Exact scattering for axial incidence on concave soft and hard paraboloids

Abstract

A scalar plane wave propagates along the axis of a concave paraboloid of revolution. The space inside the paraboloid is filled with a linear, homogeneous and isotropic medium, and the analysis is conducted in the phasor domain with a time-dependence factor exp (+jωt) and a propagation constant k. The surface of the paraboloid is either soft (Dirichlet boundary condition) or hard (Neumann boundary condition).