Generation of high-order harmonics in a high-intensity laser radiation field

An analysis is made of the generation of high-order harmonics by atoms and ions in high-intensity laser beams. A brief description is given of the main experimental relationships governing such generation, of methods for numerical solution of the Schrodinger equation for an atom in a strong field, and of some approximate models which make it possible to understand the mechanism of the effect (in particular, the 'semiclassical' model). A detailed discussion is made of an analytic quantum-mechanical theory of high-order harmonic generation in a one-electron system with the Coulomb, delta-like, and other potentials. Expressions are provided for the complex amplitudes of harmonics generated by monochromatic and bichromatic excitation. The results of simulation of high-order harmonic generation in an extended medium are given. This simulation takes into account the phases of the harmonics and their dependences on the amplitude of the fundamental-frequency field. The phase-matching problem and ways of solving it, the problem of the spectrum and duration of a pulse of a single harmonic and of the feasibility of controlling them, the problem of the total harmonic field, and other topics are considered.