Electromagnetic scattering from a circular cylinder of homogeneous dielectric coated by a dielectric shell with a permittivity profile in the radial and azimuthal directions-even TM case

Equations are formulated and numerical results presented for electromagnetic scattering from an infinitely long circular cylinder of homogeneous dielectric coated with a dielectric shell. The permittivity of the dielectric shell varies as ρ^-2 in the radial direction and as a weighted cosine in φ. Plane waves with an electric field parallel to the cylinder axis constitute the incident fields, restricting the analysis to the transverse magnetic (TM) case. This permittivity profile allows the unknown electric field in the dielectric region to be represented by a series of cosine-elliptic Mathieu functions of even integer orders with unknown expansion coefficients. The unknown expansion coefficients are determined by enforcing boundary conditions and using the orthogonal properties of the trigonometric functions and of the Mathieu functions. The far scattered field is then evaluated and numerical results for the scattered field versus different geometrical parameters are obtained and presented