法布里-培若干涉儀(Fabry-Pérot interferometer，FPI，又稱Fabry-Pérot filter)可控制穿透光波長而被廣泛應用於通訊、雷射和光譜量測。入射光的波長、入射光的入射角度、共振腔的厚度以及共振腔內材料的種類皆會影響FPI的共振條件。之前的研究者基於元件結構及調變操作簡易，使用向列型液晶(nematic liquid crystal，NLC)當作主動式材料與FPI結合，利用電場對NLC的影響形成可調變折射率的材料。但NLC折射率的改變是因其導軸旋轉，如此一來，這樣的元件其濾波特性會與入射光的偏振態相關。
本論文是利用藍相液晶(blue phase liquid crystal，BPLC)作為FPI中可調變之主動式材料。因BPLC為三維的各方同向性，可使FPI元件之濾波特性與入射光偏振態無關。在實驗中，元件的透射峰值移動現象則是因為多束反射光在可調折射率的BPLC中發生干涉現象。BPLC晶格內的液晶在外加正向電場下因克爾效應(Kerr effect)產生了local reorientation，BPLC折射率從等效折射率(niso)逐漸轉換成尋常光折射率(no)。在此我們更可使用高分子聚合方式(polymer-stabilized construction)穩固BPLC的晶格結構讓BPLC可存在室溫下，增加了使用元件的方便性。目前，我們已達到~1nm/V的調變能力且與偏振態無關。而元件的反應時間方面，上升時間加下降時間總合約1ms。

Fabry-Pérot (FP) filters are widely used in telecommunications, lasers and spectroscopy to measure the wavelengths of light. The properties of a FP filter depend on the wavelength and incident angle of the light source, the thickness of the etalon and the refractive index of the material between the reflecting surfaces. In previous studies, the nematic liquid crystal (NLC) is employed as the medium of FP filters because of its simple structure and ease of modulation. The directors of the NLC could be rotated by applying an electric field. Due to the birefringence of the NLC, the optical characteristics of the device are polarization dependent.
Blue phase liquid crystal (BPLC) is the phase between cholesteric phase and isotropic phase. It’s an optically isotropic material can function as an active index-tuning material adopted in a FP filter, and the characteristics of the BPLC-based FP filter are polarization independent. By applying an electric field, the Kerr effect can be induced due to the local reorientation of liquid crystals in BP structure, leading to the effective index change of BPLC and the transmission peak shifts. Furthermore, the effective index of BPLC approaches the ordinary index of host LCs under increasing electric fields. In addition, the BPLC using polymer network construction can be stabilized in room temperature and improves the convenience of the device. According to the experimental results, the tunability of the BPLC-based FP filter is about 1nm/V. The measured response time of the BPLC-based FP filter is 1ms.

中文摘要……………………………………………………………………………..i
Abstract………………………………………………………………………….......ii
誌謝……………………………………………………………………………….….iii
目錄…………………………………………………………………………….…….iv
圖目錄…………………………………………………………………………….….vii
表目錄………………………………………………………………………….….…xi



第一章 緒論…………………………………………………………………………1
第二章 簡介…………………………………………………………………………2
2-1 液晶簡介…………………………………………………………………2
2-1.1 何謂液晶……………………………………………………………2
2-1.2 液晶的分類…………………………………………………………3
2-2 液晶的物理特性………………………………………………………..13
2-2.1 液晶分子排列的秩序參數………………………………………..13
2-2.2 液晶分子的光學異向性…………………………………………..14
2-2.3 液晶分子的介電異向性…………………………………………..17
2-2.4 溫度對液晶分子的影響…………………………………………..18
2-2.5 液晶的連續彈性理論……………………………………………..19
2-3 Fabry-Pérot Interferometer導論………………………………………..21
2-3.1 Fabry-Pérot interferometer導論…………………………………21
2-3.2 Liquid crystal Fabry-Pérot interferometer (filter)回顧....................22
2-4 藍相液晶簡介…………………………………………………………..23
2-4.1 何謂藍相液晶……………………………………………………..23
2-4.2 藍相液晶結構……………………………………………………..24
2-4.3 高分子安定化藍相液晶理論……………………………………..25
2-4.4 藍相液晶在電場下的反應………………………………………..27
第三章 理論介紹…………………………………………………………………..29
3-1 Fabry-Pérot Interferometer簡介………………………………………..29
3-2 Fabry-Pérot Interferometer理論推導…………………………………..30
3-2.1 Multiple Beam Interference………………………………………..30
3-2.2 自由頻譜範圍(Free Spectral Range)……………………………...34
3-2.3 細度(Finesse)……………………………………………………...35
3-3 藍相液晶的Kerr effect…………………………………………………37
第四章 實驗方法與過程…………………………………………………………..40
4-1 材料介紹………………………………………………………………..40
4-1.1 液晶混和物介紹…………………………………………………..40
4-1.2 配置藥品…………………………………………………………..43
4-2 高分子安定化液晶樣品製作………………………………...………...44
4-2.1 空cell製作………………………………………………………...44
4-2.2 液晶盒sample製作………………………………………………..46
4-3 實驗量測裝置…………………………………………………………..48
4-3.1 穿透頻譜測量裝置………………………………………………..48
4-3.2 樣品偏振態之量測………………………………………………..49
4-3.3 樣品折射率變化差之量測………………………………………..50
4-3.4 樣品反應時間之量測……………………………………………..51
第五章 結果與討論………………………………………………………………..52
5-1 藍相液晶觀察與分析…………………………………………………..52
5-1.1 高分子安定化藍相液晶溫度範圍觀察分析……………………52
5-1.2 藍相液晶外加電壓觀察分析……………………………………53
5-2 高分子安定化藍相液晶相位量測分析………………………………..55
5-3 BPLC Fabry-Pérot filter穿透頻譜之電控分析………………………61
5-3.1 BPLC Fabry-Pérot filter在可見光區之穿透頻譜電控分析..........61
5-3.2 BPLC Fabry-Pérot filter在紅外光區之穿透頻譜電控分析..........63
5-4 BPLC Fabry-Pérot filter穿透頻譜之模擬分析………………………65
5-5 BPLC Fabry-Pérot filter偏振依賴性之量測…………………………71
5-6 BPLC Fabry-Pérot filter反應時間之量測………………………….74
第六章 結論與未來展望…………………………………………………………..76
參考文獻……………………………………………………………………………..77

[1] F. Reintzer, Monatsh. Chem. 9, 421 (1888).
[2] S. Singh, and D. A. Dunmur, “Liquid Crystal：Fundamentals,” World Scientific, Singapore (1990).
[3] S. Chandrasekhar, Contemp. Phys. 29, 527 (1988).
[4] Yariv, “Optical Electronics in Modern Communications,” Oxford University Press (1997).
[5] 林宗賢, “液晶光子晶體雷射現象與其光控制研究,” 國立成功大學物理研究所碩士論文, (2004).
[6] J. Li, S. Gauza, and S. T. Wu, “Temperature effect on liquid crystal refractive indices,” J. Appl. Phys. 96, 19 (2004).
[7] MEOS AG Company, FABRY PEROT RESONATOR, experiment 03.
[8] Precision Photonics Corporation, Basic Physics and Design of Etalons.
[9] J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, and S. D. Lee, “Electrically tunable optical filter for infrared wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718 (1990).
[10] J. S. Pate1, “Polarization insensitive tunable liquid-crystal etalon filter,” Appt. Phys. Lett. 59, 1314 (1991).
[11] J. S. Pate1 and M. W. Maeda, “Tunable Polarization Diversity Liquid-Crystal Wavelength Filter,” IEEE Photon. Technol. Lett. 3, 739 (1991).
[12] J. S. Patel and Y. Silberberg, “Anticrossing of polarization modes in liquid-crystal etalons,” Opt. Lett. 16, 1049 (1991).
[13] Z. Zhuang and J. S. Patel, “Behavior of cholesteric liquid crystals in a Fabry–Perot cavity,” Opt. Lett. 24, 1759 (1999).
[14] Z. Zhuang, Y. J. Kim, and J. S. Patel, “Behavior of the Cholesteric Liquid-Crystal Fabry-Perot Cavity in the Bragg Reflection Band,” Phys. Rev. Lett. 84, 1168 (2000).
[15] J. S. Patel and S. D. Lee, “Electrically tunable and Polarization insensitive Fabry-Perot & etalon with a liquid-crystal film,” Appl. Phys. Lett. 58, 2491 (1991).
[16] Jay E. Stockley, Gary D. Sharp and Kristina M. Johnson, “Fabry–Perot etalon with polymer cholesteric liquid-crystal mirrors,” Opt. Lett. 24, 55 (1999).
[17] M. Kinoshita, M. Takeda, H. Yago, Y. Watanabe, and T. Kurokawa, “Optical frequency-domain imaging microprofilometry with a frequency-tunable liquid-crystal Fabry–Perot etalon device,” Appl. Opt. 38, 7063 (1999).
[18] Z. Zheng, G. Yang, H. Li, and X. Liu, “Three-stage Fabry–Perot liquid crystal tunable filter with extended spectral range,” Opt. Express 19, 2158 (2011).
[19] Y. Bao, A. Sneh, K. Hsu, K. M. Johnson, J. Y. Liu, C. M. Miller, Y. Monta, and M. B. McClain, “High-speed Liquid Crystal Fiber Fabry-Perot Tunable Filter,” IEEE Photon. Technol. Lett. 8, 1190 (1996).
[20] E. A. Dorjgotov, A. K. Bhowmik, and P. J. Bos, “Switchable polarization-independent liquid-crystal Fabry–Perot filter,” Appl. Opt. 48, 74 (2009).
[21] J. H. Lee, H. R. Kim, and S. D. Lee, “Polarization-insensitive wavelength selection in an axially symmetric liquid-crystal Fabry-Perot filter,” Appl. Phys. Lett. 75, 859 (1999).
[22] Y. Huang, T. X. Wu, S. T. Wu, “Simulations of liquid-crystal Fabry–Perot etalons by an improved 4×4 matrix method,” J. Appl. Phys. 93, 2490(2003).
[23] H. Kikuchi, “Liquid Crystalline Blue Phases,” Springer, Berlin Heidelberg (2007).
[24] D. L. Johnson, J. H. Flack, and P. P. Crooker, “Structure and Properties of the Cholesteric Blue Phases,” Phys. Rev. Lett. 45, 641 (1981).
[25] H. Kikuchi, M. Yokota, Y. Hisakado, H. Yang, and T. Kajiyama, “Polymer-stabilized liquid crystal blue phases,” Nat. Mater. 1, 64 (2002).
[26] H. J. Coles and M. N. Pivnenko, “Liquid crystal ‘blue phases’ with a wide temperature range,” Nature 436, 997 (2005).
[27] A. Yoshizawa, M. Sato, and J. Rokunohe, “A blue phase observed for a novel chiral compound possessing molecular biaxiality,” J. Mater. Chem. 15, 3285 (2005).
[28] Y. Hisakado, H. Kikuchi, T. Naganura, and T. Kajiyama, “Large Electro-optic Kerr Effect in Polymer-Stabilized Liquid-Crystalline Blue Phases,” Adv. Mater. 17, 96 (2005).
[29] Y. Haseba, H. Kikuchi, T. Naganura, and T. Kajiyama, “Large Electro-optic Kerr Effect in Nanostructured Chiral Liquid-Crystal Composites over a Wide Temperature Range,” Adv. Mater. 17, 2311 (2005).
[30] S. Y. Lu and L. C. Chien, “Electrically switched color with polymer-stabilized blue-phase liquid crystals,” Opt. Lett. 35, 562 (2010).
[31] Boulder Nonlinear Systems, Inc. “Liquid Crystal Fabry-Perot Tunable Filter,” (2001).
[32] J. Yan, H. C. Cheng, S. Gauza, Y. Li, M. Jiao, Li. Rao, and S. T. Wu, “Extended Kerr effect of polymer-stabilized blue-phase liquid crystals,” Appl. Phys. Lett. 96, 071105 (2010).
[33] L. Rao, J. Yan, S. T. Wu, S. I. Yamamoto, and Y. Haseba, “A large Kerr constant polymer-stabilized blue phase liquid crystal,” Appl. Phys. Lett. 98, 081109 (2011).