Uniform Ray Description of Physical Optics Scattering by Finite Locally Periodic Metasurfaces

This article presents a uniform ray description of electromagnetic wave scattering by locally periodic metasurfaces of polygonal shape. The model is derived by asymptotically evaluating the critical-point contributions of a physical optics (PO) scattering integral. It is valid for metasurfaces whose bulk scattering coefficients are periodic functions of a phase parameter, which, in turn, is a continuous and smooth function of surface coordinates. The scattered field is expressed in terms of reflected, transmitted, and diffracted rays that do not generally obey conventional geometrical constraints (i.e., Snell’s law and the Keller cone). An iterative technique is presented to determine the locations of critical points on one or multiple interacting metasurfaces. Numerical results demonstrating the utility and accuracy of the asymptotic PO model are also provided.