Effective ATI channels in high harmonic generation

Harmonic generation by an atom in a laser field is described by the three-step mechanism as proceeding via above-threshold ionization (ATI) followed by the electron propagation in the laser-dressed continuum and the subsequent laser assisted recombination (LAR). An amplitude of harmonic production is given by the coherent sum of contributions from different intermediate ATI channels labeled by the number m of absorbed laser photons. The range of m-values that gives substantial contribution is explored and found to be rather broad for high harmonic generation. The coherence effects are of crucial importance being responsible for the characteristic pattern of harmonic intensities with a plateau domain followed by a cutoff region. Due to multiphoton nature of the process, an efficient summation of m-contributions can be carried out in the framework of the saddle point method. The saddle points correspond to some complex-valued labels m = m c associated with the intermediate effective ATI channels in the three-step harmonic generation process. The advantage of this approach stems from the fact that summation over large number of conventional ATI m-channels is replaced by summation over small number of effective m c-channels. The equation governing m c has a transparent physical meaning: the electron ejected from the atom on the first (ATI) stage should return to the core to make LAR possible. The effective channel labels m move along characteristic trajectories in the complex plane as the system parameters vary. In the cutoff region of the harmonic spectrum a single effective channel contributes. For lower harmonics, in the plateau domain, two effective ATI channels become essential. The interference of their contributions leads to oscillatory pattern in the harmonic generation rates. The calculated rates are in good agreement with the results obtained by other approaches.