Control of high-order harmonic generation in strong laser fields

Using solutions of the time-dependent Schr\"odinger equation for the ${\mathrm{H}}_{2}^{+}$ molecular ion, we examine various scenarios for controlling high-order harmonic generation with combinations of laser fields. It is found that (i) the harmonic generation ``plateau'' can be modified by combining a laser field with its third harmonic field, (ii) even harmonics are controllable using the combination of a laser field and a weaker second harmonic field, and (iii) the phases of high-order harmonics in a strong driving field can also be changed by additional fields. In particular, when a weak dc electric field is applied, we prove that the phase shifts of all harmonics linearly depend on the dc field strength. In addition, when an ultrastrong static magnetic field is applied collinearly with the driving laser polarization, harmonic generation efficiency is enhanced and higher harmonics beyond the usual ``cutoff'' are generated as a result of the squeezing of the transversely spreading electron wave packets. The enhancement is a confirmation of the electron-ion recollision mechanism for high-order harmonic generation.

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