Scattering of waves by a half-space of periodic scatterers using broadband Green's function.

An efficient scatterer-free full-wave solution for plane wave scattering from a half-space of two-dimensional (2D) periodic scatterers is derived using broadband Green's function. The Green's function is constructed using band solutions of the infinite periodic structure, and it satisfies boundary conditions on all the scatterers. A low wavenumber extraction technique is applied to the Green's function to accelerate the convergence of the modal expansion. This facilitates the Green's function with low wavenumber extraction (BBGFL) to be evaluated over a broadband as the modal solutions are independent of wavenumber. Coupled surface integral equations (SIE) are constructed using the BBGFL and the free-space Green's function respectively for the two half-spaces with unknowns only on the interface. The method is distinct from the effective medium approach which represents the periodic scatters with an effective medium. This new approach provides accurate near-field solutions around the interface with localized field patterns useful for surface plasmon polaritons and topological edge states examinations.