The Malyuzhinets-Popov diffraction problem revisited

TL;DR

This paper develops an asymptotic analysis of high-frequency diffraction involving a convex boundary with curvature discontinuity, introducing new special functions related to Fock's integrals.

Contribution

It introduces a modified Fock parabolic-equation method and derives novel asymptotic formulas for diffraction fields with curvature jumps.

Findings

Derived asymptotic formulas for wavefields in different diffraction regions.

Characterized penumbral fields using new special functions similar to Fock's integrals.

Provided insights into wave behavior at convex boundaries with curvature discontinuities.

Abstract

In this paper, the high-frequency diffraction of a plane wave incident along a planar boundary turning into a smooth convex contour, so that the curvature undergoes a jump, is asymptotically analysed. An approach modifying the Fock parabolic-equation method is developed. Asymptotic formulas for the wavefield in the illuminated area, shadow, and the penumbra are derived. The penumbral field is characterized by novel and previously unseen special functions that resemble Fock's integrals.