Approximation model for refractive index slight inhomogeneity reverse determination of multilayers

Thin film coatings in actual application are always characterized by some kind of, slight or large, refractive index inhomogeneity. Its accurate characterization can be vital to the process parameters calibration of coating machine, and to the design and manufacture of ultra low loss coatings. According to Schr?der approximation, the characteristic matrix of a slightly inhomogeneous thin film was derived, and an approximation model for the spectral characteristics calculation of slightly inhomogeneous multilayer coatings was presented by the matrix method. Based on the effective medium approximation theory and infinite division into large homogeneous sublayers, the effectiveness, calculation accuracy and time consumption of the approximation model were discussed in details. It shows that this model presents a fast and effective tool for the reverse determination of the refractive index inhomogeneity defect of multilayer system, and lays a foundation for the numerical optimization algorithm application into the data fitting based on the measured broadband spectral characteristics of actual multilayer coatings.