General adiabatic elimination procedure for lasers with slow relaxation of population inversion

An improved adiabatic elimination procedure, based on center manifold theory, is used to determine a two-dimensional flow which describes a large class of lasers characterized by slow relaxation of the population inversion. A detailed analysis of this model shows a) a quasi-conservative motion in a Toda potential, b) Haken second threshold for the expected parameter values, c) undamped oscillations in agreement with the Lorenz equations and d) a more accurate description of the relaxation processes than the usual rate equations. The relevance of the model to experiments is also briefly discussed. © 1986 SPIE.