Azimuthal Modulation in Cylindrical Cavities

This paper presents a classical analysis of how small, static azimuthal deformations of a cylindrical cavity’s wall affect its resonant frequencies. The author considers a radius modulation of the form R(ϕ)=R0[1+δcos⁡(m0ϕ)]R(ϕ)=R0[1+δcos(m0ϕ)] and applies perturbation theory to derive first-order frequency shifts for TM and TE modes. Key findings include a selection rule: the perturbation couples modes with azimuthal indices differing by ±m0±m0, leading to mode splitting rather than simple frequency shifts of individual modes. An explicit example is given for the TM010010 mode under m0=1m0=1 modulation, with estimated splitting on the order of 0.1% for δ=0.01δ=0.01. The results are relevant for microwave filter design and mode-selective couplers, focusing purely on classical, time-independent boundary effects. Microwave filter design has seen radical changes in the last twenty years. Tm and Te modes fundamentally underpin their resonance and potential. Perturbation theory allows for transformative analysis of mode splitting potential that could greatly increase wireless communication connectivity.