Single-longitudinal-mode laser as a discrete dynamical system

A solid-state laser running on a single longitudinal mode can show chaotic time behavior if several transverse modes are excited. The temporal development of the laser is approximated by a Kirchhoff integral together with a rate equation for the inversion. The qualitative structure of the solution of this discrete dynamical system is studied for various values of the pump rate by numerical as well as by analytical methods. With increasing pump rate we find constant, quasi-periodic, and irregular time behavior for the output power.