Control of multistability

This Review Article provides an overview of chaos in laser diodes by surveying experimental achievements in the area and explaining the theory behind the phenomenon. The fundamental physics underpinning laser diode chaos and also the opportunities for harnessing it for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient testbed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number generation. Avenues for future research and development of chaotic laser diodes are also identified.

Physics and applications of laser diode chaos

A reflection of our ultimate understanding of a complex system is our ability to control its behavior. Typically, control has multiple prerequisites: It requires an accurate map of the network that governs the interactions between the system's components, a quantitative description of the dynamical laws that govern the temporal behavior of each component, and an ability to influence the state and temporal behavior of a selected subset of the components. With deep roots in nonlinear dynamics and control theory, notions of control and controllability have taken a new life recently in the study of complex networks, inspiring several fundamental questions: What are the control principles of complex systems? How do networks organize themselves to balance control with functionality? To address these here we review recent advances on the controllability and the control of complex networks, exploring the intricate interplay between a system's structure, captured by its network topology, and the dynamical laws that govern the interactions between the components. We match the pertinent mathematical results with empirical findings and applications. We show that uncovering the control principles of complex systems can help us explore and ultimately understand the fundamental laws that govern their behavior.

Control Principles of Complex Networks

Complex phenomena in photonics, in particular, dynamical properties of semiconductor lasers due to delayed coupling, are reviewed. Although considered a nuisance for a long time, these phenomena now open interesting perspectives. Semiconductor laser systems represent excellent test beds for the study of nonlinear delay-coupled systems, which are of fundamental relevance in various areas. At the same time delay-coupled lasers provide opportunities for photonic applications. In this review an introduction into the properties of single and two delay-coupled lasers is followed by an extension to network motifs and small networks. A particular emphasis is put on emerging complex behavior, deterministic chaos, synchronization phenomena, and application of these properties that range from encrypted communication and fast random bit sequence generators to bioinspired information processing.

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Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers

Control of chaos via extended delay feedback

We present a technique for stabilizing unstable periodic orbits in low-dimensional dynamical systems that allows for control over a large domain of parameters. The technique uses a continuous feedback loop incorporating information from many previous states of the system in a form closely related to the amplitude of light reflected from a Fabry-P\'erot interferometer. We demonstrate that the approach is well suited for pratical implementation in fast systems by stabilizing a chaotic diode resonator driven at 10.1 MHz.

Stabilizing unstable periodic orbits in fast dynamical systems.

We design and implement a chaotic-based system, enabling ultra-fast random bit sequence generation. The potential of this system to realize bit rates of 160 Gb/s for 8-bit digitization and 480 Gb/s for 16-bit digitization is demonstrated. In addition, we provide detailed insight into the interplay of dynamical properties, acquisition conditions, and post-processing, using simple and robust procedures. We employ the chaotic output of a semiconductor laser subjected to polarization-rotated feedback. We show that not only dynamics affect the randomness of the bits, but also the digitization conditions and postprocessing must be considered for successful random bit generation. Applying these general guidelines, extensible to other chaos-based systems, we can define the optimal conditions for random bit generation. We experimentally demonstrate the relevance of these criteria by extending the bit rate of our random bit generator by about two orders of magnitude. Finally, we discuss the information theoretic limits, showing that following our approach we reach the maximum possible generation rate.

Fast Random Bit Generation Using a Chaotic Laser: Approaching the Information Theoretic Limit

Fast chaotic dynamics in a diode resonator are controlled using a continuous feedback scheme proposed by Pyragas [Phys. Lett. A 181, 203 (1993)]. The resonator is driven by a 10.3 MHz sinusoidal voltage (corresponding to a drive period under 100 nsec). Period-[ital k] orbits, with [ital k]=1, 2, and 4, have been stabilized by applying a vanishingly small feedback signal that is generated by continuously comparing the state of the resonator with its state one orbital period in the past. We observe that the control is effective even in the presence of a [similar to]24 nsec time lag between the sensing of the system and the application of the feedback that arises from unavoidable propagation delays through the feedback electronics.

Stabilizing unstable periodic orbits in a fast diode resonator using continuous time-delay autosynchronization

We stabilize unstable periodic orbits of a fast diode resonator driven at 10.1 MHz (corresponding to a drive period under 100 ns) using extended time-delay autosynchronization. Stabilization is achieved by feedback of an error signal that is proportional to the difference between the value of a state variable and an infinite series of values of the state variable delayed in time by integral multiples of the period of the orbit. The technique is easy to implement electronically and it has an all-optical counterpart that may be useful for stabilizing the dynamics of fast chaotic lasers. We show that increasing the weights given to temporally distant states enlarges the domain of control and reduces the sensitivity of the domain of control on the propagation delays in the feedback loop. We determine the average time to obtain control as a function of the feedback gain and identify the mechanisms that destabilize the system at the boundaries of the domain of control. A theoretical stability analysis of a model of the diode resonator in the presence of time-delay feedback is in good agreement with the experimental results for the size and shape of the domain of control.

https://www.phy.duke.edu/~qelectron/pubs/Chaos7560.pdf

Controlling chaos in a fast diode resonator using extended time-delay autosynchronization: Experimental observations and theoretical analysis

Chaotic semiconductor lasers have been proven attractive for fast random bit generation. To follow this strategy, simple robust systems and a systematic approach determining the required dynamical properties and most suitable conditions for this application are needed. We show that dynamics of a single mode laser with polarization-rotated feedback are optimal for random bit generation when characterized simultaneously by a broad power spectrum and low autocorrelation. We observe that successful random bit generation also is sensitive to digitization and postprocessing procedures. Applying the identified criteria, we achieve fast random bit generation rates (up to 4 Gbit/s) with minimal postprocessing.

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David W. Sukow

Papers

Stabilizing unstable periodic orbits in fast dynamical systems.

Fast Random Bit Generation Using a Chaotic Laser: Approaching the Information Theoretic Limit

Stabilizing unstable periodic orbits in a fast diode resonator using continuous time-delay autosynchronization

Controlling chaos in a fast diode resonator using extended time-delay autosynchronization: Experimental observations and theoretical analysis

Dynamics of a semiconductor laser with polarization-rotated feedback and its utilization for random bit generation