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We study the parametric wave interaction in qua- dratic nonlinear media withrandomized distribution of the ferroelectric domains. In particular, we discussproperties of second and cascaded third harmonic generation.  We derive analytical formulas describing emission properties of the secondand third harmonics in the presence of domain disorder and show that the latterprocess is governed by the characteristics of the constituent processes, i.e.second harmonic generation and sum frequency mixing. We demonstrate the role ofrandomness on various second and third harmonic generation regimes such asRaman-Nath and \v{C}erenkov nonlinear diffraction. We show that therandomness-induced incoherence in the wave interaction leads to deteriorationof conversion efficiency and angular spreading of harmonic generated in theprocesses relying on transverse phase matching such as Raman-Nath. On the otherhand forward and \v{C}erenkov frequency generation are basically insensitive tothe domain randomness.

Parametric wave interaction in quadratic crystal with randomized distribution of ferroelectric domains