Green´s functions for planar soft and hard surfaces derived by asymptotic boundary conditions

The Green´s functions for different realisations of planar soft and hard surfaces are developed by using the asymptotic boundary conditions and the spectral-domain approach. The geometries considered are the ideal perfect electric conductor/perfect magnetic conductor (PEC/PMC) strip surface, the strip-loaded grounded dielectric slab and the corrugated surface. In all cases the strips and corrugations are straight. The asymptotic boundary conditions are valid in the limiting sense, when the period of the strips or corrugations approaches zero. The Green´s functions developed have poles corresponding to surface waves. These are of three types: an ordinary surface wave in the grounded dielectric slab propagating radially out from the source; a strip wave propagating along the strips of the strip-loaded dielectric slab and also along the strips of the PEC/PMC strip surface; and surface waves occurring due to the corrugated surface. Fulfilment of both the soft and hard boundary conditions is discussed in both the near- and far-field regions. The strip wave of the strip-loaded dielectric slab prevents the boundary conditions in the near-field from being fulfilled, and is thus undesired. The other two surface waves are needed to realise the hard boundary condition.