Exciton polariton dispersion in superlattices

Abstract A general approach to the analysis of polariton states in superlattices is developed, based on functional methods of quantum field theory and the Legendre transforms Using the Schwinger equations for a photon and an exciton in the operator form, the equation for the polariton state vector in the complex Hilbert space is established. This equation is related to the Dyson and Bethe—Salpeter equations for the corresponding photon and exciton Green’s operators. These equations allow one to reduce the problem of determining the polariton eigenstates to the eigenvalue problem for the Hermitian operator. The proposed method is used to calculate the polariton band structure of one-dimensional superlattice based on cubic semiconductor materials. Analyzed is the corresponding fine structure of the spectrum which arises due to the exchange interaction between electron and hole in the system.