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Temporal correlations and dynamical transitions in semiconductor lasers with Optical feedback

Carlos Quintero-Quiroz, Presentation date: March 16, 2017

Author: Carlos Quintero-Quiroz
Title: Temporal correlations and dynamical transitions in semiconductor lasers with Optical feedback
Director: C. Masoller and M. C. Torrent
Presentation date: March 16, 2017
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Abstract: Optical excitable systems that mimic neuronal behavior have potential to be building-blocks of novel, ultra-fast, neuron-inspired photonic information processing systems. In par- ticular, semiconductor lasers with optical feedback (SLOF), can emit optical spikes with temporal correlations resembling those present in neuronal spike. SLOF can also generate a rich variety of dynamical behaviors, and thus, are ideal testbeds for studying dynamical transitions and testing novel analysis tools. In order to advance in the development of neuron-inspired laser processors it is important to understand how SLOF represent (or encode), in the sequence of spikes, an external input. It is also important to understand how the different dynamic regimes develop, and how they are affected by external perturbations. Hence, the aim of this Thesis is the study of temporal correlations and dynamical transitions in the dynamics of an SLOF. To do this, we perform experiments, model simulations, and use a symbolic method to analyze the obtained intensity time-series. First, we investigate how the spiking laser output encodes a weak periodic input that is implemented via direct modulation of the laser pump current. Experimental sequences of optical spikes were recorded and analyzed by using the ordinal symbolic methodology that identifies and characterizes serial correlations in data sets. When changing the frequency and amplitude of the modulation, transitions among different locking regimes are detected in the form of changes in the statistics of the ordinal patterns. A good qualitative agreement is also found with simulations of the Lang and Kobayashi model. Second, we identify the onset of different dynamical regimes that occur as the laser pump current increases. We apply three analysis tools that allow quantifying various aspects of the dynamical regime transitions. The first method is based on the analysis of the standard deviation of the intensity time-series, recorded with different oscilloscope sampling rates. The second method relies on the analysis of the number of spikes as a function of the threshold used to define the spikes. The third method is based on the ordinal analysis of the inter-spike-intervals. These tools allow us to quantitatively detect the onset of two different dynamical regimes, know as low-frequency fluctuations (LFF), and coherence collapse (CC). We also analyze the transition from a noise-dominated regime to a more deterministic (less stochastic) dynamics. For this study, in addition to the experimental laser system (an SLOF), we used as numerical examples the logistic map and the Rössler chaotic system. We find that, when the noise is strong, the permutation entropy (computed from the probabilities of the ordinal patterns) increases faster than linearly. By comparing the results of these three systems, we discuss the possibility of determining, from time series analysis, whether the underlying dynamics is dominated by noise or by deterministic processes. The results reported in this Thesis are relevant in a number of ways. The methodologies developed allow detecting parameter regions of noisy locking to an external weak periodic input and may be useful to investigate other forced excitable systems. In addition, the methods developed to detect the onset of different regimes can be valuable for analyzing regime transitions in many real world systems. Finally, the methodology for determining, for observed data, whether the underlying dynamic is mainly driven by noise or by deterministic effects can also be used in multidisciplinary applications (finances, geosciences, social systems, etc.).