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

A 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.

Figure 1

Bifurcation diagram for $\gamma \in [0,0.07]$. The extrema of the time series of the optical power vs the normalized feedback rate are shown.

Figure 2

Time series of output power (1.a) and phase-space trajectory (1.b) for $\gamma =0.028795$. Time series (2.a) is an enlargement of the boxed part, with (2.b) being its trajectory. In (1.b) and (2.b) the ellipse is the trajectory of the stable ECM about to appear.

Figure 3

Bifurcation diagram obtained by the simulation and continuation method. The simulation result is in black, and the continuation result is in orange (gray). The stable part of the branch is a thick line, while the unstable part is a thin line. Squares (circles) are saddle-node (torus) bifurcations.

Figure 4

(a) Bifurcation diagram for increasing (top line) and decreasing feedback (bottom line) plotted on the same scale but shifted vertically for clarity. (b) The frequency of the periodic solutions (stable part only) obtained by continuation vs the normalized feedback rate. Dashed vertical lines bound the bistability regions.

Figure 5

(a) and (b) Two time series of the light output power available for a normalized feedback rate of $\gamma =0.0611$ and (c) and (d) the corresponding optical spectra.