A theoretical discussion is given of the diffuse scattering of p-polarized electromagnetic waves from a vacuum-dielectric interface characterized by a one-dimensional disorder in the form of parallel, Gaussian shaped, dielectric ridges positioned at random on a planar semi-infinite dielectric substrate. The parameters of the surface roughness are chosen so that the surface is characterized as weakly rough with a low ridge concentration. The emphasis is on phase coherent features in the speckle pattern of light scattered from the surface. These features are determined from the intensity-intensity correlation function of the speckle pattern and are studied as functions of the frequency of light for frequencies near the dielectric frequency resonances of the ridge material. In the first part of the study, the ridges on the substrate are taken to be identical, made from either GaAs, NaF, or ZnS. The substrate for all cases is CdS. In a second set of studies, the heights and widths of the ridges are statistically distributed. The effects of these different types of randomness on the scattering from the random array of dielectric ridges is determined near the dielectric resonance frequency of the ridge material. The work presented is an extension of studies ͓A. B. McGurn and R. M. Fitzgerald, Phys. Rev. B 65, 155414 ͑2002͔͒ that originally treated only the differential reflection coefficient of the diffuse scattering of light ͑not speckle correlation functions͒ from a system of identical ridges. The object of the present work is to demonstrate the effects of the dielectric frequency resonances of the ridge materials on the phase coherent features found in the speckle patterns of the diffusely scattered light. The dielectric frequency resonances are shown to enhance the observation of the weak localization of electromagnetic surface waves at the random interface. The frequencies treated in this work are in the infrared. Previous weak localization studies have concentrated mainly on the visible and ultraviolet.
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