Trajectory-based analysis of low-energy electrons and photocurrents generated in strong-field ionization

The three-dimensional classical-trajectory Monte Carlo method is employed to investigate low-energy photoelectron spectra in above-threshold ionization by strong laser fields. By connecting the tunneling coordinates with the final momentum-energy spectra, we identify the effects of the Coulomb potential on electron trajectories and the final energy spectra. In addition, we verify that the photoelectron spectra, depending on the energy region, can be controlled with a two-color laser pulse by varying the phase delay. The modulations of the electron spectra and yields as well as the generated photocurrents reveal the connections among them, which support our previous work [Phys. Rev. Lett. 109, 243002 (2012)] on terahertz wave generation from two-color laser pulses.

Figure 1

(a) Energy spectra of photoelectrons collected within the angles of $\pm 6^{\circ }$ with respect to the laser polarization direction, calculated with (solid lines) and without (dot-dashed lines) the Coulomb potential, in the tunneling regime with 150 ${\text{TW/cm}}^2$, 2.0 $\mu \text{m}$ pulses. The dashed vertical lines indicate the energies of $2U_p$ and $10U_p$. (b) The low-energy region of the calculated spectra (solid line) compared with Blaga's experimental data [16] (dot-dashed line) produced by Ar under the same laser parameters. (c) Comparison of calculated angular distributions of photoelectrons with experimental data [35] in the energy region [2.25 eV, 2.75 eV], for 800 nm and 2.0 $\mu \mathrm{m}$ lasers with peak intensity of ${10}^{14}$ ${\text{W/cm}}^2$.

Figure 2

The calculated photoelectron final energy distribution with respect to the tunneling vector potential $A$ and the initial transverse momentum for electrons with trajectory weight larger than $1\times {10}^{-6}$. (a) Electrons propagate with Coulomb potential. (b) Electrons propagate without Coulomb potential. The laser parameters are the same as in Fig. 1.

Figure 3

The calculated electron trajectories (a) with and (b) without the Coulomb potential, respectively. Different colors correspond to different tunneling vector potentials $A$ ($-2.0$–2.0 a.u.) at the same initial momentum ($p_x=0.04$ a.u., $p_y=0$). (c), (d), and (e) are detailed drawings of the different kinds of trajectories around the nucleus in (a), and the nucleus is marked as a black filled circle. The laser parameters are the same as in Fig. 1.

Figure 4

As Figs. 3 and 3, but for the initial momentum $p_x=0.2$ a.u., $p_y=0$. The laser parameters are the same as in Fig. 1.

Figure 5

Modulated momentum spectra and energy spectra with the phase delay of the two-color field. (a),(b) Parallel momentum distribution; (c),(d) vertical momentum distribution; and (e),(f) energy distribution as a function of the relative phase. In the left column, electrons propagate in only the laser field, while the Coulomb potential is taken into account in the right column. The optical phases at which the yields attain maximum values are indicated by black filled circles in (e) and (f). The laser parameters of the fundamental pulse are the same as in Fig. 1 while the second harmonic pulse has an intensity of 0.005 times the fundamental.

Figure 6

Energy spectra contributed by escaping and rescattering electrons, respectively, against the phase delay of the two-color field. (a),(b) Electrons propagate with the Coulomb potential. (c),(d) Electrons propagate without the Coulomb potential. In the left column, only escaping electrons are considered, while only rescattering electrons are taken into account in the right column. Optimal phases when the yields attain maximum at each energy are indicated by the solid black circles and contour data are rescaled within each energy interval. The laser parameters are the same as in Fig. 5.

Figure 7

Electron yields collected at all angles, in a $6^{\circ }$ range parallel and antiparallel to the laser polarization as a function of the relative phase. The corresponding current along the laser polarization direction is shown in dashed lines with squares. The laser parameters are the same as in Fig. 5.