Expansion of the spectral representation function of a composite material in a basis of Legendre polynomials: Experimental determination and analytic approximations

A unique formulation is presented to derive the spectral representation function of heterogeneous two-component materials in terms of an expansion on Legendre polynomials. This approach notably simplifies the calculations needed to estimate the effective dielectric function from the spectral density function and allows one to extract it from experimental data by using quite simple analytic expressions. The spectral representation function derived by the present method agrees notably well with experimental infrared reflectance measurements obtained from several ionic compounds. In addition, we state that the infrared spectral region is the optimal one in order to determine the full relationship between the spectral density function and the effective dielectric constant of a composite material.