次波長金屬孔洞之電磁波散射

Electromagnetic Scattering of a Subwavelength Hole in a Perfect Metal Plate

陳宏文 ； 陳瑞琳 ； 郭志禹

《光學工程》 106期 (2009/06) Pp. 10-19

https://doi.org/10.30011/OE.200906.0002

摘要

本文章研究當電磁波斜向入射至有限厚度，無限延伸完美導體平板上的次波長圓形穿孔時，所形成的散射場解析解。本研究理論基礎建構在沒有外加電荷與電流下的馬克士威方程式，藉由其所具有的電磁場雙重性，將電磁場以向量與純量位勢能函數表示後求解。問題空間區分爲考慮近場表現的內部區域與探討遠域輻射的外部區域，在長波極限假設下，入射場波數與孔洞半徑乘積是一微小參數，我們利用擬合展開法，配合Fabrikant所提出之混合邊界值理論，分別求解當TM極化入射與TE極化入射時孔洞所引發之散射場多極結構，並分析多極結構強度與孔洞深度以及入射角度之間的關係。孔洞所造成的遠域散射場主次項，相當於垂直導體面之電偶極與平行導體面之磁偶極所產生之輻射電磁場。當導體板厚度無限薄時，本研究能與Bethe[1]之結果吻合。

關鍵字

擬合展開法 ； 電磁多極展開 ； 電磁散射 ； 次波長孔洞散射

並列摘要

The scattering of an oblique electromagnetic wave incident on a subwavelength circular aperture in an infinite perfect conductor plane with a finite thickness is investigated analytically. The theory is based on the duality property of source-free Maxwell equation and the resultant scattering fields are fully expressed in terms of the auxiliary scalar and vector potentials. Both of the TM and TE polarized incidence are considered. There are two regions defined by the analytical method: the near field inner region and the radiation outer region. We use the method by Fabrikant to solve the mixed boundary value problems. Because which is the product of the incident wave number and the pore radius is a small parameter, we could use the method of matched asymptotic expansion to find the multipole structure. The sophisticated three-dimensional interplay between the pore depth and the incident angle is also revealed.

並列關鍵字

Matched asymptotic expansion ； Electromagnetic multipole expansion ； Electromagnetic scattering ； Diffraction by subwavelength holes