Modified theory of coupled waves and a numerical method for the analysis of bragg mirrors with an arbitrary refractive index profile

An analytical and effective numerical approach to the analysis of the optical characteristics of Bragg mirrors with an arbitrary refractive index profile is developed. Analytical expressions obtained using the modified theory of coupled waves for the coefficients of reflection/transmission of light from/through the BM with high accuracy predict its main characteristics at both low and high contrast of the refractive index. The hybrid numerical method includes the numerical calculation of the transfer matrix for one period of the knowledge base and its analytical multiplication for an arbitrary number of periods. The developed methods are applied to the analysis of the properties of practically important BMs made on the basis of sprayed pairs of Ta$_{2}$O$_{5}$/SiO$_{2}$ dielectrics, Group III nitrides and arsenides. The characteristics of the knowledge base with smooth (gradient) interfaces are considered in detail.