Asymptotic solution with higher-order terms for scattered fields by an impedance discontinuity of a planar impedance surface

In this study, we have derived a novel asymptotic solution with higher-order terms for the scattered field by an impedance discontinuity of a planar surface. In the derivation of the asymptotic solution, we have applied the aperture field method to obtain an integral representation for the scattered field. Then we have used the saddle point technique applicable uniformly as the saddle point approaches the endpoint of the integral. It is shown that when both the source and observation points are placed sufficiently far away from the impedance surface, the asymptotic solution for the scattered field is represented by the geometrically reflected ray on a planar surface and the diffracted ray at the impedance discontinuity. We have confirmed the validity and utility of the asymptotic solution with the higher-order terms by comparing with the reference solution calculated from the numerical integration of the integral representation. We have also shown the physical interpretation of the asymptotic solution.