Unit Cell Design for Aperiodic Metasurfaces

A technique is presented for the design of printed unit cells in aperiodic metasurface environments. The method begins with a solved matrix equation governing electromagnetic scattering from a homogenized metasurface design. The matrix equation is used to find the local, inhomogeneous electric field exciting a printed-circuit unit cell geometry. The local field is then impressed onto the printed-circuit geometry and the induced surface current is numerically computed. The computed surface current is sampled at the matrix equation discretization. The matrix equation is then used to compute the electric field scattered by the printed-circuit unit cell onto its neighbors using the sampled current in place of the current of the original homogenized unit cell. The printed-circuit geometry is optimized to scatter the same field as the homogenized unit cell when excited with the local electric field computed. Two design examples are provided. Both a finite-sized, wide-angle reflecting metasurface, and a metasurface reflectarray designed to scan and collimate an incident cylindrical wave are realized with printed-circuit unit cells using the proposed approach. It is shown that the local periodicity approximation cannot be used to accurately design the unit cells of either finite-sized metasurface.