Chaotic and periodic emission of high power solid state lasers

Nonlinear, dynamical systems even with a few degrees of freedom may show chaotic or periodic behaviour, depending on the parameters of the system. Recently it was demonstrated, both experimentally and theoretically, that the temporal emission of a laser can become chaotic, if several longitudinal modes oscillate [Brunner and Paul (1983), and Abraham et al. (1982)]. The chaotic emission is caused by the nonlinear interaction of the modes and the longitudinal gain structure [Komtomtseva et al. (1982)]. In this paper it is pointed out that the transverse mode structure and the radial gain profile produced by the transversal modes, may give rise to temporal instabilities of the laser emission. If the relevant parameters of the laser oscillator — Fresnel number, resonator losses, pump rate — exceed certain critical values, the output intensity becomes unstable. The damped relaxation oscillation changes into undamped periodic oscillation or, with increasing values of the above parameters, into chaotic emission. The theory, using the nonlinear Kirchhoff-Fresnel integral equation and the rate equation approach, is confirmed by experimental results.