Localization effects in the scattering of light from a randomly rough grating

We calculate the resonant scattering of p-polarized light incident on a randomly rough grating ruled on a medium characterized by a dielectric constant \ensuremath{\epsilon}(\ensuremath{\omega})=${\ensuremath{\epsilon}}_{1}$(\ensuremath{\omega})+i${\ensuremath{\epsilon}}_{2}$(\ensuremath{\omega}), where ${\ensuremath{\epsilon}}_{1}$(\ensuremath{\omega})-1 and \ensuremath{\Vert}${\ensuremath{\epsilon}}_{2}$(\ensuremath{\omega})\ensuremath{\Vert}\ensuremath{\ll}\ensuremath{\Vert}${\ensuremath{\epsilon}}_{1}$(\ensuremath{\omega})\ensuremath{\Vert}. Particular emphasis is placed on determining the contribution to the scattering that arises from the localization of surface polaritons due to the surface roughness. This localization is found to contribute a maximum to the angular dependence of the intensity of the nonspecularly reflected light in the antispecular direction.