Experimental study of the complex dynamics of semiconductor lasers with feedback via symbolic time-series analysis

Abstract

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.