Theory of diffraction by holes of arbitrary sizes

High-gradient accelerating radio frequency (RF)] cavities are currently being developed in several national laboratories for applications in high-energy physics. Ultra-high accelerating gradients, reaching up to the GV/m range, can be achieved using ultra-compact accelerating structures operating in the sub-terahertz (sub-THz) regime. However, accurately measuring the key RF parameters of such compact structures presents significant experimental challenges, and even minor inaccuracies can lead to substantial errors. Additionally, RF simulations for these cavities often require extensive computational resources. Among the most critical parameters to determine is the reflection coefficient. To provide a fast and accurate analytical estimation, we have developed an electromagnetic theory describing the coupling between a resonant cavity and an RF waveguide. This approach is based on Bethe’s small-aperture polarization method, further developed by Collin. An exact analytical expression for the reflection coefficient is presented, formulated as a function of the physical parameters of the cavity waveguide system and applicable to arbitrary geometries, materials, and frequencies.