Various numerical schemes for self-action problems are considered. We describe a method for construction of an accurate and efficient projection-difference scheme in cylindrical coordinates. Numerical results for transformation of a self-focused pulse spectrum are presented.

Self-focusing leads to bifurcations of transverse solitary waves in sodium vapor (2D) and to second-order spatial solitons in a GaAs planar waveguide gain medium (1D). Transverse patterns in vertical-cavity surface-emitting lasers are shown to contain field vortices under some conditions. Good agreement is found between experimental data and computations.

Injection of a cw narrow-band laser beam into a lasing vertical- cavity surface-emitting laser results in the appearance of new frequencies on the way to injection locking as predicted by our theoretical model. Injection also causes a local asymmetric modification of the lasing line, resulting in a new gain peak at a lower frequency and a dip on the high-frequency side. The peak and dip move out directly as the intracavity injected power, as predicted by our quantum mechanical theory.

The numerical simulations of two coaxial laser beams, pump and probe, propagating in a three-level absorber are presented. The fixed-pump beam frequency and the variable-probe beam frequency are near-resonant to the adjacent transitions. Depending on the ratio of the population relaxation rates, either absorption or amplification of the probe field may occur, both demonstrating symmetric Rabi-splitted spectra of the absorption coefficient if the on-resonance pump intensity is high enough. In contrary to this, the spectra of the probe beam transmitted intensity are shown to be asymmetric due to the frequency-sensitive saturated refraction induced by the pump beam. The competition of level population changes and Rabi splitting is shown to cause the nontrivial induced lenses responsible for the complicated dependence of spectral asymmetry upon the pump intensity.

A novel numerical method to solve Fokker-Planck equations in quantum optics is presented, based on a Monte Carlo simulation of the probability diffusion process. The method is especially useful for multimode analysis and hence for studying realistic models of nonlinear optical systems. Two simple examples are given: the first is a 1D Fokker-Planck equation in the number representation, which describes a simple model of optical amplifier; the second is a 2D equation in the P-function representation-the quasi-probability for normal-ordered averages-which corresponds to the customary Van der Pol model of the laser threshold. In this case also the field correlation function and spectrum are numerically simulated.

Propagation of noncollinear generated second harmonic and sum frequency beams of ultrashort light pulses has been studied. An interference maximum in the far-field intensity distribution of the beams has been observed. The position of the maximum depends on the time delay between the interacting pulses. On the basis of this effect a technique to measure the lengths mismatch of two cavities and a technique to measure the time delay between two pulses with differing frequencies in a single laser shot have been developed.

We analyze the temporal development of a seed signal propagating in an ensemble of three-level atoms initially pumped by a two- photon excitation pulse. In an incoherently prepared system, the medium acts as a two-level system. Such a system is scale- invariant and therefore its dynamics are uniquely determined by the value of (alpha) L. On the other hand, a coherently prepared system is not scale invariant, leading to more complicated dynamics. We show that at low optical gain the amplification is reduced when the pumping is coherent. We further show that at high inversion there is an exponential increase in the radiation emitted from the lower transition in an initially prepared coherent system.

The calculation of quasi energies for atoms in strong resonance radiation fields and magnetic field as functions of detunings permits one to define whether or not the saturation due to the pump or probe field occurs. Where there is no saturation due to the probe field, different types of rotation of polarization plane of the probe field in alkaline atoms are calculated.

Coherent effects in polarized systems of nuclear or electron spins using a microscopic model are studied, but not the Bloch equations. It is shown that the spin system in a resonance circuit can emit a coherent superradiant pulse when the system is initially in an essentially unstable state, at a time much shorter than the spin dephasing time T₂ when the coupling of the system with the circuit is sufficiently strong, and at the time longer than T₂ when this coupling is weak. The important role if dipole spin-spin interactions is elucidated.

A method of integro-differential equation associated with the optical loch equations is proposed to consider the problem of nonlinear transient reflection (refraction) of two laser noncomplanar pulses. It is a 3D boundary-value problem of a semiclassical nonlinear resonant transient optics for the phase memory effects exhibited by surface atoms in response to pulses of fields resolved in space and time. A generalized Lorentz- Lorenz formula and a theorem of extinction of nonlinear transient optics are used to investigate generalized reflection and refraction laws.

We develop the group-theoretical approach for analytically solving the time-dependent Schrodinger equations for multilevel atoms driven by amplitude- and/or frequency-modulated concurrent laser fields. The time evolution of externally driven N-level atoms is calculated in an explicit matrix form. The exact analytical conditions for complete population transfer and its return are simply connected with the parameters of the symmetry. We consider in detail the case of a four-level system driven by concurrent laser pulses of different forms.

The concept of nonlinear resonance was associated formerly with the exact resonance between the external periodic field and the eigenfrequency at some energy, or alternatively between partial oscillatory degrees of freedom for a many-dimensional system. It is shown here that for the broad class of systems, the exact resonance is not necessarily needed for the nonlinear resonance to take place. The examples of physical systems are given. The problems of dynamical stochasticity and fluctuational transitions between stable states are discussed.

Initial conditions corresponding to the stationary evolution of a two-mode two-boson model with interaction between modes and self- action in one of them have been considered. On this basis the possibility of the steady squeezing for both Bose fields has been established. The estimations of the squeezing parameters have been obtained.

A new quantitative time-series characteristic is described and discussed. Power spectrum entropy renormolized to a given value of mean effective energy is used as a measure of relative degree of order of the time series. This criterion is tested for some well-known systems and phenomena. A perspective of this parameter used as a characteristic of system behavior is illustrated by way of application of this criterion to real signals analysis.

A method of reconstruction of dynamical systems on one realization is applied to a real biological system-the isolated frog's heart. The reconstruction is made without consideration to either physical or biological properties of the system. A 2D map qualitatively describing the behavior of the system is obtained. The equations are examined.

We apply the dynamical symmetry method for treating quantum atomic dynamics both in a prescribed laser field and in a self- consistent radiation field. In the framework of such an approach a new reasonable criterion for 'quantum chaos' that is connected with the behavior of the dynamical-group parameter in the pseudophase plane can be introduced in addition to the known criteria. For the simplest SU(2) model (an ensemble of two-level atoms), it is shown that the atomic dynamics essentially depend on a field polarization. The motion of SU(2) parameter g in the plane Re g - Im g is quite regular for a circular polarization and is ergodic for a linear one.

Berry's phases are derived for the generalized quasi-energy states of a multilevel quantum system driven by a strong biharmonic classical field. It is shown that when the frequencies of the two field harmonics are varied the earlier considerations of Breuer and Holthaus may not be applied in a straightforward manner. The additional contributions to the geometric phase are evaluated and shown to vanish in the adiabatic limit.

Polarization coherent states (PCS) are considered as generalized coherent states of SU(2)_p group of the polarization invariance of the light fields. In terms of PCS the polarization quasi probability functions are defined, which determine the quasi classical description of the statistical polarization properties of quantum light fields. The geometric phases of PCS are introduced in a way analogous to that used in the classical polarization optics.