以全向量虛軸有限元素波束傳播法分析表面電漿子波導與微結構光波導

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各種波導。我們分析了在非對稱 環境的金屬條狀波導、長程介電加載的表面電漿子波導、六孔圓形空 氣孔洞光纖以及三孔環狀空氣孔洞光纖。針對不同的邊界設定，我們 計算波導之有效折射率、傳播長度以及模態場型。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和結構參數變化 對於洩漏模態計算結果的影響。對於長程介電加載的表面電漿子波導， 我們計算得知此結構在波長為1.55 μm時，傳播長度可超過6 mm，並 討論不同的金屬寬度，對於模場的侷限性及傳波長度的影響。最後， 藉由六孔圓形空氣孔洞光纖以及三孔環狀空氣孔洞光纖結構，此兩種 結構在損耗上差距，我們研究在不同的邊界設定下，對於計算結果收 斂的影響。

In this thesis, the full-vectorial fi nite-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 various waveguides. The asymmetric metal stripe waveguide, the long-range dielectric-loaded SPP waveguide, the six-circular-air-hole fi ber, and the three-annular-shaped-air-hole fi ber are investigated. The eff ective indices, propagation lengths, and modal fi eld pro files are calculated for various boundary settings. In the asymmetric metal stripe waveguide with a thin gold stripe layer on glass substrate surrounded by air, we analyze the leaky modes for which the calculations are refined by using different values of the PML reflection coeffi cient and structure parameters. The long-range dielectric-loaded surface plasmon polariton waveguide (LR-DLSPPW), in which a thin and narrow metal stripe is sandwitched between a square dielectric ridge and a dielectric fi lm supported by a low-index substrate, supports a fundamental long-range dielectricloaded surface plasmon polariton waveguide mode with a propagation length over 6 mm at the wavelength of 1.55 m. Various widths of the Au stripe are examined to understand different guided-mode characteristics. In the two microstructured air-hole fi bers, the convergence of the e ffective refractive indices under di fferent boundary settings is studied.