Effect of multiple time delays on intensity fluctuation dynamics in fiber ring lasers.

The effect of time delay on nonlinear oscillators is an important problem in the study of dynamical systems. The dynamics of an erbium-doped fiber ring laser with an extra loop providing time-delayed feedback is studied experimentally by measuring the intensity of the laser. The delay time for the feedback is varied from approximately 0.3 to approximately 900 times the cavity round-trip time, over four orders of magnitude, by changing the length of fiber in the delay line. Depending on the delay, we observe either regular oscillations or complex dynamics. The size of the fluctuations increases for delays long compared with the round-trip time of the laser cavity. The complexity of the fluctuations is quantified by creating spatiotemporal representations of the time series and performing a Karhunen-Loève decomposition. The complexity increases with increasing delay time. The experiment is extended by mutually coupling two fiber ring lasers together. The delay time for the mutual coupling is varied from approximately 0.2 to approximately 600 times the cavity round-trip time, over four orders of magnitude again. In this case the fluctuations are generally larger than the single laser case. The complexity of the dynamics for the mutually coupled system is less at short delays and larger at long delays when compared to the uncoupled case. The width of the optical spectra of the coupled lasers also narrows.