Electromagnetic scattering by optically anisotropic magnetic particle

The Mie theory for electromagnetic scattering by spherical particle is extended to the case of magnetic particle with gyromagnetic type of permeability. Specifically, we first construct for the magnetic induction B_I inside the particle a new set of vector basis functions, which are the solution of the wave equation for B_I and expanded in terms of the usual vector spherical wave functions (VSWF’s) with different values of wave vector k_l. The relationship between k_l and the frequency is obtained as the eigenvalues of an eigensystem determined by the permeability tensor. The incident and scattered fields are expanded as usual in terms of the VSWF’s. By matching the boundary conditions, a linear set of coupled equations for the expansion coefficients are obtained and then solved for the solution to the scattering problem. Preliminary numerical results are presented for the case in which the scattering is due solely to the optical anisotropy within the particle. The scattering efficiency is found to exhibit miscellaneous dependence on the incident angle, the polarization, the degree of anisotropy, as well as the size parameter. In addition, the possibility of the photonic Hall effect for one Mie scatterer is confirmed.