Complex intermittent dynamics in large-aspect-ratio homogeneously broadened single-mode lasers
The paper reports results of numerical simulations of a model of an one-dimensional laser cavity described by a system of the Maxwell-Bloch equations for three variables: population inversion, medium polarization, and electric field. The simulated regimes correspond to a large-Fresnel-number regime, when the dynamics is controlled by the nonlinearity and diffraction, rather than boundary conditions. The simulations are performed above the second laser threshold, where the uniform plane-wave states, which appear above the first laser threshold, become unstable. The observed dynamics is very different in cases of negative and positive detuning \(\delta\) of the electromagnetic field in the cavity mode relative to the atomic intrinsic-transition frequency in the Maxwell-Bloch equations. In the case of \(\delta < 0\), the dynamics is regular, being characterized by quasi-periodic oscillations (with two basic frequencies); the respective first-return Poincaré map displays a simple pattern in the form of a closed loop. In the case of \(\delta > 0\), the dynamical picture is drastically different, displaying strongly pronounced intermittency. It resembles the known case of the cycling chaos, characterized by random jumps of the effective dynamical trajectory between several unstable closed trajectories of the saddle type. Five such trajectories are identified. While the system moves along any of them, the dynamics is laminar (quite regular and smooth) for an extended period of time; jumps between the trajectories are characterized by sudden bursts of dynamical chaos. A remarkable feature of the reported regime is the fact that the five saddle-loop trajectories are always visited in one and the same order.
scientific article; zbMATH DE number 2175338