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We analyze the effect of optical feedback on the dynamics of a passively mode-locked ring laser operating in the regime of temporal localized structures. This laser system is modeled by a system of delay differential equations, which include delay terms associated with the laser cavity and the feedback loop.
Using a combination of direct numerical simulations and path-continuation techniques, we show that the feedback loop creates echos of the main pulse whose position and size strongly depend on the feedback parameters. We demonstrate that in the long-cavity regime, these echos can successively replace the main pulses, which defines their lifetime. This pulse instability mechanism originates from a global bifurcation of the saddle-node infinite-period type. In addition, we show that, under the influence of noise, the stable pulses exhibit forms of behavior characteristic of excitable systems.
Furthermore, for the harmonic solutions consisting of multiple equispaced pulses per round-trip we show that if the location of the pulses coincide with the echo of another, the range of stability of these solutions is increased. Finally, it is shown that around these resonances, branches of different solutions are connected by period doubling bifurcations. These solutions have also been studied experimentally. For the experimental realization, the gain medium consisting in 6 quantum wells embedded between a bottom totally reflective Bragg mirror and a top partially reflective Bragg mirror (1⁄2VCSEL) was considered; the 1⁄2VCSEL was then placed in an external cavity that was closed by a fast semiconductor saturable absorber mirror (SESAM) to operate the laser in the passive mode-locked regime. In particular, it was shown both, experimentally and theoretically, that the output of specific solutions can be favored by choosing certain ratios between the fundamental round-trip time and the delay time.
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