Analytic description of high-order harmonic generation by atoms in a two-color laser field

Abstract

A closed-form analytic formula describing high-order harmonic generation (HHG) in a two-color field of frequencies $\ensuremath{\omega}$ and $2\ensuremath{\omega}$ is derived quantum mechanically in the low-frequency (tunneling) limit for an electron bound by a short-range potential and generalized to the case of an active electron in a neutral atom. The HHG rates are presented as a product of an electron wave packet describing the ionization of an active electron and its propagation in a laser field up to the recombination event and an atom-specific cross section of the electron's photorecombination. In contrast to the case of a monochromatic laser pulse [Frolov et al., Phys. Rev. Lett. 102, 243901 (2009)], the two-color wave packet involves the interference of two terms (involving the Airy function) that describe the emission of harmonics during the first and second half-cycles of the fundamental laser cycle and give rise to the two-plateau structures in the HHG spectra. For the case of the H atom, we show that our analytic results are in good agreement with those obtained from a numerical solution of the three-dimensional time-dependent Schr\odinger equation. The factorization formula is used for describing the dependence of HHG rates for inert gases on the relative phase and intensities of the $\ensuremath{\omega}$ and $2\ensuremath{\omega}$ components of a laser field. It is shown that atomic structure (including electron correlation) effects can modify substantially the two-color HHG spectra of inert gases.