The irradiation of atoms by a strong, quasicontinuous IR laser field of frequency $\ensuremath{\omega}$ results in the emission of odd harmonics of $\ensuremath{\omega}$ (``IR harmonics''), by high-harmonic generation. It has been recently shown [A. Fleischer and N. Moiseyev, Phys. Rev. A 77, 010102(R) (2008)] that the addition of a weak XUV field of harmonic frequency $q\ensuremath{\omega}$ to the IR driver field leads to the appearance of a new set of higher-order harmonics (``XUV harmonics'') $q\ifmmode\pm\else\textpm\fi{}2K$ ($q,K$ integers) which were absent in the spectra in the presence of the IR field alone. Here we generalize these results by studying the generation of XUV harmonics upon the addition of an arbitrary high-frequency XUV field $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}\ensuremath{\omega}$, with frequency not necessarily a harmonic of $\ensuremath{\omega}$, and amplitude ${\ensuremath{\epsilon}}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}}^{\mathit{in}}$, which might be large. We have found that as the intensity of the XUV field increases, higher sets of XUV harmonics $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}\ifmmode\pm\else\textpm\fi{}2K,2\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}\ifmmode\pm\else\textpm\fi{}(2K\ensuremath{-}1),3\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}\ifmmode\pm\else\textpm\fi{}2K,\dots{}$. gradually appear, where each XUV harmonics set ${n}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}\ifmmode\pm\else\textpm\fi{}[2K\ensuremath{-}1+\mathrm{mod}({n}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}},2)]$ $({n}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}}=1,2,3,\dots{})$ is ${(\frac{{\ensuremath{\epsilon}}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}}^{\mathit{in}}}{{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}}^{2}{\ensuremath{\omega}}^{2}})}^{2{n}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}}}$ times weaker than the set of IR harmonics. The mechanism responsible for the appearance of the XUV harmonics is analyzed analytically using a generalization of the semiclassical recollision (three-step) model of high-harmonic generation (HHG). It is shown that the emitted HHG radiation field can be written as a series of terms, with the zeroth-order term representing the three-step recollision mechanism in its most familiar context [P. B. Corkum, Phys. Rev. Lett. 71, 1994 (1993)] and giving rise to IR harmonics in the spectra. The higher-order terms, which are responsible for the appearance of the new sets of XUV harmonics in the spectra, are shown to originate from the polarization (ac-Stark oscillations) which is induced by the XUV field on the returning electronic wave packet in the recollision process. The XUV harmonics are formed by the same electron trajectories which form the IR harmonics and have the same emission times as the IR harmonics. Due to the small quiver amplitude of the ac-Stark oscillation, they are, however, much weaker than the IR harmonics. Nevertheless, this mechanism allows an extension of the cutoff in the harmonic generation spectra without the necessity of increasing the IR field intensity, as is verified numerically by a quantum-mechanical simulation of a Xe atom irradiated by a combination of IR and XUV classical fields.
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