修正的頻域有限差分法及其應用

Abstract

本論文中我們提出一修正之頻域有限差分法, 將介質不連續情形作適當修正, 並推展到四種不同材質下的修正式, 解決有尖角存在時的數值困難。我們使用此方法作一些週期性金屬結構在長波長下異常穿透現象的模擬, 並從模擬結果中探討該現象與表面電漿子以及結構中其他模態之間的物理關聯。我們亦提出一個結合液晶特性與異常穿透現象所構成的光開關的概念, 或可用於顯示器上。最後, 我們利用數值方法計算週期性結構的波導問題, 以進一步了解週期性金屬結構之電磁特性。

In this thesis, we propose a modified finite-difference frequency-domain method, by taking account of the boundary condition at the interface of different media. We also extend further the formulas to overcome the numerical difficulty of a corner problem where different media are included around the corner. We use the method to simulate the extraordinary transmission phenomenon of periodic metallic structures at long wavelength and discuss its relation to surface plasmons, and other resonant modes of structure. We propose the concept of an optical switch by combining the properties of liquid crystal and the extraordinary transmission phenomenon, which may be useful for display applications. Finally, we also investigate the propagation characteristics of some waveguides formed by defects in metallic photonic crystals. The numerical simulation may help us understand the optical properties of periodic metallic structures.