以全向量虛軸有限元素波束傳播法分析雙軸銀奈米柱波導的模態特性

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來分析表面電漿波導上的波導傳播模態，分析的表面電漿結構分別有雙軸奈米柱鑲嵌在均勻介質的以及將雙軸奈米柱放在介質基板上兩種不同結構。在操作波長500到2000奈米波長的範圍下，我們計算了等效折射率、傳播距離、模態場型以及等效模態面積。首先，我們先探討雙軸奈米柱包含在均勻的二氧化矽以及空氣的情況，藉由比較其單軸構造的特性可以發現兩軸相鄰的奈米柱會發生耦合的現象，並且分裂出多個不同的模態。對於不同的奈米柱半徑在本文中也被調查。接著我們研究加上基座之後的影響，由事先研究的結果可以知道單軸奈米柱在基座上會有一個傳播模態以及一個洩漏模態，藉此我們發現因為耦合的效應，在雙軸在基座上的結構可以分別得到兩種傳播模態以及洩漏模態。最後，我們也調查不同半徑的影響。

In this research, we adopt the full-vectorial finite-element imaginary-distance beam propagation method (FV-FE-ID-BPM) based on the hybrid edge/nodal elements and incorporated with perfectly matched layers (PMLs) to analyze waveguide modes propagating on plasmonic waveguides composed of two parallel circular-cylinders named the double-nanowire, including that immersed in a uniform dielectric matrix and that supported by dielectric substrate. The effective refractive indices, propagation lengths, mode-field profiles, and effective mode areas are calculated for different parameters and structures over the wavelength range from 500 nm to 2000 nm. The double-nanowires immersed in uniform silica and in air are first investigated. The splitting into multiple modes due to the coupling between the two adjacent nanowires is examined by comparing with modal characteristics of the single nanowire. Different nanowire radii are also considered. The effect of including a supporting substrate is studied. Previous studies have given the fact that a single silver nanowire with a silica substrate possesses a silver/substrate guided mode and an air/silver leaky mode. The coupling phenomena of the double-nanowire case are demonstrated in this study, showing the resultant two silver/substrate guided modes and two air/silver leaky modes. Finally, the effect of using different substrate materials is discussed.