  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.
