本文研究雙頻液晶( Dual Frequency Liquid Crystal )光電元件之光電特性。在實驗中我們利用雙頻液晶製作出液晶透鏡( LC lens )。
當製作液晶透鏡時，在液晶透鏡的玻璃基板上製作一顆外觀近似雙曲線形狀的聚合物透鏡，由於此聚合物透鏡的關係，可使得外加電壓下液晶透鏡內呈現不均勻電場( inhomogeneous electric field )分佈，在此不均勻電場作用下，液晶層內的折射率會呈現如 GRIN lens般的折射率梯度分佈，當光線通過時產生透鏡之聚焦與發散的效果，另外改變外加電場之大小可控制液晶分子之排列，而改變折射率之分佈，並產生調控焦距之效果。
本論文主要探討液晶透鏡的聚焦特性、反應時間在電壓調控與頻率調控下有何差別。從實驗結果我們發現使用頻率調控比使用電壓調控在元件特性上有其良好的優點，從液晶透鏡實驗中可發現使用頻率調控操作液晶透鏡，其可調控的焦距變得更廣和反應時間變快。

We study the characteristics of the dual frequency liquid-crystal (LC) optoelectronic devices in this literary. We fabricate the LC lens with the dual frequency liquid crystal in our experiment.
In this study, we first prepare a parabolic polymer structure on the glass substrate to form a polymeric lens glass, then, fill the dual-frequency LC into the empty cell which consists of one ITO glass and the polymeric lens glass to fabricate a frequency modulation LC lens. Additionally, a hybrid surface alignment is also used for our LC lens. For the dual-frequency LC, a hybrid surface alignment is necessary to obtain a frequency modulation LC lens. Because of the polymeric lens, the electric fields are inhomogeneous distributions in the LC lens when a voltage is applied to the electrodes. In this situation, an inhomogeneous electric field is applied to the cell to create GRIN lens-like distribution of the gradient refractive index. Thus, the focusing effects occur when the light passes through the LC lens. Moreover, by changing the amplitude and frequency of the applied voltage, the focal length of the LC lens can be changed.
We mainly discuss the optical property and the response time of the LC lens based on the voltage modulation and the frequency modulation. The experimental results reveal that the frequency modulation has more advantages, such as widen range of controlled focal length and faster response time, comparing with the voltage modulation.

摘要-----------------------------------------------------------------Ⅰ
Abtract--------------------------------------------------------------Ⅱ
目錄---------------------------------------------------------------- Ⅲ
圖表目錄---------------------------------------------------------- Ⅵ
第一章 序論
§ 1-1 前言-------------------------------------------------------- 1
§ 1-2 液晶簡介-------------------------------------------------- 3
§ 1-3 液晶的分類----------------------------------------------- 4
§ 1-4 GRIN lens 導論--------------------------------------- 20
§ 1-4-1 GRIN lens 種類-----------------------------------22
第二章 液晶理論基礎
§ 2-1 液晶物理------------------------------------------------ 25
§2-1-1 液晶的光學異向性( Optical anisotropy )---- 25
§2-1-2 液晶的連續體彈性形變理論------------------------ 29
§2-1-3 電場對絕緣向列相( Nematic )液晶的影響------ 30
§2-1-4 液晶的黏滯係數( Viscosity )------------------------ 33
§2-1-5 液晶的秩序參數( Order parameter, S )--------- 34
§2-1-6 溫度對向列相( Nematic )液晶的影響------------ 36
§2-2 膽固醇液晶------------------------------------------------ 38
§2-2-1 膽固醇液晶的光學特性------------------------------ 38
§2-2-2 外在影響膽固醇液晶螺距的因素------------------ 40
§2-3 雙頻液晶--------------------------------------------------- 44
§2-3-1 雙頻液晶之介電係數----------------------------------44
§2-4 GRIN lens 理論------------------------------------------ 47
§2-5 反應時間( Response Time )的定義---------------- 58
第三章 樣品製作
§3-1 樣品的製備------------------------------------------------ 60
§3-1-1 材料介紹------------------------------------------------ 60
§3-1-2 樣品製作的過程---------------------------------------62
第四章 實驗結果與討論
§4-1 觀察液晶透鏡干涉條紋的變化---------------------- 67
§4-1-1 儀器架設與檢測方法--------------------------------- 67
§4-1-2 實驗結果與討論--------------------------------------- 69
§4-2 液晶透鏡相位分佈的計算------------------------------ 84
§4-2-1 計算聚合物透鏡的高度與斜率--------------------- 84
§4-2-2 計算液晶透鏡的相位--------------------------------- 87
§4-2-3 實驗結果與討論--------------------------------------- 92
§4-3 液晶透鏡焦距的計算------------------------------------ 98
§4-4 液晶透鏡的聚焦性質-----------------------------------102
§4-4-1 儀器架設與量測方法--------------------------------102
§4-4-2 實驗結果與討論--------------------------------------104
§4-5 量測液晶透鏡的反應時間( Response time )----105
§4-5-1 儀器架設與量測方法--------------------------------105
§4-5-2 實驗結果與討論--------------------------------------108
第五章 結論-----------------------------------------------------113
參考文獻---------------------------------------------------------115

[1] S. Sato, Jpn. J. Appl. Phys. 18, 1679 (1979).
[2] S. Suyama, M. Date, and H. Takada, Jpn. J. Appl. Phys. Part 1 38, 480 (2000).
[3] M. Hain, R. Glockner, S. Bhattacharya, D. Dias, S. Stankovic, and T. Tschudi, Opt. Commun. 188, 291 (2001).
[4] T. L. Kelly, A. F. Naumov, M. Yu. Loktev, and M. A. Rakhmatulin, Opt. Commun. 181, 295 (2000).
[5] Oleg Pishnyak, Susumu Sato, and Oleg D. Lavrentovich, Appl. Opt. 45, 4576 (2006).
[6] Bin Wang, Mao Ye, and Susumu Sato, Jpn. J. Appl. Phys. 45, 7813 (2006).
[7] Shin Masuda, Shogo Fujioka, Michinori Honma, Toshiaki Nose, and Susumu Sato, Jpn. J. Appl. Phys. Part 1 35, 4668 (1996).
[8] Toshiaki Nose, Shin Masuda, Susumu Sato, Jianlin Li, Liang-Chy Chien, and Philip James Bos, Opt. Lett. 22, 351 (1997).
[9] Mao Ye, Bin Wang, and Susumu Sato, Appl. Opt. 43, 6407 (2004).
[10] Hongwen Ren, Yun-Hsing Fan, Sebastian Gauza, and Shin-Tson Wu, Jpn. J. Appl. Phys. 43, 652 (2004).
[11] Yi-Hsin Lin, Hongwen Ren, Kuan-Hsu Fan-Chiang, Wing-Kit Choi, Sebastian Gauza, Xinyu Zhu, and Shin-Tson Wu, Jpn. J. Appl. Phys. 44, 243 (2005).
[12] Hongwen Ren, and Shin-Tson Wu, Opt. Express. 14, 11292 (2006).
[13] Hongwen Ren, David W. Fox, Benjamin Wu, and Shin-Tson Wu, Opt. Express. 15, 11328 (2007).
[14] Hongwen Ren, Yun-Hsing Fan, and Shin-Tson Wu, J. Phys. D：Appl. Phys. 37, 400 (2004).
[15] Hongwen Ren, and Shin-Tson Wu, Appl. Phys. Lett. 82, 22 (2002).
[16] V. V. Presnyakov, and T. V. Galstian, Mol. Cryst. Liq. Cryst. 413, 435 (2004).
[17] Vladimir V. Presnyakov, and Tigran V. Galstian, J. Appl. Phys. 97, 103101 (2005).
[18] P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed., Clarendon Press, Oxford (1993).
[19] L. M. Blinov and V. G. Chigrinov, Electrooptics Effects in Liquid Crystal Materials, Springer-Verlag, New York (1994).
[20] 松本正ㄧ、角田市良, 液晶的基礎與應用, 劉瑞祥譯, 國立編譯館 (民國85年).
[21] B. Bahadur, Liquid Crystals-Applications and Uses, Vol. 1, World Scientific, Singapore (1990).
[22] Eugene Hecht, OPTICS, 3rd ed., Addison Wesley, San Francisco (2002).
[23] Andrew J. Lovinger, Karl R. Amundson and Don D. Davis, Chem. Mater. 6, 1726 (1994).
[24] Grant R. Fowles, Introduction to Modern Optics, 2nd ed., University of Utah, New York (1975).
[25] 朱自強、王仕璠、蘇顯渝, 現代光學教程,四川大學出版社, 成都(1990).
[26] Iam-Choon Khoo, Liquid Crystals-Physical Properties and Nonlinear Optical Phenomena, John Wiley & Sons Press, New York (1995).
[27] Iam-Choon Khoo and Shin-Tson Wu, Optics and Nonlinear Optics of Liquid Crystals, World Scientific, Singapore (1993)
[28] Hermann A. Haus, Wave and Fields in Optoelectronics, Englewood Cliffs, New Jersey (1989).
[29] 閻吉祥、魏光輝、哈流柱、林永昌、江先進, 矩陣光學, 兵器工業出版社, 北京 (1995).
[30] S. Jobling, Y. Williams, J. Liou, and I. C. Khoo, NSF EE REU PENN STATE Annual Research Journal Ⅲ, 92 (2005).