Electromagnetic Wave Diffraction on Axially Symmetric System of Two Spherical Caps

Abstract

ABSTRACT A mathematically rigorous solution is obtained for the diffraction problem of electromagnetic waves on an axially symmetric system of two infinitely thin perfectly conducting spherical caps. This screen configuration is a model of both open resonators with spherical mirrors and two mirror spherical antennas. The initial boundary problem is equivalently reduced to the infinite system of linear algebraic equations of the form (I + H)x = b with the compact operator H in the Hilbert space l 2; the reduction is done using the variables separation technique in the local coordinates, theorems on addition of the Debye potentials, and the regularization technique for dual series equations involving the Jacobi polynomials. The spectrum of complex eigen frequencies of an open resonator with spherical mirrors is calculated, and classification is established for its own modes. Application boundaries are obtained for quasi-optical models of open resonators. A new theoretical model is suggested for the phenomenon of the intermode interaction in an open resonator with spherical mirrors.