Electromagnetic transmission resonances for a single annular aperture in a metal plate

We present a theory for the reflection phase and amplitude of the lowest-order TEM mode in an annular aperture at the end of a metal plate. This reflection coefficient determines the frequency and peak width of the Fabry-Perot transmission resonances. The theory assumes that the width of the aperture is subwavelength; however, the annular radius can be quite large, and we show that the theory reproduces the reflection of a linear slit in the limit of infinite radius. Finite-difference time-domain calculations agree well with the theory, in terms of both the transmission resonance frequency values and the extracted reflectivity. The theory presented shows that both the phase and amplitude of reflection can vary substantially with changes in geometry and frequency, and that both are modulated by transverse resonances. This work has implications for filters, near-field aperture probes, sensors, and metamaterials.