Two-color phase control of high-order harmonic generation in intense laser fields

We present a time-independent generalized Floquet approach for nonperturbative treatment of high-order harmonic generation (HG) in intense onea (i) determination of the complex quasienergy eigenvalue and eigenfunction by means of the non-Hermitian Floquet formalism, wherein the Floquet Hamiltonian is discretized by the complex-scaling generalized pseudospectral technique [Wang, Chu, and Laughlin, Phys. Rev. A 50, 3208 (1994)], and (ii) calculation of the HG rates based on the approach that implies the classical treatment of the electromagnetic field and quantal treatment of the atom. The method is applied to the nonperturbative study of HG by the hydrogen atom in strong laser fields with the fundamental frequencies 532 and 775 nm and their third harmonics. The results show a strong dependence on the relative phase δ between the fundamental frequency field and its harmonic. For the intensities used in calculations (1×${10}^{13}$ and 5×${10}^{13}$ W/${\mathrm{cm}}^2$ for the fundamental frequency 532 nm and 1×${10}^{13}$ and 3×${10}^{13}$ W/${\mathrm{cm}}^2$ for the fundamental frequency 775 nm, the harmonic intensity being 10 and 100 times weaker), the total photon emission rate has its maximum at δ=0 and minimum at δ=π. However, this tendency, while valid for the first several HG peaks, is reversed for the higher HG peaks. The HG spectrum for δ=π is broader and the peak heights decrease more slowly compared to the case of δ=0. These results have their analog in the multiphoton above-threshold detachment study performed recently for ${\mathrm{H}}^{\mathrm{-}}$ ions [Telnov, Wang, and Chu, Phys. Rev. A 51, 4797 (1995)].