Effective dielectric functions of alkali halide composites and their spectral representation

In the electrostatic approximation inhomogeneous samples with characteristic scale of inhomogeneities much smaller than the wavelength of light can be characterized by an effective dielectric function eeff. This paper analyzes in which cases simple mixing formulas can be used to calculate eeff from the dielectric functions of the consituents. These considerations are compared with reflectance measurements of alkali halide composites in the far infrared. In many cases it turns out that it is essential to employ the general ansatz of the Bergman spectral representation in order to describe all effects due to the geometrical arrangement of the phases in a proper manner. It is necessary to adjust Bergman's spectral density to measurements. This can be done by use of a Monte-Carlolike algorithm. Further on we try to answer the question how to extract the dielectric function of one of the constituents from measurements of the effective dielectric function.