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研究生:吳承祐
研究生(外文):Cheng-Yu Wu
論文名稱:雷射穿透膽固醇液晶的遠場繞射圖形
論文名稱(外文):Far field diffraction patterns of laser beam through the cholestric liquid crystal
指導教授:林家弘林家弘引用關係
指導教授(外文):Ja-Hon Lin
口試委員:吳俊傑賴暎杰謝文峰
口試委員(外文):Jin-Jei WuYin-Chieh LaiWen-Feng Hsieh
口試日期:2012-07-26
學位類別:碩士
校院名稱:國立臺北科技大學
系所名稱:光電工程系研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:英文
論文頁數:50
中文關鍵詞:液晶非線性光學Z-scan遠場繞射圖案Fresnel-Kirchhoff積分
外文關鍵詞:Liquid crystalnonlinear opticsZ-scanfar field diffraction patternFresnel-Kirchhoff integral.
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在這個研究中,我利用鈦藍寶石雷射作為量測光源來研究向列型液晶和膽固醇液晶的非線性光學特性。首先我利用Z-scan的量測來得到液晶的非線性折射率,在此量測中,分別採用線性偏振進行向列型液晶和左旋偏振光進行膽固醇液晶的量測,發現所得到的歸一化穿透率都是先上後下的圖形,因此非線性折射率變化為負值,推論主要是由於熱透鏡的效應所造成;接著我將液晶樣品在透鏡前後移動,觀察高斯光束經過液晶樣品後的遠場繞射圖形,發現當液晶樣品在透鏡焦點前,曲率半徑為負的高斯光束經過此一個自散焦介質後,在遠場會形成一個中央亮紋及一個較弱強度光環的繞射圖案,此外當液晶樣品移到透鏡的焦點後,此時入射高斯光束波前的曲率半徑變為正值,觀察遠場繞射的圖案,發現它的中央亮紋的強度變弱,而外圍環的強度會變強,類似一個甜甜圈的圖案。由於高斯光束在焦點位置,曲率半徑和光束的大小變化相當大,我藉由克希荷夫繞射積分公式並考慮此兩參數可以得到高斯光束經過液晶後遠場繞射圖形的強度變化,由此公式模擬得到在焦點前曲率半徑為負值,因此經過自散焦的介質可以得到中心亮紋,在焦點後曲率半徑為正值,因此經過自散焦的介質則遠場繞射圖案將是中央暗紋。這個研究結果有助於我們利用液晶來設計實用的非線性光幅限制器作為感測器的保護裝置。

In this work, we use Ti:sapphire laser as light source to study the nonlinear optical characteristics of the liquid crystal (LC). First, we measure the nonlinear refractive indices of LC by the Z-scan measurement. During this measurement, we use linear polarization light beam to measure nematic liquid crystal (NLC) and left-handed circular polarization beam to measure cholestric liquid crystal (CLC) , respectively. Owing to the thermal lensing effect, the measured normalized transmittance reveals peak-valley trace means that the nonlinear refractive index change is negative. Then, we move the LC in z direction before and after the focal point of lens to observe the far field diffraction patterns (FFDP) as Gaussian beam passing through the LC cell. The incident Gaussian beam will have negative wave-front curvature when the LC is put before the focal point of the lens. The FFDP displayed a central bright spot surrounded by a ring with lower intensity when the Gaussian beam passed through a self-defocusing medium. After LC cell moved after the focal point of the lens, the curvature of incident Gaussian beam through the LC will become positive. From FFDPs, the intensity of central bright spot will reduce and the outer ring will increase, resemble to a donut pattern. It is needed to consider the variation of the radius of curvature and beam radius due to apparent change for the Gaussian beam around the focal point. The variation of FFDPs as the Gaussian beam through the LC cell can be calculated using the Kirchhoff diffraction integral. After calculation, we can summarize that the central bright spot can be obtained while the self-defocusing medium is before the focal point and the wave-front curvature is negative. If the self-defocusing medium is after the focal point, the far field diffraction patterns will become a central dark pattern as the wavefront curvature is negative. The investigated results will help us to design practical nonlinear optics limiters of protective devices sensor by LC.

Outline
Chinese abstract i
English abstract iii
Acknowledgment v
Content vi
List of tables vii
List of figures ix
Chapter 1 Introduction 1
1.1Kinds of liquid crystals 1
1.1.1 Thermotropic liquid crystals 1
1.2 Far field diffraction pattern through the nonlinear
medium 4
1.3 Motivation 5
Chapter 2 Theory background 6
2.1 Z-scan measurement 6
2.1.1 Nonlinear absorption and nonlinear refraction
coefficient 6
2.1.2 Z-scan technique 8
2.2 Thermal lensing model 12
2.3 Fresnel-Kirchhoff far field diffraction theory 13
Chapter 3 Experiment 16
3.1 Sample preparation 16
3.2 Experimental setup 16
3.2.1 Transmittance spectrum measurement 16
3.2.2 Z-scan measurement 17
Chapter 4 Results and discussion 19
4.1 Nematic liquid crystal (Horizontal alignment) 19
4.1.1 Nonlinear refractive index of NLC 19
4.1.2 Evolution of far field diffraction pattern 23
4.2 35% chiral doped cholesteric liquid crystal 27
4.2.1 Nonlinear refractive index of CLC 27
4.2.2 Evolution of far field diffraction pattern 32
4.3 31% chiral doped cholesteric liquid crystal 38
4.3.1 Nonlinear refractive index of CLC 39
4.3.2 Evolution of far field diffraction pattern 41
Chapter 5 Conclusions 45
References 47

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