Lyapunov method and analysis of the emerging repetitively pulsed regime in semiconductor lasers with delayed feedback

We study the nature of transition from stationary lasing to pulse-periodic oscillations when the phase of the delayed feedback and the diode laser pump current change. The appearance of oscillations can take place under the scenarios of soft or hard excitation of oscillations. We propose a semi-analytical approach to identify the nature of the transition and to determine the dynamic characteristics and stability of the arising spike regime with a change in the external parameters. Direct integration of the Lang — Kobayashi equations showed an acceptable accuracy of this approach.