Regular and stochastic self-modulation of radiation in a ring laser with a nonlinear element

It is shown that a ring laser with a second-harmonic generator can double the number of stable states, resulting in self-modulation of the radiation. The system is described by a one-dimensional mapping that can be used to trace analytically the transition to stochasticity and to make universal calculations of those values of the bifurcation parameter at which the character of the selfmodulation changes.