Abstract
We solve exactly the three-dimensional time-dependent Schr\"odinger equation for the ${\mathrm{H}}_{2}^{+}$ molecular ion in a combination of intense short laser pulses and static magnetic fields using a newly developed adaptive grid method. This allows for a study of the control of high-order harmonic generation in molecules by various orientations of the magnetic and laser fields in order to control electron recollision with nuclei. In particular, we find regimes of pure even harmonic or even and odd harmonic generation for particular field and frequency configurations. Furthermore, magnetic fields are found to extend harmonic generation plateaus to higher order as a result of further nonlinear coupling between charges and fields.
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