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

Abstract

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.

Delayed dynamical systems: networks, chimeras and reservoir computing

“…For example, in a semiconductor laser with time-delayed feedback through an external mirror, the photon lifetime is significantly shorter than the feedback time, which can cause the laser intensity to oscillate chaotically [9]. From an experimental point of view, delay systems are particularly attractive because the complexity of the dynamics usually increases with the delay [10][11][12], which is typically easy to control.…”

Complex dynamics and synchronization of delayed-feedback nonlinear oscillators

“…The question of isochronal synchronization of these nonlinear oscillators (Fischer et al 2006;Klein et al 2006;Rogers-Dakin et al 2006;Schwartz & Shaw 2007;Zhou & Roy 2007;Franz et al 2008) is central to possible applications in sensor networks (Sorrentino & Ott 2008, 2009a. We thus consider coupled oscillators in §4, where the many different configurations, in which even two oscillators may be coupled, are outlined.…”

Mathematical models of light waves in Brillouin-scattering fiber-optic gyroscope resonator

“…Pump light from the laser enters the fiber resonator through the fiber coupler, and an increase in the optical power induces first-order Stokes light waves, B 1 and B 2 , that propagate in a direction opposite to that of the pump light P 1 and P 2 . Both the Sagnac effect in the BFOG and changes to the resonant frequency will produce a difference in the resonance frequencies of B 1 and B 2 [9,10], which results in interference, and the interference signal is processed by the detection circuit. As the power of the pump light exceeds the Brillouin scattering threshold power, an increase in the pump power will result in an increase in the power of the first-order Stokes light [5,7] and stimulate the production of second-and higher-order Stokes light waves.…”