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- Title
Diffraction of an obliquely incident electromagnetic wave by an impedance right-angled concave wedge.
- Authors
Antipov, Y.A.
- Abstract
Scattering of a plane electromagnetic wave by an anisotropic impedance right-angled concave wedge at skew incidence is analysed. 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 θ-function. The electric and magnetic field components are expressed through the Sommerfeld integrals, and the incident and reflected waves are recovered.
- Subjects
ELECTROMAGNETIC waves; RIEMANN-Hilbert problems; ELLIPTIC integrals; ELECTRIC fields; MAGNETIC fields
- Publication
Quarterly Journal of Mechanics & Applied Mathematics, 2014, Vol 67, Issue 1, p1
- ISSN
0033-5614
- Publication type
Article
- DOI
10.1093/qjmam/hbt021