Cascading nonlinearities in optical four-wave mixing

In a crystal without inversion symmetry there exist two-step indirect contributions to third-order nonlinear optical processes (cascading). Contributions to optical four-wave mixing occur through optical rectification and linear electro-optic effects. In contrast to cascading by second-harmonic generation, which has to satisfy strict phase-matching conditions, optical rectification is always allowed. In polar KNbO3 crystals we measured four-wave mixing in several geometries to evaluate the direct contribution of the third-order polarizabilities and the cascaded contribution. We present a theoretical model and show experimentally that the cascading effect is large and that contributing polarization gratings must be transversely polarized.