On the features of the Optical Rogue Waves observed in the Kerr lens   mode locked Ti:Sapphire laser
  Kerr lens-mode-locked Ti:Sapphire lasers are known to display three coexistent modes of operation, that can be described as: continuous wave (CW), transform limited pulses (P1) and positive chirped pulses (P2). Optical rogue waves, in the form of pulses of high energy appearing much often than expected in a Gaussian distribution, are observed in the chaotic regime of the mode P2, but not of P1. These high energy pulses appear in an unpredictable way, but it is observed that their separation (if measured in number of round trips) can take only some definite values, which received the name of "magic numbers". The existence of optical rogue waves in P2 and not in P1, and also of the magic numbers, are correctly reproduced by a numerical simulation based on a five-variables iterative map. But, a successful numerical simulation provides limited insight on the physical causes of the observed phenomena. We present evidence that optical rogue waves in this laser follow a modulational instability, and that an initial condition in P1 rapidly evolves into P2 if the parameters' values are beyond that instability's threshold. The magic numbers are residuals of the periodic orbits of the "cold" cavity when it is perturbed by the opposite effects of a dissipative term, due to the presence of transversal apertures, and an expansive term, due to the Kerr effect. 
Alejandro A. Hnilo, Marcelo G. Kovalsky and Jorge R. Tredicce
physics.optics