Gaussian Beam Scattering By Spherical Uniaxial Anisotropic Medium

The scattering of Gaussian beam by spherical uniaxial anisotropic medium is studied in this paper. Based on the Maxwell's equations and the electric-field differential equations for uniaxial anisotropic media, the analytical expansion of interior fields in terms of spherical vector wave functions of the anisotropic sphere are derived by making the Fourier transform and using the expansion coefficients of plane wave factors. The incident on-axis Gaussian beam and scattering field are also expanded in terms of spherical vector wave functions. By virtue of the continuous boundary conditions, the expansion coefficients of the scattering fields of an uniaxial anisotropic sphere irradiated by on-axis Gaussian beam are derived.The spatial distributions of radar cross sections (RCS) are analyzed numerically and the effects of beam width, size parameters as well as permittivity tensor factorsεtandεzon the RCS are studied. It is indicated that the effects on RCS by the permittivity tensorεand permeability tensorμcan be equivalent and the dualistic relation between them is still valid in uniaxical anisotropic medium. Numerical results for some special cases are obtained. The results degenerated to the cases of plane wave and the case of isotropic medium. They are in good agreement compared with those by XFDTD methods and the Mie theory, respectively.With similarly, solution to off-axis Gaussian beam scattering by spherical uniaxial anisotropic medium is also obtained, combining the expansion of incident off-axial Gaussian beam in terms of spherical vector wave functions. The spatial distribution of RCS and the effects of size parameters, permittivity tensor as well as coorsinates of the sphere in the system of the Gaussian beam are studied. The newly obtained results are in good agreement with present references.Scattering by uniaxial anisotropic medium irradiated by Gaussian beam nonparallel to the primary optical axis is also analyzed preliminary. Utilizing the Maxwell's equations and Fourier transform, the eigenvectors for electromagnetic fields are derived in the coordinate with the primary optical axis as it's z′-axis. By coordinate rotation transform, the electromagnetic fields in the anisotropic medium are expanded with spherical vector wave functions in the spherical coordinate where the incident Gaussian beam and the scattering field are also expanded. Then the expansion coefficients are derived by applying the boundary conditions. The correctness of the theory is verified by degenerating to the case of Gaussian beam incidence parallel to the primary optical axis.