Spectral Dependence of Modulation Instability

We consider the spectral dependence of modulation instability. In addition to the usual Maxwell-Boltzmann, or Gaussian, distribution, we consider Lorentzian, exponential and rectangular power spectra. We show that each distribution gives its own threshold for instability, and that the rectangular spectrum gives the counterintuitive trend of increasing perturbation period as the profile narrows (becomes more coherent). Theoretical results are confirmed experimentally by mapping the plasma problem to the equivalent statistical optics system $^{2,3}$.