，光可以在液晶波導中侷限住。
在量測方面，以偏光顯微鏡的觀測並推測在未施加電壓時的液晶導軸排列方向與波導的光傳播方向平行，當達到最大電壓時，其波導中心區域的液晶導軸方向，幾乎平行電場；但波導邊緣的液晶卻與波導的光傳播方向夾45度角。接著量測液晶波導傳播特性，其輸出光強度的趨勢會隨著電壓的增大，先衰減，再逐漸變大，當外加電壓18 Vpp時，液晶波導的最大衰減量為22 dB，可做為光開關。在100 Vpp以上的高外加電壓，其液晶波導輸出光能量與偏振相關，由於液晶導軸方向平行於外加電場，當入射光偏振態感受到液晶折射率為ne，其侷限效果較佳，所以輸出端的光強度較高，其傳遞損耗也較低。

In this study, we fabricate the liquid crystal waveguides (LCWs) by infiltrating liquid crystal into hollow waveguides whose cladding layer is SiO2 layer. The electrical modulation of the LCWs can be achieved by dielectric properties of liquid crystals.
The light propagates in LCWs by the total internal reflection because the index of cladding layer made by SiO2 is higher than core layer. We design the cladding thickness of LCWs is 4 ?m and operate the wavelength at 1550 nm by the Fresnel equation and by beam propagation method. The simulation results show that the LCWs provides a good confinement no matter the refractive indices of core is no, ne or n ̅.
The light is well confined and polarization-dependent when the external voltage is over 100 Vpp. In low external voltage, the output intensity can be changed by different external voltage. The devices can serve as an electrically tunable liquid crystal switch with over 22 dB attenuation at 18 Vpp.

[1]S. E. Miller, "Integrated optics: an introduction.," Bell Syst. Tech. J.48, pp. 2059-2068 (1969)
[2]羅仕守, "新型中空光波導研製與應用," 國立中央大學, 光電科學研究所(2005)
[3]B. E. A. Saleh and M. C. Teich, "Fundamentals of Photonics. " (Weily, 1991)
[4]J. B. Jensen, L. H. Pedersen, P. E. Hoiby, L. B. Nielsen, T. P. Hansen, J. R. Folkenberg, J. Riishede, D. Noordegraaf, K. Nielsen, A. Carlsen, and A. Bjarklev, “Photonic crystal fiber based evanescent-wave sensor for detection of biomolecules in aqueous solution,” Opt. Lett. 29, p. 1974(2004)
[5]V.J. Cadarso, A. Llobera, C. Fernandez-Sanchez, M. Darder and C. Dominguez, “Hollow waveguide-based full-field absorbance biosensor,” Sens. Actuators B: Chem. 139, p. 143(2009)
[6]E. A. J. Marcatili and R. A. Schmeltzer, "Hollow metallic and dielectric waveguide for long distance optical transmission and laser," Bell Syst. Tech. J. 43, pp. 1783-1809 (1964)
[7]H. Schmidt and A. R. Hawkins, " Optofluidic waveguides: I. Concepts and implementations, " Microfluid Nanofluid, 4, pp. 3-16 ( 2008)
[8]A. R. Hawkins and H. Schmidt, " Optofluidic waveguides: II. Fabrication and structures," Microfluid Nanofluid, 4, pp. 17-32 (2008)
[9]A. Datta, I.Y. Eom, A. Dhar, P. Kuban, R. Manor, I. Ahmad, S. Gangopadhyay, T. Dallas, M. Holtz, H. Temkin, and P. K. Dasgupta, “Microfabrication and characterization of teflon AF-coated liquid core waveguide channels in silicon,” IEEE Sens. J. 3, pp. 788-795 (2003)
[10]A. d’Alessandro, B. Bellini, D. Donisi, R. Beccherelli, and R. Asquini, “Nematic liquid crystal optical channel waveguides on silicon,” IEEE J. Quantum Electron. 42, pp. 1084-1090 (2006)
[11]D. Donisi, B. Bellini, R. Beccherelli, R. Asquini, G. Gilardi, M. Trotta, and A. d’Alessandro, “A switchable liquid-crystal optical channel wavguide on silicon,” IEEE J. Quantum Electron. 46, p. 762 (2010)
[12]D. B. Wolfe, R. S. Conroy, P. Garstecki, M. A. Fischbach, K. E. Paul, M. Prentiss, and G. M. Whitesides, “Dynamic control of liquid-core/liquid-cladding optical waveguides,” Proc. Natl. Acad. Sci. 101, p. 12434 (2004)
[13]W. Risk, H. Kim, R. Miller, H. Temkin and S. Gangopadhyay, “Optical waveguides with an aqueous core and a low-index nanoporous cladding,” Opt. Exp. 12, p. 6446 (2004)
[14]J. B. Shellan, P. Agmon, P. Yeh, and A. Yariv, “Statistical analysis of Bragg reflectors,” J. Opt. Soc. Am. 68, p. 18 (1978)
[15]Chii-Chang Chen, Hua-Kang Chu, “Method for fabicating distributed bragg reflector waveguide,” US patent: 7,783,151 B2, Aug. 24, (2010)
[16]M. A. Duguay, Y. Kokubun, and T. L. Koch, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49, p. 13 (1986)
[17]D. Yin, D. W. Deamer, H. Schmidt, J. P. Barber, and A. R. Hawkins, “Integrated optical waveguides with liquid cores,” App. Phys. Lett. 85, p. 3477 (2004)
[18]H. Schmidt, D. Yin, J. P. Barber, and A. R. Hawkins, “Hollow-core Waveguides and 2-D waveguide arrays for integrated optics of gas and liquids,” IEEE J. Sel. Topics Quantum Electron. 11, p. 519 (2005)
[19]R. Bernini, G. Testa, L. Zeni, and P. M. Sarro, “ntegrated optofluidic Mach-Zehnder interferometer based on liquid core waveguides,” App. Phys. Lett. 93, p. 011106 (2008)
[20]T. T. Larsen, A. Bjarklev, D. S. Hermann, J. Broeng, "Optical Devices based on liquid crystal photonic bandgap fibres, " Opt. Express. 11(20), pp. 2589-2596 (2003)
[21]F. Du, Y. Q. Lu, and S. T. Wu, "Electrically tunable liquid-crystal photonic crystal fiber, " App. Phys. Lett. 85, pp. 2181-2183 (2004)
[22]M. W. Haakestad, T. T. Alkeskjold, M.D. Nielsen, L. Scolari, J. Riishede, H. E. Engan, and A. Bjarklev, "Electrically tunable photonic bandgap guidance in a liquid-crystal-filled photonic crystal fiber, " IEEE Photonic. Tech. Lett. 17, pp. 819-821 (2005)
[23]T. R. Wolinski, K. Szaniawska, S. Ertman, P. Lesiak, A. W. Domanski, R. Dabrowski, E. Nowinowski-Kruszelnicki, and J. Wojcik, "Influence of temperature and electrical field on propagation properties of photonic liquid-crystal fibres, " Meas. Sci. Technol. 17, pp. 985-991 (2006)
[24]T. R. Wolinski, S. Ertman, A. Czapla, P. Lesiak, K. Nowecka, A. W. Domanski, E. Nowinowski-Kruszelnicki, R. Dabrowski, and J. Wojcik, "Polarization effects in photonic liquid crystal fibers, " Meas. Sci. Technol. 18, pp. 3061-3069 (2007)
[25]K. S. Hsiao, and C. Y. Ko, "Light-controllable photoresponsive liquid-crystal photonic crystal fiber, " Opt. Express. 16, pp. 12670-12676 (2008)
[26]粘珊綺, "電調變液晶波導," 國立中央大學, 光電科學研究所(2010)
[27]D. P. Cai, S. C. Nien, H. K. Chiu, C.C. Chen and C.C. Lee, "Electrically tunable liquid crystal waveguide attenuators," Opt. Express. 19, pp. 11890-11896 (2011)
[28]F. L. Pedrotti, S.J., L. M. Pedrotti, and L. S. Pedrotti, "Introduction to optics, 3rd edition." (Prentice-Hall, 2007)
[29]RSoft Design Group, "BeamPROP 6.0-User Guide."
[30]P. J. Collings, and M. Hird, "Introduction to liquid crystals- Chemistry and Physics, " (Taylor & Francis, 1997)
[31]D. J.R. Cristaldi, S. Pennisi, F. Pulvirenti, “Liquid Crystal Display Drivers: Techniques and Circuits.” (Springer,2009)
[32]田民波, "TFT液晶顯示原理與技術." (五南圖書出版股份有限公司,2008)
[33]P. Y. Amnon Yariv, "Optical Waves in crystals, " (John Wiley & Son, 1984)
[34]默克光電科技股份有限公司
[35]J. Li, S. T. Wu, S. Brugioni, R. Meucci, and S. Faetti, "Infrared Refractive indices of liquid crystals. " J. Appl. Phys. 97, p. 073501 (2005)
[36]S. Brugioni, and R.Meucci, "Refractive indices of the nematic mixture E7 at 1550nm. " Infrared Physics & Technology. 49, pp. 210-212, (2007)
[37]“Refractive index database.”, http://refractiveindex.info/
[38]G. P. Bryan-Brown, E. L. Wood, I. C. Sage, “Weak surface anchoring of liquid crystals” Nature 399, p. 338 (1999)
[39]T. Alkeskjold, J. Lægsgaard, A. Bjarklev, D. Hermann, A. Anawati, J. Broeng, J. Li, and S.T. Wu, “All-optical modulation in dye-doped nematic liquid crystal photonic bandgap fibers”, Opt. Express. 12, p. 5857 (2004)
[40]Vladimir V. Presnyakov, Zhijian J. Liu, and Vladimir G. Chigrinov, “Infiltration of photonic crystal fiber with liquid crystals”, Proc. SPIE 6017, p. 60170J (2005)
[41]J. Beeckman, R. James, F. A. Fernandez, W. De Cort, P. J. M. Vanbrabant, and K. Neyts, “Calculation of fully anisotropic liquid crystal waveguide modes,” Journal of Lightwave Technol. 27, pp. 3812-3819 (2009)
[42]M. Y. Chen, S. M. Hsu, and H. C. Chang, “A finite-difference frequency-domain method for full-vectorial mode solutions of anisotropic optical waveguides with arbitrary permittivity tensor,” Opt. Express 17, pp. 5965-5979 (2009)
[43]C. C. Huang, “Solving the full anisotropic liquid crystal waveguides by using an iterative pseudospectral-based eigenvalue method,” Opt. Express 19, pp. 3363-3378 (2011)
[44]M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama,“Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulatorphotonic crystal slabs,” IEEE J. Quantum Electron. 38, pp. 736-742 (2002)
[45]李正中, "薄膜光學與鍍膜技術." (藝軒圖書出版社, 2006)