Laser-assisted photoionization beyond the dipole approximation

We present a theoretical study of atomic laser-assisted photoionization emission beyond the dipole approximation. By considering the nonrelativistic nondipole strong-field approximation (nondipole Gordon-Volkov wave function), we analyze the different contributions to the photoelectron spectrum, which can be written in terms of intra- and intercycle factors. We find that our nondipole approach not only exhibits asymmetric emission in the direction of light propagation, but also allows emission in dipole-forbidden directions. The former feature can be rooted in both intra- and intercycle interference processes, while the latter stems from a dependence of the sideband energy on the emission angle with respect to the propagation direction. Our theoretical scheme, presented here for He atoms in the $1s$ quantum state, is general enough to be applied to other atomic species and field configurations.

Figure 1

Intercycle factor for case A (see Table 1) parameters and $N=2$, within the (a) dipole and (b) and (c) nondipole approximations. The vertical dashed lines indicate the position of the SB in the dipole approximation: $E_n^D$ for (a) and (b) $n=-30,-25$ and (c) $n=64,67$.

Figure 2

(a) Nondipole LAPE PES (with $N=1$) of $\mathrm{He}\left(1s\right)$ for case A (see Table 1) in logarithmic scale and arbitrary units. (b) Asymmetry factor (26).

Figure 3

Intracycle factor for LAPE of $\mathrm{He}\left(1s\right)$ for the nondipole case A (see Table 1) at (a) fixed emission angles and (b) fixed energy values.

Figure 4

Schematic classical limits in the momentum space $(k_x,k_z)$. Green dashed lines depict the dipole results (see Ref. [17]).

Figure 5

Intracycle factor for case D as a function of the photoelectron energy at fixed emission angles. (a) The photoelectron momenta are $\mathbf{k}=k\widehat{z}$ ($\theta =0$) and $\mathbf{k}=k\widehat{y}$ ($\theta =\pi /2$). The black dashed vertical lines indicate the semiclassical limit at $E_{\text{low}}=1.6$ a.u. and $E_{\text{up}}=3.6$ a.u. (b) The blue solid line shows $\mathbf{k}=k\widehat{x}$ and the orange dashed line shows the quadratic approximation (31). The black dashed vertical lines indicate the semiclassical limit at $E_{\text{low}}=0.2$ a.u. and $E_{\text{up}}=11$ a.u. At $v_0^2/2=3.6$ a.u. (blue dashed vertical line) the PES shows a minimum.

Figure 6

Intracycle factor at the emission direction (a) $\mathbf{k}=k\widehat{z}$, (b) $\mathbf{k}=k\widehat{y}$, and (c) $\mathbf{k}=k\widehat{x}$, for different laser parameters according to cases B–E (see Table 1).

Figure 7

Intracycle factor at the emission directions $\widehat{z}$ (purple solid line) and $-\widehat{z}$ (orange dashed line) for case E (see Table 1). The dashed vertical lines indicate the classical limits at $E_{\text{low+}}=1.06$ a.u., $E_{\text{low}-}=1.13$ a.u., and $E_{\text{up}}=4.09$ a.u.