We use a nonperturbative method to solve the time-dependent Schrödinger equation for an electronic state of an atom subject to a very intense (>${10}^{13}$ W/${\mathrm{cm}}^2$) laser. The oscillating, time-dependent dipole induced by the laser serves as a source for the photoemission. Calculations of single-atom photospectra reveal peaks at the odd harmonics of the incident laser field superimposed on a broad continuous background. We discuss a series of calculations for the hydrogen atom and a short-range Yukawa potential containing a variable number of bound states. At intensities up to a few times ${10}^{13}$ W/${\mathrm{cm}}^2$ at 1064 nm, we achieve stable, converged spectra that agree very well with previously published results. As the intensity increases to ${10}^{14}$ W/${\mathrm{cm}}^2$, the ionization rate increases to about 1% of the laser frequency, and converged results become extremely difficult to obtain, even for impractically large integration volumes. These difficulties are caused by a rising background due to electron density far from the nucleus and the increasing importance of the interaction of the wave function with the edges of the grid. We discuss the implications of our findings for calculations at high intensity and suggest alternative ways to calculate harmonic emission rates in the strong-ionization regime.

• Received 8 November 1991

DOI:https://doi.org/10.1103/PhysRevA.45.4998