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

The problem of diffraction of a plane polarized wave by perfectly cond ucting cones of arbitrary cross sections is considered. Using the Deby e scalar potentials and the Sommerfeld transformation, the exact solut ion is constructed in the form of Sommerfeld's integrals with the stan dard phase and the functions on subdomain N of the unit sphere as ampl itudes. By investigating Sommerfeld's integrals in a high-frequency ap proximation using the combination of the stationary phase method and t he propagation of singularities of the amplitude analysis, a rather co mplete description of diffraction processes is obtained. The formulae for the amplitude of the spherical outgoing wave diffracted by the con e's vertex are obtained in terms of spectral characteristics of the Be ltrami-Laplace operator on N. Examples are considered to illustrate th e proposed approach.