Generalized soft-and-hard surface

Soft-and-hard surface (SHS) is a mathematical idealization of the tuned corrugated boundary. The boundary conditions are defined by a single real vector parallel to the corrugations. The SHS boundary was recently generalized by replacing the real vector by a complex vector and its conjugate. In the present study, the SHS boundary is generalized one step further by defining it in terms of two complex vectors tangential to the surface. It is shown that in analogy to the previous special cases; there exist two eigenpolarizations, TE and TM with respect to the two vectors for plane waves of any angle of incidence. These two specially polarized waves see the boundary as a simple perfect magnetic or electric conductor surface, respectively. Because the same is true for TE and TM parts of fields radiated by finite sources, it is possible to apply the classical image theory for the computation of fields in the presence of a planar generalized SHS boundary. A principle of realization of such a boundary is briefly discussed. If the two vectors defining the boundary can be realized in practice, a device transforming any given polarization to any other polarization in reflection appears feasible.