Momentum spectra of electrons rescattered from rare-gas targets following their extraction by one- and two-color femtosecond laser pulses

We have used velocity-map imaging to measure the three-dimensional momenta of electrons rescattered from Xe and Ar following the liberation of the electrons from these atoms by 45 fs, 800 nm intense laser pulses. Strong structure in the rescattering region is observed in both angle and energy, and is interpreted in terms of quantitative rescattering (QRS) theory. Momentum images have also been taken with two-color (800 nm $+$ 400 nm) pulses on Xe targets. A strong dependence of the spectra on the relative phase of the two colors is observed in the rescattering region. Interpretation of the phase dependence using both QRS theory and a full solution to the time-dependent Schrödinger equation shows that the rescattered electrons provide a much more robust method for determining the relative phase of the two colors than do the direct electrons.

Figure 1

VMI electron momentum image after inversion from Xe target using two-color laser pulses at an intensity of 8.8 × 10${}^{13}$ W/cm${}^2$ (800 nm pulse intensity).

Figure 2

Left-hand column: Inverted electron momentum spectra from Xe for laser intensities of (a) 5.5, (b) 7.7, and (c) 10.0 (in units of 10${}^{13}$ W/cm${}^2$). Events with energies less than 4$U_p$ are not plotted. Middle column: the same data plotted in terms of $p_r$ and ${\theta }_r$. Right-hand column: Energy spectra for electrons within a 10${}^{ˆ}$ angle of the polarization vector.

Figure 3

Similar to Fig. 2, but for Ar at intensities of (a) 7.7, (b) 10.0, and (c) 12.8 (in units of 10${}^{13}$ W/cm${}^2$).

Figure 4

Angular distributions $\mathit{\sigma }$($p_r,{\theta }_r$) extracted from the middle columns of Figs. 2 and 3 (with additional intensities added). The left-hand column is for Xe, the right-hand one for Ar. The value of $p_r$ in a.u. is given in each figure. The laser intensities, in units of 10${}^{13}$ W/cm${}^2$, are shown in the insets.

Figure 5

Comparison of the angular distributions $\mathit{\sigma }$($p_r,{\theta }_r$) from Fig. 4 with theoretical calculations from two different electron-ion potentials for different values of $p_r$. The experimental data for this comparison have been smoothed to remove the ATI structure. The laser intensities, in units of 10${}^{13}$ W/cm${}^2$, are shown in the insets.

Figure 6

(a) Wave form for a two-color field given by Eq. (4) for various values of the relative phase. [Electric field (blue); vector potential (green).] (b) Results of classical ADK model described in the text. Positive values of $E/U_p$ correspond to the emission of electrons in the negative $\mathit{z}$ direction.

Figure 7

Schematic of two-color setup.

Figure 8

Density plots of the yield of HATI electrons in the negative $\mathit{z}$ direction from Xe as a function of the two-color phase $\mathit{\varphi }$. (a) Experimental result. (b) TDSE theoretical calculation. (c) QRS volume-integrated result. See text for details.

Figure 9

Similar to Fig. 7 but extended in scale to include the direct electrons. (a) Experiment; (b) TDSE calculation.