  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.
