Plasma mirrors for ultrahigh-intensity optics

Transcription

1 Plasma mirrors for ultrahigh-intensity optics C. Thaury, F. Quéré, J-P. Geindre 2, A. Levy, T. Ceccotti, P. Monot, M. Bougeard, F. Réau, P. d Oliveira, P. Audebert 2, R. Marjoribanks 3 & Ph. Martin Service des Photons, Atomes et Molécules, Commissariat à l Energie Atomique, DSM/DRECAM, CEN Saclay, 99 Gif-sur-Yvette, France 2 Laboratoire pour l Utilisation des Lasers Intenses, CNRS, Ecole Polytechnique, Palaiseau, France 3 Department of Physics and Institute for Optical Sciences, University of Toronto, 60 St. George Street, Toronto, Ontario M5S A7, Canada Attosecond bunching of Brunel electrons Movie shows the temporal evolution of the electrons (x,p x ) phase space density obtained from a 2-dimensional Particles-In-Cells simulation with the CALDER code. x is the spatial coordinate along the target normal (horizontal axis in movie), and p x the momentum component along this normal (vertical axis in movie). The plasma occupies the half space x > 2λ. This phase space density is taken at a given y along the target surface, and around the peak of a p polarized, W/cm 2, laser pulse (non-relativistic interaction regime). A fraction of the Brunel electrons are observed to bunch temporally as they return to the plasma. The different steps of this bunching process are detailed on Fig.. λ λ Figure : Two images of the plasma electrons (x p x ) phase space density at two different times, extracted from movie. Numbers () to (6) indicate the different steps in the bunching and spreading of attosecond electron bunches. Step (4) corresponds to the optimum bunching. Figure shows two images extracted from movie, and thus illustrates the temporal evo-

2 lution, in the (x,p x ) phase space, of Brunel electrons born in different optical cycles of the laser field. Using these images and movie, the following mechanism can be inferred for the formation of attosecond electron bunches in the plasma. Electrons are pulled out of the plasma () when the laser electric field E L points inward (E L > 0). These are the so-called Brunel electrons. As E L decreases and then changes sign, electrons are pushed back toward the plasma (2). Just like recolliding electrons in strong-field atomic ionization 2, the energy of returning Brunel electrons has a maximum as a function of the initial time of escape 3, 4. Electrons that left the plasma first, just after the zero-crossing of E L (E L = +ɛ), have been almost equally accelerated and then slowed down by the field, and end up with small velocities one laser cycle after their release (some of them even keeping negative velocities and never returning to the plasma). At the other extreme, the last electrons that left the plasma, just before E L decreases, have hardly been accelerated by the laser field, and therefore also return the plasma with a velocity close to 0. In between, electrons that have been significantly accelerated toward vacuum by the laser field, and then pushed backward the plasma by the combination of the laser and space charge electric fields, return with the maximum energy. Thus, Brunel electrons are distributed along an arch in phase-space (2-3). In the half of the arch closer to the bulk part of the plasma, the resulting spatial dispersion in energy is such that the fastest returning electrons progressively catch up with the slowest ones, which had smaller excursions in vacuum. As a result, the trajectories of these Brunel electrons eventually cross, and Brunel electrons in this first half of the arch bunch temporally (4), as they penetrate the plasma. This bunching is only temporary, since the fastest electrons eventually overtake the slowest ones, leading to a spreading of the electron bunch (5-6).. O. Coulaud, M. Dussere, P. Henon, E. Lefebvre, J. Roman, Optimization of a kinetic laserplasma interaction code for large parallel systems. Parallel Computing 29, 75 (2003) 2. Y. Mairesse,et al. Attosecond Synchronization of High-Harmonic Soft X-rays. Science 302, 540 (2003) 3. F. Brunel, Not-so-resonant, resonant absorption. Phys. Rev. Lett. 59, (987). 4. G. Bonnaud, P. Gibbon, J. Kindel, and E. Williams, Laser interaction with a sharp-edged overdense plasma. Laser Part. Beams 9, (99) Acknowledgements The authors would like to thank E. Lefebvre for providing the PIC code CALDER, used to calculate the electrons phase-space density. 2

3 Supplementary figure Double Plasma Mirror set-up (a) 3D view of the DPM implementation, and of the two AR-coated plates (inset). (b) Optical scheme of the DPM.

4 Supplementary figure 2 Images of the laser focal spot (a) with and (b) without the DPM.

5 !!" # Supplementary figure 3 Optical set-up used to measure the far-field spatial profile of the highorder harmonics generated on a solid target.

6 Supplementary figure 4 CWE harmonic spectra from gold, aluminium, silica and plastic targets, at W/cm 2. These spectra extend up to orders 20-2 for aluminium and silica, and 5 for plastic. The corresponding frequencies match the plasma frequencies of fully-ionized solid-density aluminium (n e = cm 3 = 460 n c 2 2 n c ), of fully-ionized solid-density silica (n e = cm 3 = 400 n c = 20 2.n c ), and that of fully-ionized solid density plastic (for the target we used, n e cm 3 = 225 n c = 5 2.n c ). Hydrodynamic simulations confirm that these low-z targets are fully ionized, and at solid-density, in our experimental conditions. In the case of gold, the maximum harmonic order is around n = 26, indicating that the target is only partially ionized, as expected for such a high-z target. The * symbols indicate incoherent plasma line emission, also observed at low temporal contrast (without DPM).

7 (a) (b) Supplementary figure 5 Raw images of HHG spectra on the MCP detector, obtained on (a) a silica target at W/cm 2 and (b) a plastic target at W/cm 2. The difference in spectral width between CWE and ROM harmonics beyond the 5th order is striking.