Coulomb rescattering in nondipole interaction of atoms with intense laser fields

We investigate the ionization dynamics of atoms irradiated by an intense laser field using a semiclassical model that includes magnetic Lorentz force in the rescattering process. We find that the electrons tunneled with different initial transverse momenta (i.e., perpendicular to the instantaneous electric field direction) distributed on a specific circle in the momentum plane can finally converge to the same transverse momentum after experiencing Coulomb forward scattering. These electron trajectories lead to a bright spot structure in the two-dimensional transverse momentum distribution, and particularly in the long-wavelength limit, a nonzero momentum peak in the direction antiparallel to the laser propagation (or radiation pressure) direction. By analyzing the subcycle dynamics of rescattering trajectories, we unveil the underlying mechanism of the anti-intuitive peak. Beyond the strong-field approximation and the dipole approximation, we quantitatively predict the spot center and the peak position. Our results are compared with a recent experiment and some theoretical predictions are given.

Figure 1

The electron momentum distributions of an Xe atom on the $p_y-p_z$ plane (upper row) and the momentum distributions along the propagation direction (lower row). The laser parameters are as follows: (a) and (d) 3400 nm, ellipticity $\rho =0.0$ (LP); (b) and (e) 3400 nm, $\rho =0.1$; (c) and (f) 3400 nm, $\rho =1.0$ (CP). Laser intensity is the same for all panels, 0.06 $\mathrm{PW}/{\text{cm}}^2$. The distributions of the initial transverse momentum after tunneling are plotted in dashed green.

Figure 2

Contour plots of the asymptotic momentum $P_{zf}$ [(a) and (c)] and $P_{yf}$ [(b) and (d)] versus the initial transverse momentum at a fixed tunneled phase $\omega t_0=0.3$ for a 3400 nm LP field. Panels (a) and (b) are without Coulomb potential, while panels (c) and (d) are with Coulomb potential.

Figure 3

The evolution of the electron trajectories originating near the saddle point: (a) the evolution of $p_z$; (b) the motion along the laser propagation direction. The vertical dashed purple line throughout (a) and (b) indicates the moment when the electron returns, i.e., $x\left({\eta }_r\right)=0$.

Figure 4

The peak shift of $p_z$ distribution versus the laser intensity. The experimental results with a 3400 nm LP laser are plotted with black diamonds with error bars. Numerical simulation results with 3400 and 5000 nm lasers are plotted with green circles and red squares, respectively. The analytical formulas with or without Coulomb correction are plotted with dashed or solid lines, respectively.