A Hybrid Multiple Scattering Approach for Efficient Scattering Modeling of 2-D Periodic Gratings

Existing approaches for modeling the scattering properties of periodic artificial structures often rely on full-wave simulations, or analytical algorithms only applicable to canonical shapes, such as spheres and circular cylinders. They typically tend to be inefficient or inadequate when it comes to complex structures, especially considering optimization problems and wide-band simulations. Therefore, in this letter, an efficient hybrid approach for evaluating the scattering properties of 2-D arbitrarily-shaped gratings with 1-D periodicity (2D1D) has been proposed. The scattering matrix (T-matrix) of a single scatterer with an arbitrary shape is extracted from a surface integral equation as discretized by a Nystrom approach. The efficient evaluation of the cylindrical wave expansion coefficients of the periodic Green's function is next incorporated along with the obtained T-matrix in a multiple scattering theorem formulation to handle the scattering modeling of 2D1D gratings. The effectiveness of the proposed method are demonstrated through several numerical examples, in comparison with results obtained from a full-wave solver Comsol. The developed approach can be used as a powerful tool for the scattering simulations and optimizations of periodic gratings.