Space-time and space-averaged equations for a two-mirror laser: theory and numerical results

A theoretical model is considered for an unsteady three-level (single-mode) laser. By use of the rotating wave approximation, the usual semiclassical equations are transformed into a system of first-order space-time (ST) equations. The space oscillations of the population difference (hole-burning effects) and the motion of the atoms are included in the treatment. After the introduction of several assumptions, the ST equations are transformed to a set of time-dependent space-averaged (SA) equations. The numerical calculations were performed for a pulsed two-mirror laser with a finite phase memory decay constant and for resonance and nonresonance frequencies. The calculations show that the SA equations give almost the same results as the much more complicated ST equations.