Two approaches to solving the problem of diffraction by a cylindrical body with a coordinate-dependent refractive index

An algorithm based on solving a two-dimensional integral equation for the problem of diffraction by an infinite cylindrical body with a coordinate-dependent refractive index is proposed. For the diffraction by a circular cylinder, rigorous approach reduced to solving the Helmholtz equation by expanding the field in a combined basis of splines and trigonometric functions is used. The comparison of two methods for the case when the squared wavenumber depends parabolically on the x-coordinate is performed. The method on the basis of the integral equation was tested on a problem of plane-wave scattering by a cylinder with an elliptic or a rectangular cross section under the assumption that the wavenumber of the medium inside the cylinder may be constant. A special case of the diffraction by an inhomogeneous circular cylinder from a metamaterial is also considered.