Multiphoton ionization and high-order harmonic generation of H$_{2}^{+}$ in intense ultrashort elliptically polarized laser fields

We present an \textit{ab initio} 3D calculation of multiphoton ionization (MPI) and high-order harmonic generation (HHG) of the hydrogen molecular ion subject to intense elliptically polarized laser pulses. The numerical procedure involves the extension of the generalized pseudospectral (GPS) method for non-uniform spatial discretization of the Hamiltonian and wave functions in prolate spheroidal coordinates; the time propagation scheme is based on the split-operator technique in the energy representation. The calculations are performed for the ground and first excited electronic states of H$_{2}^{+}$ at the equilibrium internuclear separation $R = 2$ a.u. as well as for the stretched molecule at $R = 7$ a.u. The dependence of the HHG spectra on the ellipticity parameter is analyzed. The spectral and temporal structures of the HHG signal are studied by means of the wavelet time-frequency analysis. The results provide new insights regarding the detailed HHG mechanisms in elliptically polarized laser fields.