Instability due to cross-phase modulation in the normal-dispersion regime

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Abstract
The interaction of two light waves, having different frequencies and propagating in a dispersive nonlinear medium, is studied using the method of Zakharov (Zh. Eksp. Teor. Fiz. 51, 1107 (1966) [Sov. Phys. JETP 24, 740 (1967)]). This method does not require the sidebands of the incident waves to have frequencies comparable to those of the incident waves, as do the coupled nonlinear Schrödinger equations that are normally used to model this interaction. It is shown that cross-phase modulation does not necessarily lead to instability of the incident waves. In particular, two light waves propagating in the normal-dispersion regime of a conventional single-mode fiber are stable. However, cross-phase-induced modulational instability can occur in a conventional fiber when one of the light waves propagates in the anomalous dispersion regime. The dispersion curve associated with a dispersion-flattened fiber has two regions in which dispersion is normal, separated by a region in which dispersion is anomalous. Cross-phase-induced modulational instability can occur in a dispersion-flattened fiber when the two light waves propagate in different normal-dispersion regimes.

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