A spectral representation for the dielectric properties
of layered materials*

Anthony Roy Day

Physics Department
Marquette University
Milwaukee, WI 53201

We present a spectral representation for the effective dielectric function of a sample that consists of two homogeneous layers joined with a rough interface. This spectral representation is closely related to the Bergman-Milton spectral representation for bulk composites, and is easily extended to multilayered materials. By comparing the layered system to a reference layered system that has a flat interface we form a surface spectral function that captures all the effects of surface structure on the effective dielectric function of the layered sample, and is independent of the dielectric functions of the two layers. Because of the anisotropy of the layered system there are two surface spectral functions, one for the case where the applied field is parallel to the interface, and one for the case where the applied field is perpendicular to the interface. We discuss a reciprocity relationship between these two spectral representations and present sum rules that are directly related to the degree of surface roughness. We present numerical calculations of the surface spectral function for some model geometries, including the Gaussian random surface that has been extensively used to study light scattering from rough surfaces, and show that the simulations verify the sum rules and reciprocity relationships. We show how the surface profile and interactions between layers of the multilayered materials are related to the features of the surface spectral function and we discuss the possibility of determining the spectral function directly from reflectivity measurements.

* Work done in collaboration with M. F. Thorpe (Michigan State University), A. R. McGurn (Western Michigan University) and D. J. Bergman (Tel Aviv University).