Nonconservation of Topological Charge and Cusps in a One-Dimensional Laser Scheme.

An analysis was made of the field structures in a coaxial laser with fast saturable absorption. In such an efficiently one-dimensional scheme, the integer topological index (charge) naturally arises: the phase incursion of the field envelope when bypassing the aperture, divided by $2\ensuremath{\pi}$. The topological charge is the winding number for the phase curve introduced for the electric field envelope with increase of the coordinate for fixed time. In the framework of the generalized Ginzburg-Landau equation, shown are finite numbers of plane-wave modes, stable with respect to weak perturbations, and solitonlike modes with inhomogeneous intensity distributions and different topological charge. It was found that the topological charge could change during transient to steady state. The events of these changes alternate with formation of cusps of the phase curve occurring when extrema of the field intensity and phase coincide.