雙奈米狹縫金屬光柵光反射與穿透之模型化與分析

Modeling and Analysis of Optical Reflection and Transmission of Double Nano-slit Metallic Gratings

林孫戎(Sun-Jung Lin)

指導教授 ： 黃鼎偉

國立臺灣大學/電機資訊學院/光電工程學研究所/碩士(2011年)

https://doi.org/10.6342/NTU.2011.00461

摘要

雙奈米狹縫金屬光柵為每個週期存在兩個奈米狹縫的金屬一維週期性結構。光波入射雙奈米狹縫金屬光柵反射和穿透的特性會隨著兩個狹縫的參數和兩個狹縫模態的能量耦合程度變化。本篇論文推導出來解析模型分析光波入射雙奈米狹縫金屬光柵反射和穿透的特性。雙奈米狹縫金屬光柵的金屬狹縫區域類似金屬和介電物質交錯排列五層平板波導，因為金屬和介電物質交錯排列五層平板波導存在兩種表面電漿子模態，所以光波入射雙奈米狹縫金屬光柵可能會在金屬狹縫區域激發兩種表面電漿子模態。本篇論文推導出來金屬和介電物質交錯排列五層平板波導的模態特性方程式，求解模態特性方程式可以得到兩種表面電漿子模態的等效折射率。金屬狹縫區域類似Fabry-Pérot共振腔，兩種表面電漿子模態在金屬狹縫區域各自獨立來回反射，發生干涉現象。如果滿足共振條件，反射率譜和穿透率譜就會出現尖峰。利用兩種表面電漿子模態互相為正交的關係可以展開邊界條件關係式，推導出來光波入射雙奈米狹縫金屬光柵反射和穿透的解析模型。我們使用解析模型計算的結果和電磁模擬軟體使用嚴格耦合波分析(RCWA)數值模擬的結果相當吻合。雖然只有考慮Fabry-Pérot共振模態影響的解析模型不會完全精確，但是可以幫助我們具備對於雙奈米狹縫金屬光柵在近紅外光波長區段光反射與穿透現象的物理直覺，並且大幅減少計算時間，快速得到計算結果。

關鍵字

奈米狹縫 ； 金屬光柵 ； 表面電漿子 ； Fabry-Perot共振腔 ； 反射 ； 穿透

並列摘要

Double nano-slit metallic gratings are one-dimensional periodic structures which have two nano-slits within each grating period. The characteristics of optical transmission and reflection as the light is incident onto the double nano-slit metallic gratings will be dominated by the properties of each nano-slit and the optical coupling between of the nano-slits. In this thesis, an analytical model of the optical transmission and reflection properties for the light incidence onto nano-slit metallic gratings was derived. The metal nano-slit region of double nano-slit metallic gratings are similar to the five-layer planar waveguides of staggered metal and dielectric materials, which has two surface plasmon modes. Thus, when the light is incident onto the double nano-slit metallic gratings, two surface plasmon modes may be excited in the metal nano-slit region. The modal characteristic equation of the metal-dielectric staggered five-layer planar waveguides was also derived and the solution to the modal characteristic equation yields the effective refractive indices of the two surface plasmon modes which can be used to describe the propagation characteristics of these two surface plasmon modes in the metal slit region. The Fabry-Pérot interference may occur as the two surface plasmon modes bounces back and forth independently along the metal nano-slits due to the abrupt reflective index change at the top and bottom interfaces. In case of resonance, dips in the reflectivity spectrum and peaks in the transmittance spectrum will appear. The orthogonality of the two surface plasmon modes as well as the boundary condition were then used to derived the analytical model of the optical transmission and reflection of the double nano-slit metallic gratings. The results obtained by using the analytical model are in good agreement with those by using rigorous coupled wave analysis (RCWA). Although the analytical model is not completely accurate, it allows us to obtain new physical insight into the behavior of the surface plasmon modes in the double nano-slit metallic gratings and to calculate the numerical solutions with a considerably reduced computation time.

並列關鍵字

Nano-slits ； Metallic gratings ； Surface plasmons ； Fabry-Perot resonators ； Reflection ； Transmission

參考文獻

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