Unveiling the complex organization of recurrent patterns in spiking dynamical systems.

Complex systems displaying recurrent spike patterns are ubiquitous in nature. Understanding the organization of these patterns is a challenging task. Here we study experimentally the spiking output of a semiconductor laser with feedback. By using symbolic analysis we unveil a nontrivial organization of patterns, revealing serial spike correlations. The probabilities of the patterns display a well-defined, hierarchical and clustered structure that can be understood in terms of a delayed model. Most importantly, we identify a minimal model, a modified circle map, which displays the same symbolic organization. The validity of this minimal model is confirmed by analyzing the output of the forced laser. Since the circle map describes many dynamical systems, including neurons and cardiac cells, our results suggest that similar correlations and hierarchies of patterns can be found in other systems. Our findings also pave the way for optical neurons that could provide a controllable set up to mimic neuronal activity.

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

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.

Stochastic logic gate that exploits noise and polarization bistability in an optically injected VCSEL.

We study numerically the dynamics of a vertical-cavity surface-emitting laser (VCSEL) with optical injection and show that the interplay of polarization bistability and noise yields a reliable logic output to two logic inputs. Specifically, by encoding the logic inputs in the strength of the light injected into the suppressed polarization mode of the VCSEL (the so-called 'orthogonal' injection), and by decoding the output logic response from the polarization state of the emitted light, we demonstrate an all-optical stochastic logic gate that exploits the ubiquitous presence of noise. It gives the correct logic output response for as short as 5 ns bit times when the dimensionless spontaneous emission coefficient, ß(sp), is within the range 10(-4)-10(-1). Considering that typical values of ß(sp) in semiconductor lasers are in the range 10(-5)-10(-4), the VCSEL-based logic gate can be implemented with nowadays commercially available VCSELs, exploiting either their intrinsic noise, or external and background noise sources.

10-fold detection range increase in quadrant-photodiode position sensing for photonic force microscope.

We propose a technique that permits one to increase by one order of magnitude the detection range of position sensing for the photonic force microscope with quadrant photodetectors (QPDs). This technique takes advantage of the unavoidable cross-talk between output signals of the QPD and does not assume that the output signals are linear in the probe displacement. We demonstrate the increase in the detection range from 150 to 1400 nm for a trapped polystyrene sphere with radius of 300 nm as probe.

Stochastic resonant damping in a noisy monostable system: theory and experiment.

Usually in the presence of a background noise an increased effort put in controlling a system stabilizes its behavior. Rarely it is thought that an increased control of the system can lead to a looser response and, therefore, to a poorer performance. Strikingly there are many systems that show this weird behavior; examples can be drawn form physical, biological, and social systems. Until now no simple and general mechanism underlying such behaviors has been identified. Here we show that such a mechanism, named stochastic resonant damping, can be provided by the interplay between the background noise and the control exerted on the system. We experimentally verify our prediction on a physical model system based on a colloidal particle held in an oscillating optical potential. Our result adds a tool for the study of intrinsically noisy phenomena, joining the many constructive facets of noise identified in the past decades-for example, stochastic resonance, noise-induced activation, and Brownian ratchets.