Theory of resonant light scattering through exciton-polaritons

Abstract

There are apparently two different formalisms of the resonant Brillouin or Raman scattering cross section through exciton-polaritons: one which has been introduced by Brenig, Zeyher, and Birman (BZB) and which is based on the distorted-wave Born approximation; and a second, conventional one which is based on the factorization approximation for sequential scattering events. Starting from the previously derived results of the inner product and orthonormality condition of the normal modes of exciton-polaritons extending over the whole space consisting of a semi-infinite semiconductor and vacuum, the BZB cross section has been rederived very naturally. Through the use of the reciprocity relation between transmissivities from the vacuum to the semiconductor and vice versa, which has also been shown to hold true, the BZB cross section is verified to be equivalent to the conventional one. The correct normalization of the polariton modes or the careful treatment of the phase matching of the scattered waves at the vacuum-crystal interface is pointed out to be important for the conventional cross-section calculations. The properties and differences of the final states of the polariton scattering in the two approaches are discussed in detail. The phenomenological extension of the verification of the equivalence between the two approaches is also demonstrated for the case with nonzero exciton damping.