Phase-reversed structures in superlattice of nonlinear materials
  We present detailed description of so-called phase-reversed structures that are characterized by two grating wave vectors allowing simultaneously phase-match two parametric three-wave processes. The novelty is that the structure is realized as a definite assembly of nonlinear segments leading to detailed description of cascaded three-photon processes with the parameters of realistic structured nonlinear materials of finite length. We apply these results for analysis of the quasi-phase-matching in production of both photon triplet and four-photon states in cascaded down-conversion. The received results are matched with the experimental data. 
D.A. Antonosyan and G.Yu. Kryuchkyan
quant-ph