A review is given of a 30-year-old activity of Moscow State University's laboratory of nonlinear optics, headed by R. V. Khokhlov and S. A. Akhmanov, in the development and application of optical parametric devices.

The paper reports on results of studies on dynamic modes of operation of a laser with periodic pumping. The bifurcation diagram in a two-dimensional space of managing parameters is constructed. The obtained characteristics allow for prediction of modes of synchronous operation of two optically coupled lasers.

The possibility of generation in a nonlinear interferometer of the complex-form intensity pulsations through the concurrent resonance nonlinearities due to transitions of molecules to different energy states has been put forward and substantiated. The conditions and character of transition to the mode of dynamic chaos have been analyzed.

This paper presents a FELC/VLSI spatial light modulator which has been built as a component for optoelectronic neural networks. The device exhibits analogue optical modulation and is capable of optical memory. It is the first parallel optical device that implements a learning algorithm in its pixels.

We used a modified form of the Z-scan technique to study the various factors influencing bistability in a semiconductor doped glass filter. A strong self-focusing effect was observed and an estimate of the corresponding n₂ coefficient is obtained. A systematic modeling of absorptive bistability in a semiconductor doped glass, including both longitudinal and transverse heat diffusion as well as the effects of self-focusing, is presented and compared with experimental observations.

Dynamics of a ring laser with a field rotating mechanism were investigated for two medium models: a 2-level model and a model taking into account rotational sublevels of carbon-dioxide molecule. It was shown that spatial structure formation in the laser can be controlled by the angle of rotation.

New types of nonlinear optical systems that use the joint effects of Kerr-like nonlinearity, interference and diffraction in 2-D optical feedback are analyzed. We show that spatio- temporal instabilities in these systems can exist in the form of conditional instability. By varying several parameters of the optical system it is possible to control the nonlinear dynamics, thus creating different regimes of intermode interactions.

Transverse interactions in a passive ring resonator with Kerr slice are theoretically and numerically investigated. Using the method of nonlinear phase modulation expansion we obtained the system of equations for nonlinear modes. Stability analysis of resonator modes was carried out. We also studied intermode interactions and regular pattern formation processes in both cases of plane wave and circular aperture.

A variety of complex dynamics associated to homoclinic connections have been numerically and experimentally observed in the reflection of Fabry-Perot etalons with a partially absorbing input mirror and a trilayer spacer of alternatively opposite thermo-optic materials.

The mathematical model of an optical system with thin Kerr slice and feedback mirror and diffraction in 2-D feedback loop described by nonlinear diffusion equation and Shroedinger type equation is studied. The existence of global attractor and finiteness of its Hausdorff dimension are proved.

New types of transversal interactions in a nonlinear interferometer with Kerr slice and two dimensional feedback are analyzed. We show that interactions between the most unstable modes have wavevectors belonging to different mode instability bands (interballoon interactions) cause the formation of new types of patterns. Mode amplitude equations for these patterns are obtained. Analysis of amplitude equations is confirmed by numerical simulation.

New results of theoretical study on light beam propagation through the atmosphere are presented. Studied in detail is the action of the self-induced thermal lens and the turbulent field of refractive index fluctuations on the structure of the beam distortions.

The picosecond parametric amplification of a polychromatic image with a wavelength bandwidth of 140 nm and a gain of 15 dB has been obtained in a type I, LBO crystal. Thirty per 30 points were resolved. These results are in good agreement with a numerical study of the phase-matching conditions around the collinear degeneracy where phase-matching is non- critical for the signal beam in angle as well as in wavelength.

A tunable KTP optical parametric oscillator (OPO) operating on a single longitudinal mode of its resonator is described. Single mode operation has been achieved by using an intracavity Fabry-Perot etalon in a short-length OPO resonator. The crystal is pumped by the second harmonic of a 10 Hz, Q-switched, injection-seeded Nd:YAG laser. the tuning range observed with a crystal cut at 60 degrees is 0.75 - 0.87 micrometer for the signal beam and 1.83 - 1.37 micrometer for the idler beam. The linewidth of the OPO is 200 MHz (0.0066 cm^-1), which is very close to the Fourier limit. The total output energy (signal plus idler) was measured to be up to 0.6 mJ per pulse at a pump energy of 10 mJ.

The saturation of self-organized second-harmonic generation in optical fibers, predicted by a model we have recently derived, is verified by calculating the saturation value of the ratio I_2(omega )/I_(omega )² using experimental data of some previous experiments. It was found that the value of (I_2(omega )/I_(omega )²)_sat determined experimentally ranges from 0.3 multiplied by 10^-16 m²/W to 2 multiplied by 10^-16 m²/W, which is in reasonable agreement with the theoretical predictions. The self-organized parametric down conversion is proposed for a very effective preparation of optical fibers.

Harmonics generation of laser radiation ((lambda) equals 1.06 (mu) , (tau) equals 3 ps) in low-temperature atmospheric plasma and target plasma is investigated. Maximum efficiency was achieved for third harmonics generation ((eta) equals 10^-3). Results of odd harmonics generation (up to eleventh, (lambda) equals 96 nm) are reported.

Continuous linear laser on dyes Rhodamine 6G and DCM, operating in a mode of intracavity frequency doubling is experimentally investigated. Efficiency of radiation transformation is determined by means of a nonlinear (beta) -BaB₂O₄ crystal and Ar⁺ pump lasers of a wide power range with various cross distribution of radiation. Effective narrow- band ((Delta) (lambda) on the order of 0.01 - 0.1 cm^-1) generation in the field of 285 - 315 nm and broadband ((Delta) (lambda) on the order of 5 nm) UV-radiation in the field of 310 - 350 nm is received. Dependencies, describing influence of discrepancies of installations of crystal on the power of the second harmonic radiation, are determined.

Photoinduced second harmonic generation in titanium and cerium doped lead-silicate glasses at different infrared preparation intensities is reported. The influence of dopants on second harmonic conversion efficiency is discussed.

We report an efficient conversion of multiple transverse mode output of TEA carbon-dioxide laser into the 5 micrometer region by second harmonic and sum frequency generation in wide- aperture long AgGaSe₂ crystals. The second harmonic pulses with energy up to 350 mJ (at an external efficiency (eta) equals approximately 10%) and the sum-frequency pulses with energy up to 50 mJ ((eta) equals approximately 1.5%) have been obtained. The recent applications of this radiation are discussed.

The dependence of the speckle field was investigated in Ba₂NaNb₅O₁₅ crystals in laser beam on the orientation of the crystals, temperature and direction of growth. In the crystal with 90 degree orientation the speckle structure of the beam disappears at about 300 degrees Celsius; in the crystal with 0 degree orientation the point scattering centers disappear near the Curie point.

The influence of a longitudinal magnetic field on the behavior of the speckle-pattern of light, transmitted through an optical fiber, is investigated. The rotation of the speckle-pattern was observed. The angle of the rotation corresponds in order of magnitude and in sign to the Faraday rotation.

The static magnetization induced by an elliptically polarized optical beam in a medium with dissipation is discussed for a classical and quantized optical field in a coherent state. Exact analytical formulas that describe the dc magnetization linearly and quadratically dependent on the intensity of the optical beam with the classical field are derived for crystals and nonlinear isotropic Kerr media with dissipation. For both magnetizations the hermitian operators are also defined and then used to calculate their expectation values induced by a quantized field propagating in a Kerr medium with dissipation, which in practice is represented by an isotropic medium and by crystals with symmetries 6m2 and 6/mmm. The positive and negative role of dissipation is shown explicitly in a fully quantitative way from the exact analytical solutions. Damping of the optical wave propagating in the medium with dissipation increases the dc magnetizations. The dissipation parts of the second- and fourth-order nonlinear magneto-electric susceptibilities influencing this magnetized process decrease the dc magnetizations and even, as in the case of the nonmagnetic crystals with the symmetries 3, 3, 32, 3m and 3m, lead to the appearance of dc magnetization perpendicularly directed with respect to the light propagation direction. Because optically induced dc magnetizations depend on the Stokes parameters, their space derivatives are also derived for the medium with dissipation.

The interference structure of the laser light scattering cone behind the laser spark was observed for the first time. We propose consideration of the observed structure as a result of interference of the laser radiation, scattered by two or more self-focusing centers in laser spark air plasma. We have investigated the spatial distribution of the laser radiation scattered by the laser spark. These experiments differ from the previous ones by use of the four harmonics of Nd-laser radiation. As a source of radiation the Nd-laser installation was used with the master oscillator, operated on one transverse and longitudinal mode. The pulse duration was 10 ns, pulse energy -- up to 20 J and beam divergence -- 8 (DOT) 10^-5 rad. After the frequency conversion by means of the KDP crystals the second, third, and fourth harmonics radiation appeared with the energy up to 10 J (in fourth harmonic). In each of our experiments one laser harmonic radiation was focused into the hermetical chamber, filled with air (10 divided by 760 mm Hg). For the scattered radiation registration we photographed the scattering flat white screen, illuminated by this radiation. This screen was disposed parallel to the laser beam axis at the distance of 2 - 6 mm from it. We observed a cone-like symmetric respectively to the laser beam axis radiation scattering in the spark. That enables us to determine the maximum angle alpha of laser radiation deviation as a function of pressure p and wavelength lambda (or number of harmonic N).

The parameters of anisotropy and gyrotropy area are shown to exist in biaxial gyrotropic crystals, where local sites of wave vectors surface in the vicinity of optical axis directions have negative or zero curvature. In these directions effects of focusing and diffractionless propagation of light beams occur. At Gaussian beams example a number of focusing and diffractionless propagation schemes are presented. The description of the new type of nondiffracting light beams (spatial solitons) in photorefractive crystals in the case of phase shifted diffraction gratings is given.

The dynamics of pulsed pumped dye lasers with transversal excitation geometry with linearly polarized pumping when the absorption dipole is perpendicular to the emission dipole have been theoretically and experimentally investigated. The theoretical model is based on balance equations and takes orientational relaxation processes into account. Experimental results have been obtained on Rhodamine 6G in Ethyleneglycol under pulsed transversal polarized pumping from a N₂ laser. The theoretical and experimental results obtained allow us to call the new effect: orientational self-bleaching.

The effect of space phase self-modulation of light by a photorefractive crystal Ba₂NaNb₅O₁₅ in an external alternating electric field was experimentally observed.

We have observed lowering of reflectivity (from approximately 85% up to approximately 50 - 70%) of the cholesteric liquid crystal (CLC) mirror under the nonlinear action of circular polarized laser radiation. The possibility is considered of nonthermal but light-field induced helical pitch dilation and untwisting. It should be mentioned that it is the first experiment to our knowledge (the special laser operation was chosen, so that the changes of pitch can be accumulated) where such strong changes of reflectivity can be explained by nonthermal effects. We also observed defocusing of the reflected beam with a near Gaussian spatial profile and changing of the CLC mirror curvature, but we consider that in these experiments thermal effects are more probable.

Radiation characteristics of dye laser with Kerr medium inside the resonator are experimentally investigated. It is shown that arising additional radiation modulation led to reduction of a duration of laser pulses.

Degenerate four-wave mixing (DFWM) and phase conjugation (PC) of pulsed carbon-dioxide laser radiation on transient gratings inside its own laser medium have been studied both experimentally and theoretically. The operational mode of the e-beam controlled discharge carbon-dioxide laser has been chosen in such a way (CO₂:N₂:He equals 1:2:4, p equals 0.28 atm, t_in equals 30 microseconds) that the laser pulse length ((tau) _out approximately equals 10 - 20 microseconds) is comparable with an effective relaxation time of the upper laser level ((tau) _rel approximately 15 - 30 microseconds). The time-history of the carbon-dioxide laser and PC signal pulses, and PC reflectivity have been thoroughly investigated for different cavity Q factors and specific electrical energy inputs. It has been shown, that the formation of the PC signal under the intracavity DFWM on gain (amplitude) and thermal (phase) gratings is characterized by a complicated time history that reflects the main relaxation processes taking place inside the inverted medium. A feature of the transient PC process inside the laser active medium is the dependence of the effective relaxation time of the upper laser level on the intensity of pumping waves. PC reflectivity has been obtained by numerical calculations. A comparison of the theoretical and experimental data confirms the contribution of two different mechanisms of grating formation under DFWM inside the active medium of the carbon-dioxide laser.

Resonant backward degenerate four-wave mixing in a (Lambda) -type Doppler-broadened 3- level system using two arbitrarily intense copropagating and crosspolarized pump beams is analyzed. The saturation features of the emission spectra are shown to depend critically on the pump imbalance and in case of a balanced grating wave saturation level-crossing emission resonances arising from destructive interference effects between coherent excitation pathways are shown to appear.

The theory of frequency-degenerate six-wave mixing of ultra-short light pulses in a medium with relaxing Kerr nonlinearity is developed. The energetic and temporal output characteristics are analyzed as functions of parameters of medium and pump pulses. For certain delay time between pump pulses, the parametric gain of the signal and conjugated pulse in whole medium length is maximized. An effect of the counter-propagating pump pulse compression is predicted. The dynamics of transition between six-wave mixing and four-wave with a change of an angle between the pump and signal propagation directions is studied.

The method for greatly widening the coherent interaction region of intersecting broad-band optical bemas by tilting the coherence layers has been theoretically and experimentally studied. Efficient FWM for the spectrum width of radiation equal to 20 nm has been obtained. OPC of signal wave has been shown.

We demonstrate experimentally two regimes of an enhanced beam amplification in photorefractive waveguide. Enhancement is achieved by matching the optical activity and the reflections of the beams in waveguide. Beam amplification is assisted by stimulated photorefractive scattering.

Hologram recording and subharmonic generation by means of ac field and phase modulated laser beams are studied. Phase locked detection mechanism in the geometry when the direction of the external ac field is perpendicular to the direction of the grating vector is discussed also.

A new efficient numerical scheme for solution of problems simulating dynamics of nonlinear interaction in photorefractive crystals has been developed and tested. Using the criterion of maximal mitigation of dynamic phase distortions, the processes of two- and four-beam interaction in InP:Fe has been optimized.

The pair correlations between the instantaneous intensities of input pump superbroadband (250 cm^-1) laser radiation with femtosecond and picosecond noise structures, output depleted pump radiation and Stokes one generated through stimulated Raman scattering in compressed hydrogen have been experimentally studied under the weak and strong pump depletion by means of time-delayed four-wave mixing in Kerr-shutter configuration. Experimental results show that the Stokes radiation is well correlated with the input pump one up to the energy conversion efficiency of about 30%. Considerable suppression of the femtosecond amplitude fluctuations in the depleted pump beam has been observed upon increasing the pump depletion that indicates the possible way for preparing superbroadband light with predominant phase fluctuations using SRS. The picosecond part of cross-correlation function between the depleted pump and Stokes radiation flows has very asymmetric shape that is probably caused by the transiency in the scattering of picosecond noise spikes and by the fact that these spikes in Stokes and depleted pump radiation flows have opposite temporal shapes.

A new method for the phase measurements in Raman scattering is presented. It is based on the comparison between an object placed on the illuminating laser beam and its image on the Raman scattering beam. The knowledge of the intensity structures of the object, the image and their Fourier spectrums allows the determination of the phases.

Stimulated Raman light scattering by an atom near a macroscopic body with spectral peculiarities in the vicinity of the atomic resonance frequency is theoretically investigated. It is shown that the stimulated Raman light scattering by an atom under these conditions essentially differs from that in free space.

The effects of wide-band smooth (global) and narrow-band abrupt (local) spectral inhomogeneities on the soliton dynamics in passive and active fibers are investigated. Soliton spectral tunneling effect (SSTE) is predicted and investigated. The SSTE consists in 'infiltration' of a femtosecond soliton spectrum through a potential barrier-like spectral inhomogeneity of group velocity dispersion (GVD) including the forbidden band of positive GVD. As was mentioned, of importance is the possibility of using spectral inhomogeneities of the dispersion parameters in order to suppress the Raman self-frequency shift of femtosecond solitons. Spectral perturbation method of soliton theory is developed.

An improved algorithm of the difference schema approximating nonlinear Maxwell equations and an analysis of stability and dispersion properties of it are presented. PC simulation of Maxwell solitons and a comparison with the nonlinear Shrodinger equation theory are investigated.

The coherent amplification in active fibers in the presence of spontaneous luminescence noise is studied. Fluctuations of soliton parameters and restriction of bit rate in communication lines are analyzed.

The possibility of generation and observation of a nonlinear solitary strain wave (soliton) in different solid waveguides is of special interest in connection with undeniable potential applications in solid state physics and mechanics. The present paper deals with experimental results on the studies of soliton generation and evolution in a relatively long waveguide as well as in a waveguide of varying cross section (inhomogeneous waveguide).

Properties of guiding-center solitons in the particular points along the path of pulses through a fiber are studied. To estimate analytically the particular point of a maximal self-compression the readily available procedure is developed. We focus on the spatial position of the aforementioned point as well as on the value of a maximal compression ratio. The proposed procedure is successfully applied to interpret our experiments on picosecond guiding-center solitons in various orders. Results of our measurements proved to be in a good agreement with the numerical values obtained from the above proposed analytical procedure of estimations and also with computed data known in isolated cases.

Results of mathematical modeling and experimental investigation of spontaneous soliton generation in forward stimulated Raman scattering (SRS) are reported. The duration of measured soliton pulses varied from 15 to 30 ps corresponding to the relaxation time T₂ in compressed methane. The peculiarities of Raman solitons generation under essentially different quasi-steady-state and transient regime of SRS excitation were observed. For pump pulses with duration of 300 ps and Gaussian beam profile the probability of soliton-like pulse observation was only about 0.0034. For longer pump pulses and for pulses with top-hat beam profile that probability was considerably higher. The influence of mutual diffractive focusing of laser and Stokes beams on the process of Raman solitons generation was experimentally confirmed.

We present results of theoretical investigations of collisions of spatial solitons. For the case of large collision angles the analytic theory has been worked out. Numerical investigations of power exchange among the solitons with small collision angles were carried out. The possibility of new soliton creation after collision has been discovered.