Chaos in free electron laser oscillators

The chaotic nature of a storage-ring Free Electron Laser (FEL) is investigated. The derivation of a low embedding dimension for the dynamics allows the low-dimensionality of this complex system to be observed, whereas its unpredictability is demonstrated, in some ranges of parameters, by a positive Lyapounov exponent. The route to chaos is then explored by tuning a single control parameter, and a period-doubling cascade is evidenced, as well as intermittence.Comment: Accepted in EPJ

The Control of Dynamical Systems - Recovering Order from Chaos -

Following a brief historical introduction of the notions of chaos in dynamical systems, we will present recent developments that attempt to profit from the rich structure and complexity of the chaotic dynamics. In particular, we will demonstrate the ability to control chaos in realistic complex environments. Several applications will serve to illustrate the theory and to highlight its advantages and weaknesses. The presentation will end with a survey of possible generalizations and extensions of the basic formalism as well as a discussion of applications outside the field of the physical sciences. Future research avenues in this rapidly growing field will also be addressed.Comment: 18 pages, 9 figures. Invited Talk at the XXIth International Conference on the Physics of Electronic and Atomic Collisions (ICPEAC), July 22-27, 1999 (Sendai, Japan

A state variable for crumpled thin sheets

Despite the apparent ease with which a sheet of paper is crumpled and tossed away, crumpling dynamics are often considered a paradigm of complexity. This complexity arises from the infinite number of configurations a disordered crumpled sheet can take. Here we experimentally show that key aspects of crumpling have a very simple description; the evolution of the damage in crumpling dynamics can largely be described by a single global quantity, the total length of all creases. We follow the evolution of the damage network in repetitively crumpled elastoplastic sheets, and show that the dynamics of this quantity are deterministic, and depend only on the instantaneous state of the crease network and not at all on the crumpling history. We also show that this global quantity captures the crumpling dynamics of a sheet crumpled for the first time. This leads to a remarkable reduction in complexity, allowing a description of a highly disordered system by a single state parameter. Similar strategies may also be useful in analyzing other systems that evolve under geometric and mechanical constraints, from faulting of tectonic plates to the evolution of proteins

Physics and Applications of Laser Diode Chaos

An overview of chaos in laser diodes is provided which surveys experimental achievements in the area and explains the theory behind the phenomenon. The fundamental physics underpinning this behaviour and also the opportunities for harnessing laser diode chaos for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient test-bed 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.Comment: Published in Nature Photonic

Two-dimensional spatiotemporal complexity in dual-delayed nonlinear feedback systems: Chimeras and dissipative solitons

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos 28, 103106 (2018) and may be found at https://doi.org/10.1063/1.5043391.We demonstrate for a photonic nonlinear system that two highly asymmetric feedback delays can induce a variety of emergent patterns which are highly robust during the system’s global evolution. Explicitly, two-dimensional chimeras and dissipative solitons become visible upon a space-time transformation. Switching between chimeras and dissipative solitons requires only adjusting two system parameters, demonstrating self-organization exclusively based on the system’s dynamical properties. Experiments were performed using a tunable semiconductor laser’s transmission through a Fabry-Pérot resonator resulting in an Airy function as nonlinearity. Resulting dynamics were bandpass filtered and propagated along two feedback paths whose time delays differ by two orders of magnitude. An excellent agreement between experimental results and the theoretical model given by modified Ikeda equations was achieved. Photonic delay systems are of astonishing diversity and have created a rich field of fundamental research and a wide range of applications. Under a transformation from time into pseudo-scape, their basic architecture makes them equivalent to ring networks with perfectly-symmetric coupling. For the first time we extend this spatiotemporal analogy in experiments by adding a second delay, 100 times the length of the first delay line. Nonlinearity is provided by a tunable semiconductor laser traversing a Fabry-Pérot resonator. Visualized in 2D-space, we show the temporal evolution of different chimeras and dissipative solitons. Experimental results excellently agree with numerical simulations of the double-delay bandpass Ikeda equation. Based on the attractors of multiple fixed-point solutions, we provide insight into the mechanism structuring the system’s dynamics.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept

Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial

A new computational technique based on the symbolic description utilizing kneading invariants is proposed and verified for explorations of dynamical and parametric chaos in a few exemplary systems with the Lorenz attractor. The technique allows for uncovering the stunning complexity and universality of bi-parametric structures and detect their organizing centers - codimension-two T-points and separating saddles in the kneading-based scans of the iconic Lorenz equation from hydrodynamics, a normal model from mathematics, and a laser model from nonlinear optics.Comment: Journal of Bifurcations and Chaos, 201

New Light on Molecular and Materials Complexity: 4D Electron Imaging

In this Perspective, 4D electron imaging is highlighted, after introducing some concepts, with an overview of selected applications that span chemical reactions, molecular interfaces, phase transitions, and nano(micro)mechanical systems. With the added dimension of time in microscopy, diffraction, and electron-energy-loss spectroscopy, the focus is on direct visualization of structural dynamics with atomic and nanoscale resolution in the four dimensions of space and time. This contribution provides an expose of emerging developments and an outlook on future applications in materials and biological sciences