Rigorous analysis of the vector diffraction problem for a cylindrical waveguide cavity (Q2754732)

A vector diffraction problem for an open semi-infinite ideally conducting cylinder with an internal disk wall is considered. Waves are excited by a non-symmetric electromagnetic field of a \(\delta\)-generator of voltage, that is placed in a thin cut on the inner surface of the cylindrical surface. The corresponding boundary-value problem of electrodynamics is formulated for Fourier transforms of scalar potentials of TM- and TE-waves. For their determination, a Wiener-Hopf equation is derived. The equation strictly takes into account interaction of waves, boundary conditions on the diffusing surface and the Meixner conditions on the edge. By application of the factorization technique, the Wiener-Hopf equation is reduced to an infinite system of algebraic equations of the second kind with exponentially decaying coefficients. For arbitrary parameters of the problem, this equation allows solution with beforehand prescribed accuracy.