Impact of feedback time-distribution on laser dynamics

Time-distributed optical feedback in semiconductor lasers has gained attention for its ability to produce high-quality chaos and effectively suppress the time-delay signature. However, the fundamental impact of the distribution of feedback in time on laser dynamics remains unexplored. In this paper, we investigate this topic by using fiber Bragg grating (FBG) feedback. We theoretically study the laser response using FBGs of different lengths but similar reflectivity, effectively stretching the impulse response over a longer period while maintaining its overall shape. We observe that above a critical value corresponding to a grating length of approximately $1$\,cm, fluctuations in laser stability emerge. We attribute this phenomenon to the damping of relaxation oscillations when the zeros of the FBG reflectivity spectrum align with the laser side lobes around the relaxation oscillation frequency. We also uncover an asymmetrical dynamical behavior of the laser for positive and negative frequency detuning. We deduce that this asymmetry is a characteristic feature of FBG feedback and delve into the specificities that trigger such behavior.