On the role of spatial dispersion in boundary conditions for perfect non-specular reflection

Exact solutions for perfect anomalous reflection through metasurfaces have been recently developed in terms of both ideal nondispersive impenetrable boundary conditions (BCs) and penetrable BCs on top of a grounded slab. The second model is more accurate for the description of metasurfaces realized in PCB technology. Focusing on this particular class of metasurfaces, this paper investigates the connection between the two solutions, with the aim to clarify the role of spatial dispersion. It is shown that the two solutions can be related through an equivalent transmission network where transmission lines with different wavenumbers are associated to the incident and reflected waves. Finally, numerical analyses are carried out to assess the impact of neglecting spatial dispersion, as it is done in designs based on a linear phase gradient of the local reflection coefficient.