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We present theoretical studies of high-order harmonic generation in a rare-gas medium. The experimental results obtained at Saclay with a 1064 nm Nd-YAG laser in the 1013 W cm-2 intensity range are summarized. The harmonic emission strengths first decrease rather steeply for the first orders, then form a long plateau up to the 21st harmonic in xenon, or up to the 33rd harmonic in argon, before decreasing again rather abruptly. The theoretical description of these experiments consists first in the calculation of the photoemission spectra emitted by a single atom. The spectra are obtained by numerically integrating a time-dependent Schrôdinger equation for the laser-excited rare-gas atom. Second, one must account for collective effects in the medium, described by Maxwell’s equations. A theoretical framework for describing the generation and propagation of harmonics in strong laser fields is developed. A numerical solution of the propagation equations for the harmonic fields in xenon at 1064 nm provides results which agree well with experimental data. We discuss the role of phase matching in the high-order harmonic generation experiments. The main conclusion is that phase matching is determined not only by the variation of the phases of the interfering fields in the non-linear medium, but also by the variation of the amplitudes throughout the medium. We find orders of magnitude improvement in phase matching in a strong-field regime compared with the perturbative limit. © 1991 IOP Publishing Ltd.

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Journal of Physics B: Atomic, Molecular and Optical Physics

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