Penetration Through Slots in Overmoded Cavities

A resonant cavity undergoes three distinct behaviors with increasing frequency: 1) fundamental modes, localized in frequency with well defined modal distribution; 2) undermoded region, where modes are still separated, but are sufficiently perturbed by small imperfections that their spectral positions (and distributions) are statistical in nature; and 3) overmoded region, where modes overlap, field distributions follow stochastic distributions, and the slot acts as if in free space. Understanding the penetration through slots in the overmoded region is of great interest, and is the focus of this article. Since full-wave solvers may not be able to provide a timely answer for very high frequencies due to a lack of memory and/or computation resources, we develop bounding methods to estimate worst-case average and maximum fields within the cavity. After discussing the bounding formulation, we compare its results to full-wave simulations at the first, second, and third resonance supported by the slot in the case of a cylindrical cavity. Note that the bounding formulation indicates that results are nearly independent of cavity shape: only the cavity volume, frequency, and cavity quality factor affect the overmoded region, making this formulation a powerful tool to assess electromagnetic interference and electromagnetic compatibility effects within cavities.