The modern state of research on nonlinear optical interaction of high-power laser radiation with plasmas is described in the context of spatial characteristics of radiation. It is shown that SBS and self focusing allow desirable spatial structures of laser pulses to form in plasma

Numerical analysis of geometry of a double phase conjugate mirror is carried out in frames of two-dimensional model. The role of fanning in a process of scattering is consistently taken into account. Results of the specially conducted experiment aimed at verification of theoretical predictions are discussed

Bifurcations of optical transverse solitary waves are studied for one-way propagation through a sodium vapor cell. Two types of phase encoding seed transverse bifurcations resulting in cell- exit profiles with beauty rivaling that of a kaleidoscope. The cell-exit profiles are stationary in time, reproduce completely when the power or frequency is scanned, and agree well with one- way computations. Temporal and longitudinal development of the cell-exit profiles is shown, demonstrating both the instability nature of this phenomenon and its solitary wave nature. The first evidence is also presented for a double-peaked Raman gain

Theoretical analysis of nonconventional schemes of four-wave mixing (FWM) using additional irradiation of resonance medium, which enables the realization of noncoherent optical control of the process efficiency, has been carried out. The possibility of significant increase in the phase conjugate reflectivity and decrease in the pump wave intensity, required for realization of optical bistability, has been shown. Optical control and intensification of FWM in Rhodamine 6G solution have been experimentally accomplished

The analytical expressions for radiation intensity dependence of electric permittivity of medium with elastic exciton-exciton interaction are derived. The features of nonlinear surface and guided waves propagating along a boundary of such nonlinear medium are examined

Results of experimental investigation of degenerate four-wave mixing by resonant reflection of single-frequency cw-semiconductor laser radiation from sapphire-cesium vapor boundary are presented. It is shown that characteristics of such mixing are conditioned by the peculiarities of formation and washing out of reflection dynamic gratings in a thin atomic layer

The theory of s- and p-polarized surface polaritons (SP) under conditions when optical Kerr nonlinearity and surface electrical conductivity (SEC) are simultaneously important is developed. Expressions are obtained that describe the dispersion and energy characteristics of nonlinear SP. The influence of SEC on these characteristics, as well as existence domain and spatial evolution of the surface waves, are investigated

Different types of transverse instabilities resulting in traveling and motionless spatial structures in bistable semiconductor interferometers and injection lasers are investigated on the basis of the proposed generalized theoretical mode

The instability threshold characteristics are investigated for two different optical devices, the ring cavity and the feedback mirror, with passive weakly absorbing two-level atoms cell. The linear stability analysis of the ring cavity predicts emission of several conical shells, depending on the optical arrangement and the buffer gas pressure. In the case of pure vapor, each conical shell has its own frequency. All the cones display the same frequency in the case of large buffer gas pressure. The feedback mirror device displays very different instability characteristics, with only one frequency emitted along a unique cone, in agreement with the experiment. The self-oscillation is shown to be controlled by the reflectivity properties of the cell, which behaves at threshold as a mixture of ordinary mirror and phase conjugate mirror

Thresholds of transverse instabilities arising from the mutual interaction of counterpropagating waves in a slab of Kerr medium without any cavity or mirror feedback are calculated from first principles, allowing for the effects of diffusion on the longitudinal index grating and for the field polarization. It is shown that the amplitude and polarization instabilities decouple in the linear limit under rather general conditions. Static polarization instabilities may have lowest threshold for finite transverse wave vector or on axis, depending on the Kerr constants. Analytic expressions are presented for the latter case. Numerical simulations show hexagon formation, consistent with related experiments.

The interaction of optical radiation with a semiconductor is analyzed by means of a numerical simulation. Two-dimensional effects are discussed. The influence of heat conduction on longitudinal kinks formation is considered in detail. It is shown that temperature dependence of a charge carriers lifetime can lead to periodical oscillations of electron concentration and semiconductor temperature. An influence of light-induced charge carries on switching waves is discussed. The sphere of applicability for widely known models of thermal optical bistability is determined.

The main features of field structures with characteristics of excitation in wide-aperture nonlinear interferometers driven by coherent external radiation are reviewed. Single and interacting switching waves and diffractive autosolitons are considered, including autosoliton interaction with dislocation of holding radiation wave front. The possibility of realization of digital-analogous parallel optical computing using these structures, spatial hysteresis, and reconstruction of interferometer regime under effect of radiation are discussed.

We studied the structure of absorption domains in cadmium sulfide by the following experimental techniques: the domains luminescence spectra; the transmission of a probe beam through the domain in the direction perpendicular to that of domain motion; and the radial distribution of intensity of the excitation light transmitted through the domain. The absorption domains in cadmium sulfide are found to be relaxation waves with final state in the Urbach absorption tail, their structure being analogous to that of burning waves studied in the kinetics of chemical reaction. The self-organization in this effect results in a weak dependence of the maximum domain temperature on excitation conditions. A blue shift of the luminescence line has been found for running domains with light intensity increasing.

Transverse pattern dynamics in the output of a laser are studied by numerical solution of the Maxwell Bloch equations. It was found that simple patterns involving many radial and angular modes can be simply described in terms of the motion and interaction of defects, singularities in the complex field. The complexity of the patterns and dynamics increase as the Fresnel number of the resonator is increased and as the mode spacing, gain, and cavity detuning are adjusted to bring more modes within the range of frequencies where gain exceeds loss.

The conventional FWM phase conjugation technique and the intracavity one have been studied experimentally in a gain medium of a pulsed e-beam sustained CO₂ laser. The total reflectivity of 45% for the phase-conjugate beam energy of 0.3 J is reported. The periodic temporal modulation of the laser output and of the phase-conjugate beam intensity for intracavity FWM arrangement has been observed. Two types of density gratings in the medium (temperature and acoustic ones) are used to explain experimental results.

The effective method of phase locking of a laser array with a multibeam intracavity long-range interaction (MBI) in nonlinear media is studied. The conditions under the MBI are determined when the long-range coupling is realized between the lasers (all-to-all type) and when only nearest neighbors interact (close-range coupling). A theoretical examination is given of the influence of the number of lasers, the cavity length detuning, and the coupling coefficients on the threshold gain coefficients and frequency characteristics of phase-locked and phase- unlocked modes of the laser array operation. An effect of parameters of the resonant absorbing medium on phase locking of the laser array is studied, and it is shown that the bandwidth of the synchronization is independent of the number of lasers at the optimal conditions.

By increasing the Fresnel number of F of a ring cavity with photorefractive gain, the transition from a low F regime, where few modes compete in a regular or irregular sequence, to a high F regime, where many modes oscillate simultaneously giving rise to spatio-temporal chaos is shown. The transverse field is characterized by an increasing number of topological defects, whose mean separation is related to the spatial correlation length of the field.

Spatio-temporal effects of thresholding and switching are investigated theoretically and experimentally in bistable single- and multimode cavities containing two nonlinear elements: photochromic absorber on bacteriorhodospin controlled by bleaching and coloring external beams and amplifier on organic dye pumped by periodic laser pulses.

The static and dynamical structures that emerge in lasers that operate with several transverse modes are discussed. Optical vortices form crystalline arrays and give rise to processes of creation and annihilation in pairs.

Hard excitation of particle-like field structures in passive nonlinear interferometers (diffractive autosolitons) under conditions of transverse structure instability and in the case of unstable resonator are investigated. The existence of positive and negative diffractive autosolitons in a wide-aperture laser with saturable absorber is shown.

The fine-scale thermal self-action of the laser radiation in pulsed excimer lasers is shown. The increments of the convective instability are obtained. The range of transverse modulation periods is defined, for which the instability exhibits significant temporal growth. It is shown that this effect can increase the laser divergence.

The active medium nonlinearity effect on the stability of the co-phase oscillation of a large number of optically coupled lasers are studied. The conditions of large- and small-scale inhomogeneities of the field are determined. It is shown that the random spread of laser frequency values leads to domain formation with significant difference of the field phase angle.

A review of papers devoted to investigation of instability in transverse laser beam profile with respect to amplitude-phase perturbations in pulsed CO₂ lasers is presented. Experimental and theoretical investigations in this field and methods for instability suppression are described.

On the basis of the developed theoretical method, the ordinary optical scheme of free electron laser with a hole on the exit mirror was investigated with consideration of gain saturation in a wiggler. The intracavity mode power and output radiation power were considered in relation to the radius of mirror curvature, the value of wiggler gain, hole dimensions, the range of mirror tilt angle, etc. The transverse structure of the intracavity field was calculated, and configurations with a local minimum and with 'saddle' points near the center of exit mirror were obtained. The dislocations of wavefront were obtained. Such points in degenerated cases formed rings situated far from the mirror center.

This paper provides a simple physical consideration of a new type of squeezed state of light: space-time squeezed state. As it was shown recently, spatial-multimode broadband squeezed light can generate (by homodyne detection) photon counting statistics that are regular not only in time, but also in the plane of observation. A possible advantage of application of space-time squeezed light in a number of areas of quantum optics (i.e., low-noise generation, detection of optical images, Fourier optics, and holography) is discussed from an elementary point of view.

Analysis of photonic noise in wide-aperture nonlinear interferometer excited by external radiation is presented. The possibility of spatio-temporal squeezed states generation and of effective noise suppression in a definite range of temporal and spatial frequencies is demonstrated.

The statistical analysis of the simultaneous influence of external noise and resonant frequency spread on phase locking of optically coupled lasers with a long-range interaction is performed in terms of the theory of critical phenomena. Dynamics of order parameter (amplitude of collective laser's oscillation), stability, and correlation connections between lasers for phase- locked and phase-unlocked modes are investigated. It is shown that by means of detuning of synchronous frequency from gain medium line center, the bandwidth of synchronization can be significantly increased.

It is well known way to increase the radiation power by combining beams from many lasers. However, the great increase in the intensity on the target may be obtained only if all beams are mutually coherent. The problem of making radiation of multichannel (multi-element) laser coherent was widely discussed. Several review articles were published recently [1-3] . The idea of coherent combining of a large number of phase locked beams is used in several concepts of super-high-power laser system: for chemical HF/DF lasers [4], for free electron lasers [5), for semiconducter lasers [6). The following methods to phase locking for laser array were considered: 1. frequency and phase locking of laser array to the radiation of master oscillator (MO) by adaptive optics method [7]; 2. the scheme master oscillator and power amplifier array [8; 3. phase locking of slave laser array to the injection signal from MO [9); 4. optical coupling between resonators (channels) of laser array [10]. Method of adaptive optics is attractive because it may have universal applications. However it needs design and production of many detectors, modulators, electrical serve loops and so on. Finally, it would be very complex system. The schemes 2 and 3 are at very initial stage of development. It was shown experimentally that the HF multiline radiation after the power amplifier (PA) may be coherently combined on a target with the radiation from MO [8] . The questions are leaving open of oscillator isolation and of choosing parameters of PA and MO to achieve high power and efficiency simultaneously. The amplifier array concept was not tested experimentally. There is a successful attempt at coherent combining of MO radiation with the radiation of injection locked Nd-YAG laser [11] . However, the transfer of this method to the array of injection locked lasers seems to be highly problematic due to tight tolerances for resonator length detunings. The concept of optically coupled laser array evolved very fast. So, this paper will be devoted to new results and ideas that made a progress in the concept of optically coupled lasers after the overviews [1-3] . These results relate to the problem of phase locking for two lasers and for the array of N lasers and concern the spectrum of collective modes and their stability. The dynamics of optically coupled lasers due to the resonator lengths detunings will be considered, too.

It is shown that combination mode-mode couplings are responsible for spectral instability in a ring laser. The key role of nonequidistancy in combination mode-mode coupling efficiency is proven.

Three- and four-level schemes of inversionless amplification with different types of coherent pumping is reviewed. Amplification without inversion between the 'bare' states is a result of population inversion between eigenstates of the density matrix. In particular, it can be achieved due to the coherent population trapping, i.e., effective removal from the interaction with the field a fraction of atoms at lower levels.