Analytical-numerical calculation of diffraction coefficients for a circular impedance cone

An analytical-numerical computation of diffraction coefficients is described for a semi-infinite impedance cone of circular cross section illuminated by an electromagnetic plane wave. To enable an incomplete separation of variables, both the incident and scattered fields are expressed in terms of the Kontorovich-Lebedev (KL) integrals; an inversion of the Leontovich condition on the cone's surface yields equations for the spectra, whose Fourier coefficients satisfy certain functional difference equations of the second order; the latter are then converted to integral equations of the second kind which are solved numerically; using the so obtained spectra in the KL-integrals for the scattered field and evaluating the integrals in far field leads to diffraction coefficients. Numerical results are included both for verification purposes and for displaying the diffraction behavior for different incident and diffraction angles, as well as for several cone impedances.