Ab initiostudy of high-order harmonic generation ofH2+in intense laser fields: Time-dependent non-Hermitian Floquet approach

We present a time-dependent non-Hermitian Floquet approach for the precision three-dimensional nonperturbative calculations of high-order harmonic generation (HHG) rates of the hydrogen molecular ions subject to intense laser fields. The procedure involves an extension of the complex-scaling generalized pseudospectral method for nonuniform spatial discretization of the Hamiltonian and non-Hermitian time propagation of the time-evolution operator. The approach is designed for effective and high-precision nonperturbative treatment of high-order multiphoton processes in very intense and/or low-frequency laser fields, which are generally more difficult to treat using the conventional time-independent non-Hermitian Floquet matrix techniques. The method is applied to the multiphoton ionization (MPI) and HHG calculations of $\mathrm{H}_{2}{}^{+}$ for the wavelength $532\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ at the equilibrium internuclear separation $(R=2.0\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.})$ and several laser intensities, as well as at the laser intensity $5\ifmmode\times\else\texttimes\fi{}{10}^{13}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}$ and various internuclear distances in the range between 3.0 and $17.5\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ We found that both the MPI and HHG rates are strongly dependent on $R$. Further, at some internuclear separations $R$, the HHG productions are strongly enhanced and this phenomenon can be attributed to the resonantly enhanced MPI at these $R$. Finally, the enhancement of higher harmonics is found to take place mainly at larger $R$. Detailed study of the correlation between the behavior of MPI and HHG phenomena is presented.