Optical properties of Rydberg excitons in Cu${}_2$O based superlattices

Combining the microscopic calculation of superlattice minibands and the macroscopic real density matrix approach one can obtain electric susceptibilities of the superlattice system irradiated by an electromagnetical wave. It is shown how to compute the dispersion relation, excitonic resonances positions and susceptibility of Cu${}_2$O/MgO based superlattice (SL), when Rydberg Exciton-Polaritons appear, including the effect of the coherence between the electron-hole pair and the electromagnetic field and the polaritonic effect. Using the Kronig-Penney model for computing miniband SL parameters the analytical expressions for optical functions are obtained and the numerical calculations for Cu${}_2$O/MgO SL are performed.