Vector wave function expansions of dyadic Green's functions for bianisotropic media

Abstract

An alternative set of Cartesian vector wave functions is presented to simplify the development of eigenfunction expansions of electromagnetic fields and dyadic Green's functions for bianisotropic media. With the eigenfields expanded using these functions, the determination of their expansion coefficients is facilitated via a concise 4 × 4 matrix method. Based on the complete dyadic discontinuity relations, the source consequents of dyadic Green's functions are also explicitly expressed in terms of these functions. By incorporating the modified reciprocity theorem into the discontinuity relations, more compact source consequents are found to be related directly to the eigenfields in a complementary medium. These complementary eigenfields, in turn, can be deduced readily from their original counterparts by performing certain simple transformations. This manner of incorporating reciprocity provides a clear insight into the significance of each discontinuity relation and reveals the connections between the singularities, discontinuities and the complementary eigenfield components. For illustration, the vector wave functions expansions of the eigenfields for isotropic and uniaxial bianisotropic media are discussed.