Elimination of chaos in multimode, intracavity-doubled lasers in the presence of spatial hole-burning

In this paper possibilities of a stabilization of large amplitude fluctuati ons in an intracavity-doubled solid-state laser are studied. The modificati on of the cross-saturation coefficient by the effect of spatial hole-burnin g is taken into account. The stabilization of the laser radiation by an inc rease of the number of modes, as proposed in [James et al., 1990b; Magni et al., 1993], is analyzed. It is found that when the cross-saturation coeffi cient is modulated by the spatial hole-burning the stabilization is not alw ays possible. We propose a new way of obtaining a stable steady-state confi guration based on an increase of the strength of nonlinearity, which leads to a strong cancellation of modes, so that during the evolution all modes, but for a single one, are canceled. Such a steady-state solution is found t o be stable with respect to small perturbations.