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

摘要

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 ${rm TE}$ and ${rm TM}$ 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.