The atomic photoeffect is studied in the pulsed fields of two coherent waves: a high-order harmonic wave and the fundamental wave. Expressions are derived for the intensity of the main peak and satellites in the photoelectron energy spectrum for an arbitrary delay between the pulses. The role of inelastic Coulomb rescattering of photoelectrons from the residual ion in the fundamental wave field, in the production of satellites is analysed.

The atomic photoeffect is studied in the pulsed fields of two coherent waves: a high-order harmonic wave and the fundamental wave. Expressions are derived for the intensity of the main peak and satellites in the photoelectron energy spectrum for an arbitrary delay between the pulses. The role of inelastic Coulomb rescattering of photoelectrons from the residual ion in the fundamental wave field, in the production of satellites is analysed.

We propose a new method for the amplification of high-order harmonics of laser radiation based on stimulated emission accompanying the propagation of a probe pulse of a high-order harmonic through a gas medium irradiated by a high-power pump wave. It is demonstrated that such an amplification becomes noticeable in the case when a probe wave of a high-order harmonic enters the interaction area with some delay time with respect to the pump wave. Our estimates for the gain of high-order harmonics show that this gain is proportional to the delay time, reaching unity even for rather short delay times (corresponding to several optical cycles of the pump wave).

The case is considered of a weak Gaussian harmonic pulse of frquency $(2s+1)\ensuremath{\omega}$ passed through an atomic medium collinearly with an intense Gaussian laser pulse of frequency $\ensuremath{\omega}.$ The harmonic beam may be amplified or deamplified according to the balance between stimulated emission and absorption. A simple analytic expression for the gain is derived in the tunneling limit of ionization. It predicts a positive (negative) gain for positive (negative) delay of the harmonic pulse with respect to the laser pump pulse. The gain may be significant and proportional to the delay for delays of a few laser periods, much shorter than the pulse envelopes. Possibilities for experimental observations are briefly discussed.

Amplification of high harmonics generated by atoms irradiated by a high-power laser is considered. The general expression for the gain is obtained as a function of the atomic target and the laser parameters. For high-harmonic generation in a fiber, the gain may be substantial. An experiment for the gain measurement is discussed.

We consider spontaneous generation of a high-order harmonic by an atomic beam passing through a focus produced by two coherent pump waves propagating at a small angle with respect to each other. It is demonstrated that, due to phase matching, the use of two coherent waves in a gas dispersive medium allows the efficiency of high-order harmonic generation to be considerably increased as compared with the case of a single wave with a doubled amplitude. Conditions permitting the optimization of harmonic generation are analyzed.

Amplification of high-order harmonics generated in the above-threshold ionization of atoms in the field of a high-power laser wave is considered for the first time. The relevant gain is estimated as a function of parameters of the atomic beam and the pumping wave.

The problem of the amplification of high harmonics generated during the above-threshold ionization of atoms in a high-power laser wave field is examined for the first time. An estimate of the gain coefficient as a function of the parameters of the atom beam and the pump wave is given.

For phase-locked emitters, provided a certain relation exists between the pump wave and atomic beam parameters, a saturation effect is shown to be possible for which the intensity of the high-order harmonics ceases to depend on the atomic density. By means of a simple model that includes variations in the intensity of the pump wave in the plane transverse to the focal axis, an expression is obtained for the optimum atomic density of the medium corresponding to intensity saturation. The dependence of the optimum atomic density on the laser power and harmonic number obtained is found to be in qualitative agreement with recently published experimental data.

The analytic approach is considered for clarifying the role of the Coulomb interaction in the photoelectron-ion system in the formation of the spectrum and angle distribution of photoelectrons arising under the overthreshold ionization of atoms. This approach is based on involving multiple scattering of a photoelectron on the residual ion Coulomb potential with trapping a field quantum in each scattering event. The dependence of photoelectron energy spectrum on intensity and laser wave frequency is clarified. The applicability criteria of the theory suggested are found and the possibility of its experimental check is examined.

A multiphoton photoelectric effect at a metal in an intense laser field is analyzed. The light is propagating along the surface of the metal. An interpretation is offered for the above-threshold peaks in the spectrum of photoelectrons. The Coulomb interaction of these electrons with the image potential of the electron cloud in the metal is taken into account in this interpretation. The observed electron spectrum can be explained on the basis of a multiple scattering of an electron by the image potential, with a field photon being captured in each scattering event. It is also shown that the above-threshold peaks arise in fields far weaker than the corresponding fields in the case of atoms (in above-threshold ionization).

Specific features of harmonic generation in a strong laser field are analytically considered. The proposed approach assumes a direct connection between the above-threshold ionization of atoms and harmonic generation. An expression governing harmonic intensities is derived in terms of the probability amplitudes of the above-threshold ionization of atoms corresponding to the model of multiple Coulomb scattering of a photoelectron on the potential of the residual ion (the MCS model). The results of calculations are compared with the experimental data.