各向異性光波導之有限差分頻域特徵模態分析

Abstract

本論文首先使用有限差分頻域法分析各向同性光波導，包括平板波導、埋入式方形波導、脊形波導和光纖，並引入完美匹配吸收層作為計算區域外圍的吸收邊界。此外，提出以全向量有限差分頻域法推得標準特徵方程式，以之分析各向異性平板型的光波導，並引入適用各向異性材料的完美匹配吸收層，因此得以分析洩漏式的波導。本研究分析各向異性抗共振反射光波導和各向異性平板光波導，並且準確地計算出該波導模態的有效折射係數和場形分布。為了了解這些波導的傳播特性，本研究提出在不同光軸指向下的數值結果。 最後，以全向量有限差分頻域法推得分析三維各向異性光波導的標準特徵方程式。以纖芯充填液晶的光纖為例，計算在不同的光軸指向下，基模態的有效折射係數和對應的色散係數曲線，並討論模態傳播特性。

In this thesis, the finite-difference frequency-domain (FDFD) method is first utilized to analyze isotropic optical waveguides, such as slab waveguides, channel aveguides, rib waveguides, and optical fibers. The perfectly matched layer (PML) is employed as the absorbing boundary of the computing window in the FDFD solver. Then, a full-vectorial FDFD method based standard eigenvalue algorithm is developed for the analysis of anisotropic planar optical waveguides. The PML for anisotropic media is incorporated into the formulation as the absorbing boundary condition so that leaky waveguides can be treated. Adopting this method, anisotropic planar waveguides including anisotropic antiresonant reflecting optical waveguides (ARROWs) and anisotropic slab waveguides are investigated. The effective indices and the field distributions of allowed guided modes on such waveguides can be accurately calculated. Propagation characteristics of these waveguides are studied and numerical results are shown for different optic-axis orientations. Finally, a full-vectorial FDFD method based standard eigenvalue algorithm for the analysis of three-dimensional anisotropic optical waveguides is derived. Using the full-vectorial mode solver, the effective indices and the corresponding chromatic dispersion coeffcient curves for di®erent optic-axis orientations of fundamental guided modes on a hollow core fiber filled with liquid crystal (LC) are calculated. Also, the propagation behavior of the modes on the LC-core fiber is discussed.