Two-Color Strong-Field Photoelectron Spectroscopy and the Phase of the Phase

The presence of a weak second-harmonic field in an intense-laser ionization experiment affects the momentum-resolved electron yield, depending on the relative phase between the $\omega$ and the $2\omega$ component. The proposed two-color “phase-of-the-phase spectroscopy” quantifies for each final electron momentum a relative-phase contrast (RPC) and a phase of the phase (PP) describing how much and with which phase lag, respectively, the yield changes as a function of the relative phase. Experimental results for RPC and PP spectra for rare gas atoms and ${\mathrm{CO}}_2$ are presented. The spectra demonstrate a rather universal structure that is analyzed with the help of a simple model based on electron trajectories, wave-packet spreading, and (multiple) rescattering. Details in the PP and RPC spectra are target sensitive and, thus, may be used to extract structural (or even dynamical) information with high accuracy.

Figure 1

Schematic illustration of RPC $P$ and PP $\mathrm{\Phi }$. Given a sequence of photoelectron momentum distributions (as obtained with the VMI spectrometer) for varied relative phase $\phi$, the change in electron yield (dots) for given photoelectron momentum (small square in the spectra) is fitted by $P\cos (\phi +\mathrm{\Phi })$ (red curve).

Figure 2

Experimental RPC (a) and PP (b) spectra for Ar, calculated from 66 Abel-projected VMI spectra per $\phi$ interval $[0,2\pi ]$. The 794- and 397-nm components of the 100-fs two-color pulse had intensities $\simeq {10}^{14}$ and ${10}^{12}\mathrm{W}/{\mathrm{cm}}^2$, respectively (i.e., $\xi =0.05$). In (a), $P$ has been normalized to $\max P$. Circles and vertical lines indicate $10U_{\mathit{p}}$ rescattering rings and $2U_{\mathit{p}}$ cutoffs, respectively. White numbers in (b) are referred to in text.

Figure 3

Experimental RPCs (left) and PPs (right) for Kr (top), Xe (middle), and randomly aligned ${\mathrm{CO}}_2$ (bottom). Laser intensities and color coding as in Fig. 2. The yellow dashed lines in (f) indicate the “clubs” discussed in the text.

Figure 4

(a) Final SMT photoelectron momenta for $\xi =0$, absolute value of electric field at ionization time $|\mathit{e}({\tau }_1)|$ color coded. Rings representing local maxima in final momentum $|{\overline{p}}_z|$ due to rescattering during the first, second, and third return are labeled. For better visibility, final momenta in respective opposite directions (originating from electrons emitted half a laser cycle earlier) are plotted in light gray. (b) Normalized excursion ${\overline{\alpha }}_z$ of electron rescattering at first (solid) and second return (dotted), respectively, leading to final momenta indicated as $\mathsf{x}$ in (a). SMT PP spectra for $\xi =0.05$, taking into account (c) ionization and wave-packet spreading ($s=3/2$) and (d) additionally a scattering cross section (3) (with $Z=18$ and $\mu =1/2$). Same color coding in (c) and (d) as in previous figures. White numbers in (d) analogous to Fig. 2.

Figure 5

RPC (a) and PP (b) spectra for Ar from TDSE (${10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, $\xi =0.05$). Durations of ${\sin }^2$-shaped pulses for 794 and 397 nm were 60 and 50 fs, respectively. Additionally to $2U_{\mathit{p}}$ cutoffs and $10U_{\mathit{p}}$ rings, second-return cutoff rings are included, which form boundaries for features labeled A and B. Slight left-right asymmetries visible in (a) are remnants of CEP dependence.