Axially symmetric TM-wave radiation through the ring slot in the sphere-conical resonator

The problem of radiation of the axial symmetric TM waves through the ring slot in the sphere-conical resonator is solved rigorously using the analytical regularization technique. Resonator is formed by a perfectly conducting semi-infinite conical surface with the ring slot in the wall, and with the spherical diaphragm by which one of conical sectors is closed. The slot is placed between the vertex and the diaphragm. The problem is reduced to an infinite system of linear algebraic equations (ISLAE) of the second kind which allows the solution with a given accuracy for any geometrical parameters and frequency. We analyze numerically the hemispherical resonator with conical aperture angle γ→ π /2. The dependence of the resonance modes radiation through the slot of the resonator on the geometrical parameters, as well as the features of the formation of far field patterns are investigated.