Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness

TL;DR

This paper investigates electromagnetic wave transmission through small holes in perfect conductors of finite thickness, revealing dependencies on wavelength and mode attenuation, and connecting modal and multipole expansion methods.

Contribution

It provides a detailed analysis of non-resonant transmission through small holes, including new expressions and a link between modal and multipole expansion approaches.

Findings

Transmission follows Rayleigh dependence in subwavelength regime

Fundamental waveguide mode attenuation suppresses transmission

Bethe's result is recovered for infinitesimally thin screens

Abstract

The non-resonant electromagnetic transmission of a normal-incident plane wave through a single hole in a perfect conductor metal slab of finite width is studied. The cases of rectangular and circular holes are treated in detail. For holes in the extreme subwavelength regime, in a film of finite thickness, the transmittance is shown to have the Rayleigh dependency upon the wavelength and, in addition, is mainly suppressed due to attenuation of the fundamental waveguide mode. In the limit of an infinitesimally thin screen Bethe's result is recovered for the circular hole. The numerical computations are fitted, providing expressions for the transmission in a wide region of parameters. We reformulate our results in terms of multipole expansion, interpreting the waveguide modes inside the hole as induced multipole moments. This result provides the link between the modal expansion method and the one based on a multipole expansion.