Generation of the third harmonic in periodic domain structures

An investigation is made of the characteristics of third harmonic generation in crystals with a periodic domain structure. Identification is made of those symmetry classes of crystals in the ferroelectric and paraelectric phases which ensure reversal of the sign of the nonlinear susceptibility in neighboring domains. It is shown that such a system should exhibit quasi-phase-matched third harmonic generation when the period of the structure is equal to an odd number of coherence lengths.