Simplified formulation of dyadic Green's functions and their duality relations for general anisotropic media

A simplified method to obtain the complete set of the dyadic Green's functions ( DGFs) for general anisotropic media is presented. The method is based on the k-domain representation of the fields in terms of wave matrices. The Fourier transformed Green's functions are calculated through the inverses of wave matrices. The inverses of the wave matrices, which lead to the final form of DGF, are obtained using dyadic decomposition technique. This facilitates the inverse operation significantly and gives DGFs clear vector representation, which helps their physical interpretation. The dyadic decomposition of the wave matrices has been presented for uniaxially anisotropic, biaxially anisotropic and gyrotropic media. The method of deriving DGF using the technique given in this paper is applied on a uniaxially anisotropic medium and verified with the existing results. It is shown that the knowledge of the inverse of one type of wave matrix is adequate to find the complete set of the dyadic Green's functions for a general anisotropic medium using the method presented. The duality relations of dyadic Green's functions are also developed. It is shown that once the dyadic Green's functions for one of the dual media are obtained, the DGFs for the other dual medium can be found by application of the duality relations shown in this paper.