Chaos crisis and bistability of self-pulsing dynamics in a laser diode with phase-conjugate feedback

Abstract

International audienceA laser diode subject to a phase-conjugate optical feedback can exhibit rich nonlinear dynamics and chaos. We report here on two bifurcation mechanisms that appear when increasing the amount of light being fed back to the laser. First, we report on a full suppression of chaos from a crisis induced by a saddle-node bifurcation on self-pulsing, so-called external-cavity-mode solutions (ECMs). Second, the feedback-dependent torus and saddle-node bifurcations on ECMs may be responsible for large regions of bistability between ECMs of different and high (beyond gigahertz) frequencies

Numerical study of extreme events in a laser diode with phase-conjugate optical feedback

“…For example, except for very low feedback strength, there is no steady-state externalcavity mode (ECM) in the case of PCF. Instead, ECMs are self-pulsating solutions at a frequency being a multiple of Corresponding author: emeric.rnercier@supelec.fr the external-cavity frequency [16,17], These superharmonic self-pulsating solutions have only recently been found in ex periment [18]. As recently shown theoretically [19], secondary bifurcations on these limit-cycle ECM solutions explain the occurrence of LFFs as observed experimentally [20].…”

“…The model we use is a set of rate equations adapted to the case of PCF from the Lang and Kobayashi equations [31] where quantities, including time, are normalized [16,17,19]:…”

Laser diode nonlinear dynamics from a filtered phase-conjugate optical feedback

“…α corresponds to the linewidth enhancement factor, τ is the external cavity round-trip time normalized by the photon lifetime, T is defined as the ratio of the carrier and photon lifetimes, τ r corresponds approximately to the time the light takes to penetrate the PCM normalized by the photon lifetime, P is the pump parameter above threshold, and t is the dimensionless time. In several previous theoretical studies [19,20,29], the following set of parameter values is considered…”

“…In the PCF configuration, ECMs are defined as self-pulsating intensity solutions with a period close to an integer multiple of the external-cavity round-trip time. It has been shown that ECMs emerge from Hopf bifurcations [19,20]. From the ECM limit-cycle solutions, LFFs emerge through secondary bifurcations [23].…”

“…Depending on the feedback strength, steadystate solution [19], external-cavity-modes (ECMs) [19,20], chaos [21], low-frequency fluctuation (LFF) [22,23], extreme events [24], and undamped oscillations with frequency close to the laser relaxation frequency [25] can be observed. Of particular physical interest are the ECMs that have been investigated both theoretically [17,19,20] and experimentally [26]. In the PCF configuration, ECMs are defined as self-pulsating intensity solutions with a period close to an integer multiple of the external-cavity round-trip time.…”