以全向量虛軸有限元素波束傳播法分析金屬光波導與金屬條狀表面電漿子波導

Abstract

本篇論文中，我們以曲線混合型元素為基底的全向量有限元素虛軸波束傳遞法以及完美匹配層來分析表面電漿波導。我們分析了金屬方形波導、圓形波導、金屬孔洞光纖以及在非對稱環境的金屬條狀波導。金屬方型與圓形波導在可見光波段的性質與其在微波波段時可被視為完美電導體的性質不同，我們研究了邊長以及半徑對於增加截止波長的影響。金屬孔洞光纖是一個類似光子晶體的結構，但在其最內圈灌入金屬，因此不僅存在光子晶體的模態，也會存在表面電漿模態。我們分析了以上結構的等效傳播常數。最後在非對稱環境的金屬條狀波導裡，我們分析了完美匹配層中的反射係數對於洩漏模態的影響。

In this thesis, the full-vectorial finite element imaginary-distance beam propagation method (FE-ID-BPM) based on the hybrid edge/nodal elements and the perfectly matched layers (PMLs) is used to analyze some surface plasmonic waveguides. The metallic rectangular waveguide, the metallic circular waveguide, the metallic holey fiber, and the asymmetric metal stripe waveguide are investigated. The rectangular and circular waveguides in nano-scale perform differently from the perfectly electric conductor (PEC) waveguides popularly used at microwave frequencies. The extended cutoff wavelengths of TE-like modes and TEM-like mode as well as the effects of the wall width, wall height, and wall radius are discussed. The metallic holey fiber is a photonic-crystal-fiber-like (PCF-like) structure with metal injected to a certain air ring, for which the complicated modes include the surface plasmon (SP) modes and the fundamental PCF mode. The effective refractive indices at optical wavelengths of these modes are analyzed. Finally the asymmetric metal stripe waveguide is studied, and especially the leaky modes for which the calculations are refined by using different values of the PML reflection coefficient.