Theory of laser diodes with weak optical feedback II 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. B10, 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.