Experimental and numerical study of the symbolic dynamics of a modulated external-cavity semiconductor laser

Abstract

Abstract:We study the symbolic dynamics of a stochastic excitable optical system with periodic forcing. Specifically, we consider a directly modulated semiconductor laser with optical feedback in the low frequency fluctuations (LFF) regime. We use a method of symbolic time-series analysis that allows us to uncover serial correlations in the sequence of intensity dropouts. By transforming the sequence of inter-dropout intervals into a sequence of symbolic patterns and analyzing the statistics of the patterns, we unveil correlations among several consecutive dropouts and we identify clear changes in the dynamics as the modulation amplitude increases. To confirm the robustness of the observations, the experiments were performed using two lasers under different feedback conditions. Simulations of the Lang-Kobayashi (LK) model, including spontaneous emission noise, are found to be in good 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 external forcing, and the noise that sustains the dropout events.

Effects of periodic forcing on the temporally correlated spikes of a semiconductor laser with feedback

“…1a in [7]. A semiconductor laser (Sony SLD1137VS), with a solitary threshold current I th =28.4 mA, temperature-and current-stabilized with an accuracy of 0.01 C and 0.01 mA, respectively, using a combi controller (Thorlabs ITC501), emitting at 650 nm, has part of its output power fed back to the laser cavity by a mirror 70 cm apart (the external cavity round-trip time is 4.7 ns).…”

“…We analyze the experimental and numerical ISI sequences by using ordinal analysis [34], as in [6,7]. Each ISI sequence, {∆T i }, is transformed into a sequence of ordinal patterns (OPs), which are defined by considering the relative length of D consecutive ISIs and assigning them a symbol that indicates their relative length, in the same order as they appear in the sequence.…”

“…Because information processing in the brain is associated with the excitable action potentials that propagate through neuronal axons [2], many efforts are being done to develop excitable devices that could mimic neuronal behavior in bio-inspired information processing networks. Particularly, semiconductor lasers with optical injection [3][4][5], optical feedback [6,7] or saturated absorber [8][9][10][11] have been investigated with this purpose.…”

“…Recently we studied experimental and simulated ISI sequences [6,7] employing a symbolic method of time-series analysis referred to as ordinal analysis [34]. This methodology is capable of identifying the presence of serial correlations in datasets, and by analyzing the statistics of the different symbols (ordinal patterns, OPs), it can capture subtle variations in temporally correlated data [35][36][37][38].…”

“…In [6,7] we analyzed the role of external forcing on the sequence of optical spikes by gradually increasing the modulation amplitude at a fixed modulation frequency. Here we address the role of the modulation frequency.…”