平面波輔助邊界積分方程法應用於週期性金屬/介質結構之數值模擬

本論文針對具一維週期之二維電磁繞射問題提出一新穎的數值方法：平面波輔助邊界積分方程法。本方法乃基於傳統邊界積分方程法之架構，並結合平面波展開的概念，充分利用兩種數值技巧的優點。吾人藉積分方程以規範週期性結構中具複雜幾何的區域之電磁場，並以平面波的線性組合描述垂直於週期方向之延伸背景中的波動行為。由於以自由空間格林函數及週期性邊界條件取代一般常用的週期性格林函數，本法可免於週期性格林函數級數展開之收斂困難。此外，基於局域線性基底展開之離散技巧，本方法之準確性與收斂性在不等分割之應用上亦得到驗證。此不等分割之應用使本法適於模擬具細微結構的電磁問題。針對表面電漿波異常穿透之相關議題，吾人藉數值模擬探討兩類含金屬材質之光柵的繞射問題。在第一類光柵（波浪狀多層結構）問題中，吾人探討了由耦合表面電漿波引起的光穿透增強效應，並將其與第二類光柵（具狹縫之金屬薄層）問題中主導增強穿透的狹縫共振效應作比較。在第二類光柵問題中，吾人解釋了由狹縫共振效應引發的增強性穿透之發生頻率與光柵結構參數間的關係，並以此光柵之其他變形的模擬結果進一步加強吾人的解釋。

關鍵字

平面波展開；積分方程法；表面電漿子

並列摘要

A novel hybrid numerical technique is proposed for analyzing general 2D electromagnetic problems with 1D gratings. The proposed method combines the conventional boundary integral-equation method (BIEM) with the plane-wave-expansion technique, taking the benefit from either method. In the framework of the proposed method, the BIEM is in charge of formulating the major part of the problem containing the grating structure, while the plane-wave expansion is for describing the nature of the outgoing wave and truncating the computation domain in the direction perpendicular to the grating extension. The free space Green’s function with the periodic boundary condition is used to replace the commonly used periodic Green’s function for dealing with the periodicity of the problem. This circumvents the convergence difficulty of the periodic Green’s function. The performance of the PW-BIEM with the non-uniform mesh is also verified, showing the capability of the PW-BIEM in modeling the grating structure with fine geometry. With the proposed method, the transmission behavior of the wavy layered structure with a substrate-metal-cover-air architecture is investigated. The enhanced transmission due to the mechanism of the coupled surface plasmon polariton (SPP) is discussed and compared with another enhancement mechanism, cavity resonance effect, of the slit grating. For slit gratings, in addition to that of the rectangular type, the modified slit gratings are also simulated. The transmission behavior is discussed and interpreted.

並列關鍵字

plane-wave expansion ； boundary integral-equation method ； surface plasmon polariton

參考文獻

[1] Baida, F. I., D. V. Labeke, and B. Guizal, “Enhanced confined light transmission by single subwavelength apertures in metallic films,” Appl. Opt., vol. 42, pp. 6811-6815, 2003.

[2] Balanis, C. A., Advanced Engineering Electromagnetics (John Wiley & Sons, New York, 1989).

[3] Bonnand, C., J. Bellessa, C. Symonds, and J. C. Plenet, “Polaritonic emission via surface plasmon cross coupling,” Appl. Phys. Lett., vol. 89, pp. 231119(1)-231119(3), 2006.

[4] Bonod, N., S. Enoch, L. Li, E. Popov, and M. Nevière, “Resonant optical transmission through thin metallic films with and without holes,” Opt. Express, vol. 11, pp. 482-490, 2003.

[5] Brolo, A. G., R. Gordon, B. Leathem, and K. L. Kavanagh, “Surface plasmon sensor based on the enhanced light transmission through arrays of nanoholes in gold films,” Langmuir, vol. 20, pp. 4813-4815, 2004.

國際替代計量

平面波輔助邊界積分方程法應用於週期性金屬/介質結構之數值模擬

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