Localization in frequency for periodically "kicked" light propagation along a dispersive single mode fiber

Summary form only given. We consider in this work propagation in a dispersive optical fiber, of broad light pulses which are repeatedly "kicked" by a sinusoidal RF modulation at equidistant locations along the fiber. The naive expectation about the evolution of the spectrum and the buildup of sidebands (harmonics) is that their number diffusively increases with the number of kicks, and the spectrum continuously broadens. We show in this work that this scenario doesn't occur, but rather a special mechanism of localization, which causes the spectrum to be confined. It is similar to localization in the phase space of quantum kicked rotor, which is related to Anderson localization for electrons in solids.