Accurate Retrieval of Target Structures and Laser Parameters of Few-Cycle Pulses from Photoelectron Momentum Spectra

We illustrate a new method of analyzing three-dimensional momentum images of high-energy photoelectrons generated by intense phase-stabilized few-cycle laser pulses. Using photoelectron momentum spectra that were obtained by velocity-map imaging of above-threshold ionization of xenon and argon targets, we show that the absolute carrier-envelope phase, the laser peak intensity, and pulse duration can be accurately determined simultaneously (with an error of a few percent). We also show that the target structure, in the form of electron-target ion elastic differential cross sections, can be retrieved over a range of energies. The latter offers the promise of using laser-generated electron spectra for probing dynamic changes in molecular targets with subfemtosecond resolution.

Figure 1

(a) Electric field and vector potential of a 760 nm five-cycle laser pulse at $1\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ for CEP $\phi =0$. (b) Left and right wave packets calculated for the laser pulse in (a) for xenon. (c, d) The evolution of left and right wave packets with CEP, respectively. (e, f) Theoretical left and right high-energy photoelectron energy spectra calculated by the QRS model vs CEP. The spectra have been obtained by angular integration over a cone of 10° along the laser polarization axis.

Figure 2

(a, b) Volume-integrated left and right high-energy Xe photoelectron spectra from the QRS model for a laser pulse at 760 nm, pulse duration of 6.7 fs, and peak intensity of $1.1\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ and different CEP. The peak intensity and pulse duration are obtained from the best fit to the experimental data of Kling et al. [8], shown in (c) and (d) for left and right electron spectra, respectively. All data are from integrating over 10° along the polarization axis. The remaining small discrepancy is partly because the CEP values in the experimental data are not at exactly the same values as in the theory (see text).

Figure 3

(a) Peak energies vs the CEP from the electron spectra on the left for a Xe target. Red crosses represent experimental data shown in Fig. 2c; blue asterisks connected by a line represent best theoretical fits; other symbols show how the peak energies change when peak intensity or pulse duration are varied from the best fit (see text). (b) Similar analysis using an Ar target.

Figure 4

(a) Differential elastic scattering cross sections for ${\mathrm{Xe}}^{+}$ ions by free electrons with incident momentum of $p_r=1.2\mathrm{a}.\mathrm{u}.$. Solid line: theoretical result calculated from a model potential for Xe. Dashed lines: DCS’s extracted from experimental data of 8 with different CEP’s. (b) Similar to (a) except for Ar, for $p_r=0.9\mathrm{a}.\mathrm{u}.$. (c) Elastic scattering DCS’s of ${\mathrm{Ar}}^{+}$ ion by free electrons with $p_r=1.1\mathrm{a}.\mathrm{u}.$ over a large angular range. The lines are from three different theoretical calculations (see text). The symbols are from an electron-${\mathrm{Ar}}^{+}$ collision experiment [22] for small angles and from the present HATI spectra for large angles. The theoretical curves do not include experimental angular resolutions.