THEORY OF LASER-DIODES WITH WEAK OPTICAL FEEDBACK .2. LIMIT-CYCLE BEHAVIOR, QUASI-PERIODICITY, FREQUENCY LOCKING, AND ROUTE TO CHAOS

The nonlinear behavior of the deterministic equations that describe the optical feedback system is investigated. An analytic expression for the amplitude of the self-pulsations that occur when the relaxation oscillations (RO's) become undamped is derived and compared with numerical results. For small amplitudes a square-root law, which is typical for Hopf bifurcations, is found. For increased feedback levels a second Hopf bifurcation occurs, and a frequency related to the second type of RO predicted by the small-signal analysis of part I [J. Opt. Soc. Am. B 10, 130 (1993)] emerges. Frequency-locked and quasi-periodic solutions arise. The occurrence of a third frequency is a precursor of chaotic motion. The transition to chaos is determined by a switching between two unstable attractors.