Transmission of an evanescent wave through a subwavelength aperture in a PEC screen

The diffraction of a wave by an aperture in a plane screen is an old and fundamental problem in optics and electromagnetic theory. In a typical theoretical formulation for the electromagnetics problem, a circular aperture is placed in a perfectly conducting (PEC) plane screen of infinitesimal thickness lying in the xy plane. The incident field is a time-harmonic plane wave propagating in a direction lying in the xz plane. This case is referred to as the transverse-electric (TE) case because the incident electric field is normal to the plane of incidence (the plane determined by the normal to the screen and the direction of propagation). For the transverse-magnetic case (TM), the incident magnetic field is normal to the plane of incidence. The objective of an analysis is often to determine the total time-average power transmitted through the aperture, and a convenient parameter for quantifying it is the transmission coefficient. We consider two fundamental questions: what is the transmission coefficient for an evanescent plane wave through an electrically small aperture? can the transmission coefficient for an evanescent plane wave be significantly greater than that for a propagating plane wave? The paper aims to answer both of these questions.