Recently, the existence of robust three-dimensional light bullets (LBs) waspredicted theoretically in the output of a laser coupled to a distant saturableabsorber. In this manuscript, we analyze the stability and the range ofexistence of these dissipative localized structures and provide guidelines andrealistic parameter sets for their experimental observation. In order to reducethe complexity of the analysis, we first approximate the three-dimensionalproblem by a reduced equation governing the dynamics of the transverse profile.This effective theory provides an intuitive picture of the LB formationmechanism. Moreover, it allows us to perform a detailed multi-parameterbifurcation study and to identify the different mechanisms of instability. Itis found that the LBs experience dominantly either homogeneous oscillation orsymmetry breaking transversal waves radiation. In addition, our analysisreveals several non-intuitive scaling behaviors as functions of the linewidthenhancement factors and the saturation parameters. Our results are confirmed bydirect numerical simulations of the full system.
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