1304.3968 (Y. A. Antipov)

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

Y. A. Antipov

Scattering of a plane electromagnetic wave by an anisotropic impedance concave wedge at skew incidence is analyzed. In the case of a right-angled wedge, the problem reduces to two symmetric order-2 vector Riemann-Hilbert problems (RHPs) which are solved exactly. The problem of matrix factorization leads to a scalar RHP on a genus-3 Riemann surface. Its closed-form solution is derived by the Weierstrass integrals, and the associated Jacobi inversion problem is solved in terms of elliptic integrals. It is shown that the solvability of the physical problem is governed by the location of the four zeros of the product of two quadratic polynomials associated with the two vector RHPs. The coefficients of these polynomials are expressed through the wave number, the impedance parameters and the angle of incidence. In the case when the solution is unique, the reflected, surface and diffracted waves are recovered.

View original: http://arxiv.org/abs/1304.3968