以全向量虛軸有限元素波束傳遞法研究五角形銀奈米柱波導及其耦合結構

Studies of Pentagonal Silver Nanowires and Their Coupling Structures Using a Full-Vectorial Imaginary-Distance Finite-Element Beam Propagation Method

劉弘煒(Hung-Wei Liu)

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(2018年)

https://doi.org/10.6342/NTU201801892

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五角形銀奈米柱波導。當操作波長500到2000奈米的範圍內，我們分析等效折射率、傳播長度和模態場型。一開始我們研究小半徑五角形與圓形銀奈米柱波導之差異。與圓形結構相比，五角形結構的操作波長較長，特定的模態適合應用於訊號傳導。接著我們研究在不同幾何形狀下銀奈米柱波導的光集中強度。最後，在奈米柱半徑增大的情形下，當放在SiO2 基板上時，同時擁有傳播模態和洩漏模態性質的混合洩漏模態會產生。鑲嵌在SiO2 介質裡面時，多個複雜的偶合模態與不同的奈米柱間距衍生出命名的模糊與統一等問題，藉由研究圓形銀奈米柱波導耦合原理，我們探討出具有物理意義和統一性的命名規則並能將此規則應用於五角形銀奈米柱波導。

關鍵字

有限元素虛軸波束傳遞法 ； 表面電漿 ； 五角形銀奈米柱 ； 圓形銀奈米柱 ； 傳播模態 ； 洩漏模態 ； 混合洩漏模態 ； 模態命名 ； 耦合原理

並列摘要

In this research, we adopt the full-vectorial finite-element imaginary-distance beam propagation method (FE-ID-BPM) based on the hybrid edge/nodal elements and incorporate perfectly matched layers (PMLs) to analyze pentagonal silver nanowire plasmonic waveguides including that immersed in SiO2 and that supported by SiO2 substrate. With the operating wavelengths ranging from 500 nm to 2000 nm, the effective refractive indices, propagation lengths, and mode- field profi les are investigated for different radii and gap widths in this research. The difference between small-radius pentagonal and circular silver nanowire waveguides are first investigated. Compare to circular structures, pentagonal structures possess wider operating
wavelength range and are suitable for signal transmitter devices for certain modes. Next, optical energy concentration due to different geometrical structures of silver nanowires is discussed. Finally, large-radius silver nanowire systems are studied. When supported by a SiO2 substrate, a hybrid leaky mode is observed and certain unique optical properties are calculated. When immersed in SiO2 matrix, the uncertainty of naming the coupled modes occurs. By analyzing the coupling origins, systematical coupled mode naming rules are proposed.

並列關鍵字

Finite-element imaginary-distance beam propagation method (FE-IDBPM) ； Surface plasmon polaritons (SPPs) ； Pentagonal silver nanowires ； Circular silver nanowires ； Guiding modes ； Leaky modes ； Hybrid leaky mode ； Mode naming rules ； Mode assembling theory

參考文獻

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