以全向量虛軸有限元素波束傳遞法分析五角形和正方形銀奈米波導之模態特性

Modal Analysis of Pentagonal and Square Silver Nanowires Using a Full-Vectorial Imaginary-Distance Finite-Element Beam Propagation Method

許新茂(Hsin-Mao Hsu)

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(2017年)

https://doi.org/10.6342/NTU201702863

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兩種不同表面電漿波導上的模態特性，此兩種分別為正方形銀奈米柱波導和五角形銀奈米柱波導，並各自鑲嵌在SiO2介質裡面以及放在SiO2介質上面。在操作波長500到2000奈米的範圍下，我們計算了等效折射率、傳播長度和模態場型。一開始我們先探討五角形銀奈米柱波導的特性，當鑲嵌在SiO2介質裡面時，主要場型會集中在尖角處；而放在SiO2基板上則會發現傳播模態和洩漏模態的主要場型會各自集中在不同的介面。最後我們利用正方形銀奈米柱來研究耦合現象，假如在單軸正方形銀奈米柱上發現一個模態，那麼在雙軸正方形銀奈米柱上就會發現因為耦合效應而產生的不同兩個模態。

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 ； 正方形銀奈米柱 ； 傳播模態 ； 洩漏模態

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 the incorporated perfectly matched layers (PMLs) to analyze two different plasmonic waveguides, which are pentagonal silver nanowire waveguides and square silver nanowire waveguides including that immersed in SiO2 and that supported by SiO2 substrate. With the operating wavelength range from 500 nm to 2000 nm, the effective refractive indices, propagation lengths, and mode-field profiles are calculated for different parameters and structures in this research. The pentagonal silver nanowire waveguides are first investigated. When immersed in SiO2, the major fields are concentrated near the corners. But when supported on a SiO2 substrate, the major fields of guiding modes and leaky modes are confined near different interfaces, respectively. Finally, the coupling effect in square silver nanowire waveguides is studied. If one mode is found in a single square silver nanowire, two individual modes will be found in the double square silver nanowire due to the coupling effect.

並列關鍵字

Finite-element imaginary-distance beam propagation method (FE-IDBPM) ； Surface plasmon polaritons (SPPs) ； Pentagonal silver nanowires ； Square silver nanowires ； Guiding modes ； Leaky modes

參考文獻

Barnes, W. L., A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature., vol. 424, pp. 824--830, 2003.

Berenger, J. P., "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys., vol. 114, pp. 185--200, 1994.

Bierwirth, K., N. Schulz, and F. Arndt, "Finite-difference analysis of rectangular dielectric waveguide structures," IEEE. Trans. Microwave Theory Tech., vol. 34, pp. 1104--1113, 1986.

Boltasseva, A., Valentyn S. Volkov, Rasmus B. Nielsen, Esteban Moreno, Sergio G. Rodrigo, and Sergey I. Bozhevolnyi, "Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths," Opt. Express, vol. 16, pp. 5252--5260, 2008.

Cavendish, J. C., D. A. Field, and W. H. Frey, "An approach to automatic three-dimensional finite element mesh generation," Int. J. Number. Meth. Eng., vol. 21, pp. 329--347, 1985.