光子晶體結構是種由材料折射率或介電常數以週期性排列而組成的結構，此種結構會產生光子能帶，能完全的阻擋光波通過進而控制光波的傳播，因此可以利用此光子晶體結構來設計各種低損失的光波導與光學元件。本文主要以平面波展開法、時域有限差分法和廣義瓊斯矩陣法作為分析的工具，詳細計算所設計的光子晶體光波導與內含液晶材料的光子晶體光波導之各種特性。本文將液晶材料與光子晶體光波導結構互相搭配結合，應用液晶的可調變光電特性與光子晶體結構優良的光波導特性，設計出各種可調式光電元件，包括可調式光子能帶、可調式光子晶體偏振選擇器、可調式光子晶體干涉器、可調式光子晶體耦合器、可調式光子晶體共振器及可調式光子晶體波長分波多工器等，並使用數值模擬的計算來證明各元件的特性與可行性。這些可調式光子晶體光電元件可以應用在未來的積體光學光迴路和光通訊系統中。

　Photonic crystals are artificial dielectric or metallic structures in which the refractive index modulation gives rise to stop bands for optical waves within a certain frequency. The waveguide creates a band of conduction inside the bandgaps. These crystals have many potential applications because of their ability to control lightwave propagation. Such structures can be use to design highly efficient new optical devices. We investigated the properties of the photonic crystal waveguides and the tunable photonic crystal devices with liquid crystals numerically by using the plane wave expansion method, the finite-difference time-domain method, and the extended Jones matrix method. The design and analysis of tunable photonic crystal devices, such as tunable photonic bandgap, tunable photonic crystal field-sensitive polarizer, tunable photonic crystal waveguide Mach-Zehnder interferometer, tunable photonic crystal waveguide coupler, tunable photonic crystal channel drop filter, and tunable wavelength division multiplexing are discussed. The novel tunable components may provide novel application in the photonic integrated circuits and optical communication systems.

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