Pulse shaping in strong-field ionization: Theory and experiments

Intense ultrafast pulses cause dissociative ionization and shaping the pulses may allow control of both electronic and nuclear dynamics that determine ion yields. We report on a combined experimental and theoretical effort to determine how shaped laser pulses affect tunnel ionization, the process that precedes many strong-field phenomena. We carried out experiments on Ar, ${\mathrm{N}}_2$, ${\mathrm{H}}_2\mathrm{O}$, and ${\mathrm{O}}_2$ using a phase-step function of amplitude $\frac{3}{4}\pi$ that is scanned across the spectrum of the pulse. In addition, we changed the amount of chirp in the pulses. Semiclassical as well as fully quantum mechanical time-dependent Schrödinger equation calculations are found to be in excellent agreement with experimental results. We find that precise knowledge of the field parameters in the time and frequency domains is essential to afford reproducible results and quantitative theory and experiment comparisons.

Figure 1

Experimentally measured relative difference of the ion yields obtained as a function of scanning the chirp of pulses with a step at +0.025 rad/fs (filled symbols) or −0.025 rad/fs (open symbols).

Figure 2

Experimentally measured relative difference, defined by Eq. (13), of the ion yields obtained as a function of the position of the phase step for a given positive (pink shading under curve) or negative (blue shading under curve) chirp value indicated in each plot.

Figure 3

Experimentally measured ratios $Y_{+}/Y_{-}$ or $Y_{-}/Y_{+}$ of the ion yields obtained as a function of scanning the position of the phase step for a given positive or negative chirp value indicated in each plot. The numerator and denominator are chosen so that values are always greater than 1.

Figure 4

Results of simulations and TDSE calculations for Ar atoms. We performed intensity averaging for each curve labeled “IA.” The chirp value is $+600\mathrm{f}{\mathrm{s}}^2$. The simulations and calculations are scaled to match the right peak in the experimental data, which is shown for comparison.

Figure 5

Time-frequency Wigner (top) and Husimi (bottom) representations of 40-fs TL pulses shaped with a $\frac{3}{4}\pi$ step at ${\omega }_0$ and at ${\omega }_0$ $-0.03\mathrm{rad}/\mathrm{fs}$. The plots are calculated using Eq. (14).

Figure 6

Time-frequency representations of a laser pulse with a $\pm \frac{3}{4}\pi$ phase step. The pulses in the left four plots (a), (b), (e), and (f) have zero chirp in addition to the phase step, whereas those in the right plots (c), (d), (g), and (h) have $+600\mathrm{f}{\mathrm{s}}^2$ chirp. The “blue” plots indicate a positive detuning of the step position from the central frequency to +0.03 rad/fs, and the “red” ones indicate a negative detuning to −0.03 rad/fs. Furthermore, the “(+)” labels indicate a $+\frac{3}{4}\pi$ spectral phase step, and “(−)” labels indicate a $-\frac{3}{4}\pi$ step. The plots are calculated using Eq. (14).