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The two most commonly used models for passively modelocked lasers with fastsaturable absorbers are the Haus modelocking equation (HME) and thecubic-quintic modelocking equation (CQME). The HME corresponds to a speciallimit of the CQME in which only a cubic nonlinearity in the fast saturableabsorber is kept in the model. Here, we use singular perturbation theory todemonstrate that the CQME has a stable high-energy solution for an arbitrarilysmall but non-zero quintic contribution to the fast saturable absorber. As aconsequence, we find that the CQME predicts the existence of stable modelockedpulses when the cubic nonlinearity is orders of magnitude larger than the valueat which the HME predicts that modelocked pulses become unstable. Thisintrinsically larger stability range is consistent with experiments. Ourresults suggest a possible path to obtain high-energy and ultrashort pulses byfine tuning the higher-order nonlinear terms in the fast saturable absorber.

Nonlinear Stabilization of High-Energy and Ultrashort Pulses in Passively Modelocked Lasers with Fast Saturable Absorption