Suppression of ionization in short high-frequency laser pulses of high intensity

A numerical technique for the solution of the time-dependent Schrödinger equation in three spatial dimensions is proposed to study the time evolution of hydrogen atoms subject to ultraintense short laser pulses. The method makes use of the Kramers-Henneberger transformation, and through a variable substitution, all of position space is discretized and the correct boundary condition at infinity is implemented. Calculations for 6-fs pulses with a ${\sin }^2$-shaped envelope show that stabilization of the atom against ionization does occur at high laser frequency and intensity, but that it is much less efficient than predicted by one-dimensional model calculations.