Applying the Kontorovich-Lebedev transform to the analysis of electromagnetic diffraction by wedges

Abstract

The presence of edges on the surface of a target may considerably influence the scattered field. The corresponding edge corrections are derived from the solution of the canonical problem of diffraction by an infinite wedge. If the refraction index takes different values inside and outside the wedge, no closed-form solution has been found so far despite multiple attempts and the use of a broad variety of methods. The Kontorovich-Lebedev transform has been successfully applied in the past to a number of scalar problems of diffraction by wedges. This paper applies the method to a vector problem of electromagnetic diffraction by a dielectric wedge. The boundary-value problem is reduced to a system of singular integral equations. It is shown that the equations can be approximately solved by perturbation method when the refraction index is near unity.