Dyadic Green´s function in a general rotationally symmetric material with electrical anisotropy using spherical vector wave function expansion

This paper presents an eigenfunction expansion of the dyadic Green´s function in a general rotationally symmetric medium with electrical anisotropy using spherical vector wave functions. As usual, the dyadic Green´s function in the spectral domain consists of the solenoidal and nonsolenoidal contributions from the rotational and irrotational wave eigenfunctions. It is visible from the final expansion that the parameters of the medium have close and intricate relationships with the properties of the Green´s function, hence, influencing the nature of the propagating waves. The formulation in the paper reveals that the singularity term due to the irrotational vector wave function present in the full eigenfunction expansion is somewhat similar to that of an isotropic case except that the permittivity in the expansion is now a tensor. Like the chiral medium, this particular anisotropic medium exhibits the ability to support the propagation of oppositely polarized waves. This result is due to the fact that the permittivity tensor has some specific off-diagonal non-zero components. Although not straightforwardly implied from its constitutive relations, the mode splitting can be observed in the final expression of the Green´s functions.