Nonlinear dynamics in semiconductor ring lasers with negative optoelectronic and incoherent optical feedback

In this work, we study theoretically the dynamical behavior of two semiconductor ring lasers (SRLs). One is subject to negative optoelectronic feedback and the other laser is subject to incoherent optical feedback. Relying on asymptotic methods, we are able to reduce the original set of five equations used to describe the dynamical behavior of SRLs with negative optoelectronic feedback (SRL-NOEF) or incoherent optical feedback (SRL-IOF) to two equations and one map with time delay valid on time-scales longer than the relaxation oscillations (ROs). The equations of the reduced models turn out to be the same for both systems. As we vary the feedback strength, the devices under consideration in this work display both continuous wave operation and a period-doubling route to chaos. The two counter-propagating intensities of both systems exhibit in-phase chaotic behavior for small delay times comparable to the period of relaxation oscillations. For delay times significantly longer than the period of ROs, the two counter-propagating modes show in anti-phase chaotic oscillations. Moreover, for long delay times, we find that the counter-propagating intensities of both systems depict the same dynamical behaviors when their feedback strengths are increased.