Stochastic and Deterministic Dynamics in a Semiconductor Laser with Optical Feedback

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Semiconductor lasers have been widely utilized in optical communications and optical data storage. However, in many important applications a small amount of the output light may be reflected back into the laser cavity resulting in large intensity fluctuations and a broadened laser linewidth. Here we experimentally and numerically characterize the subtle influence that spontaneous emission in the laser cavity has on shaping the instabilities produced by the time-delayed optical feedback from external reflections.

In the first experiment, we estimate the relative role played by deterministic and stochastic influences in the semiconductor laser at high injection currents under the influence of reflective feedback over a large range of feedback strengths. An empirical mode decomposition method is utilized to provide a physically significant definition of the Hilbert phase. Hurst exponent measurements of the Hilbert phase fluctuations show a clear transition from regular Brownian motion to fractional Brownian motion as the amplitude of coherent feedback is incremented in the experiment and model equations.

At lower injection currents noise is believed to play a much more crucial role in the intensity dropout dynamics witnessed by the system. In a second experiment we adapt a methodology commonly used to evaluated escape phenomena in the theory of large fluctuations to elicit deterministic features shared by many dropouts in an experimental an simulated intensity time series. The optimal path of dropout derived from this analysis demonstrates epochs both before and after the dropout where the system dynamics exhibits a chaotic itinerancy between external cavity lasing modes supported by the system.

Finally, we numerically investigate the role of additive noise in the selection of a chaotic instability supported by the semiconductor laser with time-delayed optical feedback for different parameter settings. We find that a single instability is preferred by the system over a larger region of the parameter space as the amplitude of the noise term is increased in the model equations. An experimental characterization of this stability region serves as a sensitive indicator of the amount of Langevin noise relevant in numerically describing stochastic influences present in the evolution of the light dynamics.