Femtosecond dynamics of energetic electrons in high intensity laser-matter interactions

Highly energetic electrons are generated at the early phases of the interaction of short-pulse high-intensity lasers with solid targets. These escaping particles are identified as the essential core of picosecond-scale phenomena such as laser-based acceleration, surface manipulation, generation of intense magnetic fields and electromagnetic pulses. Increasing the number of the escaping electrons facilitate the late time processes in all cases. Up to now only indirect evidences of these important forerunners have been recorded, thus no detailed study of the governing mechanisms was possible. Here we report, for the first time, direct time-dependent measurements of energetic electrons ejected from solid targets by the interaction with a short-pulse high-intensity laser. We measured electron bunches up to 7 nanocoulombs charge, picosecond duration and 12 megaelectronvolts energy. Our ’snapshots’ capture their evolution with an unprecedented temporal resolution, demonstrat- ing a significant boost in charge and energy of escaping electrons when increasing the geometrical target curvature. These results pave the way toward significant improvement in laser acceleration of ions using shaped targets allowing the future development of small scale laser-ion accelerators.

A direct experimental evidence of these processes requires sub-picosecond measurements of charge density near the surface or alternatively tracing down the escaping electrons. So far this task remained elusive and only indirect time integrated measurement of radiated electromagnetic pulses 17,18 or magnetic fields 19 were reported.
In the following we provide temporally resolved measurements of energetic electrons ejected from solid targets during the interaction with a short-pulse high-intensity laser. We measured the total charge and the temporal profile of electron pulses with up to 7 nC charge and 12 MeV energy with picosecond duration. The results show that, when using high-power ultra-short laser pulses focused on different target geometries (namely planar, wedged and tip shapes), there is a significant increase in the charge and energy of the escaping electrons when the geometrical target curvature is increased. It represents a direct evidence of the growth of the electrostatic potential induced near the target surface and thus an enhancement of the accelerating gradient for the emitted ions.

Setup of the experiment
The experiment, depicted in Fig. 1, has been performed with the FLAME laser at the SPARC_LAB test-facility 20 by focusing its high-intensity ultra-short-pulses (up to 4 J energy and 35 fs pulse duration) on solid targets of different thicknesses and shapes. Snapshots of the emitted electrons are provided by an Electro-Optical Sampling (EOS) device 21 , a temporal diagnostics commonly used in accelerator facilities 22,23 , able to provide single-shot and non-destructive measurements for the longitudinal profile of charged particle beams. The EOS system we employed makes use of a 500 μm-thick ZnTe electro-optic crystal installed 1 mm downstream the target. Being this distance much larger than the Debye length (less than 1 μm in our experimental conditions), only the highly energetic ejected electrons that escape the potential barrier are able to reach that location. A probe laser (35 fs duration), directly split from the main laser, illuminates the crystal while simultaneously the electron cloud is moving below it. Such ultra-short probe laser allows to achieve less than 100 fs as temporal resolution, mainly limited by the implemented electro-optic crystal 24 . The high resolution EOS diagnostic technique allows us to operate on the same time scale of the process, determined by the duration of the driving laser pulse 10 .
The EOS diagnostics exploits the large electric fields associated to relativistic charged particles. When they move near the electro-optic crystal, their Coulomb field E b (t) makes the crystal birefringent. As a consequence, if a linearly polarized probe laser simultaneously passes through the crystal, its polarization is rotated by an angle Γ (t) ∝ r 41 E b (t)d, where d and r 41 are the crystal thickness and electro-optic coefficient, respectively. The probe polarization is thus modulated according to the electron bunch temporal profile. Our EOS system exploits a probe laser directly split from the main laser, ensuring a jitter-free synchronization, and implements the spatial encoding technique 25 in which the bunch longitudinal profile is encoded along the probe transverse profile. The encoding is obtained when the probe laser crosses the crystal with an angle, that in our case is θ i = 28°. In such way the bunch longitudinal coordinate t i is related to the laser transverse one x i by the relation t i = x i tan θ i /c, with c the vacuum speed of light. Being 6 mm the diameter of the probe laser, it follows that the resulting active time window provided by the EOS is about 10 ps. The process ends by converting the induced modulation in the probe polarization in a modulation in its intensity (readable by a CCD camera) by means of a linear polarizer installed downstream the EOS crystal, whose optical axis is rotated by 90 with respect to the initial probe laser polarization. More details about the laser system and the implemented EOS diagnostics are presented in sec.

Results
Previous reports of ion acceleration by high intensity short pulse lasers have demonstrated a significant energy enhancement of the accelerated ion when structured targets [26][27][28] were used instead of the conventional planar target in the Target Normal Sheath Acceleration (TNSA) scheme. The underlying interpretation of these results is that, during the interaction of the laser pulse with sharp structured targets, higher quantity of electrons escape the target leaving behind a stronger potential well, which in turn can accelerate the ions to higher energies. In order to prove this conjecture a direct time-resolved measurement of the escaping electrons is required. We therefore employed our method and investigated the influence of target shape on the amount and energy of the escaping electrons by using a 10 μm-thick aluminum foil, a wedged shape of stainless steel razor blade and a tip shape of a needle. Measuring the charge quantity and energy of the escaping electrons by means of the EOS detector provides the required evidence for the field-enhancement conjecture. The energy information, in particular, is estimated by exploiting the single-shot feature of the EOS system, allowing to use it as a time of flight monitor 25 .
The results, summarized in Fig. 2 have been obtained by focusing the FLAME laser on different target shapes. The geometry of our EOS setup (the bunch is moving below the crystal and normally to it while the probe laser propagates laterally from right to left) determines the curved shape of the retrieved signals. The snapshots show that the escaping energetic electrons from the planar and blade targets present a secondary, broadened temporal structure (see Fig. 2(d,e), respectively). The duration and energy of the electron bunch is derived by measuring the bunch time of flight up to the EOS detector and by fitting it with numerical EOS simulations. In the case of the planar foil target, the resulting snapshot in Fig. 2(a) shows the presence of a first emitted bunch with approximately 1.2 nC charge and 7 MeV energy followed by a second broadened structure carrying a larger amount of particles (about 3 nC). If we assume that the delay (about 1.5 ps, see Fig. 2(d)) is due to different bunch velocities, the latter one has about 1 MeV energy. For the wedged target, the snapshot in Fig. 2(b) shows a similar structure. The first bunch now carries a larger amount of electrons (2 nC) at the same energy (7 MeV) while the charge in the second bunch is strongly reduced to 0.3 nC. The temporal delay in this case is about 2 ps, as reported in Fig. 2(e). Electron bunches coming from the tip target are shown in Fig. 2(c). In this case the interaction with laser produced a much larger number of released electrons (about 7 nC) at higher energies (about 12 MeV). Due to the large amount of charge, the birefringence induced in the ZnTe crystal leads to a rotation of the probe laser polarization larger than π/2 and the EOS signal in Fig. 2(f) is consequently distorted. The overlaying red line shows the retrieved charge profile. These results provide a direct evidence of charge and energy boost when using sharp tips. Another feature, possibly attributed to this target shape, consists in the presence of a second smaller bunch (B2), carrying about 3 nC charge. The difference in the slope of the two signals in Fig. 2(c) may be due to the fact that B2 is emitted along a different path, rotated by ≈ 50 with respect to B1. It follows that B2 traveled for a longer distance (about 600 μm) and its signal is delayed by about 2 ps, as reported in Fig. 2(f).

Particle-In-Cell Simulations.
The experimental results shown in Fig. 2

are in agreement with
Particle-In-Cell (PIC) simulations. We conducted a numerical study in order to reproduce the interaction of a high-intensity short-pulse laser with wedged targets by using the 2D particle-in-cell (PIC) code TURBOWAVE 29 . The sketch of the interaction is reported in Fig. 3. Numerical simulations of the reported experiment include detailed description of the interaction near the surface and reveal the formation of the electron cloud and ejection of the fast energetic electrons. The simulations consist in a surface with micron-scale target local perturbations (consistent with electron scanning microscope images of the blade material used in the experiment) interacting with laser intensity of 10 18 W cm −2 , a spot diameter of 10 μm and an overall 30 fs duration. The simulation region is 40 × 40 μm 2 with 10 −2 μm cell size in order to reproduce the surface roughness. Considering the pre-pulse effect on the target, the blade is considered as a Fe 5+ plasma and each cell of the plasma region contains initially 512 particles. This resolution enables a proper description of the expected high gradients in the density and generated potential. Figure 4 shows the electron spectrum as function of energy obtained by placing a virtual screen in proximity of the target. The blue (red) points represent the electron distribution 100 fs (350 fs) after the laser hits the target surface. The semilog plot demonstrates that the majority of the electrons are slow (below 3 MeV) because they continue to stay near the target while the time increases. There is also a smaller component of trapped electrons up to about 4 MeV energy. On the contrary, electrons with higher energy are able to escape. They were close to the target 100 fs after the interaction but for later times they moved away, i.e. towards the EOS detector (1 mm far from the target). This is represented by the lack of red points at high energy in Fig. 4. It follows that only the high energy component of the emitted electrons is able to reach and be detected by the EOS monitor, while the low energy one is locked close to the target. These results are in agreement with measurements, consisting of detected electrons with energies larger than 6 MeV.

Discussion
In conclusion we reported, for the first time, the dynamics of energetic electrons in short-pulse high-intensity laser matter interactions at sub-picosecond level. Our measurements provide 'snapshots' of the electron cloud evolution with an unprecedented resolution better than 100 fs. We have measured a significant increase in the charge and energy of the escaping electrons (corresponding to the increase in the potential barrier) for sharp structured targets. These results demonstrate the field enhancement conjecture previously predicted and can be used as a guideline in order to achieve higher energies for positively charged ions with respect to what is currently obtained through conventional laser acceleration schemes.  Methods Laser and experimental area. The FLAME facility consists in a 100 TW Ti:Sapphire chirped-pulse amplification (CPA) laser system delivering 35 fs, at 0.8 μm with energies up to 4 J at 10 Hz repetition rate. The experimental layout of the target area is shown in Fig. 5. The laser beam is focused by means of f/10 off-axis parabolic mirror with focal length f = 1 m. The focal spot is optimized using a deformable mirror, allowing to reach a focus dimension on target of the order of 25 μm. About 60% of the initial laser energy lie within such focal spot. The probe laser, used for the EOS diagnostics, is split before the last multi-pass amplifier and re-compressed to 35 fs duration. The laser-target interaction occurs in a high vacuum environment (10 −6 mbar) in order to avoid self-focusing effects and reduce contaminations that could affect the experiment. The synchronization of the main and probe lasers in correspondence of the EOS crystal is obtained by means of an α-cut BBO crystal installed on the ZnTe holder. The time overlapping is then retrieved by using a 3 fs resolution delay-line and looking for light emission by second-harmonic generation (SHG).
Electro-Optical Sampling. In order to retrieve the main properties of the emitted electrons (charge, energy and duration) from the measured EOS signals, a numerical simulation code has been developed in MATLAB environment. It starts calculating the transverse electric field E V (t) of a gaussian electron bunch travelling at energy E in vacuum at distance r from the ZnTe crystal. The simulation then takes into account the dispersive propagation of such field in the ZnTe crystal 30 , with thickness d. Being n(ω) and κ(ω) the ZnTe refractive and absorption indices in the Fourier domain 31 , the propagating field is given by  where A tr (ω) = 2/(n(ω) + iκ(ω) + 1) is the amplitude transmission coefficient. The sampling is performed by a copropagating probe laser pulse whose initial linear polarization gradually becomes elliptical due to the electro-optic effect induced by the propagating field 24 . Being λ L the laser central wavelength, the overall phase delay cumulated by the probe laser at the end of the crystal is given by the convolution where n 0 and r 41 are the ZnTe optical refractive index calculated in λ L and its electro-optic coefficient, respectively.
represents the normalized (dimensionless) laser electric field, also assumed to be gaussian. The process terminates by simulating the signal output (∝ sin 2 (Γ (t)/2))) on the CCD camera. Figure 6 shows the resulting encoding process as detected by the CCD camera. The probe laser laterally enters into the crystal while the bunch, moving normally and near to it, induces a local birefringence. The bunch electric fields gradually penetrate the crystal and the localized birefringence moves vertically with a speed c/n 0 . This leads to an overlap of the probe and the birefringence along a curved path and thus a circular shape in the EOS output signals. Since the shape and strength of the detected signals depends on the bunch parameters used to calculate E v (t), by comparing the experimental data with the simulated one it is possible to extrapolate such information.
The calibration of the EOS system been performed by focusing the Flame laser (with an intensity of about 5 × 10 18 W cm −2 ) on the edge (about 1 μm-thick) of a wedged target. The resulting time-resolved signals, recorded at different delays of the probe laser, are shown in Fig. 7(a-c). The signal corresponds to a total charge of 2.1 nC of energetic electrons that have been ejected from target and traveled up to the EOS crystal in the form of 'bunch' with 1 ps duration and approximately energy 15 MeV energy. The reproducibility of the results is proved by looking at the three frames of Fig. 7(a-c), obtained by delaying the probe with respect to the main pulse: the signal structure remains unaltered while it moves in time (from the up-right to the down-left corner). This is confirmed in Fig. 7(d-f) where the numerical simulation of the EOS output is provided for such electron bunches. The energy information is obtained by using the EOS as a time of flight monitor 23,25 . Being Δ t TOF the particle time of flight, we can estimate the bunch velocity as v = d/Δ t TOF and its energy as E = γm e , where γ = − v c 1/ 1 ( / ) 2 is the relativistic Lorentz factor, c is the speed of light and m e is the electron rest mass. Unlike conventional time-integrated spectrometric techniques, this method is able to provide energy measurements resolved in time. (a-c) Experimental measurements obtained by focusing the main laser on the edge of a wedged target at different probe laser delays (Δ t). The electron bunch is moving above the upper side of the crystal and normally to it. By measuring its time of flight we determined a mean energy of 15 MeV. The signal amplitude corresponds to 2.1 nC charge and the resulting bunch duration is 1 ps (rms). (d-f) Expected EOS signals assuming such bunch parameters. The lack of uniformity in the experimental signals, if compared with the simulated ones, is due to inhomogeneities in both the ZnTe crystal and probe laser spot.