Daniel Hennequin

Bio: Daniel Hennequin is an academic researcher from Lille University of Science and Technology. The author has contributed to research in topics: Saturable absorption & Laser. The author has an hindex of 15, co-authored 54 publications receiving 777 citations. Previous affiliations of Daniel Hennequin include University of Pisa & Centre national de la recherche scientifique.

Chaos in a CO2 laser with modulated parameters: Experiments and numerical simulations.

Abstract: A laser with parameters modulated at a frequency f may respond not only at that frequency and its harmonics nf, but also at that of its subharmonics f/n. When the order n of its subharmonics increases indefinitely, the response of the laser becomes irregular, though the system remains deterministic. Many approaches have been used to characterize these different behaviors and the associated attractors, in a ${\mathrm{CO}}_{2}$ laser containing an elasto-optic modulator. A quite important similitude has been remarked between the bifurcation diagram of the laser and that of the logistic map ${x}_{n+1}$=1-\ensuremath{\mu}${x}_{n}^{2}$. More complex chaotic features have also been observed, e.g., generalized bistability between different attractors, and crisis when a chaotic attractor collides with an unstable periodic cycle. The influence of the rate of change of the driving parameters has also been studied. The experimental results show excellent agreement with those provided by the two-level model of the laser.

Two-dimensional optical lattices in a CO2 laser

Abstract: Using a cavity with a large Fresnel number, a nontrivial large-scale order resulting from global multimode-interaction dynamics is found in the transverse structure of a ${\mathrm{CO}}_{2}$ laser beam. Two-dimensional optical lattices displaying several hundred phase singularities each have been observed. The symmetry properties of these far-field patterns and their associate temporal spectra are studied as a function of two control parameters: the Fresnel number and the transverse intermode spacing.

Laser chaotic attractors in crisis

Abstract: Different crises, i.e., abrupt qualitative changes in the properties of attractors, have been observed in a C${\mathrm{O}}_{2}$ laser with internal modulation. They are shown to be related to crossing between a stable or unstable periodic cycle and the strange attractor resulting from the period-doubling cascade observed at low modulation levels. Depending on the operating conditions, boundary and interior crises have been observed.

Homoclinic orbits and cycles in the instabilities of a laser with a saturable absorber

Abstract: The phase-space evolution for the instabilities in a CO/sub 2/ laser with an intracavity saturable absorber is investigated experimentally. The different scenarios corresponding to limit cycles, homoclinic orbits and cycles involving two unstable points, and chaotic behavior are investigated. A theoretical analysis of the experimental results is sketched out.

Regular and Chaotic Dynamics

Abstract: This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The book is intended as a self consistent treatment of the subject at the graduate level and as a reference for scientists already working in the field. It emphasizes both methods of calculation and results. It is accessible to physicists and engineers without training in modern mathematics. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects. It can be used as a graduate text for a two semester course covering both Hamiltonian and dissipative dynamics.

Critical exponents for crisis-induced intermittency

Abstract: We consider three types of changes that attractors can undergo as a system parameter is varied. The first type leads to the sudden destruction of a chaotic attractor. The second type leads to the sudden widening of a chaotic attractor. In the third type of change, which applies for many systems with symmetries, two (or more) chaotic attractors merge to form a single chaotic attractor and the merged attractor can be larger in phase-space extent than the union of the attractors before the change. All three of these types of changes are termed crises and are accompanied by a characteristic temporal behavior of orbits after the crisis. For the case where the chaotic attractor is destroyed, this characteristic behavior is the existence of chaotic transients. For the case where the chaotic attractor suddenly widens, the characteristic behavior is an intermittent bursting out of the phase-space region within which the attractor was confined before the crisis. For the case where the attractors suddenly merge, the characteristic behavior is an intermittent switching between behaviors characteristic of the attractors before merging.In all cases a time scale \ensuremath{\tau} can be defined which quantifies the observed post-crisis behavior: for attractor destruction, \ensuremath{\tau} is the average chaotic transient lifetime; for intermittent bursting, it is the mean time between bursts; for intermittent switching, it is the mean time between switches. The purpose of this paper is to examine the dependence of \ensuremath{\tau} on a system parameter (call it p) as this parameter passes through its crisis value p=${p}_{c}$. Our main result is that for an important class of systems the dependence of \ensuremath{\tau} on p is \ensuremath{\tau}\ensuremath{\sim}\ensuremath{\Vert}p-${p}_{c}$${\ensuremath{\Vert}}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}}$ for p close to ${p}_{c}$, and we develop a quantitative theory for the determination of the critical exponent \ensuremath{\gamma}. Illustrative numerical examples are given. In addition, applications to experimental situations, as well as generalizations to higher-dimensional cases, are discussed. Since the case of attractor destruction followed by chaotic transients has previously been illustrated with examples [C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 57, 1284 (1986)], the numerical experiments reported in this paper will be for crisis-induced intermittency (i.e., intermittent bursting and switching).

Chaos, strange attractors, and fractal basin boundaries in nonlinear dynamics.

Abstract: Recently research has shown that many simple nonlinear deterministic systems can behave in an apparently unpredictable and chaotic manner. This realization has broad implications for many fields of science. Basic developments in the field of chaotic dynamics of dissipative systems are reviewed in this article. Topics covered include strange attractors, how chaos comes about with variation of a system parameter, universality, fractal basin boundaries and their effect on predictability, and applications to physical systems.