Green´s functions for corrugated surface derived by asymptotic corrugation boundary conditions

The Green´s functions for corrugated surfaces have been derived by using the asymptotic corrugation boundary conditions. The assumption is that the periodicity of the corrugations are small compared to the wavelength. The Green´s functions are derived in the spectral domain. The poles of the spectral Green´s functions give the information about surface waves. In a wide frequency range there are no surface waves in the direction transverse to the corrugations. At the frequency defined by /spl lambda//sub 0/=4d/spl radic/(/spl epsi/r-1) the surface wave is strongly localized in and propagating along the corrugations passing near the source, and its magnitude does not decay with distance. For other frequencies the surface waves spread and their magnitude decays. The presented Green´s functions are helpful in analysing plane corrugated surfaces when the plane wave model is not sufficient, e.g. when the source is near the surface.