Abstract

Semiconductor lasers subject to delayed optical feedback from external reflectors and operating close to threshold exhibit complex output oscillations characterized by sudden intensity drops (low frequency fluctuations or LFF). LFF is often described as a dynamical regime consisting of many unstable external cavity modes (ECMs). But recent experimental and numerical studies suggest that LFF may already appear for a low number of ECMs [1]. As the feedback rate increases from zero, each ECM sequentially appears, undergoes a Hopf bifurcation followed by more complicated bifurcations until transient or sustained LFF is observed. Using a new continuation method specially designed for delay-differential equations, we have found that successive ECMs are connected by closed branches of periodic solutions See figure Bifurcation diagram of the ECMs and three Hopf bifurcation branches The figure represents the maximum of the modulus of the electrical field vs the feedback rate η Same equations and same values of the parameters as in [1]. Square dots indicate Hopf bifurcation points. Stable and unstable ECM branches of solutions are represented by full and dashed lines, respectively Successive branches of periodic solutions are connecting one stable and one unstable Hopf points. They change stability at torus bifurcation points (not shown in the figure)

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