for measuring and retrieving the CEP was applied, which exploits this observed shift (see fig. 7.13d) is the single-shot Stereo-ATI technique. Two CEP asymmetry parameters were defined. These ranges are indicated by the green and brown areas on the time-of-flight and energy spectra for the cosine and sine waveforms of the laser pulse in fig. 7.13b and c. The time-of-flight spectra for CEP retrieval were used because those are the raw unprocessed signals from the measurement apparatus. Parameter x was calculated as (PL−PR)/(PL+PR), wherePLandPR are the integrated signals. ywas calculated analog.
The two Parameter CEP asymmetry curves obtained in this way are shifted against each other by approximately 60◦.
Figure 7.14: Mapping the CEP of non-phase-stabilized consecutive laser pulses. Consecu-tive single laser shots from a non-phase-stabilized laser at 3 kHz repetition rate represented on a parametric plot in which the axesxandyare the phase asymmetry parameters derived for two TOF ranges in the ATI spectra.
Instead of the conventional linear representation (phase asymmetry versus phase), new insight can be gained by plotting these sine-like phase asymmetries on a Lissajous like parametric plot with each axis corresponding to one of the two CEP asymmetries. In fig.
7.14, laser shots with a random CEP are shown in that representation. With the two phase asymmetry parameters, the CEP of each shot (in the entire 2π range) is mapped to one point on the ellipse-like curve, which implies that there is no phase uncertainty. The reason for a slightly deformed ellipse is due to the fact that the phase asymmetry curves are not perfectly sine shaped and that the responses are not exactly identical if the two electron detector are not identical, what they never are.
(e,2e) process can be clearly seen in neon and RESI plays a much less important role (cf.
[188]). As mentioned above in neon mostly the (e,2e) process is contributing to the NSDI.
Therefore we can concentrate on its phase dependence.
Figure 7.15: Longitudinal momentum distribution of neon at four different CEPs. The shift in the momentum distribution in dependence of the CEP is very pronounced. This data was measured with sub 4 fs pulses and a peak intensity of approximately 5·1014 W/cm2.
The neon data presented here was measured with a pulse length of approximately 4 fs, at a center wavelength of 750 nm and a peak intensity of approximately 5.2±1.3·1014 W/cm2. This intensity was extracted from the position of the maxima in the double hump structure that are located at ±2 UP. Unfortunately the intensity estimation with this position has a large uncertainty.
In figure 7.15 the CEP-dependent change of the double hump structure of the dication recoil momentum is very pronounced for NSDI of neon. The individual panels are inte-grated over a segment of the CEP circle. A very large asymmetry with the right hump dominating the spectrum between 260◦ and 270◦ can be seen, this changes into a rise of the left hump between 210◦ and 220◦. The emphasis shifts further on to the left in the next plotted segment between 150◦ and 160◦ and at a phase between 120◦ and 130◦ the right hump is mostly suppressed, while the left one is very strong. The most striking fea-ture in this measurement is the almost completely transfer of events from one side of the distribution to the other.
If now the momentum is plotted against the phase (see figure 7.16) one can see a continuously change of the signal from one direction to the other and then back again.
The phase effect is extremely pronounced.
The asymmetry parameter is a measure of the asymmetry of the momentum distribution
Figure 7.16: Left: Plot of the ion momentum distribution in polarization direction vs. the phase. The depletion of one of the two maxima near ±2 a.u. at a phases of 100◦ and 280◦ is nicely pronounced. Right: Asymmetry parameter vs. phase. The asymmetry follows a almost perfect sine function.
in polarization direction 2. It compares the number of counts in the left channel and the right channel with each other while a maximum asymmetry has the absolute value of 1.
As one can see in the right picture of figure 7.16 the asymmetry is nicely pronounced and follows a sine function in a nearly perfect way. This measurement was the high signal-to-noise measurement of the CEP-dependent asymmetry in neon, which became only feasible with the implementation of the phase-tagging concept described in 7.2.2. It was possible to achieve much higher statistics as in previous measurements and additionally we were able to measure all phases at once and did not have the risk that a shift in the laser parameters falsifies our results.
If the double ionization events are integrated over all momenta, the dependence of the double ionization yield on the CE-phase can be explored. Naively one would expect that the double ionization yield depends on the maximum electric field in the laser pulse. If this shape is now compared to the measured doubly charges ion yield in figure 7.17 it can be seen that this expectation is only applicable in a limited way. The minima can be found at the integer multiple ofπ while the maxima are shifted in respect to the minima byπ/2.
7.3.2 Argon
In the double ionization of argon, which was also measured with sub 4 fs pulses at a peak intensity of approximately 1.6±0.4·1014 W/cm2, the double hump structure is not visible.
It is known [164], that in argon RESI is a much more important process at low intensities than (e,2e) Therefore in argon a different CEP dependence might be expected than in neon. The intensity is again estimated from the 2Up cutoff in the longitudinal momentum.
2L−R
L+R, where L is the integral over the events with a negative momentum and R is the ion yield with a positive momentum.
Figure 7.17: Integrated ion yield of the double ionization of neon in dependence of the phase.
The phase effects of the RESI contribution have not been investigated before and until now there are also no theoretical predictions. Triggered by our results calculations are in progress.
Figure 7.18: Comparison of the experimental CEP-dependent Ar2+ yield (black squares) with theoretical predictions (colored lines) for three different intensities from Micheau et al. [213]. The error bars indicate the statistical error of the experimental data.
Employing the phase-tagging approach, for the first time the CEP dependence of the Ar2+ ion yield for constant pulse duration and intensity has been measured (see figure 7.18). The intensity in our measurement 1.6(±0.1)×1014 W/cm2 is determined from the 2Upcutoff in the longitudinal momentum (along the laser polarization axis) of H2O+, which was present as background in the jet in our experiments on argon. The experimental Ar2+
ion yield data in figure 7.18 is compared to recently published theoretical results by Micheau et al. [213]. They calculated the Ar2+ yield for a 5-cycle pulse centered at 800 nm at three intensities of (1.4, 1.6, 2.0)×1014 W/cm2. The theoretical curve for 1.6×1014 W/cm2
agrees best with the data presented here, consistent with the experimentally determined intensity. The calculations predict minima in the Ar2+ yield at approximately 3/4π and 7/4π, which are independent of intensity in this range [213]. In figure 7.18, we choose ϕ0 in the experimental data such that the dip in the total Ar2+ yield occurs at the same phase as in the theoretical curves. Although the yield is clearly CEP dependent, it has a ±π inversion symmetry. However, this ambiguity can be eliminated with the phase-dependent Ar2+ momentum spectra.
As can be seen in figure 7.19, for argon the momentum distribution is shifting from the left to the right as a function of the CEP, but the shift is not as pronounced as for neon (cf. 7.15). In figure 7.19 the red curve is integrated over a phase between 113◦ and 117◦ and the blue one, with a phase between 299◦ and 303◦, show a very nice asymmetry and differ significantly from the distribution with an integrated phase plotted in black.
Figure 7.19: Longitudinal ion momentum distribution of the double ionization of argon measured with sub 4 fs pulses at a peak intensity of 1.6·1014 W/cm2.The integral over all phases is plotted in black. One can see that the dip between the two humps is filled up.
In red is the momentum distribution at a phase between 113◦ and 117◦ and in blue at a phase between 299◦ and 303◦.
If we draw our attention to figure 7.20, on the right the longitudinal momentum is plotted versus the phase. In contrast to the neon measurement we do not see islands of high count rate instead we can see a band that shifts up and down. This may be understood if the large contribution of the RESI process is taken into account, which should have a phase dependence that is similar to the single ionization via tunneling [211]. There the main part of the phase dependence is a shift in the high momentum part similar to what can be observed here.
On the right side of figure 7.20 the asymmetry parameter is plotted against the phase and it follows a sine curve just as with the (e,2e) process in neon. If only the large momenta are taken into account for the asymmetry parameter, the behavior of the asymmetry is about the same as in neon.
Figure 7.20: Left: Longitudinal ion momenta vs. the phase for argon. Right: Asymmetry parameter versus the phase. The momenta chosen for the evaluation of the asymmetry parameter are between ±1 a.u. and ±2 a.u..