We show that violation of the "spectral condition" leads to a drift in stability of a soliton from its initial location, and show how to determine the speed of the drift.

We develop a general approach to the problem of the propagation dynamics of higher-order multipole spatial solitons in nonlocal nonlinear media. By introducing the generalized Hermite-Laguerre-Gaussian ansatz similar to the corresponding linear modes, we construct nonlocal solitons by means of the variational approach and then find them numerically as stationary states. We then study the example of a tripole-like structure with nonzero angular momentum and investigate the stable propagation of such a beam in optical media with a nonlocal Gaussian response. Our results provide the first example of a self-trapped multi-vortex beam in self-focusing nonlinear media.

We find the Lax pair for a system of reduced Maxwell-Bloch equations that describes the propagation of two-component extremely short electromagnetic pulses through the medium containing two-level quantum particles with arbitrary dipole moments.

Formation of the bright and dark solitons in N-core of the optical coupler is the important problem for the creation of effective optical lines of the communication. This problem is connected to the finding of the solution of the nonlinear Schrodinger equation taking into account the interaction between the cores of the fiber. Basing on elementary mathematical model of N-core of the optical fiber coupler with the linear interaction between the next cores the conditions of formation of the solitons in 2 - core fiber coupler is investigated. For the certain type of the soliton solution the necessary and sufficient conditions of existence of the solitons are received. The parametrical space and the physical sense of the received conditions is defined. It is shown, that for the certain parameters of optical systems, the solitons spread with identical speed and width, but the amplitudes of the interacting solitons can be both one polarity, and opposite. The method based on solution of the system of the connected Schrodinger equations determines the necessary and sufficient conditions of the existence of solitons and it can be used for research of problems of formation and propagation of the bright (or dark) solitons in N- core optical couplers.

The analysis of the coupled Klein-Gordon equations system of the second order for an optical media with the Kerr nonlinearity is carried out. The conditions of existence of the pulse propagation in a form of dark solitons are formulated.

Possible approaches to observe optical bistable behavior of SiO₂ opal matrices are discussed. They include mirrorless schemes exploiting transmission oscillations at the stop-band edge or sharp structure impurity resonances and layouts with opal inside Fabry-Perot interferometer.

We will show that, in three-mode approximation, an exact analytic solution of a steady-state parametric frequency conversion problem can be obtained by analytic solution of independent nonlinear Schrodinger equations with corresponding coupled boundary conditions.

Bistable lasing in twin coupled microcavities is demonstrated analytically and numerically, underlying a new principle of a multiple-wavelength microlaser where the lasing wavelength is switched by locking into the desired mode in a multimode resonator. The bistability appears due to an interplay between coherent and incoherent mode interaction processes, assisted by similarity between the spatial intensity distribution of the modes in the gain region. The wavelength switching dynamics in a model system of twin defects in a photonic crystal is explained on the basis of the theoretical analysis presented.

We show the speed of response of a photorefractive self-pumped phase-conjugate mirror can be considerably (6 - 20 times) accelerated by special training procedures. Efficiency of some such procedures is compared and analyzed.

We have found that to achieve dynamic photorefractivity regime the external electric field (>20 V, >1 s) should be applied to the cell with photoconducting orienting layers prior to its operation. These conditions are automatically fulfilled for low-frequency ac electric field. Investigations have shown that only normal (transverse) rolls possess resonance interplay with periodic charge pattern induced by optical interference field on photoconducting orienting layers. If charge of ITO electrodes prevents separated charges to move back, neither transverse rolls, nor dynamic photorefractivity are observed.

In this work are presented results of numerical modelling of recording of transient concentration holographic gratings by the thermodiffusion mechanism in the condensed medium. The principal opportunity of parameters management of grating at change shape of temperature field is shown. The way of management in parameters of holographic gratings in reoxan medium (the register oxidized medium with anthracene), based on thermodiffusion effect is offered.

The modulational instability of continuous waves in nonlocal random focusing and defocusing media with saturable nonlinearity is described. It is shown that nonlocality with a sign-definite Fourier image of the medium response function reduces significantly the growth rate peak and bandwidth of instability caused by stochasticity. Contrary, nonlocality can increase modulational instability growth rate for a response function with negative-sign bands.

The reflection mechanisms are analyzed for the incoherent light beams interacting in a medium with thermal nonlinearity. The propagation geometry of the light beams within a cell with absorbing organic dye is determined, and the intensities of laser radiation associated with the nonlinear reflection effect are estimated. It is demonstrated that on nonlinear reflection one can observe transformation of the spatial structure of a signal beam. The reflected light beam occupies the region associated with the geometric reflection of the signal beam from the reference one. It is found that a thermal lens formed when a laser is operating in the pulsed mode is transformed as a vertical thermal "plate" due to the convection currents of the dye solution.

The coherent nonlinear interaction of three-four electrostatic waves is considered analytically and numerically. The excitation and nonlinear evolution of the electrostatic two-stream or Farley-Buneman (FB) plasma instabilities in the collisional plasma are investigated. Basing on the magnetohydrodynamics (MHD) system equations for collisional plasmas with magnetized electrons and non-magnetized ions, the evolution equations for the electron density are obtained.. It is shown that three-four wave coherent interaction is one of the effective physical mechanism which leads to nonlinear stabilization of the growing high-frequency waves and to the formation of local density structures of the charged particles. The different scenarios of the stabilization of the two-stream instability (as a periodic, multi-periodic, nonlinear cnoidal, shock waves and quasi-stochastic behavior) are possible in the collisional plasma. If the plasma system is in the weakly supercritical regime, the explosive instability may also occur. The different examples of the nonlinear temporal evolution of the FB instability are represented. The result of the numerical models allows analyzing feasibility of scenarios of the two-stream plasma instability in the plasma.

Three-wave coupled states, appearing with Bragg collinear light scattering in a periodically modulated two-mode square-law nonlinear medium with linear losses under action of optical pump, are revealed and investigated. The localization conditions and spatio-temporal distributions of their optical components are studied theoretically in both stationary and non-stationary regimes and observed within the acousto-optical experiments in a two-mode calcium molybdate crystalline waveguide.

Experimental results of self-compression of femtosecond pulses under filamentation in argon and xenon are presented. The mode of a self-compression in xenon is realized for the first time. The dependence of the spectrum broadening from pressure of these gases, input energy and focusing parameters are studied in detail. The spectral and temporary profiles of the first and the second filaments at multiple filamentation are analyzed. Features of multiple filamentation are revealed in xenon. For the first time experimentally the effect of restriction a number of filaments and effective swapping of energy from one filament to another (more than 70 % of energy in two-filament mode without increasing of their amount is founded). The possible mechanism of the phenomenon related with the saturation of the third order nonlinearity in xenon and influence of the higher fifth-order susceptibility χ⁽⁵⁾ are discussed.

An analytic approach to describe subpicosecond soliton dynamics is presented. It is argued that the modified nonlinear Schrödinger (NLS) equation containing a nonlinearity dispersion term should be considered as a true basic integrable model in the subpicosecond region, instead of a perturbed NLS equation. Unique features to improve performance characteristics of optical systems in the subpicosecond region by matching properly soliton and medium parameters are illustrated by several examples, among which are dispersion-managed solitons and solitons in a nonlocal Kerr medium.

Intra-cavity and output spectra broadened in the low-Q cavity Raman fiber laser are measured and modeled. The approach of the optical wave turbulence is implemented for the description of the spectral broadening owing to the multiple four-wave mixing processes between numerous longitudinal modes. The predictions of the theory are in a good agreement with performed experiments for the different output fiber Bragg grating reflection coefficients in all power range.

Mechanism of a laser radiation transformation under which frequency of initial signal is doubled and then reduced to the red part of spectrum is suggested. This mechanism is implemented in the bi-axial crystals as the result of cascade process: an initial wave generates the second harmonic, which generates a video pulse. Such process is accompanied by the continuous transformation down of the second harmonic frequency under condition of Zakharov-Benney resonance.

It has been shown that during the few light field cycle pulses propagation in the nonlinear dielectric media with dispersion it is possible for the highly intensive light kern slowly changing with the distance passed in the media to be formed. The transverse sizes of the kern can be comparable with the central wave length. The difference of the phase velocity of the kern and its surrounding light shell makes it possible for the phase surface branching to occur.

The spectral widening of radiation of femtosecond Cr4+:forsterite laser in high nonlinear optical fiber is studied. Generation of spectral supercontinuumin near infrared range in the variable dispersion fiber obtained by femtosecond pulses of Cr4+:forsterite laser working in the self synchronization regime is realized.

We study pattern formation in a paraxial model for an unidirectional ring resonator filled with a semiconductor sample and driven by a coherent injected field beyond the mean field limit (MFL). We perform numerical simulations to describe the three-dimensional dynamics of the coherent field profile. For fast media spontaneous self-confinement leads to the formation of 3D dissipative addressable spatial solitons, we show that for carrier dynamics compatible with GaAs/GaAlAs MQW devices longitudinal self-confinement is hindered by the slow carrier interband dynamics.

Switching of thin-film semiconductor Fabry-Perot with the resonance in visible region by short UV pulse is demonstrated. Design of reconfigurable optical switch with wavelength conversion is discussed. Visualization and analysis of the fine-structured UV images are possible, and resolution of the system for detecting minor local differences of object and etalon images can be increased to submicron range.

Conditions for bistability and solitons stability are defined in semiconductor laser with active and passive layers of quantum dots. It is demonstrated the way to design of base optical parameters which are critical for stability of spatial solitons. The possibility of localized structures formation from coherent excitons in thin semiconductor film is analyzed.

This paper gives analytical treatment and experimental details on on/off-bistability in vertical-cavity surface-emitting lasers with frequency-selective feedback by a grating. In particular, the conditions for the coexistence of lasing and nonlasing states and an abrupt turn-on behaviour at threshold are derived using an envelope approximation. The theoretical and experimental results are in satisfactory agreement.

The theoretical model of vortex light beams interaction with nonlinear cavity has been developed. Different steady-state and transient modes have been studied analytically and numerically, and the possibility of realization and control over periodical and rotating diffractive optical patterns has been revealed and discussed.

We present a theoretical analysis of the dynamics of lasers with delayed optical feedback where the time delay is periodically varied due to vibration of external mirror. Parameter regions have found of stable generation, periodic and quasiperiodic oscillations in dependence on characteristics of vibration.

Poincare maps are derived to describe antiphase spiking in class B multimode lasers. Analytical conditions are determined for phase synchronization and clustering of spikes associated with different longitudinal laser modes. Stabilization of splay states is proved in presence of small external signal.

Mathematical model of a nonlinear process (light field interaction with crystal having thermal-dependent optical activity, e.g. CdP₂) was introduced for four-mirror resonator. Maps of dynamic regimes were calculated. Crystal parameters, which are favorable for nonlinear-dynamic cryptography of optical range, were discovered.

We propose a study of dynamics of edge-emitting semiconductor laser subjected to external optical feedback. The external cavity contains a mirror and a second semiconductor device, which can work as an amplifier or an absorber. The existence of regimes of regular or chaotic pulsations are discussed.

We consider the influence of the local-field correction on the characteristics of attractors in a model of a single-mode homogeneously broadened laser. It is shown that the local-field correction changes the Lyapunov spectrum in a non-trivial way. The symmetry breaking leads to a shift of the chaotic behavior of the system towards the range of negative detunings from resonance, while for the positive detuning up to a certain value, it is possible to realize only a periodical regime of lasing.

On the basis of the experimentally confirmed model complemented by symmetry and bifurcation analyses the nonlinear dynamical phenomena have been studied in a single-mode anisotropic-cavity diode-pumped Nd:YAG laser. Bistability of regular and chaotic asymmetric attractors as well as noise-sensitive operation have been revealed.