НЕОБРАТИМЫЙ ГИСТЕРЕЗИС ТРЕХМЕРНЫХ ТОПОЛОГИЧЕСКИХ ЗАПУТАННЫХ ЛАЗЕРНЫХ СОЛИТОНОВ

Abstract

In a laser medium with saturable amplification and absorption or in a laser with such a medium and a sufficiently large cavity length, the authors previously demonstrated a class of dissipative three-dimensional topological solitons (Veretenov et al., 2016, 2017). Such solitons have “skeletons” – a set of several closed and unclosed vortex lines, on which the field turns to 0 and the phase of which bypass is incremented by a multiple of 2π. It is significant that the regions of the scheme parameters in which different types of topological solitons exist and are stable, overlap. Accordingly, the question arises about the nature of changes in the structure of solitons and their skeletons with a slow change in the parameters. The answer to this question, mainly in the framework of numerical modeling, is the subject of this report. The initial equation is the generalized Ginzburg-Landau complex equation for a slowly varying envelope of the field, with the longitudinal coordinate along the path of preferential propagation z (Veretenov et al., 2017) serving as an evolution variable. The control parameter is the coefficient of linear (unsaturated) field gain g0. The initial value of this parameter corresponds to the central part of the stability region of the original soliton (for definiteness, the “Solomon soliton”). Then g0 slowly increases, crossing the stability boundary, after which it stabilizes and slowly decreases, eventually returning to its original value. We demonstrate that as a result of such a hysteresis cycle, the soliton does not return to the initial one — its structure is drastically simplified. This is reflected in a decrease in the values of various topological indices, as well as in a decrease in the field energy and an increase in the energy of the active medium (minus its constant background). At the g0 reduction stage, the topological characteristics do not change (two “soliton-apples”). The transient process includes a series of elementary reactions of reconnection of the vortex lines and detachment of closed loops after a strong bend of the “parent” vortex line. In addition, during the transition process, a number of new types of localized topological metastable structures arise. The analytical part of the research was supported by the RAS Presidium Program “Nonlinear Dynamics: Fundamental Problems and Applications”. Numerical modeling was carried out with the support of the grant of the RNF 18-12-00075.