Description of Kerr lens mode-locked lasers with Poincare maps in the complex plane

We study the Kerr lens mode-locking (KLM) laser operation from the point of view of the spontaneous appearance of a new stable solution in a perturbed non-linear system. A description of KLM is possible in terms of a five var iables iterative map. For usual values of the laser parameters, the complet e map can be simplified to two maps with complex variables and one map with a real variable, which become uncoupled after a transient has evolved. Aft er appropriate scaling, the two complex maps have the same form. This simpl ifies the calculation of the fixed points and their stability. It is found that, for appropriate parameters' values, KLM arises even in the absence of spatial apertures or bandwidth limitations. Hence, the Kerr perturbation m odifies the system from non-dissipative to dissipative, this meaning a cont raction of the phase space. It is also found that the phase space can expan d for other parameters' values or initial conditions. If apertures are incl uded in the model, the convergence to the mode-locked solution is faster an d the size of its basin of attraction enlarges, but the dynamics remain ess entially the same. (C) 2001 Published by Elsevier Science B.V.