Scaling Behavior of Laser Population Dynamics with Time-Delayed Coupling: Theory and Experiment

Abstract

We study the influence of asymmetric coupling strengths on the onset of light intensity oscillations in an experimental system consisting of two semiconductor lasers cross coupled optoelectronically with a time delay. We discover a scaling law that relates the amplitudes of oscillations and the coupling strengths. These observations are in agreement with a theoretical model. These results could be applicable to the population dynamics of other systems, such as the spread of disease in human populations coupled by migration.

Amplitude death: The emergence of stationarity in coupled nonlinear systems

“…A related experimental study of chaos control in lasers by Bielawski et al [132] stabilizes the unstable steady state of a fiber two-level class B laser. Delayed coupling with delayed feedback has been shown to induce AD in a laser system [133], and Roy and coworkers [16,17] have experimentally verified a number of issues in the dynamics of coupled systems, including amplitude death.…”

“…Indeed it would not be possible to couple two lasers through their intensity fluctuations directly. As it happens, in a model of the semiconductor laser, the current and the fluctuations are, in a sense, conjugate variables that have constitute the chaotic oscillator system [16,17]. The largest three Lyapunov exponents for the above system is shown in Fig.…”

“…Coupling via conjugate variables is natural in a variety of experimental situations, and indeed the above system was inspired by the experiments of Kim and Roy [16,17] on coupled semiconductor laser systems where the photon intensity fluctuations from one laser were used to modulate the injection current of a second identical laser and vice versa. Indeed it would not be possible to couple two lasers through their intensity fluctuations directly.…”

“…2. In many practical situations AD, is desirable, as for example in laser applications [16,17,18,19,20,21] where a constant output is needed and fluctuations should be suppressed. There are also other situations where oscillations need to be maintained, as for instance in brain functioning [22,23].…”

Isochronal synchronization of delay-coupled systems

“…Incoherent delay-coupled semiconductor systems [18], and 2. Coupled spatio-temporal systems consisting of coupled fiber ring lasers [19] with delay [20].…”