Amplification of Ultrashort Laser Pulses by Brillouin Backscattering in Plasmas S. Weber, 1,2 C. Riconda, 3 L. Lancia, 4,5 J.-R. Marque `s, 6 G. A. Mourou, 1 and J. Fuchs 6 1 IZEST, Ecole Polytechnique–CEA, 91128 Palaiseau, France 2 Institute of Physics of the ASCR, ELI-Beamlines, 18221 Prague, Czech Republic 3 LULI, Universite ´ Pierre et Marie Curie-Ecole Polytechnique-CNRS-CEA, 75252 Paris, France 4 SAPIENZA, University of Rome, Dipartimento SBAI, 00161 Rome, Italy 5 INFN-Sezione Roma-SAPIENZA, University of Rome, 00185 Rome, Italy 6 LULI, CNRS-Ecole Polytechnique-Universite ´ Pierre et Marie Curie-CEA, 91128 Palaiseau, France (Received 9 December 2012; published 31 July 2013) Plasma media, by exciting Raman (electron) or Brillouin (ion) waves, have been used to transfer energy from moderately long, high-energy light pulses to short ones. Using multidimensional kinetic simulations, we define here the optimum window in which a Brillouin scheme can be exploited for amplification and compression of short laser pulses over short distances to very high power. We also show that shaping the plasma allows for increasing the efficiency of the process while minimizing other unwanted plasma processes. Moreover, we show that, contrary to what was traditionally thought (i.e., using Brillouin in gases for nanosecond pulse compression), this scheme is able to amplify pulses of extremely short duration. DOI: 10.1103/PhysRevLett.111.055004 PACS numbers: 52.38.Dx, 52.35.Fp, 52.38.Bv, 52.65.Rr Since the conception of the laser, there has been a constant push towards increasing the power and focused intensity of the produced light pulses. Doing so has indeed proven to open many new possibilities for fundamental science (e.g., nonlinear optics, compact particle accelera- tion) and applications (e.g., nonthermal precision machin- ing, medicine). Moreover, with higher intensity lasers, one can produce even shorter pulses through nonlinear effects [1], giving access to faster processes [2]. Fast progress on the increase of laser power has relied on solid state optics using techniques such as CPA (chirped pulse amplification) [3] or OPCPA (optical parametric chirped pulse amplification) [4]. These optics are, however, limited by a very low damage threshold [5] of the order of a few 100 mJ per cm 2 . Further progress relies on increasing the beam diameter, which increases the costs for the optics. By contrast, amplifiers based on plasma gratings resulting from laser-matter interaction, a medium unaffected by damage and extremely compact, present many advanta- geous properties that allow us to directly amplify extremely short laser pulses. The scheme, which is limited by strong nonlinear effects as will be discussed below, exploits energy transfer, mediated by the plasma, between a long, high energy, pump pulse and a short, low-intensity seed pulse. It can also be thought of as the scattering of one electro- magnetic wave onto the plasma wave in order to reinforce or amplify the other electromagnetic wave. The plasma wave can be either an electronic (Raman) or an ionic wave (Brillouin). The coupling requires precise momentum (k pump ¼ k seed þ k plasma ) and energy (! pump ¼ ! seed þ ! plasma ) conservation conditions. Both processes can be described by similar coupled equations [6,7], although they require quite different plasma and laser conditions. Much effort has been put in the Raman amplification of short pulses [7–10], producing up to 3 mJ, 50 fs, 10 16 W=cm 2 in a plasma channel [11]. Extrapolating these results, amplification of centimeter wide laser beams to 10 18 W=cm 2 was studied [12]. However, (1) this requires wide and long (> 10 mm) quasihomogeneous plasmas [8,12,13], (2) since ! plasma depends on the plasma density, any change in the latter strongly affects the process effi- ciency, and finally (3) the large frequency difference between ! pump and ! seed implies that one or the other has to be at a precise frequency that does not correspond to standard laser technologies. In general stimulated Raman backscattering (SRS) is favored by low tempera- tures in conjunction with very low plasma densities. Brillouin amplification has been considered in the past for fluids and gases. However, due to the characteristic phonon period of the order of 100 ps and the ionization breakdown of the material its use is very limited (see [6] and references therein). Using stimulated Brillouin back- scattering (SBS) in plasmas avoids the breakdown and reduces the characteristic time scale to the ion-acoustic wave period of the order of a few picoseconds. Further improvement is obtained by SBS amplification in the only recently studied strong-coupling (sc) regime [6,14]. It is suited for very short pulses and eases considerably some of the following technical difficulties: (1) pump and seed can be at the same frequency, in fact the amplification process is self-organizing by selecting the good frequencies, (2) the coupling is set not by a natural resonant mode but by a forced nonlinear oscillation, and since the energy transfer is fast, the interaction length is short (sub-mm), (3) the process is stable with respect to frequency mismatches associated to density inhomogeneities and it is also not PRL 111, 055004 (2013) PHYSICAL REVIEW LETTERS week ending 2 AUGUST 2013 0031-9007= 13=111(5)=055004(5) 055004-1 Ó 2013 American Physical Society