Computing the scattering from periodic, rough surfaces without including evanescent modes

For many decades, the issue of scattering of electromagnetic waves from periodic surfaces has been of great interest. When dealing with scattering on any surface, boundary conditions need to be met, and in order to satisfy these, non-propagating modes called evanescent waves have to be accounted for. In the case of scattering from a periodic surface, the scattered modes can be represented by a finite set of discrete, propagating modes and an infinite set of evanescent discrete modes. These evanescent modes decay rapidly and do not contribute in the far field, yet there are an infinite set of them that need to be accounted for. In this research, a new technique is developed which estimates a modal sub-space which is orthogonal to all the evanescent modes at the boundary. By projecting the boundary conditions on to this sub-space, the propagating scattered fields can be found in terms of the incident fields without calculating the evanescent modes. This technique accomplishes this by estimating the sub-space in terms of only the propagation constants and surface slopes. The proposed method reduces the complexity of the scattering problem significantly by eliminating the need to calculate the evanescent modes..