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Modulational instability in a nonlinear optical fiber induced by a spatial inhomogeneity

Development of the modulational instability is analyzed in an effectively inhomogeneous one-wave or two-wave fiber in the situation when the instability sets in at some critical point and grows down the fiber. In the one-wave case, it is assumed that the dispersion coefficient, being a linear function of the spatial coordinate, changes its sign at the critical point. In the two-wave case, the fiber itself is homogeneous, while an effective inhomogeneity is produced by energy transfer between the two waves via the stimulated Raman scattering. In addition, it is assumed that the pump-wave belongs to the normal-dispersion region, while the Stokes wave lies in the region of the anomalous dispersion; the instability sets in when the ratio of powers of the two waves passes through a certain critical value. In both cases, the frequency of the disturbance which is expected to play a dominant role at the nonlinear stage is found, provided that the initial disturbances are white-nose-like. In particular, it is demonstrated that, in the two-wave case, the solitons produced by the modulational instability from cw can be especially short.