High-order harmonic generation in the presence of a static electric field

We consider high-order harmonic generation by a linearly polarized laser field and a parallel static electric field. We first develop a modified saddle-point method which enables a quantitative analysis of the harmonic spectra even in the presence of Coulomb singularities. We introduce a classification of the saddle-point solutions and show that, in the presence of a static electric field which breaks the inversion symmetry, an additional classification number has to be introduced and that the usual saddle-point approximation and the uniform approximation in the case of the coalescing saddle points have to be modified. The theory developed offers a simple and accurate explanation of the static-field-induced multiplateau structure of the harmonic spectra. The longer quantum orbits are responsible for a long extension of the harmonic plateau, while the larger initial electron velocities are the reason of lower harmonic emission rates.