F. T. Arecchi

Instabilities in lasers with an injected signal

We consider a laser with an injected signal, in which the polarization can be adiabatically eliminated, we study the stability of the steady-state solutions, and we discuss the time-dependent solutions. For the laser alone, the only possible solution is constant intensity. However, the introduction of an external field, with an amplitude that does not satisfy the injection-locking condition, destabilizes the system. In such a case, numerical results show the existence of a self-Q-switching process, which induces relaxation oscillations. The frequency of the giant pulses is directly related to the amplitude of the external field, whereas the frequency of the relaxation oscillations depends on the damping rates. We show also that, depending on the value assigned to control parameters, the interaction between these frequencies leads to a chaotic behavior through intermittency or period-doubling bifurcations. Finally, topological equivalence between our laser system and a unidimensional circle map is shown for some values of control parameters.

Deterministic chaos in laser with injected signal

Abstract Dynamic behaviour of an homogeneously broadened laser with injected signal is analyzed for a model in which the polarization is adiabatically eliminated. Detuning between the atomic resonant frequency, the cavity resonance and the frequency of the external signal is considered. We show that a transition to chaos via intermittency is possible for parameters appropriate for CO2 lasers.

Non-Gaussian Statistics and Extreme Waves in a Nonlinear Optical Cavity

A unidirectional optical oscillator is built by using a liquid crystal light valve that couples a pump beam with the modes of a nearly spherical cavity. For sufficiently high pump intensity, the cavity field presents complex spatiotemporal dynamics, accompanied by the emission of extreme waves and large deviations from the Gaussian statistics. We identify a mechanism of spatial symmetry breaking, due to a hypercycle-type amplification through the nonlocal coupling of the cavity field.

THE CONTROL OF CHAOS: THEORETICAL SCHEMES AND EXPERIMENTAL REALIZATIONS

Controlling chaos is a process wherein an unstable periodic orbit embedded in a chaotic attractor is stabilized by means of tiny perturbations of the system. These perturbations imply goal oriented feedback techniques which act either on the state variables of the system or on the control parameters. We review some theoretical schemes and experimental implementations for the control of chaos.

Roll-hexagon transition in a Kerr-like experiment

A transition between hexagons and rolls is observed in an optical diffractive system containing a LCLV acting as a Kerr-like non-linearity. A rotation of 180° in the optical feedback is responsible for the appearance of new stable structures as negative hexagons and rolls. The stability of the different patterns is discussed by means of a simple model based on coupled normal form equations.

High-dimensional chaos in delayed dynamical systems

Abstract We introduce a general class of iterative delay maps to model high-dimensional chaos in dynamical systems with delayed feedback. The class includes as particular cases systems with a linear local dynamics. We report analytic and numerical results on the scaling laws of Lyapunov spectra with a number of degrees of freedom. Invariant measure is computed through a self-consistent Frobenius-Perron formalism, which allows also a recalculation of the maximum Lyapunov exponent in good agreement with the one measured directly.

On chaos in lasers with modulated parameters: A comparative analysis

Abstract Modulation of the laser excitation rate and modulation of the cavity losses are shown to result in the same dynamical phenomena for lasers in which the polarization can be adiabatically eliminated. However, to obtain the same results, the degree of modulation of the excitation must be larger than the degree of modulation of the looses.

Differences in polarization dynamics of the electromagnetic field in xenon and neon lasers

Abstract We have experimentally observed the appearance of oscillations in the state of polarization of a constant-total-intensity, quasi-isotropic, HeXe, single-“geometrical”-mode laser operating at λ = 3.51 μm. Similar oscillations, accompanied by oscillations in the total intensity, have been detected also in a HeNe laser operating at λ = 3.3922 μm under the same experimental conditions. While the oscillations in the HeXe laser are understandable in terms of competition between the field amplitudes of two modes of different polarization, those in the HeNe may involve the atomic dynamics as well.

Instabilities in a semiconductor laser with delayed optoelectronic feedback

Abstract A single mode CW semiconductor laser with an optoelectronic feedback gives a modulated output, with a sharp frequency peak depending on the feedback delay. A theoretical model, with few parameters assigned from the experiment, yields quantitative agreement with observations.

Swept dynamics of a CO2 laser near threshold: Two- versus four-level model

Abstract The swept behavior of a single mode homogeneously broadened CO 2 laser has been characterized by applying a triangular modulation to an electro optic modulator inside the optical cavity. We observe a dynamical hysteresis effect depending on the modulation depth and on the sweep rate. Our experimental results can be explained in the framework of a four level molecular model which takes into account the coupling between the two resonant levels and the rotational manifold.