具次波長孔隙之金屬波導管中之異常穿透現象：數學分析

Abstract

全透射現象能夠發生在具有次波長孔隙之矩形波導管中且遠低於小孔隙的截止頻率，最近此一發現被刊載在期刊中[1]，為了了解波傳遞過程中的物理意義，我們利用嚴謹的模態匹配法來分析在具次波長孔隙之金屬矩形波導管中的模態散射特性，在此，我們將次波長孔隙看成一個有限厚度的波導管，因此這整個結構可以被視為三個波導管的串接，而此三個波導管分別為輸入和輸出的矩形波導管及一個次波長的波導管。而在波導管不連續面的輸入和輸出的關係能夠藉由電磁場的邊界問題被嚴謹的演繹出來。而穿透波和反射波的散射特性可以經由傳輸線網路分析的理論解析出來，根據散射分析的方法，此波導管結構的複數頻率亦可被用來解釋此一異常全穿透現象。

As was reported recently in the literature [1], the total transmission through a sub-wavelength hole in a rectangular waveguide can occur in the low frequency far away from the cutoff frequency of the hole. To understand the physical insight of wave propagation process, the rigorous mode-matching method was employed to analyze the scattering characteristics of waveguide modes in a rectangular waveguide inserted with a metal plate having a sub-wavelength hole. Here, the sub-wavelength hole is regarded as a waveguide with finite thickness, thus, the overall structure can be considered as a cascade of three waveguides, which are the input- and output- rectangular waveguide and the sub-wavelength waveguide, respectively. Moreover, the input-output relation at the waveguide discontinuity can be rigorously formulated by taking into account the electromagnetic boundary-value problem. The scattering characteristics including the transmittance and reflectance are determined using the method of transmission-line network analysis. In addition to the scattering analysis, the complex frequency of the wave structure is also considered to explain such an extraordinary total transmission phenomenon.