Impact of High-Order Effects on Soliton Explosions in the Complex Cubic-Quintic Ginzburg-Landau Equation

Soliton explosions are one of the most striking phenomena observed in mode-locked lasers. They were first predicted theoretically in a one-dimensional complex cubic-quintic Ginzburg-Landau equation (CQGLE) [1] in the case of anomalous linear dispersion and then were verified experimentally in a Kerr lens mode-locked Ti:sapphire laser [2], In this regime, a localized pulse circulating in the cavity experiences an abrupt structural collapse at certain points of the time evolution subsequently recovering its original shape. The experimentally observed explosions are similar but not identical to each other and the times between them appear to be randomly distributed. Among other reported features is the existence of symmetric and asymmetric explosions in a wide range of system parameters. Exploding solitary pulses have been recently observed in an all-normal-dispersion Yb-doped mode-locked fiber laser operated in a transition regime between stable and noise-like emission [3] and the experimental results have been successfully compared with realistic numerical simulations based on a model of complex pulse propagation in optical fibers. In [4], the connection of this model with the CQGLE with additional higher-order nonlinear and dispersive effects (HOEs) was established and the existence of periodic one-side explosions was reported. However, despite significant theoretical interest (see e.g. [5]), the impact of HOEs on the dynamics of a localized pulses and on the onset of soliton explosions have not been extensively studied so far.