本篇利用Z-scan的方式探討藍相液晶之非線性光學性質。其目的為探討藍相(blue phase)液晶中，由於熱效應和液晶分子轉動所引發的非線性效應。Z-scan技術是一個常被用來量測材料的非線性吸收係數及非線性折射係數的方法，其原理是基於樣品的非線性折射率會產生自聚焦效應或自發散效應的現象。
對一般的向列型液晶而言， 向列相(nematic phase)比起同均相(isotropic phase)具有更大的非線性效應，但由於液晶本身具有異向性的緣故， 因此在向列相藉由光引致的非線性效應具有與偏振相關的特性。不同於向列相，藍相由於其對稱的結構，所以具有光學等向性，因此藍相具有與偏振無關特性並且能夠提供一個大的非線性效應。
量測非線性項n2值的實驗如下：首先將一道線性偏振的氬離子雷射光，經過透鏡聚焦在z方向，並且在樣品後面放置偵測器，接著將樣品沿著z方向在焦點前後移動，並同時接收其光訊號，最後再經由數學關係式推導出代測物質的非線性折射率n2值。本實驗研究純藍相液晶及摻雜偶氮染料藍相液晶二種材料，並分別在藍相以及同均相的狀態下量測對應的非線性折射率n2值。由實驗結果發現在藍相的狀態時，摻雜偶氮染料藍相液晶的非線性項n2 值比起純藍相液晶的非線性項n2值 ，大約大了2~3個數量級。此外，從實驗結果也證實，藍相的非線性項n2值確實是大於同均相的非線性項n2值。
本研究證實藍相液晶藉由氬離子雷射引致出非線性效應，而且z-scan可以幫助量測出此非線性項n2值。

This study researches the nonlinear optical properties of the blue phase liquid crystals using the Z-scan technique. The purpose is to investigate the non-linear effect of the blue phase liquid crystals induced by the thermal and the liquid crystal reorientation effect. The Z-scan technique is common method to measure the non-linear index n2 and the non-linear absorption coefficient of materials. The measurement of the optical Kerr constant using Z-scan is based on the principle of spatial beam distortion due to the self-focusing or self-defocusing.
For typical nematic liquid crystals, the nonlinear effect in the nematic phase is large than that in the isotropic phase. However, due to the anisotropic properties of the liquid crystal, the light-induced nonlinear effect in the nematic phase is polarization dependency. Unlike nematic phase, the blue phase is optical isotropic duo to its symmetric structure, and therefore blue phase are polarization independent and provide a larger non-linear effect.
The experiments to measure the nonlinear refractive index n2 are as follows: firstly, a linearly polarized Ar+ laser light (λ=532nm) is focused in the z direction onto the sample via lens, and the detector was set behind the sample. Sequentially, the light intensity is recorded while the sample is scanned near the beam waist of the green laser. Finally, the non-linear index n2 of the material is derived from mathematical calculation. The study investigated two kinds of material, pure blue phase liquid crystal and dye-doped blue phase liquid crystal, and measured their non-linear index n2 in the blue phase and isotropic phase, respectively. The experimental results show that the non-linear index n2 of dye-doped blue phase liquid crystal is 100~1000 times as large as this of the pure blue phase liquid crystal at the blue phase. Besides, compared with isotropic phase in the blue phase liquid crystal, the blue phase actually possesses larger non-linear index n2.
This experiment confirms that the nonlinear effect can be induced using linearly polarized Ar+ laser, and the nonlinear refractive index n2 can be measured using Z-scan technique.

誌謝…………………………………………………………………………………….iii
摘要…………………………………………………………………………………….iv
Abstract…………………………………………………………………………...…….v
目錄……………………………………………………………………………………vii
圖次……………………………………………………………………………………ix
表次……………………………………………………………………………………xi
第一章 液晶簡介………………………………………………………………..….1
1-1 前言………………………………………………………………...….1
1-2 何謂液晶………………………………...…………………………….1
1-3 液晶分類……………………………………………………………….2
1-3-1　向列型液晶………………………………………………..…..3
1-3-2　膽固醇液晶……………………………………………..……..4
1-3-3　藍相液晶………………………………………………...…….5
1-4 液晶的物理特性……………………………………………………….7
1-4-1 秩序參數…………………………………………………………..8
1-4-2 光學異向性………………………………………………………..9
1-4-3 溫度對向列型液晶之影響…………………………………….....13
1-4-4 介電常數異向性……………………………………………….....13
1-4-5 液晶的連續彈性體理論……………………………………….....15
1-4-6 黏滯係數異向性……………………………………………….....16
1-4-7　Freedericksz transition…………………………………………..18
第二章 理論………………………………………………………………………..19
2-1 光引致分子轉向效應……………………………………….………..19
2-1-1 正力矩效應……………………………………….…………….19
2-1-2 負力矩效應……………………………………………………..21
2-1-3 光激發偶氮染料同素異構化反應……………………….…….22
2-1-4 光致熱效應……………………………………………….…….23
2-2 Z-scan　Techniqe…………………………………………....………..24
2-2-1 非線性光學………………………………………….………….24
2-2-2 Z-scan的非線性吸收係數和非線性折射係數…………..……27
2-2-3 Z-scan的理論………………………………………….……....31
第三章 實驗方法與過程…………….………………………………….….…….36
3-1 材料介紹……………………………………………………………..….36
3-2 樣品製作……………………………………………………………..….37
3-3 配向之檢驗－光學顯微鏡目測法………………………………..…….41
第四章 實驗光路架設與實驗方法………………………………………….…..42
4-1 實驗光路之架設……………………………………………….……......42
4-2 實驗架構與流程…………………………………………………...……43
第五章 結果與討論……………………………………………………………...46
5-1 向列型液晶之Z-scan量測……………………………………………..46
5-2 藍相液晶（blue phase）之Z-scan量測…………………………...…..56
5-3 向列型液晶摻雜偶氮染料（Azo-Dye doped Liquid Crystals）
之Z-scan量測…………………………………………………….……..59
5-4 藍相液晶（blue phase）摻雜偶氮染料之Z-scan量測…………..…..65
第六章 結論…………………………………………………….……………….69
第七章 參考文獻………………………………………………………………..71

[1] B. Bahoadur,” Liquid Crystals-Applications and Uses”, World Scientific Press, Singapore, (1990).
[2] 陳文政, “摻雜奈米粒子及偶氮染料的液晶薄膜之光配向研究及應用” ,國立中山大學, 光電工程研究所, (2009)
[3] 劉鵠儀, “摻雜偶氮材料於藍相液晶之光學調控研究” ,國立中山大學, 光學工程研究所, (2010)
[4] H.-S. Kitzerow, P. P. Crooker, S. L. Kwok, J. Xu and G. Heppke, Phys. Rev. A 42, 3442, (1990).
[5] P. P. Crooker, in Chirality in Liquid Crystals (Eds: H.-S. Kitzerow, C.Bahr). Springer, New York, 186-222, (2001).
[6] H. Kikuchi, M.Yokota, Y. Hisakado, H. Yang, and T. Kajiyama, Nat. Mater. 1, 64, (2002).
[7] H. J. Coles, and M. N. Pivnenko, Nature 436, 997, (2005).
[8] S. Meiboom, J. P. Sethna, P. W. Anderson, W. F. Brinkmann, Phys. Rev. Lett. 46, 1216 (1981).
[9] A. Yariv, “Optical Electronics in Modern Communications”, 5th Ed., Oxford University Press, New York, (1997).
[10] M. Lu and K. H. Yang, SID Tech. Digest, 31, 338, (2000).
[11] M Blinov and V.G. Chigrinov, “Electrooptic Effects in Liquid Crystal Materials”, Springer-Verlag, New York, (1994).
[12] A. Yariv, “Optical Electronics in Modern Communications”, 5th Ed., Oxford University Press, New York, 1997.
[13] I. -C. Khoo, “Liquid crystals : physical properties and nonlinear optical phenomena”, John Wiley & Sons, Inc, (1995).
[14] E. B. Priestley, P. J. Wojtowicz and P. Sheng, “Introduction to Liquid Crystals”, Princeton, New Jersey, (1975).
[15] Peter J. Collings and Michael Hird, “Introduction to Liquid Crystals Chemistry and Physics”, Taylor and Francis, London, (1997).
[16] Giovanni Barberoan and Luiz Roberto Evangelista, “Adsorption phenomena and anchoring energy in nematic Liquid Crystals”, Taylor and Francis, Boca Raton, (2006).
[17] I. Jánossy, A.D. Lloyd and B. S. Wherrett, Mol. Crys. Liq. Cryst., 179, 1, (1990).
[18] I. Ja’nossy, L. Csillag and A.D. Lloyd, Phys. Rev. A, 44, 8410, (1991).
[19] I. Ja’nossy and T. Kosa, Opt. Lett., 17, 1183, (1992).
[20] I. Ja’nossy and A.D. Lloyd, Mol. Crys. & Liq. Cryst., 203, 74, (1991).
[21] I. Ja’nossy, Phys. Rev. E, 49, 8410, (1994).
[22] Dennis Gabor, Nature, 161, 777, (1948).
[23] W. M. Gibbons, P. J. Shannon, S. T. Sun, and B. J. Swetlin, Nature, 351, 49, (1991).
[24] W. M. Gibbons, T. Kosa, P. Palffy-Muhoray, P. J. Shannon and S. T. Sun, Nature, 377, 43, (1995).
[25] W. Y. Y. Wong, T. M. Wong and H. Hiraoka, Appl. Phys. A65, 519, (1997).
[26] H. Hervel, W. Urbach, and F. Rondelez, J. Chem. Phys. 68, 2725, (1978).
[27] C.-R. Lee, T.-S. Mo, K.-T. Cheng, T.-L. Fu and A. Y.-G Fuh, Appl. Phys. Lett., 83, 4285, (2003).
[28] A. G. Chen and D. J. Brady, Opt. Lett., 17, 441, (1992).
[29] T. V. Gastyan, V. Drnoyan, S. M. Arakelian, Phys. Lett. A, 217, 52, (1996).
[30] 陳錦慧, “利用Z-scan技術研究偶氮染料摻雜液晶聚合物之非線性光學性質” ,國立成功大學, 物理研究所, (2008)
[31] 林蕙琪, “利用雙光子Z-掃描技術研究偶氮染料摻雜液晶薄膜之非線性光學性質” ,國立成功大學, 物理研究所, (2008)
[32] A. Owyoung, IEEE J. Quantum Electron., QE-9, 1064, (1973).
[33] W.E. Williams, M.J. Soileau, and E.W. Van Stryland, Opt. Commun., 50, 256, (1984).
[34] J. D. Gaskill, “Linear systems, Fourier Transforms, and Optics”, John Wiley& Sons, Inc., New York, (1978).
[35] D. Weaire, B. S. Wherrett, D. A. B. Miller and S. D. Smith, Opt. Lett., 4, 331, (1979).