Physical Limits and Optimal Synthesis of Beyond Diagonal Anomalous Scatterers

Realizing metasurfaces for anomalous scattering is fundamental to designing reflector arrays, reconfigurable intelligent surfaces, and metasurface antennas. However, the basic cost of steering scattering into non-specular directions is not fully understood. This paper derives tight physical bounds on anomalous scattering using antenna array systems equipped with non-local matching networks. The matching networks are explicitly synthesized based on the solutions of the optimization problems that define these bounds. Furthermore, we analyze fundamental limits for metasurface antennas implemented with metallic and dielectric materials exhibiting minimal loss within a finite design region. The results reveal a typical 6dB reduction in bistatic radar cross section (RCS) in anomalous directions compared to the forward direction. Numerical examples complement the theory and illustrate the inherent cost of achieving anomalous scattering relative to forward or specular scattering for canonical configurations.