本論文利用膽固醇液晶之手紋結構，並搭配圓形摩擦配向的方式製作廣角變化之圓形光柵。膽固醇液晶在低電壓以及適當的d/p值(液晶盒厚度對螺距之比值；d/p≤3)條件下可形成近似於相位型光柵之週期性條紋結構，此結構在不同的d/p值下，可分為螺距無法改變的Developable-modulation (DM) type (d/p=0.5~1) 以及螺距可調整的Growing-modulation (GM) type (d/p=1.5~3)。本實驗乃控制樣品的d/p值大小使膽固醇液晶之手紋結構為GM type，因此可藉由調控外在電壓來改變手紋結構之螺距，進而達到繞射角度調控之效果。在本研究當中樣品之d/p值為2.5時可以得到最廣角變化的特性，繞射角變化最大值可達到20.9。此外由於光柵條紋排列方向為對稱之同心圓結構，因此具有無偏振依賴之特性。基於上述優點，此元件不僅在入射光偏振態的篩選上比一維光柵來的彈性，在繞射角調控上也可藉由微小的外在電壓而達到廣角調控的效果，在光學開關元件的應用上具有很大的潛力。

A widely tunable circular grating based on the fingerprint texture of cholesteric liquid crystals (CLC) has been investigated by using circular alignment method. The phase-grating like fingerprint texture of CLCs can be obtained by operating at the low voltage under a suitable d/p ratio (d/p≤3) and two types of the fingerprint texture are defined with various range of d/p ratio. Fingerprint texture with d/p ratio of 0.5~1.0 is the developable-modulation (DM) type and the stripes simultaneously appear across the whole sample. For the cell with d/p ratio of 1.5~3.0 is growing-modulation (GM) type and the stripes slowly extend to the whole sample along the rubbing direction from defects. In this study, the pitch of CLC sample fabricated with GM type can be easily tuned by varying voltage. The tuning maximum angle of second-order diffraction achieves 20.9 with the CLC sample under the condition of d/p=2.5. Moreover, the circular grating has the polarization-independent property because its stripe exhibits the circular symmetrical structure. According to above characteristics, the CLC circular grating is polarization-insensitive and can be potentially applied in optical switching devices for widely tunable feature.

論文審訂書 i
致謝 ii
中文摘要 iii
英文摘要 iv
目錄 v
圖次 vii
表次 ix
第一章 簡介 1
1-1 前言 1
1-2 液晶簡介 2
1-2-1 液晶起源 2
1-2-2 何謂液晶 3
1-2-3 液晶的分類 ...............…………………………………………………4
1-3 液晶物理 9
1-3-1 液晶分子排列的秩序參數 9
1-3-2 液晶的光學異向性 9
1-3-3 液晶的連續體彈性形變理論 11
1-3-4 液晶的介電異性………………………………..…………………….11
第二章 實驗相關理論 13
2-1 電場對膽固醇液晶之影響 13
2-2 手紋結構之理論與應用 15
2-3 繞射 16
2-4 繞射光柵 19
2-5 繞射光柵分類 20
第三章 樣品製作與實驗架設 22
3-1 材料介紹 22
3-2 樣品製作 23
3-3 實驗儀器架設 26
3-3-1液晶盒厚度量測 26
3-3-2偏光顯微鏡觀察條紋變化 26
3-3-3繞射效率量測 27
3-3-4繞射角變化量測 28
3-3-4無偏振依賴性量測 29
第四章 實驗結果與討論 30
4-1顯微鏡下之條紋變化 30
4-2電控繞射角變化 34
4-3繞射效率 36
4-4無偏振依賴量測 39
第五章 總結與未來展望 41
參考文獻 42

[1] L. M. Blinov and V. G. Chigrinov, “Electrooptic Effects in Liquid Crystal Materials,” Springer-Verlag, New York (1994).
[2] P. G. de Gennes and J. Prost, “The Physics of Liquid Crystals,".Clarendon Press,” Oxford University Press, New York (1993)
[3] C. Khoo, “Liquid Crystals-Physical Properties and Nonlinear Optical. Phenomena,” John Wiley & Sons Press, New York (1995).
[4] C. W. Oseen, “The theory of liquid crystals”, Trans. Faraday Soc. 29, 833 (1933).
[5] I. A Yao, C. H. Liaw, S. H. Chen and J. J. Wu, “Direction-tunable cholesteric phase gratings,” J. Appl. Phys. 96, 1760 (2004).
[6] C. T. Kuo, R. H. Chiang and C. H. Lin, “Electrically switchable cholesteric gratings based on slit electrodes,” Opt. Express 22, 9759 (2014).
[7] M. Zhu, G. Carbone and C. Rosenblatt, “Electrically switchable, polarization-independent diffraction grating based on negative dielectric anisotropy liquid crystal,” Appl. Phys. Lett. 88, 253502 (2006).
[8] C. V. Brown, Em. E. Kriezis and S. J. Elston, “Optical diffraction from a liquid crystal phase grating,” J. Appl. Phys. 91, 3495 (2002).
[9] M. S. Giridhar, K. A. Suresh and G. S. Ranganath, “Optical diffraction in nonuniform cholesteric liquid crystals: phase-grating mode,” J. Opt. Soc. Am. A 19, 1 (2002).
[10] H. Sarkissian, S. V. Serak, N. V. Tabiryan, L. B. Glebov, V. Rotar, and B. Ya. Zeldovich, “Polarization-controlled switching between diffraction orders in transverse-periodically aligned nematic liquid crystals,” Opt. Lett. 31, 2248 (2006).
[11] S. N. Lee, L. C. Chien and S. Sprunt, “Polymer-stabilized diffraction gratings from cholesteric liquid crystals,” Appl. Phys. Lett. 72, 885 (1998).
[12] I. A. Yao, Y. C. Lai, S. H. Chen, and J. J. Wu, “Relaxation of a field-unwound cholesteric liquid crystal,” Phys. Rev. E 70, 051705 (2004).
[13] C. H. Lin, R. H. Chiang, C. T. Kuo, and C. Y. Huang, “Rotatable diffractive gratings based on hybrid-aligned cholesteric liquid crystals,” Opt. Express 20, 26837 (2012).
[14] S. W. Kang, S. Sprunt and L. C. Chien, “Structure and morphology of polymer- stabilized cholesteric diffraction gratings,” Appl. Phys. Lett. 76, 3516 (2000).
[15] D. Subacius, P. J. Bos and O. D. Lavrentovich, “Switchable diffractive cholesteric gratings,” Appl. Phys. Lett. 71, 1350 (1997).
[16] J. E. Anderson, P. Watson, T. Ernst, and P. J. Bos, “Computer simulation evidence of the transient planar state during the homeotropic to focal conic transition in cholesteric liquid crystals,” Phys. Rev. E 61, 3951 (2000).
[17] Andy Y. G. Fuh, C. H. Lin and C. Y. Huang, “Dynamic Pattern Formation and Beam-Steering Characteristics of Cholesteric Gratings,” Jpn. J. Appl. Phys. 41, 211 (2002).
[18] D. Subacius, S. V. Shiyanovskii, Ph. Bos1 and O. D. Lavrentovich, “Cholesteric gratings with field-controlled period,” Appl. Phys. Lett. 71, 3323 (1997).
[19] J. Chen, P. J. Bos1, H. Vithana and D. L. Johnson, “An electro‐optically controlled liquid crystal diffraction grating,” Appl. Phys. Lett. 67, 2588 (1995).
[20] H. C. Jau, T. H. Lin, C. W. Chen, and Andy Y. G. Fuh, “Direction switching and beam steering of cholesteric liquid crystal gratings,” Appl. Phys. Lett. 100, 131909 (2012).
[21] S. H. Kima and L. C. Chien “Short Pitch, Cholesteric electro-optical device stabilized by nonuniform polymer network,” Appl. Phys. Lett. 86, 161118 (2005).