Semiconductor lasers under external perturbations can manifest a broad variety of complex dynamics in their output power, from periodicity to high dimensional chaos. One of their characteristic behaviors, when submitted to optical feedback, is their excitability. These optical excitable devices, that mimic neuronal behavior, can serve as building-blocks for novel, brain-inspired information processing systems. Neuronal systems represent and process the information of a weak external input through correlated electrical spikes. Semiconductor lasers with low to moderate optical feedback, i.e. in the low frequency fluctuations (LFF) regime, display optical spikes with intrinsic temporal correlations, similar to those of biological neurons. Here we study the laser optical spiking dynamics under the influence of direct pump current modulation, focusing on the influence of the modulation frequency and amplitude. We characterize time correlations in the sequence of optical spikes by using symbolic ordinal analysis. This powerful tool allows detecting symbolic patterns in the laser output, and to quantify the effect of the frequency and amplitude of the modulation on the patterns probabilities. The experimental results are in good qualitative agreement with simulations of the Lang and Kobayashi model.
We investigate the symbolic dynamics of an excitable optical system under periodic forcing. Particularly, we consider the low-frequency fluctuation (LFF) dynamics of a semiconductor laser with periodically-modulated injection current and optical feedback. We use a method of symbolic time-series analysis that allows us to unveil serial correlations in the sequence of intensity dropouts. By transforming the sequence of inter-dropout intervals into a sequence of ordinal patterns and analyzing the statistics of the patterns, we uncover correlations among several consecutive dropouts and we identify definite changes in the dynamics as the modulation amplitude increases. We confirm the robustness of the observations by conducting the experiments with two different lasers under different feedback conditions. The results are also shown to be robust to variations of the threshold used for detecting the dropouts. Simulations of the Lang-Kobayashi (LK) model, including spontaneous emission noise, are found to be in good qualitative agreement with the observations, providing an interpretation of the correlations present in the dropout sequence as due to the interplay of the underlying attractor topology, the periodic forcing, and the noise that sustains the dropout events.
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