  The optical power spectrum is the prime observable to dissect, understand and
design the long-time behavior of arrays of optically coupled semiconductor
lasers. A long-standing issue has been identified within the literature on
injection locking: how the thickness of linewidth and the lineshape waveform
envelope correlates with the deterministic evolution of the slave laser
oscillator and how the presence of noise and the dense proximity of coexisting
limit cycles are shaping and influencing the overall spectral behavior. In
addition we are critically interested in the regions where the basin of
attraction has self-similar and fractal-like behavior, still, the long-time
orbits are limit cycles, in this case, period-one (P1) and period-three (P3).
Via numerical work, we find that the overall optical power spectrum is deeply
imprinted with a strong influence from the underlying noise when the system
lives in the region of the P1 and P3 limit cycles. Additionally, a qualitative
comparison is made between the stochastic Langevin simulations and the recorded
optical power spectra taken from older experiments that we revisit. Finally, we
point to a possible set of next-generation applications in photonics and
quantum technologies where such findings may have substantial implications.
