Self-Sufficient Algorithm of the Method of Surface Integral Equations in the Problems of Electromagnetic Scattering by Magneto-dielectric Cylinders

A self-sufficient algorithm is proposed for solution of a 2D problem of plane electromagnetic wave scattering by a homogeneous magneto-dielectric cylinder of arbitrary cross section. The algorithm is based on a system of surface integral equations for a combination of auxiliary surface electric and magnetic currents, approximation of the original contour of the cross section by a polygon, and a constant approximation of the auxiliary currents on each side of the polygon. The auxiliary currents are determined as a result of solution of a system of linear algebraic equations obtained from the boundary conditions for the fields in the collocation points located in the middle of each side of the polygon. The self-sufficiency of the algorithm is provided by verification of fulfillment of one more system of integral equations written on the basis of the theorem of equivalence for tangential components of the fields on the surface of the cylinder calculated with use of the auxiliary currents determined above. Effectiveness of the algorithm is demonstrated by means of its application for solution of the problem of wave scattering on focusing magneto-dielectric lenses including the lenses made of material with negative index of refraction.