Novel two-dimensional periodic Green's function for the efficient analysis of structures made of elements perpendicular to the dielectric substrate by complex images

Here, a simple, accurate and rapidly convergent method based on complex images (CI) technique is developed to derive a closed-form Green's function for periodic structures perpendicular to a substrate. The Green's function is represented in a two criteria form, based on the distance of the field point from the source point. That is, for the small field point to source point distances, it is given in terms of a CI representation, while for the larger field point to source point distances, the contribution of the poles in the spectral domain function is used through the application of the residue theorem. The main advantage of the derived Green's function lies on its accuracy, ease of computation, and fast convergence. The usage of the derived closed-form Green's functions in the mixed potential integral equation (MPIE), an efficient method for analysing periodic structures, has been introduced. The proposed method is applied to several examples, and the results are in good agreement with the simulations in commercial software.