Abstract
A class-A laser with square pump profile, assumed to be operating on the three modes of the Gauss-Hermite family m + n = 2, shows in the control parameters plane domains of spatial mono-, bi-, tetra- and esa-stability. The analysis of the laser generalized free energy during the laser switch-on dynamics allows to determine the bifurcation tree of the stable states and their basins of attraction. We define a similarity parameter between two arbitrary transverse field configurations and identify the conditions under which this parameter exactly predicts the final stationary configuration to which the system evolves starting from any given initial condition. An example demonstrates the reliability of the similarity parameter in a case of spatial tetrastability.
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