圓柱體系統的多重散射分析

表面電漿共振是發生在介質和金屬交界面的能量異常增強現象，在二維的問題中，只發生在磁場極化方向和入射方向垂直的平面波。本論文主要使用多重散射法模擬二維金屬奈米圓柱的散射現象。多重散射法是一種用來分析圓柱結構的解析法，可以提供快速以及準確的計算。本研究探討在三百至八百奈米波長範圍內，具真實金屬材料奈米圓柱的散射現象。對單根銀圓柱，本研究探討圓柱半徑對散射場強度、散射截面積的值、以及散射截面積峰值所在的波長的影響。針對兩根銀圓柱，則研究入射光的方向、兩根圓柱的間距以及圓柱半徑對散射的影響。對於在一排多根圓柱且入射波為垂直方向入射波的情況，若圓柱間距足夠大，則散射會趨向收斂特性。對於一排圓柱而入射波為平行方向入射情況，本研究特別關注其導波特性。在多排圓柱的情況，本研究特別探討行距與列距對於散射截面積的影響。本研究亦探討了二維光子晶體的特性。首先使用平面波展開法求得三角晶格及四方晶格的能帶圖，接著使用了多重散射法加以計算有限大小光子晶體的光波穿透特性，並與能帶圖做比較，相關的光子晶體共振腔和直線型缺陷波導也加以討論。

關鍵字

表面電漿共振；多重散射法；散射截面積；圓柱；二維光子晶體

並列摘要

Surface plasmon resonance is an extraordinary energy enhancement phenomenon which occurs on the interface between dielectric and metal. In the two-dimensional (2-D) case, such resonance is only excited by the transverse-magnetic (TM) polarized wave with which the magnetic field is perpendicular to the 2-D plane. This research mainly concerns the scattering phenomena of 2-D metallic nanocylinders simulated using the multiple scattering method. The multiple scattering method is an analytical solution method for analyzing scattering by cylinder structures, which can provide fast calculations and accurate results. We investigate scattering by nano-cylinders with real metallic material in the wavelength regime of 300 nm-800 nm. For a single silver cylinder, the dependence on the cylinder radius of the intensity of the scattered field, the value of the scattering cross section (SCS), and the wavelength at which the maximum field value occurs is studied. For two silver cylinders, the scattering is seen to be affected by the direction of incident wave, the distance between the two cylinders, and the radius of cylinders. By increasing the number of cylinders in a single row at normal incidence, the scattering approaches a convergent behavior if the distance between adjacent cylinders is large enough. For waves incident parallelly onto a row of cylinders, the waveguiding behavior is particularly paid attention to. For multi-row structure, the effect on the SCS of the distance between cylinder rows and the gap size between columns is investigated in detail. We also investigated characteristics of 2-D photonic crystals (PCs) composed of circular cylinders. The plane-wave expansion (PWE) method is employed to obtain the photonic bandgaps (PBGs) for triangular lattice and square lattice. Then the multiple scattering method is used to obtain transmittance spectra for finite PCs for comparison with the PWE method calculated PBGs. Examples of PC cavity and line defect are also discussed.

並列關鍵字

Surface plasmon resonance ； Multiple scattering method ； Scattering cross section ； Cylinder ； 2-D photonic crystal

參考文獻

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國際替代計量

圓柱體系統的多重散射分析

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