臺灣博碩士論文加值系統

在此論文中，我們主要是討論使用偶氮染料參雜的聚乙烯醇膜以光配向方法來做偏振光柵。首先是將氬離子雷射分為兩道光後將此兩道光轉變為兩道相反的圓偏振光，之後以此兩道光打在光配向膜上，兩道光將會因為干涉而使配向膜達到連續轉動配向的效果，這種光柵稱為偏振光柵。之後，我們以氦氖雷射探測偏振光柵繞射特性並且量測繞射零階與一階的強度與偏振狀態，並且使用有限差分時域法模擬這些特性，實驗結果與理論符合。
有限差分時域法是將瑪克士威爾方程式以數值方式表示，也因如此，在空間中或在物質中，光行進的行為將可被呈現。實驗中所使用的液晶是一種單光軸材料，其折射率可以以介電常數來代表。在有限差分時域法中將不同指向的液晶以介電常數代入後，液晶光學模擬得以進行。之後再藉由傅立葉轉換將遠場各階繞射強度與偏振算出。為了準確的模擬偏振光柵的繞射行為，液晶配向不完美的部分亦被考量在內。

A liquid crystal polarization grating (LCPG) is fabricated based on the photoalignment of azo-dye-doped polyvinyl alchohol film. Pumping two argon-ion laser beams having mutually orthogonal circular polarization on the film to form continuous rotation alignment of LCs, a polarization grating is fabricated. The diffraction characteristics of the fabricated LCPG are investigated by probing it with a helium-neon laser. The polarization and intensity of the zeroth- and first-order of the diffracted beams are measured. Then these characteristics of the diffracted beams are compared and consistent with theory simulated using the finite-difference time-domain (FDTD) method.
The FDTD method is a numerical method for modeling the Maxwell’s equations. It can be used to describe the light propagation in space or in mediums. Since the liquid crystal used in the experiment is a uniaxial material, we set the dielectric tensor to represent the refractive index of the liquid crystal with different orientations in FDTD model. The light propagation within the liquid crystal can be simulated. Using Fourier transform, the diffraction characteristics of the LCPG are calculated.

摘要 Ⅰ
Abstract Ⅱ
Acknowledgement Ⅲ
Contents Ⅳ
List of Figures Ⅶ
List of Tables ⅩⅠ

Chapter 1 Liquid Crystal 1
1.1 What are Liquid Crystals? 1
1.2 Categories of Liquid Crystals 3
1.3 Liquid Crystal Phases 4
1.3.1 Nematic Phase (N) 4
1.3.2 Cholesteric Phase (N*) 5
1.3.3 Smectic Phase (Sm) 6
1.4 Physics of Liquid Crystal 7
1.4.1 Birefringence 7
1.4.2 Temperature Effect on Refractive Indeces 9
1.4.3 Elastic Continuum Theory 10
1.4.4 Electric Field Effect 11

Chapter 2 Theory 13
2.1 Photoalignment 13
Photo-isomerization 13
2.2 Holography 14
2.2.1 Recording Process 15
2.2.2 Reconstruction 16
2.3 Laser-induced Holographic Gratings 18
2.4 Numerical Integration 22
2.5 Fourier Theorem 22
2.5.1 Fourier Transform 23
2.5.2 Discrete Fourier Transform 24

Chapter 3 Experiment 26
3.1 Materials Used 26
3.2 Cell Preparation 28
3.3 Polarization Grating’s (PG) Fabricating Process 29
3.4 Cell Observation 30
3.4.1 Correction 31
3.4.2 Discussion of the Imperfect Structure 32
3.5 Measurements of Diffractive Polarizations and Efficiencies 33

Chapter 4 Simulation Methods 35
4.1 Introduction 35
4.2 Jones Matrix Method 35
4.2.1 Jones Matrix Manipulation 37
4.2.2 Formulation of One Dimensional (1D) LC Cell 38
4.2.3 Formulation of Two Dimensional (2D) LC Cell and the Diffraction Simulation 39
4.3 Finite-Difference Time-Domain (FDTD) Method 40
4.3.1 Fundamental Concepts 40
4.3.2 One Dimensional (1D) Formulation 41
Courant Number 42
4.3.3 Three Dimensional (3D) Formulation 44
4.3.4 Choice of Physical and Simulation Parameters 48
4.3.5 Dielectric Tensor of LC and Rotation Matrix 49
An Alternative Method 51
4.3.6 Absorbing Boundary Conditions for FDTD Method 52
4.3.7 Periodic Structure and Periodic Boundary Conditions 53
Test of the Periodic Boundary Conditions 53
4.3.8 Near-to-Far-Field Transformation 54
Simulation of Diffraction Efficiencies of a Grating 55
4.3.9 Simulation of the Wave Propagation in the 90° Twist Nematic (TN) LC Cell 56
4.4 Choice of Optical Simulation Methods 58

Chapter 5 Simulations 59
5.1 Simulation of the Twist Nematic (TN) Grating 59
5.2 Simulation of the Polarization Grating (PG) 60
5.3 Simulation of the Polarization Grating (PG) Having One Unidirectional Aligning Surface 68
5.3.1 Perfect Structure 68
5.3.2 Imperfect Structure 69
5.3.3 Comparisons and Discussions 71

Chapter 6 Conclusions and Prospections 73
6.1 Conclusions 73
6.2 Prospections 73

Reference 75

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