Dyadic Green’s Function for the Tensor Surface Conductivity Boundary Condition

Dyadic Green's function (DGF) for the tensor surface conductivity boundary condition (TSCBC) is formulated in this paper. Electrically biased spatially dispersive graphene sheet, densely packed graphene strips under electric bias, and magnetically biased graphene nano-patch array can be treated as the special cases of the formulation by assigning proper values to the components of the surface conductivity. In the proposed problem, due to the anisotropic nature of surface conductivity, TE and TM modes are coupled. Based on this fact, scattering Green's functions in the upper and lower regions of the interface are expanded in terms of an appropriate linear combination of vector wave functions. The unknowns are obtained after applying the necessary boundary conditions on the tangential components of the electric and magnetic Green's functions. The validity of the technique is verified by calculating the propagation constant of surface waves, and reflectance and transmittance of a plane-wave by graphene-based structure for the electric and magnetic biases along with the spatially dispersive sheets. It is important to note that the numerical simulation of graphene interface with tensor surface conductivity using commercial software packages is challenging due to the lack of efficiently developed models in their libraries.