Exploiting the Ewald method for calculating the T-matrix of arbitrary periodic arrays

In this study a 3D robust, systematic, semi-analytical method to characterize electromagnetic scattering from periodic arrays of discrete scatterers is presented. The proposed method is based on the multiple-scattering T-matrix in connection with the Ewald method. The formulation is systematic, quite general, easily traceable, and fast. Its high speed of analysis makes it well suited to design optimizations. The formulation is well developed for obliquely incident plane waves, and can be extended to Gaussian beams by means of suitable plane wave decomposition. For validating the proposed method, an example of a scattering problem is solved, and the resulting scattering spectrum, and the total field are compared with those obtained using the method of moments. To the best of our knowledge no report on derivation of the T-matrix of a 3D (or even 2D) periodic array from the T-matrix of the isolated element, based on Ewald method has been reported before.