Electromagnetic scattering from an anisotropic impedance half-plane at oblique incidence: the exact solution

• Published in: Quarterly journal of mechanics and applied mathematics Vol. 59; no. 2; pp. 211 - 251
• Main Author: Antipov, Y. A.
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.05.2006; Oxford Publishing Limited (England)
• ISSN: 0033-5614; 1464-3855
• DOI: 10.1093/qjmam/hbj004

Scattering of a plane electromagnetic wave from an anisotropic impedance half-plane at skew incidence is considered. The two matrix surface impedances involved are assumed to be complex and different. The problem is solved in closed form. The boundary-value problem reduces to a system of two first-order difference equations with periodic coefficients subject to a symmetry condition. The main idea of the method developed is to convert the system of difference equations into a scalar Riemann–Hilbert problem on a finite contour of a hyperelliptic surface of genus 3. A constructive procedure for its solution and the solution of the associated Jacobi inversion problem is proposed and described in detail. Numerical results for the edge diffraction coefficients are reported.