摘要

　　本論文中，以有限元素法模擬一維光子晶體，討論其能隙和晶體結構之間的關係。如適當地破壞光子晶體之週期性，製造出缺陷，則能在光子晶體能隙之中開闢出缺陷模態( defect mode )，在光波無法穿透的波段之開出可通過的波長。利用缺陷模態的概念，我們可設計出可取出一個或多個所需波長之光子晶體濾波器。

　　利用三個缺陷之間微弱的耦合，使其缺陷模態重疊，製造出平坦可通過之波段( pass band )。如此，耦合缺陷模態外形更接近長方形，藉此優化濾波器。此外，亦設計含四個耦合缺陷來優化雙缺陷之光子晶體濾波器。

　　將向列型液晶( nematic liquid crystal )當成缺陷引入一維光子晶體結構，如此，可以外加電場改變其光學性質，使其缺陷模態發生變化。利用此可控制的缺陷模態，進一步設計出光開關。

Abstract
In this dissertation, we present the finite element method to simulate the optical response of a finite one-dimensional (1D) photonic crystal (PhC). We discussed the relation between the photonic bandgap and the parameters of the photonic crystal structure. We can find a defect mode that let the light wave with specific wavelength pass through the structure by introducing a defect into a periodic PhC. Utilizing the concept of defect mode, we can design a photonic crystal filter which can take out the light wave with one or more wavelength.

We can create a flat pass band by utilizing the three coupled defects to make their defect modes overlapping, therefore, the shape of the coupled defect mode can be much closer to a rectangle. In addition, we optimized the two-wavelength filter with four coupled defect modes.

A nematic liquid crystal defect layer is introduced into a 1D PhC and the refractive index of the liquid crystal can be controlled by an external electric field. Thus, the defect mode can be tuned. By making use of the tunable defect mode, we can design an optical switch further.

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