Phenomenological theory of damped and undamped intensity oscillations in lasers

The usual phenomenological laser rate equations for the population inversion and the light intensity (Statz-deMars equations) are generalized to take into account intensity-dependent losses and Einstein coefficients. Sufficient conditions are given for these generalized equations in order to have only physically admissible solutions. The solutions either tend towards an equilibrium value in an aperiodic or oscillatory way or display an undamped periodic behavior. The theory is applied to the three-level laser and the four-level laser, without and with a saturable absorber asQ-switch. The applicability of the theory to various problems is discussed.