We consider the MI of optical beams in media with a purely quadratic (or x⁽²⁾) nonlinearity, analysing in detail the instability gain spectra when linear and nonlinear quasi-phase-matching (QPM) gratings are present. Because such spectra can now be measured in the laboratory², studying their profiles has direct experimental relevance.

We find that, due to the periodicity, novel low- and high-frequency bands appear in the gain spectrum, each with fundamentally different physical origins. The high-frequency gain bands are a general feature of gain spectra for QPM gratings, related to the inherent MI in the non-phase-matched, gratingless x⁽²⁾ material. In contrast, the low-frequency bands depend critically on the modulation depths and periods, and can totally disappear for particular gratings. Induced by the phase-matching periodicities, they are accurately predicted by a simple average theory.

Our results show that when the low-v gain bands are suppressed, dark solitons can propagate stably over experimentally relevant distances, due to the residual high-v gain being typically small. This increases the potential utility of dark solitons in applications, allowing their particular advantages to be exploited¹.

REFERENCES:

1. Y. S. Kivshar and B. Luther-Davies, "Dark optical solitons: physics and applications", Phys. Rep. 298, 81-198 (1998).
2. H. Fang, R. Malendevich, R. Schiek, G.I. Stegeman, "Measurement of modulational instability gain of second-order nonlinear optical eigenmodes in a one-dimensional system", Phys. Rev. Lett. 86, 4528-4531 (2001)