Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies

Vector potential formulation and parametric studies of electromagnetic scattering problems of a sphere characterized by the rotationally symmetric anisotropy are studied. Both epsilon and mu tensors are considered herein, and four elementary parameters are utilized to specify the material properties in the structure. The field representations can be obtained in terms of two potentials, and both TE (TM) modes (with respect to r) inside (outside) the sphere can be derived and expressed in terms of a series of fractional-order (in a real or complex number) Ricatti-Bessel functions. The effects due to either electric anisotropy ratio (Ae=epsilont/epsilonr) or magnetic anisotropy ratio (Am=mut/mur) on the radar cross section (RCS) are considered, and the hybrid effects due to both Ae and Am are also examined extensively. It is found that the material anisotropy affects significantly the scattering behaviors of three-dimensional dielectric objects. For absorbing spheres, however, the Ae or Am no longer plays a significant role as in lossless dielectric spheres and the anisotropic dependence of RCS values is found to be predictable. The hybrid effects of Ae and Am are considered for absorbing spheres as well, but it is found that the RCS can be greatly reduced by controlling the material parameters. Details of the theoretical treatment and numerical results are presented.