Theory of high-harmonic generation by low-frequency laser fields

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.