臺灣博碩士論文加值系統

本論文主要目的為透過翻模複製法製作菲涅耳波帶片(Fresnel zone plate，FZP)，並將其與液晶材料結合後以電壓控制達成相位型菲涅耳液晶透鏡。實驗中針對不同厚度之菲涅耳液晶透鏡的繞射效率、偏振特性，以及成像效果等光學特性進行研究。
由於向列型E7液晶的短軸折射率與固化的NOA65光學膠折射率差異極小(~0.0023)，入射光進入奇、偶區時幾乎感受不到兩區間之折射率變化，因此可藉此光學特性與外加電場控制液晶分子轉態，達到菲涅耳液晶透鏡ON/OFF切換之目的。
菲涅耳液晶透鏡使用的液晶配向有水平配向(Homogeneous alignment，HA)和90度扭轉配向(90° twisted nematic alignment，TN)兩種類型。HA菲涅耳液晶透鏡為偏振相關元件，其焦點處光強度與入射光偏振方向相關；而TN菲涅耳液晶透鏡則為偏振無關元件。
由於NOA65二階結構是立體建立於玻璃基板上，奇、偶區液晶層厚度不同會造成相位分佈不均，使入射光因為感受到相位差而產生繞射，讓光線匯聚；當施加一電壓於液晶盒時，奇區因具有NOA65層結構導致液晶層感受到的電壓較偶區液晶層為小，故其液晶分子轉動程度亦較小，如此，奇、偶區對入射光便產生明顯的相位差及繞射現象。
根據理論，相位型二階菲涅耳透鏡的繞射效率為40.5%；而本研究結果在無間隙子與12μm厚度間隙子的HA菲涅耳液晶透鏡最大繞射效率分別為37.4%及37.15%，12μm、18μm及24μm的TN菲涅耳液晶透鏡最大繞射效率分別為23.76%、28.94%及35.28%。

In this thesis, the main investigation is to fabricate electrically switchable phase Fresnel liquid crystal lens (FLCL) by means of molding duplication. The optical performance of the fabricated phase FLCL is mainly measured and investigated including maximum diffraction efficiency, correlation of polarization, and imaging result.
The experiment interprets a phase FLCL that which is based on preformed polymer relief structure but uses two different kinds of aligned liquid crystal film, homogeneous alignment (HA) and twisted nematic alignment (TN) individually.
Experimental results the phase FLCL with homogeneous alignment has polarization dependent feature, polarization insensitive for 12μm and 18μm cell gap experiment sample with TN alignment, and polarization independent for 24μm cell gap FLCL lens with TN alignment.
At present, the high diffraction efficiency is available in this study, 37.15% and 35.28% for HA and TN phase FLCL individually, which is very close to the theoretical maximum value 40.5%.
Due to high diffraction efficiency and the refractive index of cured NOA65 (Norland Optical Adhesive 65) is matching to ordinary axis refractive index of nematic liquid crystal E7, the phase FLCL could successfully have not only the same focusing function with traditional convex glass lens, but also could be ON/OFF switch by additional electric field.

摘要 I
Abstract III
致謝 XI
目錄 XIII
圖目錄 XVI
表目錄 XXIII
第一章 緒論 1
1.1 前言 1
1.2 菲涅耳透鏡介紹及文獻回顧 3
1.2.1 菲涅耳透鏡 3
1.2.2 文獻回顧 8
1.3 研究動機 23
第二章 液晶物理特性簡介 24
2.1 單光軸雙折射性(Uniaxial birefringence) 24
2.2 連續彈性體理論(The elastic continuum theory)[21] 27
2.3 電場對液晶的影響 29
2.4 Freedericksz transition[22] 31
第三章 實驗原理 33
3.1 菲涅耳波帶片(Fresnel zone plate) 33
3.2 菲涅耳透鏡理論[24] 35
3.3 Mauguin Limit定理 42
第四章 實驗材料與裝置 45
4.1 實驗材料 45
4.1.1 向列型液晶E7 45
4.1.2 光學膠(Norland Optical Adhesive 65，NOA65)[26] 46
4.1.3 聚二甲基矽氧烷(Polydimethylsiloxane，PDMS) 47
4.2 菲涅耳液晶透鏡製作 48
4.2.1 設備與材料 48
4.2.2 菲涅耳光罩設計 49
4.2.3 實驗樣品製作步驟 50
4.3 實驗裝置架設 61
4.3.1 液晶配向狀態觀測 62
4.3.2 繞射效率與偏振相關性量測 63
4.3.3 透鏡成像與擷取 65
第五章 實驗結果與討論 66
5.1 利用黃光微影製程製作菲涅耳二階結構 66
5.2 液晶層厚度對水平配向菲涅耳液晶透鏡特性之影響 68
5.2.1 水平配向菲涅耳液晶透鏡於正交偏光顯微鏡下配向狀態觀測 69
5.2.2 水平配向菲涅耳液晶透鏡繞射效率量測與偏振特性探討 71
5.2.3 水平配向菲涅耳液晶透鏡成像效果觀察 73
5.3 液晶層厚度對90度扭轉配向菲涅耳液晶透鏡特性之影響 78
5.3.1 90度扭轉配向菲涅耳液晶透鏡於正交偏光顯微鏡下配向狀態觀測 78
5.3.2 90度扭轉配向菲涅耳液晶透鏡繞射效率量測 81
5.3.3 90度扭轉配向菲涅耳液晶透鏡對於入射光偏振方向之關係 83
5.3.4 90度扭轉配向菲涅耳液晶透鏡成像效果觀察 85
5.4 不同波長入射光對菲涅耳液晶透鏡成像之影響 90
第六章 結論與未來展望 92
6.1 結論 92
6.2 未來展望 94
參考文獻 96

[1]W. Hu, A. K. Srivastava, X. W. Lin, X. Liang, Z. J. Wu, J. T. Sun, G. Zhu, V. Chigrinov, and Y. Q. Lu, “Polarization independent liquid crystal gratings based on orthogonal photoalignments, Applied Physics Letters, Volume 100, Issue 11, 111116(2012).
[2]F. Fan, A. K. Srivastava, V. G. Chigrinov, and H. S. Kwok, “Switchable liquid crystal grating with sub millisecond response, Applied Physics Letters, Volume 100, Issue 11, 111105 (2012).
[3]H. C. Jau, T. H. Lin, Y. Y. Chen, C. W. Chen, J. H. Liu, and A. Y. G. Fuh, “Direction switching and beam steering of cholesteric liquid crystal gratings, Applied Physics Letters, Volume 100, Issue 13, 131909 (2012).
[4]M. Honma and T. Nose, “Highly efficient twisted nematic liquid crystal polarization gratings achieved by microrubbing, Applied Physics Letters, Volume 101, Number 4, 041107 (2012).
[5]L. Lu, V. Sergan, T. Van Heugten, D. Duston, A. Bhowmik, and P. J. Bos, “Tunable Polymer Localized Liquid Crystal Lenses for Autostereoscopic 3D Displays, SID Symposium Digest of Technical Papers, Volume 43, Issue 1, page 383-386(2012).
[6]S. Sato, T. Nose, R. Yamaguchi, and S. Yanase, “Relationship between lens properties and director orientation in a liquid crystal lens, Liquid Crystals, Volume 5, Issue 5, page 1435-1442(1989).
[7]S. Sato, “Applications of Liquid Crystals to Variable-Focusing Lenses, Optical Review, Volume 6, Issue 6, page 471-485(1999).
[8]L. Shi, P. F. McManamon, and P. J. Bos, “Liquid crystal optical phase plate with a variable in-plane gradient, Journal of Applied Physics, Volume 104, Issue 3, 033109(2008).
[9]S. Somalingam, K. Dressbach, M. Hain, S. Stankovic, T. Tschudi, J. Knittel, and H. Richter, “Effective spherical aberration compensation by use of a nematic liquid-crystal device, Applied Optics, Volume 43, Issue 13, page 2722-2729 (2004).
[10]G. Q. Li, D. L. Mathine, P. Valley, P. Ayras, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications, PNAS, Volume 103, Number 16, page 6100-6104(2006).
[11]Joshua Naaman Haddock, “Liquid Crystal Based Electro-Optic Diffractive Spectacle Lenses and Low Operating Voltage Nematic Liquid Crystals, The University of ARIZONA(2005)
[12]Eugene Hecht, Optics, 4th ed. (Addison Wesley, 2002), Chapter 10
[13]王中原, “Studies of polarization-independent liquid-crystal Fresnel lenses with high diffraction efficiency, 國立中山大學物理學系研究所碩士論文(2009)
[14]Jian Gang Lu, Xiong Fei Sun, Yue Song, and Han Ping D. Shieh, “2-D/3-D Switchable Display by Fresnel-Type LC Lens, Journal of Display Technology, Volume 7, Number 4(2011)
[15]Hongwen Ren, Yun Hsing Fan, and Shin Tson Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals, Applied Physics Letters, Volume 83, Issue 8, 1515(2003)
[16]Yun Hsing Fan, Hongwen Ren, and Shin Tson Wu, “Switchable Fresnel lens using polymer-stabilized liquid crystals, Optics Express, Volume 11, Issue 23, page 3080(2003)
[17]Liang Chen Lin, Hung Chang Jau, Tsung Hsien Lin, and Andy Y. G. Fuh, “Highly efficient and polarization-independent Fresnel lens based on dye-doped liquid crystal, Optics Express, Volume 15, Issue 6, page 2900(2007)
[18]S. J. Hwang, T. A. Chen, K. R. Lin, S. C. Jeng, “Ultraviolet-light-treated polyimide alignment layers for polarization independent liquid crystal Fresnel lenses, Applied Physics B, Volume 107, Issue 1, page 151-155(2012)
[19]Yimin Lou, Linsen Chen, Chinhua Wang, and Su Shen, “Tunable-focus liquid crystal Fresnel zone lens based on harmonic diffraction, Applied Physics Letters, Volume 101, Number 22, 221121(2012)
[20]Toralf Scharf, “Polarized Ligh in Liquid Crystal and Polymers, Chap. 2, John Wiley ＆ Sons (2007)
[21]F. C. Frank, “On the theory of liquid crystals, Discussions of the Faraday Society, Volume 25, page 19-28(1958)
[22]Deng Ke Yang, Shin Tson Wu, “Fundamentals of Liquid Crystal Devices, Chap. 5, John Wiley ＆ Sons (2006)
[23]Eugene Hecht, Optics, 4th ed. (Addison Wesley, 2002), Chapter 5
[24]Jurgen Jahns, Susan J. Walker, “Two-dimensional array of diffractive microlenses fabricated by thin film deposition, Applied Optics, Volume 29, Issue 7, page 931(1990)
[25]Lam Choon Khoo, “Liquid Crystals, 2nd. Edition, Chap. 1, John Wiley ＆ Sons (2007)
[26]Norland Products Inc. P.O. BOX 145, North Brunswick, NJ, 08902, USA
[27]Yimin Lou, Qingkun Liu, Hui Wang, Yaocheng Shi, and Sailing He, “Rapid fabrication of an electrically switchable liquid crystal Fresnel zone lens, Applied Optics, Volume 49, Issue 26, page 4995(2010)
[28]Sihai Chen, Xinjian Yi, Hong Ma, “A novel method of fabrication of microlens arrays, Infrared Physics ＆ Technology, Volume 44, Issue 2, page 133-135(2003)