Stability analysis of cavity solitons governed by the cubic-quintic Ginzburg-Landau equation

A theoretical model is proposed to describe the formation of two-dimensional solitons in a laser cavity, extending the concept of the mode locking of temporal solitons in fibre lasers to spatial mode locking in nonlinear crystals. A linear stability analysis of the governing model based upon radial symmetry is performed to characterize the multi-pulsing instability of the laser as a function of gain. It is found that a stable n-pulse solution of the system bifurcates into a (n + 1)-pulse solution through the development of a periodic solution (Hopf bifurcation), and the results are consistent with simulations of the full model.