Coexisting periodic attractors under the influence of noise in injected photonic oscillators

Abstract

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.