Modified Finite-Difference Frequency-Domain Method and Its Applications

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.第一章 簡介…………………………………………………………..…1 第二章 數值方法……………………………………………………….3 2.1 時域有限差分法(FDTD)……………………………...………3 2.2 頻域有限差分法(FDFD)…………………………………...…8 2.3 電通密度( )與電場強度( )的關係與處理……….…...…11 2.4網格截斷方法(Mesh Truncation)……………………………..14 2.4.1週期性結構…………………………………………...14 2.4.2 完美匹配層(Perfectly Matched Layer (PML))………15 2.5不同材質交界面(interface)的處理……………………………20 2.5.1平均折射率……………………………………………21 2.5.2 介面算子(interface operator)邊界修正……………...22 2.5.3 滿足邊界條件下FDFD修正式……………………..29 第三章 數值方法驗證比較與結果………………………….36 3.1 數值驗證與比較……………………………………………...36 3.2 十字型結構…………………………………………………...37 3.3 溝槽式反射結構與穿透結構………………………………...41 3.4 金屬光子晶體………………………………………………..49 3.5 光開關設計…………………………………………………..51 第四章 結論………………………………………………………..….91 附錄……………………………………………………………………92 參考文獻………………………………………………………………9