Modulational-instability gain bands in quasi-phase-matched materials

Full text: Quadratically nonlinear materials are of significant technological interest in optics because of their strong and fast cascaded nonlinearities, which are accessed most efficiently with quasi-phase-matching (QPM) techniques. We study the gain spectra of modulational instabilities (Ml) in quadratic materials where the linear and nonlinear properties are modulated with QPM gratings. The periods and intensity-dependence of the Ml can now be measured in the laboratory. Using an exact Floquet theory, we find that novel low- and high-frequency bands appear in the gain spectrum (gain versus transverse spatial frequency). The high-frequency gain bands are a general feature of gain spectra for QPM gratings. They form part of an extensive series of bands that correspond to Ml in the non-phase-matched, quickly varying components of the fields. The low-frequency bands correspond to Ml in the phase-matched DC components of the fields and are accurately predicted by a simple average theory. This theory includes the effect of the quickly varying components as induced cubic terms, which can be strong enough to suppress the low-frequency bands, in which case dark solitons and other broad beams may be effectively stable, since the high-frequency bands are typically small