The spectral function of composites: the inverse problem

The dielectric function of a composite depends on the geometry of the compo site and the dielectric functions of the constituent materials. In the Berg man-Milton spectral representation for a two-component composite, all of th e relevant geometric information can be captured in a spectral function whi ch is independent of the material properties. Extracting the spectral funct ion from experimental values of the dielectric function would be a compact way of presenting a large body of data and highlight the role of geometry i n determining the electrical properties of the composite. We show that know n constraints on the spectral function make it possible to solve the invers e problem of determining the spectral function directly from experimental m easurements of the reflectance if one of the components has a resonance and data are taken in the restrahlen band, where the real part of the dielectr ic function of the optically active material is negative. We demonstrate th e method using numerical simulations of the reflectance of a model system w ith physically reasonable values for the dielectric functions of the two co mponents. Our results show that the spectral function determined by this me thod is stable against the introduction of noise and agrees with that previ ously calculated directly for the same model geometry. We suggest that this technique will be useful when used with real experimental data.