We present a simple, analytic, and fully quantum theory of high-harmonic generation by low-frequency laser fields. The theory recovers the classical interpretation of Kulander et al. in Proceedings of the SILAP III Works hop, edited by B. Piraux (Plenum, New York, 1993) and Corkum [Phys. Rev. Lett. 71, 1994 (1993)] and clearly explains why the single-atom harmonic-generation spectra fall off at an energy approximately equal to the ionization energy plus about three times the oscillation energy of a free electron in the field. The theory is valid for arbitrary atomic potentials and can be generalized to describe laser fields of arbitrary ellipticity and spectrum. We discuss the role of atomic dipole matrix elements, electron rescattering processes, and of depletion of the ground state. We present the exact quantum-mechanical formula for the harmonic cutoff that differs from the phenomenological law ${\mathit{I}}_{\mathit{p}}$+3.17${\mathit{U}}_{\mathit{p}}$, where ${\mathit{I}}_{\mathit{p}}$ is the atomic ionization potential and ${\mathit{U}}_{\mathit{p}}$ is the ponderomotive energy, due to the account for quantum tunneling and diffusion effects.

We present experimental results of harmonic generation using a 1-ps ${10}^{15\mathrm{-}}$W/${\mathrm{cm}}^2$ Nd-glass laser. We see up to the 29th harmonic in Xe, 57th in Ar, and at least up to the 135th harmonic in Ne (160 eV), being then limited by our monochromator’s resolution. The conversion efficiencies in Xe, Ar, Ne, and He are compared and different ways of optimizing the number of photons by defocusing the laser beam or increasing the density are discussed.

We demonstrate that high-order harmonics generated by an atom in intense laser field form trains of ultrashort pulses corresponding to different trajectories of electrons that tunnel out of the atom and recombine. Propagation in an atomic jet allows us to select one of these trajectories, leading to a train of pulses of extremely short duration.

A recently formulated theory of high-order harmonic generation by low-frequency laser fields [Anne L’Huillier et al., Phys. Rev. A 48, R3433 (1993)] allows us to study the phase of the induced atomic dipole moment. We show that this phase exhibits a piecewise-linear dependence on the laser intensity. This dependence can be interpreted in quasiclassical terms, and is related to the action acquired by the electron during its motion in the laser field. The value of the phase, however, is also affected by the quantum effects of tunneling, diffusion, and interference. The phase of the dipole moment considerably influences the conversion efficiency, as well as the coherence properties, of the harmonics generated in macroscopic media.

We study the conditions for optimal coherence of harmonics emitted by atoms in strong laser fields. The variation of the phase of the atomic dipole moment induces a dramatic dependence of the spatial and spectral coherence on the focusing geometry. However, these coherence properties can be controlled and optimized by moving the laser focus position relative to the nonlinear medium.