Rigorous Formulation of the Scattering of Plane Waves by 2-D Graphene-Based Gratings: Out-of-Plane Incidence

The plane wave scattering by 2-D gratings is studied by a rigorous mode-matching technique. Specifically, the grating considered in this work is made of periodically patterned graphene. Due to the 2-D periodicity, the electromagnetic fields in the uniform medium are expressed in terms of characteristic Floquet solutions, with each space harmonic representing a plane wave solution consisting of both TE and TM constituents. By imposing the boundary condition on the tangential components of the electromagnetic fields at the graphene interface via the conductivity tensor of graphene, one can set up an input-output relation expressed in terms of the generalized scattering matrix. For a planar multilayer structure consisting of a finite stack of 2-D graphene-based gratings, the overall scattering characteristics can be obtained by cascading each of the input-output relations of the 2-D grating successively.