Laser autosolitons: Bifurcation analysis, stability and interactions
N.N. Rosanov 
, S.V. Fedorov , G.V. Khodova and A.G. Vladimirov 
Institute of Laser Physics,
Research Center "S.I. Vavilov State Optical Institute"
S. Petersburg, Russia
Research Institute of Physics, S. Petersburg State University
S. Petersburg, Russia
Localized structures of light in nonlinear-optical passive and active (laser) systems are an object of numerous investigations because of their scientific interest and high potential for different applications [1-3]. Especially rich is variety of localized optical structures, so called "optical autosolitons", in dissipative systems under conditions of bistability. For lasers, bistability may be realized when saturable absorber is inserted inside the laser cavity; in the case of wide-aperture laser such localized structures - "laser autosolitons" - were predicted and investigated in [4,5]. In this paper we review the recent studies of spatial and spatio-temporal laser autosolitons with different geometrical dimensionality D=1 (a planar waveguide configuration), 2 and 3 ("laser bullets" in active nonlinear media with frequency dispersion) and present some new results of the autosolitons' investigations.
In general, the autosolitons are described by nonlinear partial differential equations of Ginzburg-Landau type. For stationary autosolitons, reduction to a set of ordinary differential equation is possible. For the 1D stationary laser autosolitons, we give bifurcation analysis and classification of autosolitons on the base of study of these equations' fixed points and heteroclinic trajectories that join these points. Different types of single and multiple autosolitons are demonstrated, and the intervals of their stability have been found. With increasing of pump, the stationary autosolitons lose their stability transforming into nonstationary (pulsing) autosolitons. A simlpified description is given of the autosoliton's interaction with the scheme inhomogeneities and of interaction of different autosolitons.
For laser autosolitons of the higher dimensionality, we present an approximate approach based on their average description and results of their computer simulations. In the case D=2, there are stable stationary laser autosolitons with axially-symmetric intensity distribution and different values of the topological index 0, 1, 2, ... (i.e., with the wavefront dislocations of different order). We demonstrate a good agreement in their characteristics obtained from the approximate approach and by computer simulations. Besides, there are stable 2D-autosolitons with asymmetric intensity profile rotating with constant angular velocity. Regimes of weak and strong interactions of the 2D-laser autosolitons are presented. We give also results of the approximate treatment of the fundamental laser bullets and discuss potential applications of these localized structures.