Ab initio study of high-order harmonic generation of H-2(+) 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 H-2(+) for the wavelength 532 nm at the equilibrium internuclear separation (R=2.0 a.u.) and several laser intensities, as well as at the laser intensity 5 X 10(13) W/cm(2) and various intemuclear distances in the range between 3.0 and 17.5 a.u. We found that both the MPI and HHG rates are strongly dependent on R. Further, at some intemuclear 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.