Nonlinear stabilization of high-energy and ultrashort pulses in passively modelocked lasers

The two most commonly used models for passively modelocked lasers with fast saturable absorbers are the Haus modelocking equation (HME) and the cubic-quintic modelocking equation (CQME). The HME predicts an instability threshold that is unrealistically pessimistic. We use singular perturbation theory to demonstrate that the CQME has a stable high-energy solution for an arbitrarily small but nonzero quintic contribution to the fast saturable absorber. As a consequence, we find that the CQME predicts the existence of stable modelocked pulses when the cubic nonlinearity is orders of magnitude larger than the value at which the HME predicts that modelocked pulses become unstable. Our results suggest a possible path to obtain high-energy and ultrashort pulses by fine tuning the higher-order nonlinear terms in the fast saturable absorber.