Dyadic green's functions for general two-layer anisotropic geometry with source embedded inside the anisotropic layer

Over the last decade, several methods [1-8] have been developed to obtain the dyadic Green's functions (DGFs) of layered anisotropic media. The most commonly used methods to find the DGFs are the Fourier transform method with differential formulation [6], the method of eigen-function expansion [7], the matrix formulation [8], and the dyadic decomposition techniques [5, 9-11]. In [8], the dyadic Green's function is formulated based on the tangential electric field and current at the interface, which is not suitable for the problem with z-directed current. The dyadic decomposition techniques as discussed in [5, 9-11] are more general and can provide the complete set of the dyadic Green's functions but only the case when the source is in the free space has been considered. If the source is located in a biaxial slab, then reciprocity theorem for the Green's function can be invoked to obtain the DGFs as in [12]. However, the reciprocity holds true only when the slab is filled with reciprocal medium such as uniaxial medium, biaxial medium, etc. For non-reciprocal medium such as the gyroelectric or gyromagnetic medium, the reciprocity relation for the Green's function no longer holds. The DGFs for source located in a non-reciprocal slab cannot be obtained using the reciprocity theorem.