Complex dynamics of photonic delay systems: a story of consistency and unpredictability

Abstract

[eng] - Introducció Photonic systems are powerful test-beds for the investigation of complex dynamics emerging from delays in feedback or coupling. The aim of this thesis was to study two relevant properties of photonic delay systems with direct applications in current information processing and encryption systems: consistency and unpredictability. We characterized the ability of laser systems with delay to exhibit, on the one hand, reliable complex dynamics when an external stimulus is applied, and on the other hand, unpredictable complex behavior, depending on the operating conditions. Consistency properties have been studied as a necessary condition for the implementation of Reservoir Computing schemes. The property of unpredictability has been exploited in the application of random bit generation. - Contingut de la investigació For the characterization of the consistency properties, we used three different experiments based on a semiconductor laser systems with delay that followed the drive-response scheme. Through the analysis of the responses to a repeated drive, a consistent or inconsistent behavior can be identified. In the first setup, we investigated consistency of a semiconductor laser to its own time-delayed feedback, so that the drive was the self-generated complex signal, and the response system was the semiconductor laser itself. A high accuracy in the repetition of the drive was achieved with the design of a fiber-optic setup with two feedback loops. This allowed us the extraction of measures like the sub-Lyapunov exponent. We extended the study to the use of a semiconductor laser system with excitability properties subject to

electrical input pulse trains. Here, two different pulse trains modulating the pump current of the laser were used as drives, while the semiconductor laser with delayed feedback operating in the chaotic regime of Low Frequency Fluctuations acted as response system. The purpose of this experiment was to study the possibility and requirements to induce a consistent response, particularly the power drop-out, with the injection of a short pulse. To complement the investigations on consistency, the last drive-response scheme used was an electro-optic intensity oscillator driven by 3 scalar signals: an harmonic waveform, a sequence of pulses, and recorded time-traces from the autonomous dynamics. Under certain conditions, the response system can show hysteresis and coexistence of multistable states. We introduced new tools to quantify consistency and identified common features of the setups investigated. Our study showed that when the autonomous dynamics were periodic or period doubled, a consistent response was obtained independent of the drive. In cases of bistable dynamics, new sorts of consistency were discovered, like reproducible time-position transitions between the two states. The last Chapter of this thesis was devoted to the use of the unpredictable dynamics for the generation of random bits. A semiconductor laser with polarization rotated feedback was utilized to provide chaos characterized by randomness-like features, including a flat broad spectrum, suppression of the delay echoes of the autocorrelation function and no recurrences in the temporal oscillations. Nevertheless, we found that other factors like the data acquisition and the postprocessing of the signal also affected the randomness of the finally generated bits. The validity of our guidelines was proven with our random bit generator, enhancing its generation rate up to 160Gbit/s. - Conclusió With this work, we explored the emerging complex behavior in laser systems with delay. In particular, we characterized their ability to display a consistent behavior, and deterministic chaos that can lead to unpredictable dynamics. We introduced new tools and measures to quantify consistency, and guidelines for an optimum performance of a random bit generator. Altogether, our results represent a significant contribution to the areas where these two properties play a role, such as information processing and secure optical communications.