Nonlinear dynamics in lasers affects the selection of stable steady states, the response to fluctuations, spontaneous dynamical pulsations, the selection and stability of spatial patterns, and the erratic evolution which is sometimes termed chaotic or turbulent. This invited overview reviews some recent examples of these phenomena, indicating how methods of dynamical analysis can help to explain complicated behaviors.

This paper addresses two related issues: (1) control of chaos and, (2) controlling symbolic dynamics for communication. For control of chaos, we discuss the idea for realizing desirable periodic motion by applying small perturbations to an accessible parameter of the system. The key observations is that a chaotic attractor typically has embedded densely within it an infinite number of unstable periodic orbits. Since we wish to make only small controlling perturbations to the system, we do not envision creating new orbits with very different properties from the already existing orbits. Thus we seek to exploit the already existing unstable periodic orbits and unstable steady states. Our approach is as follows: We first determine some of the unstable low-period periodic orbits and unstable steady states that are embedded in the chaotic attractor. We then examine these orbits and choose one which yields improved system performance. Finally, we apply small controls so as to stabilize this already existing orbit. For the issue of communication, we describe an experiment verifying that the injection of small current pulses can be used to control the symbolic dynamics of a chaotic electrical oscillator to produce a digital communication waveform.

A distributed time-domain model is used for a numerical analysis of the dynamics of a passively mode locked laser diode under external modulation at a frequency close to the round-trip frequency of the laser. The possible dynamical regimes of the laser are identified as synchronization locking, frequency mixing and chaotic dynamics, including a special case of quasi-locking. For the locked regime, steady-state parameters are defined, the crucial role of group-velocity dispersion in achieving locking demonstrated and stages of the locking dynamics and corresponding time constants identified.

In a multi-level laser the pump process usually involves several intermediate levels as well as spontaneous relaxations and an external pump field. These details of the atomic excitation are often irrelevant and can be summarized by an effective heat-bath description and a two-level- laser model instead. Under certain circumstances, however, the heat-bath approximation will be too crude and it cannot account for phenomena such as intensity-noise squeezing and sub- Poissonian field statistics. We show how in the general situation the multi-level description can still be reduced to a two-level description in terms of a non-Markovian master equation. In steady state the atomic excitation is then described by a rate matrix rather than a single rate. The matrix or operator nature of the pump process gives rise to a correlation of the excitation rates with the statistical moments of the laser field. This correlation represents a correction to the standard laser model. In particular, it can be identified as the physical origin of the phenomenon of dynamic noise reduction in multi-level lasers.

New asymptotic approximations of the equations modeling the stability of two coupled lasers are investigated. We show that instabilities leading to intensity oscillations are possible. We discuss the validity of each approximation and the mechanisms leading to these instabilities. For two coupled solid state lasers, an instability occurs when the frequency detuning surpasses a critical value and the difference between the phases of the laser fields is forced to be unbounded in time. For two coupled semiconductor lasers, it is the strong coupling between the phase and the laser intensity that is the mechanism leading to period doubling instabilities.

Theory is given for class B laser systems to find periodic unstable orbits due to large losses perturbations. The method allows to determine nonlocal organization of phase space, in particular, boundaries of attractive basins of attractors and stable manifold of repellers.

Dynamical and fluctuation characteristics of radiation from a solid-state non-plane cavity ring laser were experimentally studied under self-modulation lasing by variations of the system parameters, such as pump power, laser crystal temperature, magnetic field magnitude. The effect of crystal temperature on frequency of self-modulation oscillations was determined. The influence of radiation ellipticity on the relaxation frequencies is discussed.

On the basis of experimental data we have concluded theoretical analysis of the influence of amplitude and phase component of inverse population grating on both pike and cw oscillation of solid state laser with passive optical isolator.

Formation and propagation of a new type of quasi-soliton in laser system was investigated. It was shown that the interplay between linear phase shift from the center of the luminescence band and nonlinear effect of the self-phase modulation enables to create the conditions for the self-ordering of the laser field. This technique is capable to generate stable ultra-short pulse trains. Analysis of the quasi-soliton stability allows to describe the cascade of oscillation effects in laser system accompanying the increase of the pump energy.

The theory of semiconductor ring laser is developed. It is found that both carrier diffusion and linewidth enhancement factor, which are specific for semiconductors, influence highly the laser behavior. In particular, the stable bidirectional lasing with comparable counterrunning wave intensities appears. The effect of cavity phase nonreciprocity (rotation) on the laser behavior is investigated. It is shown that information about phase nonreciprocity value is contained both in the relaxation oscillation spectra of unidirectional lasing and in the difference of counterrunning wave frequencies in bidirectional regime. This feature gives a possibility to use such laser as a compact gyroscope.

We have analyzed theoretically different chaos control schemes for a modulated class-B laser including discontinuous and continuous delayed feedbacks. The analysis is based on the detailed analytical and numerical studies of unstable manifolds evolution in phase space. A prescription for optimal control is proposed.

In recent years a remarkable similarity between semiclassical laser equations and Schrodinger equation was noticed, which results, in particular, in `geometric' properties of the phase of laser field. The goals of the present paper are to realize the origin of this analogy and to reveal some of its new physical outcomes for multimode lasers.

Antiphase chaotic switches and chaotic oscillations of orthogonal linearly polarized eigenstates, influenced by spontaneous emission noise in a single-mode He-Ne laser with anisotropic cavity, have been observed experimentally and explained theoretically. Both of these effects occur in the laser driven by sinusoidal gain modulation across the bifurcation point, which corresponds to the laser first threshold.

We have carried out a series of numerical experiments on the dynamic behavior of J=0 yields J=1 yields J=0 lasers optically pumped by a linearly polarized laser field and operating either: (1) with a strongly anisotropic cavity yielding fixed linear laser field polarization at any angle (theta) with that of the pump beam, or (2) with an isotropic cavity and an axial magnetic field. In the first case (1) we show that by changing (theta) the steady-states experience a smooth monotonic variation, but the dynamic states undergo a complex sequence of bifurcations. In case (2) we find that the laser field is always linearly polarized, but for some parameter settings we report the first observation that the plane of polarization together with the laser intensity change chaotically.

Switching between linearly polarized states of slightly different optical frequencies is found in the fundamental transverse mode pattern is described as the injection current is increased. Polarization switchings obtained here as the injection current is increased in a semiconductor rate equation model incorporating a vector electric field, birefringence and the linewidth enhancement factor, are similar to previously reported experimental results for the fundamental mode. Polarization properties of higher order Gauss-Hermite modes are also analyzed.

Experimental results containing the dynamical behavior of the Nd-doped optical fiber laser are presented. It is found that the state of pump polarization affects the intensity ratio of polarization modes. The intensity fluctuation spectrum of each polarization mode reveals three relaxation peaks. The model of a class B laser with two orthogonal elliptically-polarized modes is eligible for explanation of the main experimental features of relaxation oscillation peaks.

The theoretical model which describes nonlinear laser dynamics taking into account the vectorial character of generated field has been analyzed. The parameter region in which spontaneous polarization symmetry breaking is possible for such nonlinear system has been found. In this region two different polarized states are stable, i.e. bistability takes place in it. Such bistability can be named as undetermined one inasmuch as the evolution of this system from noise to one of two possible stable states is determined by the process of spontaneous emission and is not predicted in each single case. Spontaneous mirror symmetry breaking up to full chiral purity is typical for the system under consideration, it is a property that differentiates living things from inorganic nature.

Polarization hysteresis and switching as well as automodulation of the intensities of two running orthogonal plane-polarized waves in each direction have been found experimentally in single-isotope He-Ne ring laser ((lambda) equals 1,15 micrometers ) with small linear phase and amplitude anisotropy in the cavity.

We describe main properties of optical wavefront dislocations, or optical vortices. The problem of vortices birth and annihilation is analyzed. Holographic method for vortices creation is discussed. We report at the first time four-wave mixing experiments with screw dislocation wavefronts.

It is shown, that spiral interferograms can be used for diagnostics of screw dislocations. The connection between the type of spiral line, the type of defect and the values of wavefronts curvatures of interfering beams is established. The spherical wave is considered as reference wavefront. The results of analysis for isolated dislocation are integrated on case of defects set. It is shown, that the diagnostics of coherent fields with defects as screw dislocation requires the preliminary study of wavefront topology. The outline of execution of such testing is offered.

Phase singularities in laser beams carry angular momentum due to the associated helical wavefront structure. This angular momentum can be transferred to absorbing particles trapped in the beam, setting them into rotation.

We report experimental and numerical investigation of optical vortices nucleation in a wavefront of a laser beam passed through LiNbO₃ crystal with light-induced self- defocusing nonlinear lens and through SBN crystal with self-focusing nonlinear lens.

The analysis of the free generation dynamics of solid-state lasers with an intracavity Kerr nonlinear element is presented. Nonlinear diffraction losses, which result from self-focusing and defocusing of intracavity radiation, have been determined. The stability of stationary operation has been investigated. It is shown, that in the case of the fast defocusing nonlinearity index the resulting instability can also produce undamped spikes of intensity as in the case of focusing nonlinearity. Main peculiarities of operation regimes are determined.

The modal properties of a laser resonator consisting of an array of sources and a diffractive mode-selecting mirror are presented. The modal discrimination is optimized by selection of cavity parameters, and can be enhanced by additional diffractive elements. We find that the modal properties differ significantly from a conventional Talbot cavity. Because of the diffractive mode-selecting mirror, these are virtually no edge effects and the fundamental mode loss is very small. The modal discrimination is maximized at a round-trip cavity length of both one-half and one Talbot distance. There is an optimum array fill factor that depends on the cavity length and the array size. Finally, if the cavity length and fill factor are optimized, there is no loss of discrimination with increasing numbers of elements in the array.

In this paper, we present an original detection method using three fast detectors to monitor the spatio-temporal dynamics of a bimode CO₂ laser with saturable absorber. We observe that the time dependent components of the modal amplitudes increase as the frequency degeneracy lift between the TEM₀₁ and TEM₁₀ modes is reduced. Just before locking the system undergoes a period-doubling cascade leading to chaos. We record the temporal evolution of the modal amplitudes and the optical phase difference between the two modes in the specific regimes within the period-doubling cascade. Numerical simulations are in good agreement with the experiments, in particular they confirm the existence of the period-doubling cascade.

Different behaviors of isophase curves presenting zero values of the real and imaginary parts of the transverse varying scalar electric field of a laser are presented. We illustrate how phase singularities (isophase crossings) might evolve by variation of the amplitudes of superposed Laguerre-Gaussian cavity modes. These show the formation of closed loops and kinks. Numerical simulations of the transverse pattern dynamics give similar forms of phase singularity motion and evolution.

Transversely 2D laser autosolitons--localized structures of light in wide-aperture lasers with saturable absorption--with different topological indices and rotating axially non-symmetrical intensity distribution are analyzed by means of computer simulations. Four different types of collisions of laser autosolitons are presented.

Model equations for a ring class B laser operating in three Gauss-Laguerre modes are derived and studied. Bifurcation mechanisms leading to the appearance of low-frequency antiphase oscillations of mode intensities are investigated. The spontaneous phase symmetry breaking effect leading to transverse patterns with rotating crystal generated by four optical vortices is described.