脊狀波導模態色散特性及不連續色散特性的研究

Abstract

在本論文中,首先介紹時域有限差分方法,當時域有限差分應用在求得波導 特徵值時,在延著傳播方向我們應用已知的相位移特性使得一個三維的時 域有限差分網格減化成二維的網格.應用此簡易的二維時域有限差分方法 和相關的頻譜分析技巧,我們可以求取矩形波導和脊狀波導的模態色散特 性,如此一來,不但可以減少記憶體空間和中央處理單元時間,同時還可以 將時域有限差分應用到選擇性頻譜分析方面.最後我們在脊狀波導中間部 份加上鐵佛龍介質,探討此種結構對脊狀波導的頻寬有何影響.接下來,我 們將應用時域有有限差分和適當的吸收邊界條件求解脊狀波導內有不連續 散射體的問題,在本論文中,由薄介質問題所獲得的結將用來證實時域有限 差分是可以有效地應用在解決上述的問題. In this thesis, we calculate the modal dispersion characteristics of ridged waveguide with and without inhomogeneous dielectric-slab by employing a two-dimensional finite-difference time-domain method in conjuction with discrete Fourier transform technique.By introducing a plane shift along the propagation direction, a three-dimensional Yee' s mesh can be reduced to two-dimensional mesh. Now it is possible to calculate the propagation constant of hybrid modes by using only a two-dimensional FDTD mesh.This step not only allows the frequency selective application of the finite- difference time-domain method woth suitable absorbing boundary conditions to solve the electromagnetic field scattering problem in a ridged waveguide with discontiuity. Results obtained for the problem of a thin dielectric slab is used to verify the validity of the FDTD.