Dynamics of the modulation instability spectrum in optical fibers with oscillating dispersion

A simple analytical model is developed to analyze and explain the complex dynamics of the multipeak modulation instability spectrum observed in dispersion oscillating optical fibers [M. Droques et al., Opt. Lett. 37, 4832 (2012)]. We provide a simple expression for the local parametric gain, which shows that each of the multiple spectral components grows thanks to a quasi-phase-matching mechanism due to the periodicity of the waveguide parameters, in good agreement with numerical simulations and experiments. This simplified model is alsosuccessfullyusedtotailorthemultipeakmodulationinstabilityspectrumshape.Thesetheoreticalpredictions are confirmed by experiments.