Exponentially Converging Nyström Methods in Oblique Diffraction of Arbitrarily Polarized Waves by Bianisotropic/Chiral Cylinders With Arbitrary Smooth Cross Section

Abstract

We study oblique diffraction of arbitrarily polarized plane waves by a uniform homogeneous bianisotropic cylinder with arbitrarily shaped smooth boundary. Following a boundary integral equations formulation we develop a 4 × 4 system of combined field integral equations and another 4 × 4 system of Muller-type Fredholm integral equations. Both these systems, having the tangential to the surface of the cylinder components of the electric and magnetic fields as the unknowns, are of the second kind and uniquely solvable. Efficient discretization via simple and rapidly converging Nystrom algorithms enables one to obtain highly accurate results even for electrically large objects. The proposed solution technique: a) fully accounts for the singular nature of the kernels; b) yields simple closed form expressions for all matrix elements; and c) appears to converge exponentially versus matrix size. The analogous diffraction problem for an arbitrarily shaped smooth chiral cylinder may be treated as a simple special case of the present analysis.