Математика, 2005, ¹1 NONLINEAR SCATTERING OF LASER PULSE BY ELECTRON IN PERIODIC POTENTIAL P. A. Golovinski, P. A. Preobrahzenski Voronezh University of Construction and Architecture The classical model of a nonlinear scattering of intense pulse of laser radiation by an electron, taking place in a periodic potential field, is discussed. <...> On the basis of the approximation of Kapitza-Dirac the complete analytical solution in the case of compressed pulse is obtained. <...> The form of scattered radiation and its spectral distribution for various forms of initial laser pulses are found. 1. <...> INTRODUCTION The process of the high harmonic generation as the result of the action of intense laser radiation on various systems (atomic and molecular gases, metal films, glass structures, carbon nano tubes and others) is a subject of this study. <...> The progress in this area has given, in particular, sources of a coherent ultra-violet radiation and cutting of duration of a scattered pulse up to atto second. <...> Qualitatively, the mechanism of harmonic generation on atomic gases for a low-frequency field is explained on the basis of the semiclassical Corkums model (Corkum 1993). <...> According to this model the electron generates harmonics during the scattering on the potential of the atomic core after nonlinear ionization. <...> The motion of an electron, in this model, is considered as propagation of a wave packet in a field of an electromagnetic wave (Rae and Barnett 1993). <...> The difficulties of complete quantum consideration of the high harmonic generation in strong laser fields are not completely overcome till now, though the satisfactory consideration of the process is obtained both for atomic gases, and for gases of diatomic molecules (Chin and Golovinski 1995, Chin et al 1995). <...> The harmonic generation in periodic structures (crystals) was considered theoretically in (Kalman and Brabec 1995, 1996). <...> In © Golovinski P. A., Preobrahzenski P. A., 2005. these papers the field of strong laser radiation was taken as classic, and the remaining part of the problem was solved as quantum. <...> The high harmonic generation in such model arises as a result of a spontaneous radiation of electrons scattered on ions of a lattice, at a motion under the action of a strong laser field. <...> Thus, however, the plasma effects, essential in available experiments were not taken into account, and this impedes comparison of results of the theoretical investigations with the experimental data. <...> Recently serious successes <...>