Self-pulsing in a Laser Model with Discrete Gain and Loss

A new model of a multimode homogeneously broadened unidirectional ring cavity laser is presented. Gain and loss are modelled as discrete elements taking the form of a thin laser medium of negligible extent and a partially reflecting mirror forming a cavity with a finite round-trip time. In this way, an exact analytic solution to the stability problem of the c.w. state can be obtained. It is shown that a second threshold exists for any mirror transmissivity and, when using a semitransparent mirror, that it can be reached by pumping seven times above laser threshold. Numerical solutions are presented, including periodic, quasi-periodic and chaotic oscillations. Well known mean-field limit self-pulsations are here predicted for any mirror transmissivity and suitable pump parameter, and are shown to be particular cases of a more general class of instabilities involving excitation of one or more cavity modes by Rabi frequency modulation; the resulting dynamics reflect a complex interaction among the excited modes and the Rabi frequency modulation. The present model predicts, in particular, transition to chaos from a frequency locked limit cycle or from a two-dimensional torus.