由於技術不斷的創新，特殊的液晶結構不斷的演進，因此光波傳播演算法需求必須更為精密。液晶結構內之光波傳播模擬在1941年已由瓊斯矩陣法(Jones matrix method)根據精密電磁波理論來演算，其液晶結構的光波場計算，一般是基於層與層介質間的近似計算來達成。但是當液晶分子指向矢(director)配列富有明顯變化時，則分析結果將會失真，因此廣角光束傳播法被發展出來克服一些液晶分子指向矢形變如彎曲/展曲(bend/splay) 的液晶結構光波場模擬限制。此方法為廣角結構，且軸近似區域不會受限制，可用於加電壓後液晶分子指向矢傾斜的液晶結構。
本論文藉由應用EMMANOUIL E. KRIEZIS 與STEVE J. ELSTON所提出的廣角光束傳播法[1]，適合用來分析光在異向性液晶介質的光傳播特性。並且討論一些特殊的液晶分子結構，如均質結構(Homogenous cell)、畫素邊緣(Pixel edge cell)、雙區域結構(Two-domain structures)與共平面切換(In-Plane switching)。尤其討論共平面切換(In-Plane switching)，可提供工程上的應用參考。

Special liquid crystal structures are found and used in today’s fast growing technology. The optical wave propagation simulation within liquid crystal structure was discussed by using the electromagnetic wave theory from Jones matrix method in 1941.Generally, the optical wave propagation method is driven by the fact the currently used methods applied to liquid crystal devices rely on the stratified medium approximation. As a consequence, when the liquid crystal molecules devices show large variations of the director orientation, the method fails to accurately predict the optical field. An appropriate Wide Angle Beam Propagation Method is developed to circumvent these limitations in the case of liquid crystal devices exhibiting the bend/splay deformation. The method is a wide-angle scheme ,and is therefore not restricted to the paraxial appropriations region. The method is tested on tilted liquid crystal structures in this study.
This thesis adopted the method proposed by EMMANOUIL E. KRIEZIS and STEVE J. ELSTON [1]. They proposed a Wide Angle Beam Propagation Method suitable for analyzing the optical propagation in anisotropic involving liquid crystal. We extend the method to analyze some different liquid crystal structures. which are Homogenous cell、 Pixel edge cell、 Two-domain structures and In-Plane switching . A special attention is focused on In-Plane switching. This work can help design in liquid crystal displays.

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