Dissipative light bullets: From stationary light bullets to double, quadruple, sixfold, eightfold and tenfold bullet complexes

Abstract

In this work, we analyze stabilization of three dimensional spatiotemporal solitons (“dissipative light bullets”) in highly nonlinear doped Kerr media with higher-order dispersion terms. The analytical approach based on variational analysis and numerical simulations shows that dissipative light bullets can be formed for a large range of parameters and can be stabilized under certain conditions. A set of evolution equations and expression for potential function have been derived using variational method. The fixed points are investigated by the means of Lyapunov’s method. We have highlighted the evolution of physical parameters (amplitude, widths, chirps and phase) of the dissipative optical bullets and analyzed their dynamics. A potential well has been generated into a single point due to the exact balance between repulsive and attractive potentials, justifying the stability of the fixed point. As a result, stable and robust dissipative light bullets are formed during a self-organizing propagation due to the cross compensation of various linear and nonlinear effects. Among them, we have stationary dissipative light bullets, bounded by the well known double and quadruple bullet complexes, and the new rich variety of bullet complexes like sixfold, eightfold and tenfold, respectively.Using the natural control parameter of the solution as it evolves, named the total energy Q, we have shown by numerical simulations that, as soon as we evolve from two to ten bullet complexes, the total energy increases considerably and that, for localized solutions with an symmetric initial condition, the energy increases but remains finite and converges to a constant value when a stationary solution is reached. Furthermore, It has been demonstrated in this work that, using an elliptic initial condition, solutions may be stable or unstable.