High-order harmonic generation and above-threshold ionization in H: Calculations using expansions over field-free state-specific wave functions

Abstract

We have computed the above-threshold ionization and the emitted harmonic spectra of H interacting with short laser pulses, with photon energies ranging from 1.16 to 5.44 eV and with peak intensities ranging from 6\ifmmode\times\else\texttimes\fi{}${10}^{13}$ to 7\ifmmode\times\else\texttimes\fi{}${10}^{14}$ W/${\mathrm{cm}}^{2}$, by solving the time-dependent Schr\"odinger equation (TDSE). The method of solution involves the expansion of the time-dependent wave function \ensuremath{\Psi}(r\ensuremath{\rightarrow},t) over the exact wave functions of the discrete and the continuous spectrum, computed numerically, and the subsequent integration of the resulting coupled first-order differential equations by a Taylor series expansion technique. This state-specific approach (SSA) to the solution of the TDSE allows systematic understanding of convergence as a function of the number and type of the field-free states for each value of the laser frequency (\ensuremath{\omega}) and peak intensity (${\mathit{I}}_{0}$). For example, the method allows practical numerical study of the degree of participation of high (n,l) (l=0,1,...,n-1) Rydberg, as well as of high-energy scattering states for each partial wave. For the harmonic spectra, comparisons are made between the results obtained by the SSA and those obtained in recent years by a number of researchers from the application of finite-difference grid methods. As regards economy, a general observation is that in the SSA the necessary number of partial waves is smaller than that required in the grid methods. Predictions are made for the case of \ensuremath{\Elzxh}\ensuremath{\omega}=2 eV, ${\mathit{I}}_{0}$=2\ifmmode\times\else\texttimes\fi{}${10}^{14}$ W/${\mathrm{cm}}^{2}$, in the context of a study of the effect of the pulse shape on the harmonic-generation spectrum. It is shown that the number of harmonics and the appearance of the plateau depend on the duration of the peak intensity.