Theory of stability and bifurcation in a multi-quantum well laser with opto-electronic delayed feedback

This paper presents an opto-electronic feedback multi-quantum well laser system and outlines our study of the dynamics and bifurcation in a multi-quantum well laser due to the opto-electronic delayed feedback effect. We point out theoretically the conditions of stability and Hopf bifurcation of the laser. The relaxation oscillation frequency of the system is educed to be the function of the feedback level, delayed time and in-current. The route from stability to bifurcation is numerically simulated via varying the delayed time, feedback strength and in-current. The results show that the induced dynamics can be grouped into four distinct types or modes (stable, periodic pulsed, undamped oscillating or beating, and chaos), where the frequency and intensity varying with the delayed time in the two periodic regions are analyzed detailedly to find that the pulsing frequency is reduced with the long delayed time while the pulsing intensity is added with the long delayed time. And the chaotic pulsing frequency is increased with the large in-current. In addition, the carrier transport between the barrier region and the active region can characterize the dynamics in the laser to produce stable, periodic pulsed, beating and chaotic states by altering the carriers transport or escape rate value.

► The dynamics and stability in a multi-quantum well laser is investigated when an opto-electronic feedback presents. ► The characteristic of oscillation frequency, the condition of stability and Hopf bifurcation of the system are analyzed. ► The route from stability to bifurcation is numerically calculated by varying the delayed time, feedback strength and in-current. ► There are four distinct types of dynamics including stable, periodic pulsed, undamped oscillating or beating, and chaos in the system. ► The pulsing frequency and the chaotic pulsing frequency are analyzed.