Model calculations of high-harmonic generation in molecular ions

One electron bound by a three-dimensional two-center zero-range potential is embedded in an electric field with sinusoidal time dependence and arbitrary polarization and orientation with respect to the axis of the two-center potential. In the absence of the field, the model supports up to two bound states, which have a large transition dipole moment. Hence, the physical systems best described by the model are molecular ions such as ${\mathrm{H}}_2^{+}.$ Rates for high-harmonic emission are calculated analytically up to one final quadrature. In terms of the rescattering picture, harmonic emission can be attributed to two different mechanisms: electrons recombine either at the center they started from or at the other one. The latter case allows for three topologically different classes of orbits, which lead to different spectral ranges of harmonics. Two of them are similar to atomic (one-center) harmonic generation, but have different cutoff laws that are no longer proportional to the ponderomotive potential. In the third the electron moves directly from one center to the other. This leads to strong harmonic emission at comparatively low frequencies similar to emission from a two-level atom with the cutoff proportional to the field amplitude rather than the intensity. The molecular dipole phase in this case is almost independent of the field intensity and, at constant intensity, the phases of neighboring harmonics are locked. Different orientations of the two-center system with respect to the field with various polarization configurations are investigated. Most of the observed features lend themselves to interpretation in terms of the simple man’s model.