THE HIGH-FREQUENCY DIFFRACTION OF ELECTROMAGNETIC-WAVES BY CONES OF ARBITRARY CROSS-SECTIONS

The problem of diffraction of a plane polarized wave by perfectly conducting cones of arbitrary cross sections is considered. Using the Debye scalar potentials and the Sommerfeld transformation, the exact solution is constructed in the form of Sommerfeld's integrals with the standard phase and the functions on subdomain N of the unit sphere as amplitudes. By investigating Sommerfeld's integrals in a high-frequency approximation using the combination of the stationary phase method and the propagation of singularities of the amplitude analysis, a rather complete description of diffraction processes is obtained. The formulae for the amplitude of the spherical outgoing wave diffracted by the cone's vertex are obtained in terms of spectral characteristics of the Beltrami-Laplace operator on N. Examples are considered to illustrate the proposed approach.