Time-resolved reflectivity measurements on a plasma mirror with few-cycle laser pulses

We present time-resolved reflectivity measurements on a plasma mirror and demonstrate the contrast improvement of sub-10-fs pulses. Detailed characterization of the spatial peak and the average reflectivity, the spatial and temporal properties of the reflected pulses for p- and also for s-polarization are discussed. A complete third-order correlation is measured to compare the temporal structures of the pulses before and after the plasma mirror. Simulation of the hydrodynamic expansion of the plasma supports the measured pulse properties after the reflection.


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Institute of Physics ⌽ DEUTSCHE PHYSIKALISCHE GESELLSCHAFT higher throughput without limitation on the input energy [2]. In this method, the pulses are sent on to a transparent target. While the prepulses/pedestal are transmitted, the main peak is so intense that its leading edge ionizes the target and forms a plasma on the target surface. This plasma then reflects the remaining part of the incident pulse. This way the contrast between the leading part of the pedestal or prepulses and the main pulse can be improved significantly in the reflected beam. Several investigations have been performed to study the reflectivity of the plasma mirror [11] and the reflected beam profile [12]- [14]. To reach even better contrast improvement a double plasma mirror pulse cleaner has been tested [14]. Although intense few-cycle pulses with a sufficiently high contrast will open up new prospects for many applications [15,16], the previous experimental studies were done using pulses with 25 fs duration or longer and no experiment has been done in the sub-10-fs regime. Previous time-dependent reflectivity studies resulted in 200-1000 fs rise time [17]- [19] for the formation of a reflecting plasma surface with 60 fs or longer pulse durations.
In this paper, we report on the performance of a plasma mirror with 7 fs incident pulses. The reflectivity of the plasma mirror is measured for both pand s-polarization at 45 • angle of incidence, and the reflected pulses are characterized both spatially and temporally. A complete high dynamic range third-order correlation of the reflected pulses, which allows us to obtain the time-resolved reflectivity of the plasma mirror, are presented for the first time to the best of our knowledge.
The experiment was carried out with a broadband Ti:sapphire laser system based on chirpedpulse amplification with three multi-pass amplifier stages and a hollow-fibre compressor [20]. The system typically delivered pulses with 550 µJ energy and 7 fs duration at the central wavelength of 730 nm-the spectrum extended from 550 to 900 nm-at 1 kHz repetition rate. The output beam was guided through a vacuum beamline to the target chamber. The energy on the target was ∼350-400 µJ.
The experimental set-up is shown in figure 1. The polarization of the incident beam could be swapped between p and s before entering into the target chamber. The beam with 50 mm diameter was focused on to a glass target with an f = 150 mm, 90 • silver off-axis parabola (F/3). Three motorized stages allowed to rotate the target and translate it parallel to the surface and parallel to the incident beam (z-direction). At 1 kHz repetition rate a target lasted approximately for an hour. The reflected beam from the target was refocused with a thin achromatic lens and sent to a detector outside the vacuum chamber. We measured the reflected energy, the beam profile around the focus of the incident and the reflected beam, the spatial peak reflectivity, and the temporal structure with high dynamics of the incident and also of the reflected pulses.
We characterized the efficiency of the plasma mirror by measuring the spatial-integral or 'average reflectivity' and the 'peak reflectivity.' The average reflectivity is given by the ratio of the reflected energy to the incident energy. We calculate the peak reflectivity as the ratio of the peak fluences, which are obtained from the measured beam profiles on the target and the incident energy. As we will see, this gives the same as the ratio of the peak intensities, which is the definition of the reflectivity. Figure 2(a) shows the average reflectivity for p-polarization as a function of the average incident fluence, which is determined with respect to the spatial full width at half maximum (FWHM) area of the focused beam. The energy measured with the power meter was averaged over some thousand shots. The incident fluence was changed by either moving the target out of focus (z-scan) or decreasing the energy of the incident pulse (energy scan). Different sets of measurements are shown with different symbols in figure 2. The measurements were well reproducible and gave the same results for z-scan and for energy scan. The highest average reflectivity reached up to ∼ 40%, whereas the lowest reflectivity was as low as ∼ 0.5% because the incidence angle (45 • ) was close to Brewster's angle (∼ 56 • ). From these values, a contrast improvement of two orders of magnitude is expected. We also measured the average reflectivity with longer pulse durations, which was achieved by either chirping the pulse or clipping the spectrum. The pulse duration was increased up to 60 fs, i.e., a factor of 9, but no significant change was observed in the behaviour of the reflectivity versus fluence dependence. Therefore, we plotted the reflectivity as a function of the incident fluence in figure 2.
The average reflectivity measured for s-polarization is plotted in figure 2(b). Although the highest reflectivity reached up to ∼ 65%, the expected contrast improvement is only one order of magnitude due to the relatively high Fresnel reflectivity at s-polarization, which is 7.6% at 45 • angle of incidence for our target material. The results plotted in figure 2(b) had larger flcutuations than those in figure 2(a) due to the different laser conditions. Reducing the reflectivity with antireflection (AR) coated targets can boost the contrast improvement up to factor of 200 [12]. Therefore, using s-polarized beam with AR-coated targets is ideal for obtaining the maximal throughput (65%). On the other hand, AR-coated targets are expensive, especially when they have to be replaced frequently. Using p-polarized light solves this problem at the cost of decreased throughput (40%). The contrast improvement factors are in the same order for s-polarized light with AR-coated targets and for p-polarized light with ordinary targets, at 45 • incidence angle. Using Brewster's angle increases the improvement factor for p-polarization even more, although the alignment is more complicated. The spatial peak reflectivity for p-polarized pulses is depicted in figure 2(c) as a function of the peak fluence. The maximum value was above 60%.
The spectra of the incident and reflected pulses were also measured, but they were almost identical and no significant blue shift was observed.
To investigate the spatial characteristics of the reflected beam, we collimated it with an achromatic lens (f = 150 mm) and refocused with an f = 75 mm off-axis parabola. The image of the refocused spot was magnified with a microscope objective and captured by a charge-coupled device beam profiler. The target was moved in the focal (z) direction and the imaging system was adjusted for each measurement. The measured spot diameters are plotted in figure 3(a). The horizontal lines indicate the spot diameter without activating the plasma mirror, i.e., with low input energy. The different focus diameters for sand p-polarizations are due to different alignments of the beam line. A horizontal and a vertical lineout of the refocused beam profile are plotted for s-polarization with (solid) and without (dashed) plasma mirror in figure 3(b) when the target was in the focus (z = 0). We observed two effects on the reflected beam: cleaner beam profile and smaller refocused spot. Both changes can be explained by the fluence-dependent reflectivity of the plasma mirror. The plasma mirror reflects more efficiently at the central part of the beam, while the reflection at the surrounding area is relatively suppressed, which acts as a spatial filter resulting in a cleaner beam profile [21]. At the same time, this fluence-dependent reflectivity makes the peak narrower, which results in a smaller spot size on the plasma mirror and consequently a smaller refocused spot size.
We also investigated the temporal characteristics of the reflected beam by measuring a high dynamic range third-order correlation. The polarization of the beam incident to the target was set to p because a better contrast improvement was expected. The fluence on the plasma mirror was estimated to be ∼ 60 J cm −2 . The reflected beam was recollimated and sent into a home-made third-order correlator [22]. Figure 4 shows the measured third-order correlation of the reflected pulse together with that of the incident pulse. The negative delay represents the leading edge of the pulse. Although the measured contrast was limited by the low energy (∼ 50 µJ) sent into the correlator, the expected contrast improvement of two orders of magnitude at the pulse front is striking, for example, around −2 or at −8.5 ps. The peak appearing at −1.5 ps is an artefact Institute of Physics ⌽ DEUTSCHE PHYSIKALISCHE GESELLSCHAFT Figure 4. Third-order correlation measured with (red) and without (black) the plasma mirror. Negative delay represents the leading edge of the pulse. Although the measured contrast was limited by the low input energy (∼ 50 µJ), contrast improvement of two orders of magnitude is seen in the leading edge, for example, around −2 ps. The inset shows a second-order interferometric correlation of the 6-7 fs input pulse. from a post pulse, which appears due to the nature of correlation measurements. Also a pulsesteepening effect is evident on the rising edge [23]. On the other hand, no effect is observed on the falling edge of the pulse. Figure 4 also indicates that the plasma is generated 400-500 fs before the main pulse arrives. Therefore, the plasma mirror is efficiently generated with the pedestal of our sub-10-fs pulses, similarly to the previous experiments with longer pulses. It is apparent that the reflectivity is constant during the pulse, hence the way we attained the peak reflectivity using the fluences is correct. Since 100 µm thick crystals were used in the correlator to gain a stronger signal, the third-order correlation does not reflect the short pulse duration. A second-order interferometric correlation trace in the inset of figure 4 shows the 6-7 fs duration of the incident pulses. Figure 5 depicts the time-resolved reflectivity of the plasma mirror for p-polarization obtained by dividing the correlation of the reflected pulse by that of the incident pulse. We normalized the curve by setting the average reflectivity between 0 and 4 ps to the expected peak reflectivity of 50%. A steep rise in the reflectivity is clearly seen at −500 fs. This steep rise indicates that the plasma is generated ∼ 500 fs before the main pulse. We also see a decrease in the reflectivity ∼ 6 ps after the main pulse.
To further understand the physical process, we simulated the hydrodynamic expansion of the plasma with the simulation code medusa [24]. As the input pulse, we used a 7 fs Gaussian pulse sitting on 1.7 ps Gaussian pedestal with 2 × 10 −4 contrast and 7 fs Gaussian prepulse 8.5 ps before the main peak with 10 −4 contrast. The parameter was determined by the fit on the third-order correlation without the plasma mirror. The simulation shows that the scale length L ≡ n e /|dn e /dz| of the plasma, where n e is the electron density, is ∼ 0.03λ at the critical density when the main peak of the pulse arrives. If the scale length is too large, a plasma mirror acts similarly to a chirped mirror because different wavelengths are reflected at different depths in the plasma surface due to different critical densities. With this scale length, however, this chirping effect is negligible and the pulse duration stays the same after the plasma mirror. The simulation also shows that the scale length exceeds 0.1λ around +4 ps after the main peak. Above this scale length resonant absorption [25] takes place and reaches 60-80% at 45 • incidence angle, which explains the decrease of the reflectivity around 6 ps.
It is worth investigating whether the plasma mirror works with sub-10-fs pulses with the higher contrast. For example, applying another plasma mirror to the pulse cleaned by the first plasma mirror, which will lead to the contrast improvement of more than four orders of magnitude. Since the energy in the pedestal is much lower, the pedestal may not trigger the plasma mirror any more. What the plasma mirror does to the pulse in this case is an open question.
In conclusion, we have demonstrated the contrast improvement of sub-10-fs pulses by a plasma mirror. The reflected pulses were spatially and temporally cleaned while the spatial peak reflectivity for p-polarization reached 60% and the average reflectivity had a value of ∼ 65% (∼ 40%) for s-(p-) polarization at 45 • angle of incidence. The first measurement of the complete high-dynamic correlation revealed the temporal structure of the pulses reflected from the plasma mirror. The time-resolved reflectivity of the plasma mirror was determined with the help of these results, showing the contrast improvement of two orders of magnitude and the pulse steepening at the leading edge. Improving the contrast with the plasma mirror will lead to better performances in experiments such as high-order harmonic generation on plasma surfaces and ion acceleration.