Modulation instability with high-order dispersion: fundamental limitations of pattern formation

We theoretically and numerically investigate modulation instability in the presence of even, high -order dispersion, focusing on general trends rather than on specific results for a particular dispersion order. We show that high -order dispersion leads to increasingly poor phase matching between the three central waves (i.e. the pump and the +/- 1 sidebands) and the higher sideband orders, inhibiting in effect four -wave mixing frequency generation. For sufficiently large dispersion orders, the problem in effect can reduce to a three -wave system. Our predictions are in excellent agreement with numerical simulations and show that high -order dispersion imposes a fundamental limit on modulation instability dynamics.