Figure 1

Dipole (left) and nondipole (right) probability densities of the KH wave function in the $x-z$ plane for a $\widehat{x}$-polarized, 10-cycle pulse propagating in the positive $z$ direction (upward), with $E_0=30\mathrm{a}.\mathrm{u}.$, $\omega =2\mathrm{a}.\mathrm{u}.$, and $\varphi =0$. The snapshots are taken at $t=0$, $t=T/2$, and $t=T+25.1\mathrm{a}.\mathrm{u}.$ with $T=31.4\mathrm{a}.\mathrm{u}.$. The length of the horizontal line corresponds to 50 a.u.. The scale is logarithmic with four contours per decade.Reuse & Permissions

Figure 2

Dipole (left) and nondipole (right) electron angular distributions for a 3- (upper), 5- (second), 10- (third), and 15-cycle pulse (lower panel) linearly polarized in the horizontal direction, with $\omega =2\mathrm{a}.\mathrm{u}.$, $E_0=30\mathrm{a}.\mathrm{u}.$, and $\varphi =0$. The propagation direction, marked with an arrow, is along the positive $z$ axis. In all cases the total ionization probability lies between 0.4 and 0.5, and the ratios of probability of ionization between the nondipole and dipole cases are 1.00, 1.06, 1.17, and 1.16 for the four different pulses.Reuse & Permissions

Figure 3

As Fig. 2, but for a five-cycle pulse and for three different field strengths, $E_0=20$ (upper), $E_0=30$ (middle), and $E_0=45\mathrm{a}.\mathrm{u}.$ (lower panel). The data are averaged over the carrier-envelope phase. The total ionization probability is between 0.41 and 0.63, and the ratios of probability of ionization between the nondipole and dipole cases are 1.01, 1.06, and 1.20 for the three different pulses.Reuse & Permissions

Figure 4

Upper panel: Classical angular distribution corresponding to those classical trajectories that remain closed orbits within the dipole approximation but are unbound in the nondipole description. The data, which are averaged over the carrier-envelope phase $\varphi$, are taken for a five-cycle pulse with $E_0=45\mathrm{a}.\mathrm{u}.$ and $\omega =2\mathrm{a}.\mathrm{u}.$. Middle panel: A single classical trajectory that contributes to the third lobe in the angular distribution. Lower panel: The same trajectory in the dipole approximation. The dashed (red) and dotted (blue) curves indicate the initial and final orbits, respectively, and the full curve (black) shows the trajectories during the pulse. The linear polarization is along the $x$ axis and the pulse propagates in the positive $z$ direction.Reuse & Permissions