  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 calculated rates are in
good agreement with the results obtained by other approaches.
