  It has been a longstanding goal in quantum optics to realize controllable
sources generating joint multiphoton states, particularly, photon triplet with
arbitrary spectral characteristics. We demonstrate that such sources can be
realized via cascaded parametric down-conversion (PDC) in superlattice
structures of nonlinear and linear segments. We consider scheme that involves
two parametric processes: $\omega_{0}\rightarrow\omega_{1}+\omega_{2}$,
$\omega_{2}\rightarrow\omega_{1}+\omega_{1}$ under pulsed pump and investigate
spontaneous creation of photon triplet as well as generation of high-intensity
mode in intracavity three-photon splitting. We show preparation of
Greenberger-Horne-Zeilinger polarization entangled states in cascaded type-II
and type-I PDC in framework of consideration dual-grid structure that involves
two periodically-poled crystals. We demonstrate the method of compensation of
the dispersive effects in non-linear segments by appropriately chosen linear
dispersive segments of superlattice for preparation heralded joint states of
two polarized photons. In the case of intracavity three-photon splitting, we
concentrate on investigation of photon-number distributions, third-order
photon-number correlation function as well as the Wigner functions. These
quantities are observed both for short interaction time intervals and in over
transient regime, when dissipative effects are essential.
