Conical propagation of a surface polariton across a grating

By the use of the homogeneous form of the reduced Rayleigh equation for the electromagnetic field above and on a two-dimensional rough surface we obtain the dispersion relation for a surface polariton propagating across a classical diffraction grating when the sagittal plane is not perpendicular to the generators of the surface. This dispersion relation is exact within the domain of validity of the Rayleigh hypothesis upon which it is based. It is solved numerically, and dispersion curves are determined for several directions of propagation of the surface polariton for three different choices for the grating profile function. Particular attention is paid to the dependence on the direction of propagation of the position and width of the gap in the surface polariton dispersion curve that occurs at the boundary of the first Brillouin zone defined by the periodicity of the grating. The results obtained are compared with those of a recent experimental determination of this gap. (C) 2002 Elsevier Science B.V. All rights reserved.