Stochastic dynamics of a semiconductor laser with delayed optoelectronic feedback and noise

Semiconductor lasers(SLs), versatile tools in communication, medicine, and scientific research, demand close examination of their dynamic behavior. With their unique geometric forms and diminutive sizes, these lasers possess a heightened sensitivity to noise. In this paper, we delve into time-delay semiconductor laser systems, noise included, honing in on time-delays' effects on noisy laser equations. Carrier density (N) and laser intensity (I) constitute the core parameters that define the performance of these lasers, and we scrutinize their dynamic trajectories. A cutting-edge method fusing stochastic center manifold theory with the stochastic averaging method enables us to probe the stochastic dynamical attributes of semiconductor laser equations. We uncover that the time-delay parameter (tau 1) produces varied consequences on the laser system's stability under both positive and negative optical feedback conditions. The negative feedback typically bolsters laser performance, fostering increased stability, whereas the positive counterpart could incite instability. By deftly managing the time-delay parameter, one can fine-tune the dynamic performance of semiconductor lasers, mitigating output power fluctuations and tightening linewidths, thereby augmenting stability and spectral purity. Moreover, in the realm of positive optical feedback scenarios, adroitly modifying the time-delay parameter can quell instability to a degree, paving the way for a novel regulatory approach to optimize laser performance. This lays the groundwork for further enhancement of semiconductor laser performance, as well as curbing the detrimental effects of noise on their operation.