以全向量虛軸有限元素波束傳播法分析三角形與銀奈米圓柱波導的模態特性

Modal Analysis of Triangle-Shaped and Silver-Nanowire Waveguides Using a Full-Vectorial Imaginary-Distance Finite-Element Beam Propagation Method

陳翔鵬(Hsiang-Peng Chen)

指導教授 ： 張宏鈞

國立臺灣大學/電機資訊學院/光電工程學研究所/碩士(2015年)

https://doi.org/10.6342/NTU.2015.00985

摘要

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結構的模態特性。我們主要分析了三角形狀以及銀奈米圓柱結構的模態特性。針對不同的參數和結構，我們計算了等效折射率、傳播距離以及分析了模態場型。關於三角形波導，我們分析了Λ型以及V型兩種不同的結構，並且致力於探討三角形狀結構在小角度時的模態現象。我們對於結構在擁有不同的小角度(25⁰、20⁰以及15⁰)的情況下，計算了等效折射率以及傳播距離，並且分析了模態場型的侷限性和損耗之間的關係。至於銀奈米圓柱結構，我們討論了有基座和沒有基座的兩種結構。對於在不同的操作波長，以及不同半徑的銀奈米圓柱結構的情形下，我們分析了傳播模態的特性以及詳細計算了等效折射率以及傳播距離。另外，我們發現銀奈米圓柱在有基座的結構下，除了傳播模態，也會有洩漏模態的存在。

關鍵字

有限元素虛軸波束傳遞法 ； 表面電漿 ； 三角形波導 ； 銀奈米圓柱 ； 洩漏模態

並列摘要

Modal analysis of surface plasmon polariton (SPP) waveguides using an in-house developed finite-element imaginary-distance beam propagation method (FE-ID-BPM) is discussed in this thesis. We mainly analyze the modal characteristics of triangle-shaped and silver nanowire waveguides. The effective refractive indices, propagation lengths, and mode-field profiles are calculated for different parameters and structures. For the triangle-shaped waveguides, we discuss the propagation characteristics of the two different Λ-type and V-type structures, aiming at the investigation of structures with smaller corner angles relative to those reported in the literature. We show the effective index and propagation length versus the operating wavelength for corner angles of 25⁰, 20⁰, and 15⁰, and compare the degrees of confinement and losses for different wavelengths and corner angles. For the silver nanowires, we discuss a nanowire immersed in a medium matrix and that with a supported substrate. For different operating wavelengths and radii of the nanowires, we discuss the propagation characteristics of the guiding modes. The real part of the effective index and the propagation length are discussed in detail. Besides the guiding modes, we find there exists a leaky mode in the substrate-supported nanowire.

並列關鍵字

finite-element imaginary-distance beam propagation method (FE-IDBPM) ； surface plasmon polariton (SPP) ； triangle-shaped waveguides ； silver nanowires ； leaky modes

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