Scattering of a Plane Wave by a Homogeneous Anisotropic Elliptic Cylinder

A formal series solution to the problem of scattering of a normally incident plane wave from an infinite homogeneous anisotropic elliptic cylinder is presented. The formulation of the problem is accomplished by assuming that the permittivity and the permeability tensors of the anisotropic material referred to the elliptic cylindrical coordinate axes are mainly biaxial and diagonal, and expanding each field associated with the problem in terms of a series of suitable Mathieu functions and expansion coefficients. The incident field expansion coefficients are known, but those associated with the scattered and transmitted fields are unknown. The unknown expansion coefficients are obtained by imposing appropriate boundary conditions at the surface of the anisotropic cylinder. Numerical results are presented as normalized bistatic and backscattering widths for elliptic cylinders of different sizes and permeabilities to show the effects of the material anisotropy on scattering.