Stochastic-dynamics characterization of delayed laser threshold instability with swept control parameter

A dynamical bifurcation in which the control parameter is continuously swept through the bifurcation point is characterized in terms of a first-passage-time distribution. The generating function associated with this distribution is calculated in the cases of slow and fast sweeping rates. Our results are compared with experimental findings in an Ar laser with time-dependent cavity losses and with earlier numerical and analogical simulation results. The meaning of a delayed bifurcation in the stochastic framework presented here is elaborated.