In this paper we summarize our recent theoretical and experimental results concerning optical injection in VCSELs. First, we develop phenomenological rate equation model for the normalized photon densities of the two fundamental VCSEL modes with orthogonal linear polarization when injecting external light polarized along the direction of polarization of the nonlazing mode. We then perform a simple analytical analysis of optically induced polarization switching in VCSELs, which takes into account both the current-dependent linear dichroism and the nonlinear dichroism. We also present detailed investigation of polarization dynamics induced by optical injection using an alternative rate equation model for VCSELs which takes into account the microscopic spin-flip processes in the active medium. In particular we predict that two injection locked solutions may coexist: the first one exhibits the polarization of the master laser, while the second one corresponds to an elliptically polarized injection locking. Continuation techniques allow us to find the bifurcation scenario leading to such an elliptically locked state. We also report on our first experimental results on polarization switching and injection locking for the case of an orthogonal optical injection in VCSELs and demonstrate rich dynamical behavior. The polarization switching is accompanied by a cascade of bifurcations to timeperiodic and possibly chaotic dynamics. Our experimental results show evidence of a period doubling route to chaos.

A theoretical model is developed to describe the propagation of ultra-short optical pulses in fiber transmission systems in the quasi-linear regime, with periodically inserted in-line lumped nonlinear optical devices. Stable autosoliton solutions are obtained for a particular application of the general theory.

The polarization dynamics of a longitudinally monomode bipolarized microchip Nd:YAG laser with a small value of the cavity phase anisotropy is studied experimentally and theoretically. The chaotic behavior is observed and well described by the developed model.

The analysis of nonlinear dynamics of spherical waves interacting with a cold collisionless overdense plasma is made on the basis of 'nonuniform' Hamiltonian. The necessary conditions for the realization of self-localized states are analyzed.

Photorefractive one-dimensional photonic lattices are optically induced in iron-doped lithium niobate. Discrete linear diffraction and formation of bright gap solitons due to the spatial self-action of light beams within such lattices are experimentally investigated at wavelength of 633 nm.

We present several recent observations of temporal behavior of dissipative solitons and multi-soliton complexes in a laser ring cavity. Attractors, collisions and pulsations are discussed both in experiment and numerical simulations.

The results of theoretical and experimental investigations into degenerate and non-degenerate four-wave mixing in Fabry-Perot microresonator with dye solution as a nonlinear medium are presented. It is shown that the efficiency of holographic methods for wave-front and frequency conversion may be considerably increased due to the use of recording of dynamic holograms in nonlinear interferometers. Spatial-temporal transformation of light beams for different configurations of interaction has been performed and the methods for control of energy efficiency of intracavity dynamics gratings are discussed.

An effect of light localization in nonlinear 1-D photonic crystal (PC) with a few layers pairs is considered. Computer simulation of the femtosecond pulse propagation shown a self-formation of ultra-short high-intensity solitons, which reflect from boundaries of linear and nonlinear layers as whole if nonlinear PC layers alternate with the linear ones. The variation (up to 20%) of PC layer's length doesn't change the localization process essentially. It results in increasing of input pulse intensity for which localization takes place. This aspect is very important for observing of effect in physical experiment. The stronger variation can either increase the quantity of initial pulse energy localized in PC, either damp the localization at all under the condition of unvaried intensity of input pulse. Computer simulation based on a new approach for this class of problems proposed by authors recently. Our method has advantages in comparison to the widely used splitting method.

The theory of diffraction of planar waves on an extended Fabry-Perot interferometer with transverse sinusoidal and nonsinusoidal modulation of dielectric constant is developed. Calculations of light fields for such systems are realized. Optimal parameters of sinusoidal and nonsinusoidal interferometers-gratings are determined for their usage in devices of amplitude-phase, spatial and spectral modulation of light beams and information signal encoding devices for optical communication channels and networks. A number of devices are proposed where the interferometer-grating can operate as spatial switch due to the intensity redistribution between diffraction orders.

We present an experimental and numerical investigation of the interaction of bidirectional self-guided beams in photorefractive media. Distinct from copropagating beams, the feedback intrinsic to the counterpropagating geometry renders such configurations unstable beyond a control parameter threshold. The instability is mediated through attractive interaction between the induced waveguides and leads to dynamic states, showing telltale signs of chaotic behaviour. We demonstrate qualitative correspondance between experiment and a saturable Kerr model, investigate the dynamical bifurcation in detail and expand on the consequences of a realistic photorefractive model including nonlocality, anisotropy and self bending.

The energy efficiency of multiwave mixing and geometrical parameters of spatial solitons in photorefractive Bi₁₂TiO₂₀ crystals in conditions of pulsed and continuous-wave laser excitation have been studied experimentally. It has been found that with the use of 532 nm-wavelength laser pulses switching of the photorefractive nonlinearity mechanism requires a time interval in excess of 20 - 50 ns. And saturation is observed when the duration is over 100 ns. The formation dynamics of spatial solitons in photorefractive Bi₁₂TiO₂₀ crystals has been analyzed using radiation of a continuous-wave He-Ne laser. It has been determined that the formation conditions and dynamics are influenced by a number of factors including the radiation input geometry of a crystal, power of the light beam, orientation of its polarization relative to the crystal axes, applied electric field and its direction.

We consider a d-dimensional conductor (a superlattice) within the independent-electron one-band approach taking into account slow relaxation processes. Its nonperturbative response to time-periodic electric fields is studied in the nearly coherent regimes: a) dynamic (short-time) and b) kinetic (long-time). We provide a classification and analysis of field-induced dynamic localization and response through the dc/ac current and mean square displacement of electrons. We demonstrate that the overall localization increases in passing from the periodic regime through the commensurate to the incommensurate one (governed by the relation of field period and Bloch frequency) both in the dynamic and kinetic cases. Simultaneously, exceptional localization (for some particular values of field parameters or symmetries) typically retains its order in the small relaxation rate, but on the background of increasing overall localization becomes less pronounced, both in dynamic and kinetic regimes. In the dynamic regime exceptional localization is manifested through diffusion and dc response, in the kinetic - through diffusion and ac response. The commensurate case with long-range-overlap qualitatively resembles the periodic one; within nearest-neighbor approximation the commensurate regime becomes qualitatively analogous to the incommensurate one. We also obtain explicit analytic solutions for the dynamic and kinetic harmonic generation spectra. We demonstrate that in strong and smooth fields the harmonic spectrum has a plateau-like shape. In the kinetic regime all the harmonics vanish under "exceptional" localization, whereas in the dynamic regime there is no such effect. In a strong dc field there is an effect of weak ac harmonics amplification. Coherent control of induced localization and harmonic generation is discussed.

Complicated (chaotic and stochastic) oscillations have been found in a four-frequency ring gas class-A laser with the linear coupling of the counter-running elliptically polarized waves. The routes to symmetric and asymmetric chaos have been elucidated.

A novel multilongitudinal-mode model of the semiconductor laser with optical feedback, which generalizes the solid-state laser rate equations, is presented and compared with previously used more simple semi-phenomenological multimode models. Scopes of application of these semi-phenomenological models are found.

New method of femtosecond pulse soliton self-formation is discussed for laser radiation propagation in optical fiber with cubic nonlinear response and its time dispersion. An influence of perturbations of pulse shape and pulse phase on soliton formation is considered. The stability of each formed solitons and stability of soliton formation is investigated as well. It is shown that solitons formation is stable to small perturbations of initial pulse shape. Our computer simulation is proved by analytical results.

The influence of transverse perturbations including diffraction effects on propagation of extremely short electromagnetic pulses in medium with quadratic and cubic nonlinearities is examined. The account of transverse perturbations is based on the averaged Lagrangian method. As a result, the conditions of stable propagation with respect to self-focusing are determined.

A model of a multimode bipolarized laser has been developed. The interaction of different longitudinal modes is described within the rate equation approach, whereas the interaction of each pair of orthogonally polarized modes with identical longitudinal index is described taking into account phase-sensitive modal interaction. Comparison with experimental data has been made.

The interaction of both scalar and counter-rotating polarized steady state pulses (SSP) is studied numerically for a medium characterized by nonlinear susceptibilities of the third and the fifth order (a cubic-quintic medium with χ₃> 0, χ₅ < 0 ). The collision of two plateau-shaped solitons proved to be essentially inelastic: a number of secondary solitary waves elliptically polarized arise as a result of interaction of steady-state pulses.

Effects of spatiotemporal transformation of grating shape at nonlinear holographic recording in absorbent photopolymer have been investigated. We present an analytical model of dynamics of (N+1) spatial harmonics of spatial grating profiles with taking into consideration both record mechanisms (polymerization and components diffusion), absorption, interference pattern contrast and optional photopolymerization nonlinearity. Also we take into consideration so called additional gratings (AG) formed as a result of two waves mixing. On the base of numerical simulation we examined an influence of the material and record parameters on 2D spatial profiles of gratings.

The effects are observed of propagation of an ultimately short (in one or several oscillation) electromagnetic pulse in a medium whose resonance transition characterized both by diagonal and non-diagonal matrix elements of dipole operator. The Maxwell-Bloch set of equation is employed without the approximation of slowly varying amplitudes. The analog of MacCall and Hahn area theorem is discussed corresponding to the process of the initial ultimately short pulse break up into subpulses. A novel solution is found in the form of a stable solitary bipolar signal, whose pulse area is not zero- non-zero breather.

The steady states for ultrashort dissipative optical solitons, appearing in single-mode erbium-doped fiber amplifiers are theoretically examined. Such solitons can be shaped due to resculpturing external optical pulses by fiber amplifier in the traveling-wave regime. We consider rather simplified model related to the most desirable practically fundamental solitons and, in so doing, develop extremely extended analytical approach based on exploiting the consistency equation. The analysis performed includes the already-known data for the model selected, generalizes them, and demonstrates that erbium doped fiber amplifiers can support both dark and bright dissipative optical solitons as well as the shock waves, whose amplitude and frequency profiles are exactly described.

We study the process of appearing three-wave solitons in the form of weakly coupled states under the action of pulsed optical pump in a two-mode square-law nonlinear waveguide. The analytical model for this stimulated process with slightly mismatched wave numbers predicts sculpturing multi-pulse optical components of three-wave coupled states. Both the analysis of sculpturing multi-pulse coupled states in non-stationary regime and the experimental studies are carried out. Then, the analysis developed is exploited to realize the binary encoded digital modulation of light based on collinear three-wave coupled states. An opportunity of applying this technique of localizing multi-pulse optical components inherent in coupled states to the problem of binary modulation of light beam is experimentally demonstrated.

A new physical and mathematical formulation of the pulse evolution problem is proposed based on the inverse scattering transform method and a new spectral problem. The polarization of ultrashort pulse and level degeneracy of atoms are taken into account. The Gel'fand-Levitan-Marchenko equations and soliton solutions are obtained. The change in polarization of colliding solitons is demonstrated.

It was investigated basic features of inhomogeneous polarized vector light fields. It was shown both theoretically and experimentally, how the actual topological elements, namely singular points and lines, saddles and traversing them bifurcation lines, are jointed in the structural units (quadruples, dipoles, etc.). In turn, these units are jointed in unified polarization patterns, or topological networks. It was investigated transformations of polarization pattern under guided perturbations. Arrangement of polarization ellipses of all other points of field, i.e. morphology, is defined by polarization pattern topology.

We present the results of our theoretical investigation on passive mode-locking of fiber lasers. The mode-locking is achieved using the nonlinear polarization technique. The practical case of the ytterbium-doped fiber laser operating is analysed. A simple model is developed allowing to study several features observed in passively mode-locked fiber lasers such as bistability between the mode-lock and the continuous regime, multiple pulse operation, hysteresis phenomena, bound solitons. The dynamics of the number of pulses as a function of laser parameters is also reported. Pump power hysteresis is demonstrated.

We have demonstrated the possibility to control filamentation in the turbulent atmosphere by means of introduction of regular wavefront perturbations into the initial beam. Statistical processing of simulation results has shown that the spatial position of filaments in turbulence deviates from the similar spatial positions in the regular medium within 10% of the initial perturbation period.