Tori and their bifurcations in an optically injected semiconductor laser

We show that there is motion on a torus in the single-mode rate equations of a diode laser subject to weak optical injection. It occurs in the transition from relaxation oscillations to unlocked dynamics and corresponds to a relaxation oscillation whose amplitude is modulated. The stability of the torus depends on the linewidth-enhancement factor a. The case of an unstable torus gives rise to bistability, resulting in hysteresis when the detuning of the input signal is varied for suitable injection strength. We present the relevant dynamics by several panels, including phase plots, the time series of the power, and the field spectrum. (C) 1998 Elsevier Science B.V. All rights reserved.