Lorentz–Lorenz Model for the Inverse Problem of Inhomogeneous Layer Spectrometry

A spectrophotometric method is developed for recovery of the dispersion and spatial distribution of the refractive index of inhomogeneous layers using a complete set of experimental data for the reflection spectra of s- and p-polarized waves recorded at several angles of incidence. A Lorentz–Lorenz model is used to solve the inverse problem with the spatial density function and refractive index of the layer material represented by polynomials that are obtained by minimizing the discrepancy between the computed and experimental reflection spectra. The optimum order of the spatial polynomial is found using a criterion based on estimating the errors in the solutions. The effectiveness of this approach is tested experimentally and by numerical simulation.