G.-L. Oppo

Instabilities and spatial complexity in a laser

We discuss the emergence of spatial structures in a ring laser model with transverse effects. The emphasis of this study is on the development of a description that can capture the essential features of transverse dynamics without the need for large-scale numerical efforts. We introduce an extension of the uniform field limit and derive a set of modal equations that we solve with conventional numerical methods. Our solutions show evidence of transverse mode competition in the laser dynamics, leading to both time-dependent and multimode stationary (cooperative frequency-locking) behaviors. In the time-dependent regime we analyze the resulting spatial structures and suggest a scheme for the investigation and characterization of spatial complexity.

Spontaneous breaking of the cylindrical symmetry in lasers

Abstract We consider a homogeneously broadened ring laser with spherical mirrors in which the atomic line is resonant with three degenerate transverse modes of the resonator. Upon increasing the pump parameter, the cylindrically symmetric single-mode configuration becomes unstable and the system approaches a new stationary state characterized by three coexisting modes and an asymmetric field distribution that emerges continuosly at the instability threshold. We also show that the injection of a sufficiently strong external signal with the same spatial profile as the cylindrically symmetric mode of the cavity can restore the original symmetry of the output field.

Spontaneous spatial pattern formation in lasers and cooperative frequency locking

Abstract We discuss aspects of laser dynamics that are connected with transverse effects. We show that a laser capable of operating simultaneously in more than one transverse mode can develop temporal instabilities and pulsations at gain values close to the lasing threshold and within experimental reach, and also approach steady state configurations in which several transverse resonances develop synchronized oscillation (cooperative frequency locking). We suggest a practical scheme for the experimental verification of our predictions.

Dynamics of vibro-rotational CO2 laser transitions in a two-dimensional phase space

Abstract We describe a procedure for carrying out the adiabatic elimination of the fast variables in a model of a molecular laser that takes into account the interaction among the rotational levels. Our method yields a description of laser dynamics in terms of two essential degrees of freedom as in the usual rate equation limit; the accuracy of our results, however, is far superior to that of the traditional rate equations, as we verify by direct numerical integration of the exact and approximate dynamical systems. We also show that the rotational levels are responsible for the appearance of a purely dissipative term within the framework of the Toda potential description.

The resonance fluorescence spectrum of an atom driven by two coherent fields

Abstract The spectrum of spontaneously emitted radiation from a three-level system may undergo considerable modifications when the atom is driven simultaneously by two coherent fields. In particular, our calculations, based on the quantum regression theorem, predict the appearance of strong narrowing of the spectral features when a second transition sharing a common level with the first is driven to saturation and its spontaneous decay rate is smaller than that of the fluorescing process.

Characterization of Spatiotemporal Structures in Lasers: A Progress Report

The introduction of the transverse dependence of the field in the analysis of the dynamics of lasers has already explained the presence of temporal instabilities at low values of the pump parameter for lasers operating in the good cavity limit [1,2]. However, the relevance of these studies does not expire with the detection of chaotic motion. The interplay of spatial and temporal degrees of freedom together with the highly nonlinear character of the Maxwell-Bloch equations of motion, make lasers with large transverse section good candidates for the characterization of complex spatiotemporal patterns and perhaps also of turbulent states. Moreover, the time scale of the laser dynamics offers a clear advantage over other fields of physics where spatiotemporal phenomena have been detected, from hydrodynamics to oscillating chemical reactions.

Phase Dynamics, Phase Resetting, Correlation Functions and Coupled Map Lattices

Some of the richest dynamical phenomena occur in both space and time. In view of the substantial developments that have taken place in the understanding of the onset of chaos in spatially homogeneous systems, which are described by systems of ordinary differential equations, there is some hope that parallel developments may take place in the study of spatially distributed systems that are usually described by partial differential equations. It is safe to say that this goal has not yet been achieved. The problem is twofold: not only are the phenomena diverse so that a set of organizing features like the major routes to chaos in spatially homogeneous systems has yet to be discovered, but some of the most useful nonlinear dynamics techniques, like surface of section plots, fractal dimensions and Lyapunov numbers, lose some of their utility for these high-dimensional systems. While all of the above tools can and have been brought to bear on the problem of spatio-temporal structure there is no one definitive diagnostic method.

Spatial Symmetry Breaking in Optical Systems

One of the main issues raised by synergetics [1,2] is the emergence of spatial self-organization in nonlinear dynamical systems far from thermal equilibrium. Phenomena of this kind are often accompanied by the breaking of a spatial symmetry; for example, if an instability creates a spatial pattern in a previously homogeneous system, this corresponds to the spontaneous breaking of translational symmetry.

Instabilities in a hybrid bistable system without delayed feedback

Abstract We show that a hybrid bistable system can display oscillatory or even chaotic behavior when an amplifier is introduced in the feedback loop, despite the absence of a delay. We study the effects of bias and the amplifiers gain and bandwidth on the dynamics of the system.

Spatial Instabilities and Symmetry Breaking in Lasers

The main theme of our presentation is the general subject of pattern formation, using the laser as the main vehicle to explore the interplay between temporal and spatial phenomena and the emergence and characterization of spatial complexity. The motivation for these studies came from the realization that our understanding of a broad area of nonlinear dynamics is still rather primitive and that some concepts and working tools are in need of further development.