THEORY OF HIGH-HARMONIC GENERATION BY LOW-FREQUENCY LASER FIELDS

We present a simple, analytic, and fully quantum theory of high-harmon ic generation by low-frequency laser fields. The theory recovers the c lassical interpretation of Kulander et al. in [Proceedings of the SILA P III Workshop, edited by B. Piraux (Plenum, New York, 1993)] and Cork um [Phys. Rev. Lett. 71, 1994 (1993)] and clearly explains why the sin gle-atom harmonic-generation spectra fall off at an energy approximate ly equal to the ionization energy plus about three times the oscillati on energy of a free electron in the field. The theory is valid for arb itrary atomic potentials and can be generalized to describe laser fiel ds of arbitrary ellipticity and spectrum. We discuss the role of atomi c dipole matrix elements, electron rescattering processes, and of depl etion of the ground state. We present the exact quantum-mechanical for mula for the harmonic cutoff that differs from the phenomenological la w I(p) + 3.17U(p) where I(p) is the atomic ionization potential and U( p) is the ponderomotive energy, due to the account for quantum tunneli ng and diffusion effects.