We present a review of our work on mirror-dispersion- controlled (MDC) Kerr-lens mode-locked (KLM) Cr:LiSGaF and Cr:LiSAF lasers, aimed at studying nonlinear phenomena in the 15-fs regime. Such effects as pulse self-frequency shift a side-band generation due to high-order dispersion (HOD), are looked at in more detail. These phenomena take place in any crystalline solitary mode-locked oscillator, and represent important limitations towards achieving ultimately short pulse durations.

It is shown, that the linewidth enhancement in the semiconductor transforms essentially the ultra-short pulse parameters in cw solid-state laser with semiconductor modulator and can stabilize ultra-short pulse in the wide region of the group velocity dispersion.

We report on experimental and theoretical studies of a pulsed synchronously pumped Kerr Lens Mode-locking Ti:sapphire laser singularities as well as femtosecond pulses formation dynamics in a such system. The optimum resonator parameters were derived with the help of theoretical analysis based on nonlinear ABCD matrix formalism, conditions of pulsed synchronous pumping being taken into account. On this basis the practical recommendations for a resonator design necessary under such circumstances are offered.

Propagation of the ultrashort electromagnetic pulse in resonator media without the slowly varying envelope approximation is discussed. The models of the nonlinear medium take into account polarization states of electromagnetic wave. Steady state solutions of the relevant equations are presented.

On the basis of the analysis of the wave equations for an electrical field of radiation and without use of slowly varying envelope approximation the self-action of femtosecond light pulses in transparent media is investigated. The results of numerical simulation of spectral supercontinuum evolution, accompanying temporary broadening of intensive pulses with a spectrum in the range of normal group dispersion of medium both with only electronic nonlinearity, and with simultaneous electronic and electronic-vibrational nonlinearities are presented. The opportunity of compression of pulses with supercontinuum spectrum in light formations consisting of one cycle of an electric field is predicted. It is shown that spectral superbroadening of the elliptically polarized radiation is accompanied by nonuniform rotation of a polarization ellipse.

The dependence of the optical density of a model strongly scattering medium-aqueous milk solution on its layer thickness was investigated. IR lasers generating pulses of various short (from nanosecond to femtosecond) duration were used as the radiation sources. There were determined the dependences of the attenuation coefficients of such pulses on the solution concentration in the areas of low and more high optical densities of the solution layer for different values of radiation detector angular aperture. A modification of the two-flux Kubelka-Munk model was used to derive an expression describing the dependence of the transmission of a solution layer on its parameters when radiation detectors with a finite angular aperture are used. The absorption and scattering coefficients of the medium were obtained. A comparison of the calculations and experiments revealed a forward scattering anisotropy of short-duration laser radiation in an aqueous milk solution characteristic for the Mie's scattering.

The Sommerfeld diffraction theory is extended to the case of extremely short pulses. It is shown that in the far field the energy density distribution of the diffractional pattern is transformed into Gaussian one, when the plane wave with the uniform radial amplitude distribution and one period of oscillations falls upon the circular aperture. In the case of the focusing of the Gaussian beam with one period of oscillations the energy density distribution in the focal plane differs from the Gaussian one.

The interaction of femtosecond pulse with an extended medium of the two-level atoms or molecules is considered. It is shown that in the ultrahigh intensity layer field the atomic response is extremely nonmonochromatic due to the nonlinearity appropriate to the two-level system. The theoretical analyses shows that the two-level system tends to the generation of harmonics of the driving field. The results of the computer simulations show that in the ultrahigh fields the spectrum of the medium response is unusually broad in comparison with that for the fields of moderate intensity.

The scalar problem for a plane wave pulse spreading behind the diaphragm is solved. The calculation is carried out on the base of the non-stationary Kirchhoff-Sommerfeld integral and the expansion of pulse in terms of wavelet. The round and square diaphragm are considered. The pulse propagation under the condition of focusing is calculated. The Green function of the problem for the round diaphragm with and without nonabberative focusing is constructed.

Synchronized femtosecond pulses of different wavelength and bandwidth are used to investigate intraband and interband coherent effects in polar semiconductors. At low excitation densities the relaxation of nonthermal electron distributions by spontaneous emission of LO phonons in GaAs is monitored. Quantum kinetic behavior of the dynamics beyond the semiclassical Boltzmann equation is demonstrated for the first time. Violation of the energy conservation as well as memory effects are shown to occur on an ultrashort time scale of 100 fs. For strong excitation we present the first observation of Rabi-oscillations of the occupation density in the absorption continuum of InP. Despite high carrier densities exceeding 10¹⁸ cm^-3 dephasing time are long enough to allow for the appearance of two strongly damped Rabi-cycles at a peak intensity of the pump pulses of 17 GW/cm².

Dynamics of semiconductor microcavity modes in ZnS-Ni structure was investigated by femtosecond pump-supercontinuum probe spectroscopy in wide spectral region 1.6 - 3.2 eV. The change of reflectivity of the ZnS thin films (of 0.29 micrometer, 1.08 micrometer and 1.17 micrometer) on thick Ni film on quartz substrate was monitored. Two different pumping photon energies $HBAR(omega) _pul equals 2.75 eV and $HBAR(omega) _pu2 equals 5.5 eV were used for the excitation of the microcavity and produced different photoresponse spectra. The first pumping energy (2.75 eV) is lower than the energy gap of ZnS (3.7 eV) and the powerful laser pulse excites mainly electrons of metal (i.e. boundary of the microcavity) and of ZnS layer (by two-photon absorption). Nonequilibrium carriers of metal penetrate through Schottky electron barrier into the semiconductor. For the second pumping energy (5.5 eV) the pumping pulse is practically totally absorbed in thin surface ZnS layer of 40 nm in thickness and creates nonhomogeneous hot carriers distribution semiconductor. The differences in the processes of carrier excitation are responsible for the differences in the changes of dielectric function of ZnS and Ni and for the differences in the change of cavity modes.

The new method of investigation of Fermi surface and Fermi liquid (FL) versus non-Fermi liquid (NFL) behavior in strongly correlated electron systems by femtosecond laser spectroscopy is discussed. The method consists in the study of spectral dependence of nonequilibrium charge carriers relaxation time by femtosecond pump-supercontinuum probe technique. The usefulness of this method is demonstrated on weakly correlated electron systems in Au and Cu and strongly correlated electron system in high T_c oxide-superconductor YBa₂Cu₃O_7-(delta ) by studying the temporary changes of optical density of thin metal films in wide spectral region of probing $HBAR(omega) _probe equals 1.6 - 3.2 eV. The relaxation rate of charge carriers sharply slows down in the spectral area, related to the optical transitions into the vicinity of the Fermi level. The position of this peak gives the location of the Fermi surface (FS). The form of peak gives a unique information on the damping rate of quasiparticles near FS and thus on the FL vs NFL behavior.

Nonlinear optical effects in surface oxidized CuFe_xS_y (x equals 1,2, y equals 2,3) nanoparticles incorporated in polymeric film are studied. Surface oxidation of CuFeS₂ and CuFe₂S₃ nanoparticles results in appearance of the additional absorption band with maximum at 1.03 and 1.15 micrometer, respectively. Bleaching of this additional absorption band in CuFe₂S₃ particles and the induced absorption in all studied samples after picosecond laser excitation take place. An energy level scheme for CuFeS₂ and CuFe₂S₃ nanoparticles with long-lived trap levels in the band gap is proposed and origin of additional absorption is discussed. Characteristic times for career relaxation from conduction band to these trap levels are approximately 25 plus or minus 5 ps for CuFe₂S₃ and approximately 70 plus or minus 10 ps for CuFeS₂ oxidized nanoparticles. The relaxation of electrons from trap levels has characteristic time of more than 500 ps.

Transient spectroscopy technique based on correlation properties of the second harmonic of nanosecond Nd:YAG-laser and its first Stokes component from stimulated-Raman- scattering generator was applied for studying orientational diffusion of Cu-octaethylporphyrin and Cu-tetraphenylporphyrin dissolved in tetrahydrofuran and toluene.

In principle, a possibility has been shown to excite an atom on the target level selectively and very fast with the use of high-power laser pulses. For this aim the effect of ultrafast selective excitation which was revealed earlier for vibrational levels of a molecule can be used. The example Li atom is considered. Some pulses with different frequencies should be used to excite an atom on high energy levels.

The existing theoretical and experimental works on interference stabilization of Rydberg atoms are overviewed. Physical origin of the phenomenon, its main features and the conditions of existence, as well as the main theoretical approaches used for its description are discussed.

Different types of relativistic effects in atomic photoionization are shown to have frequency-dependent onset intensities. These phenomena can be explored analytically with the Strong-Field Approximation (SFA), which becomes accurate without need for rescattering corrections when intensities are high enough to be relativistic. Specially interesting results are that electron spin-flip amplitudes and virtual pair creation become important at intensities often not considered to be relativistic. The stabilization effect wherein transition rates decline with increasing intensity is strongly enhanced by relativity when the laser is linearly polarized. With linearly polarized light, photoelectron spectra exhibit a strong displacement towards the 'hotter' or higher-energy end of the spectrum; and both spectra and total transition rates, if calculated nonrelativistically, can be seriously in error for laser intensities I greater than 1 a.u. at typical intense-laser frequencies.

The two-dimensional quantum model is developed for describing the dynamics of an atom driven by strong few-optical-cycle laser pulse taking into account the magnetic component of exciting field. The conditions are found when magnetic field strongly suppresses high-energy photon production.

The preparation of the squeezed vibrational states in molecules may be realized due to excitation by short intensive electromagnetic pulses or by means of hot proton impact. New types of multiphoton processes have appeared: the combined multiphoton-multivibron processes, the intensity of such type transitions are apparently depended on parameters of squeezed vibrational states. The multiphoton excitation, high harmonic generation and light scattering processes in molecules are analyzed.

Modern laser technique permits to notice effects of vacuum polarization on the laser radiation parameters. The work presents a non-local theory of interaction of the laser radiation and electron-positron vacuum. The possibility of the vacuum damage by intensive radiation is considered.

Practical meaningful mono-energetic laser accelerator requires the electron bunch to be within a small proportion of the period of the accelerating field. By two laser accelerator schemes, we exemplify how the emerging picosecond terawatt (ps-TW) CO₂ laser technology helps to satisfy this requirement. These include: a staged electron laser accelerator (STELLA) experiment, which is being conducted at the Brookhaven Accelerator Test Facility (ATF), and a prospective laser wakefield accelerator (LWFA), where ps-TW CO₂ laser may offer noticeable advantages over more conventional T³ solid-state lasers.

Novel scheme providing for 7 J Nd-glass subpicosecond MultiTeraWatt laser pulse shortening down to 200 fs with intensity rise time of 100 fs for 2 order of magnitude and prepulse suppression down to quantum noise level are proposed. Non-linear optical two-stage converter consists of sequential second harmonic generator and stimulated raman scattering oscillator-amplifier.

The problem of obtaining a single attosecond pulse using high- order harmonics generation is under consideration. A method for producing an exciting light pulse with a time dependent degree of ellipticity from one-frequency linearly polarized laser pulse by means of linear optics is suggested. The whole of the field generated by limited beam of this light in gas target is calculated in the far zone. For this calculation we use an original method based on time approach of a theory of high-order harmonic generation. Suppressing low-frequency part of the spectrum (i.e. extracting the high-frequency part) by pinholes is simulated. Contrasted and intense (focused) single attosecond soft X-ray pulses are calculated. Also the generation of attosecond pulse by linearly polarized light with pulse duration close to one optical cycle was simulated.

We present a short summary of results dealing with the harmonic generation in N₂ and Ar produced by wave-mixing of parallel polarized fundamental and second harmonics of a Nd-YAG picosecond laser with special regard to the influence of phase-matching due to refractive index electrons produced by two-color multiphoton ionization. Particularly, in this work we compare the harmonic conversion efficacy and the rate of ionization by a self-correlation technique between fundamental and second harmonics of laser. We show that ion and harmonic signal exhibit the same behavior versus the relative delay of both fields. It seems to suggest, at least in our conditions, a positive influence of ionization on harmonic conversion efficiency.

High-order harmonics generated by two coaxial Gaussian beams focused at different sides of the target are focused at different points. Using this spatial structure of the harmonics one can select one harmonic from the others with a pinhole situated in the focus of the harmonic. The focusing of the harmonic is much sharper, than under single-beam generation. This provides obtaining harmonic field with greater intensities.

A theory of high-order harmonic generation by bichromatic field is proposed. The theory is valid for exciting fields with comparable intensities. Calculations carried out in the frames of the theory show that adding a high-frequency exiting field significantly enhances harmonics conversion efficiency. The possibility of phase matching of harmonics under bichromatic excitation is being discussed.

Dispersion relations of the SPP at the diffused plasma boundary have been calculated. Analytical dispersion relation taking into account spatial nonlocality has been obtained. Two-beam nonlinear excitation of SPP at the sharp plasma boundary has been investigated analytically.

Collisionless energy deposition to the gas during the ionization by subpicosecond intense laser pulse is under investigation. This deposition originates from the non- adiabatic interaction of ionization electrons with laser field (so called 'residual energy' phenomenon) and could be important in the domain of compact X-ray sources technology.

Short powerful laser pulse time profile during its propagation through the ionizing gas is under investigation. Laser pulse form steepening due to the ionization absorption is evaluated as a function of distance of the pulse penetration into the gas and of the pulse and gas parameters.

We present results on plasma formation in porous silicon (cluster like solid with mean cluster size of 3 nm, mean density 0.1 - 0.2 of crystalline silicon) by femtosecond laser pulses at intensity above 10 TW/cm². We deduced hot electron temperature as high as 8 keV and fast ions of at least 2 MeV energy.

A subterawatt fs laser complex with a power in a pulse P less than or equal to 0.15 TW is constructed. Our experiments show that axicon focusing of such laser light in transparent dielectric leads to formation of a long hollow channel with micron-order transverse dimensions. It is found that effective (approximately 10^-3) generation of harmonics of incident light takes place in plasma appearing under axicon focusing. The discussion of the results obtained is presented.

A charge-exchange pumping of laser-produced ions on a compact gas cloud is experimentally investigated. An interaction at density of neutrals approximately equals 10¹⁶ cm^-3 has been achieved for the first time. A record efficiency of charge-transfer pumping 10% has been measured which is close to maximum 25% predicted by developed analytical model. The results obtained appeared to be in good agrement with 3-D numerical simulation and are promising for future laser gain experiments.

Within accurate atomic kinetic model it is shown that the inversion state of heavy Ne-like ions in plasma is possible at electron densities n_e greater than 10²³ cm^-3 if electron temperature is high enough (T_e greater than E_ioniz/2). Near optimum plasma conditions are found for Ne-like silver lasers. New effective lasing transitions in Ne- like silver are found. Large ASE effect (gL greater than 100) is predicted for Ne-like silver plasma produced by a powerful short-pulse drive laser.

Phthalocyanine coated targets, as well as tungsten, aluminum, and carbon targets are studied. Nanosecond and picosecond neodymium lasers capable of moderate output powers are used to produce 10¹¹ to 10¹³ W/cm² of incident intensity on the targets. The laser plasma temperature and electron density are measured by recording intensities and spectral shapes of ion lines in a spectral region from 40 to 300 nm. More than ten lines including Al³⁺ at 76.8 nm, Al²⁺ at 56 nm, Al⁺ at 237 nm, C³⁺ at 253 nm, and C²⁺ at 297 nm are observed and analyzed. The measurement technique permits us to determine electron density and electron temperature dependencies on the distance form the target surface ranging from 0.5 to 5 mm, where N_e greater than or equal to 10¹⁷ cm^-3. For example, for an aluminum plasma at a distance 1 mm from the target, N_e equals 5 (plus or minus 1) 10¹⁷ cm^-3 and T_e equals 14 eV, respectively. For a new class of molecular materials (metal-phthalocyanines) an increased XUV output is observed due to effective laser radiation coupling into molecular targets. Different types of coatings (including fullerenes) are currently under investigation.

A correction to the stimulated Raman gain in a homogeneous plasma caused by influence of the anti-Stokes scattering is calculated. It is shown that for conditions of the laser fusion this correction does not exceed a few percent, and for limit of intense field of the pump it does not depend on intensity of the pumping radiation.

A new technique based on the fast frequency modulation of the laser radiation is proposed for suppression of stimulated Raman scattering in plasma in conditions of the laser fusion. It is shown that Raman gain for the backward SRS can be reduced twice providing rate of the saw-toothed form frequency modulation as high as 2% per picosecond.

Analytical theory is developed for plane linearly polarized relativistically intense electromagnetic wave propagating in cold underdense plasmas. Growth rates of the instability of these waves, both quasi-monochromatic and comprising a flux of photons with different frequencies, are calculated using a special numerical technique. For the relativistically high intensities both forward and backward Raman scattering by plasmons occurs and radiation harmonics are generated. The shape of the growth rate distribution at the center of each harmonics band is formed primarily by the fluid dynamics analog of the Compton effect and its edges are due to excitation of Langmuir noise.

The generation of ion-acoustic waves in metals irradiated by ultrashort laser pulses is studied. It is shown that non- equilibrium ion-acoustic oscillations lead to an anomalous increase of the effective electron collision frequency and fast melting of metals.

Vaporisation of condensed substances heated by laser or electron beams is widely used for various practical purposes. Theoretical description of these processes is complicated, in particular, due to non-equilibrium nature of intense evaporation which manifests itself in metastable states of condense and vapour phases as well as in Knudsen layer (KL) jump adjacent to evaporating surface. In the framework of fluid dynamics KL is considered as discontinuity where appropriate boundary conditions should be formulated to describe phase transition kinetics which depends on gas flow dynamics.