Diffraction of an obliquely incident electromagnetic wave by an impedance right-angled concave wedge

TL;DR

This paper presents an exact analytical solution for the scattering of an electromagnetic wave by an anisotropic impedance right-angled concave wedge at skew incidence, using advanced complex analysis techniques.

Contribution

It introduces a novel closed-form solution by reducing the scattering problem to a symmetric vector Riemann-Hilbert problem and solving it via elliptic integrals.

Findings

Derived a closed-form solution for the scattering problem.

Expressed electromagnetic fields through Sommerfeld integrals.

Recovered incident and reflected waves explicitly.

Abstract

Scattering of a plane electromagnetic wave by an anisotropic impedance right-angled concave wedge at skew incidence is analyzed. A closed-form solution is derived by reducing the problem to a symmetric order-2 vector Riemann-Hilbert problem (RHP) on the real axis. The problem of matrix factorization leads to a scalar RHP on a genus-3 Riemann surface. Its solution is derived by the Weierstrass integrals. Due to a special symmetry of the problem the associated Jacobi inversion problem is solved in terms of elliptic integrals, not a genus-3 Riemann \`e-function. The electric and magnetic field components are expressed through the Sommerfeld integrals, and the incident and reflected waves are recovered.