Mie scattering by a uniaxial anisotropic sphere

The field solution to the electromagnetic scattering of a plane wave by a uniaxial anisotropic sphere is obtained in terms of a spherical vector wave function expansion form. Using the source-free Maxwell's equations for uniaxial anisotropic media and making the Fourier transform of the field quantities, the electromagnetic fields in the spectral domain in uniaxial anisotropic media are assumed to have a form similar to the plane wave expanded also in terms of the spherical vector wave functions. Applying the continuous boundary conditions of electromagnetic fields on the surface between the air region and uniaxial anisotropic sphere, the coefficients of transmitted fields and the scattered fields in uniaxial anisotropic media can be obtained analytically in the expansion form of vector wave eigenfunctions. Numerical results for some special cases are obtained and compared with those of the classical Lorenz-Mie theory and the method of moments accelerated with the conjugate-gradient fast-Fourier-transform approach. We also present some new numerical results for the more general uniaxial dielectric material media.