Nonlinear dynamics of laser systems with a delay

A review is given of the work done on the nonlinear dynamics of laser systems with a delayed feedback loop when the transit time along this loop is comparable with or greater than the time constants representing the changes in the main characteristics of the system. An analysis is made of the delay in the feedback loop responsible for the lasing process itself, and also in an external feedback loop which controls one of the laser parameters. Differential–difference equations describing the lasing dynamics are formulated. The evolution of the dynamics with the change in the delay time is studied. The mechanisms and the conditions of formation of periodic pulses with different structures are determined. Asymptotic characteristics (profile, amplitude, and period) of regular regimes and the dependences of their characteristics on the delay are found. The phenomenon of multistability is demonstrated. It is shown that a hysteresis of the period, amplitude, and structure of pulses may be observed. The ways by which transitions of the dynamics to chaos take place are identified.