Modulational instability in optical fibers with variable dispersion

We study modulational instability in optical fibres whose dispersion varies with the propagation distance. We distinguish between two cases, viz. periodic and random dispersion variation. In the former case it is found that due to the parametric resonance between the dispersion modulation and the modes of the linearized system new domains of modulational instability arise for anomalous as well as normal average dispersion. In the latter case stochastic parametric resonances again lead to the occurrence of modulational instability for normal dispersion. If the dispersion is anomalous the region of modulational instability increases and the respective gain decreases in comparison with a fibre with constant dispersion.