光子晶體結構是由材料折射率或介電常數以週期性排列而組成的結構，這樣的結構會產生光子晶體能隙，能完全阻擋光波的通過。本文利用平面波展開法作為分析光子晶體能隙的工具，並利用時域有限差分法來分析光子晶體共振腔與分波器。
將原本完美的週期性光子晶體結構置入缺陷，由於局域化的現象產生共振腔，本文先針對點缺陷的共振腔做分析，將此共振腔加上波導設計成濾波器， 液晶置入此濾波器的缺陷中，應用液晶的可調變光電特性，設計出可調變的光子晶體分波器，並分析各種形狀缺陷下的品質因子與可調變的波長，來找出品質較佳分波器，以設計出更多通道的分波器。

Two dimensional photonic crystal slabs have formed photonic band gap that forbids wave propagation. With the defects in photonic crystals, the defect modes will be found at a resonance frequency within the photonic band gap. Photonic crystal waveguides and cavities are the two fundamental devices used to spatially localize the light in a planar photonic crystal. We design a channel filter of a two dimensional photonic crystal with triangular lattices.

We present a method for tuning a photonic crystal microcavity by rotating electromagnetically the director axis of the liquid crystal surrounding the microcavity. The index of the refraction can be actively modulated after infiltrating anisotropic liquid crystals into a two dimensional photonic crystal lattice of air cylinders in silicon.

By implementing the two dimensional finite difference time domain method, we demonstrate the ability to tune wavelengths of a photonic crystal filter by modulating the director axis of the liquid crystal. Multiple wavelengths can be selected. We analyze the quality factor and the resonance wavelength of a tunable channel filter to enhance the performance of the photonic crystal wavelength division multiplexer applications. The tunable cavities allow the wavelength division multiplexer to actively select many wavelengths from the waveguides.

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