Transmission of an inhomogeneous plane wave through an electrically small aperture in a perfectly conducting plane screen.

Most solutions for electromagnetic diffraction by a circular aperture in a perfectly conducting plane screen are for an incident homogeneous (propagating) plane wave. When the aperture is electrically small (dimensions small compared to the wavelength), the well-known transmission coefficient behaves as the fourth power of the diameter/wavelength. We consider the case in which the incident field is an inhomogeneous (evanescent) plane wave. Numerical calculations for the electrically small circular aperture show that the transmission coefficient for an inhomogeneous plane wave can be substantially greater than for a homogeneous plane wave at the same frequency. This observation may be helpful in explaining the increased transmission recently reported for electrically small apertures in plane screens with modifications. The numerical calculations for the electrically small aperture are in agreement with results from approximate analytical expressions that are based on the equivalent electric and magnetic dipole moments for the electrically small complementary disk.

Role of evanescent waves in power calculations for counterpropagating beams.

A general expression is obtained for the time-average power passing through a plane transverse to the direction of propagation for two counterpropagating electromagnetic beams. Each beam is represented by its plane-wave spectrum, which contains both propagating and evanescent plane waves. The expression clearly shows that, under certain conditions, the evanescent plane waves contribute to the time-average power passing through the plane. This is in contrast to the case of a single electromagnetic beam, in which only the propagating plane waves contribute to the time-average power passing through the plane. The utility of the expression is demonstrated with a practical example: a line current placed over a dielectric slab. Here the counterpropagating beams are the incident and reflected fields in the region between the current and the slab. The expression is applied to a plane in this region, and it is used to determine the time-average power associated with the evanescent waves passing through this plane. This power is then shown to be equal to the time-average power carried by the guided modes of the slab.