Lyapunov-potential description for laser dynamics

We describe the dynamical behavior of both class A and class B lasers in te rms of a Lyapunov potential. For class A lasers we use the potential to ana lyze both deterministic and stochastic dynamics. In the stochastic case it is found that the phase of the electric field drifts with time in the stead y state. For class B lasers, the potential obtained is valid in the absence of noise. In this case, a general expression relating the period of the re laxation oscillations to the potential is found. We have included in this e xpression the terms corresponding to the gain saturation and the mean value of the spontaneously emitted power, which were not considered previously. The validity of this expression is also discussed and a semiempirical relat ion giving the period of the relaxation oscillations far from the stationar y state is proposed and checked against numerical simulations. [S1050-2947( 99)02906-6].