Characteristics of the extreme events observed in the Kerr-lens mode-locked Ti:sapphire laser

Abstract

Kerr-lens mode-locked Ti:sapphire lasers are known to display three coexistent modes of operation: continuous wave, transform limited pulses (P1), and positive chirped pulses (P2). Extreme events (sometimes also called optical rogue waves), in the form of pulses of high energy appearing much often than in a Gaussian distribution, are observed in the chaotic regime of the P2 mode, but not of P1. The extreme events in P2 appear unpredictably, but their separation (measured in number of round trips) is a simple combination of the numbers 11 and 12 (which were named "magic numbers"). The existence of extreme events in P2 and not in P1, and also of the magic numbers, have been successfully reproduced by numerical simulations based on a five-variables iterative map, but the intuitive insight on the physical causes has been limited. In this paper, we present evidence that the extreme events in this laser appear if the amount of self-phase modulation on the pulses is above a certain threshold, and also that the P1 mode becomes unstable before crossing that threshold. This explains why the extreme events are observed in P2, and not in P1. Remarkably, even though the values of self-phase modulation on all the pulses (in the chaotic regime) are widely spread, the values inside the set of extreme events are relatively well defined. Finally, the magic numbers are found to be the residuals of the periodical orbits of the "cold" laser cavity when they are perturbed by the opposite effects of a dissipative term, due to the presence of transversal apertures, and an expansive term, due to the self-focusing.