plasma optics Amplification of light pulses: non-ionised media

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2 Amplification of light pulses: non-ionised media since invention of laser: constant push towards increasing focused intensity of the light pulses Chirped pulse amplification D. Strickland, G. Mourou, Optics Comm. 55, 219 (1985) G.A. Mourou et al., Phys. Today 51, 22 (1998) ionisation intensity-limit: I W/cm 2 damage threshold of gratings: 1 J/cm 2 1 EW & 10 fs 10 kj surface areas of order 10 4 cm 2 = 1m x 1m difficult to produce and very expensive plasma optics

3 Amplification of light pulses: plasma pump interaction seed NO damage threshold high-energy long pump low-intensity short seed plasma response is taken up by electron plasma wave Raman ion-acoustic wave Brillouin amplified seed depleted pump conservation equations ω pump = ω seed + ω plasma k pump = k seed + k plasma time scales Brillouin τ s ω cs ps Raman τ s ω pe fs

4 Ion-based amplification in the strong-coupling regime

5 SBS - Resonance coupling between pump and seed resonance condition would be: ω o = ω s + ω sc τ s = 13, 80fs Δω s /ω o = 0.22, 0.04 AND Δω ϒ /ω ο (10 16 W/cm 2 )/ω o = 4 x 10 3 Δω γ & ω sc << Δω s i.e. coupling is in fact provided by shortness of seed downshifting seed basically useless chirp of 6nm negligible for seed but broadens pump for Δω Υ Δω s need τ s 800 fs broad spectrum of IAW plays dominant role

6 SRS - Resonance coupling between pump and seed resonance condition would be: ω o = ω s + ω ep frequency spreads <<< participating frequencies no overlap SBS: coupling via spread; SRS: coupling via downshift as ω ep (ne = 0.05 n c ) 0.22ω o SRS-amplification via frequency spread requires Δω s ω o ω ep interesting at vey low density and very short pulses

7 Intervening characteristic time scales amplification process has to be optimised in concurrence with other plasma instabilities! 1) avoid filamentation for pump and seed: τ p,s /(1/γ fil ) < 1 with γ fil /ω o 10-5 I 14 λ 2 [μm](n e /n c ) upper limit for τ p & plasma amplifier length; I p = W/cm 2, n e = 0.05 n c τ p,max 10 ps & l p 3mm; example: plateau 150 μm; density n e = 0.3 n c ; τ seed = 60 fs τ pump = O(ps) τ pump = 300 fs filamentation is the main obstacle for the high-energy scenario

8 Intervening characteristic time scales cont d 2) amplification should be efficient: τ s /(1/γ sc ) 1 with γ sc /ω o = 3.6 x 10 2 (I 14 λ 2 [μm]) 1/3 (Zm e /m i ) 1/3 (n e /n c ) 1/3 however, amplification also works in the opposite limit but lower energy transfer 3) avoid wavebreaking in the sc-limit: τ s /τ wb < 1 with τ wb ω o 1.2 x 10 2 (m i /2m e )/ (I 14 λ 2 [μm]) induces fracturing of the seed in propagation direction & destroys amplification process

9 Intervening characteristic time scales cont d 4) avoid SRS if possible: τ p /(1/γ srs ) < 1 with γ srs /ω o 4.3 x 10 3 (I 14 λ 2 [μm]) (ne/nc) 1/4 1/γ srs 25 fs!! BUT can be controlled by plasma profile and temperature, associated energy losses small limiting condition from 2) & 3) : (1/γ sc ) τ wb a max = v osc/ c (m i /Zm e ) (n e /n c ) for n e = 0.05 n c get I max W/cm 2 From these consideration one obtains a parameter space of operation

10 Operational regime for sc-sbs strong coupling for W/cm 2 wave-breaking for W/cm 2 filamentation for W/cm 2 reference density 0.05 n c outside shaded area amplification becomes difficult high density filamentation low density weak coupling short pulse low efficiency long pulse wavebreaking S. Weber et al., PRL (2013)

11 Simulating plasma amplification parameter configurations partially motivated by ongoing experiments pump parameters: I p = W/cm 2, w = 32, 64 μm, τ p = 3.5 ps seed parameters: I s = W/cm 2, w = 22, 44 μm, τ s = fs crucial part of amplification I s (t) I p ; amplification from to on < 1mm no problem n e /n c typical gas jet profile 0.05n c 240 μm 240 μm 240 μm plasma parameters: Z = 1, Te = 500 ev, m i = 3600m e PIC as worst-case scenario: δn/n pic >> δn/n thermal NOTE: SRS & filamentation grow on noise BUT sc-sbs is controlled by seed!! x k 0 Evaluation need seed shortness energy transfer plasma profile

12 Simulation results: initial phase I s I p I s = 3 x x I s = 1 x x pump depletion obtained w/o problem

13 Simulation results: highest intensity-shortest pulse amplification of an extremely short pulse: 13 fs intensity W/cm x W/cm 2 over 700 μm τ seed < 1/γ sc low energy transfer of 6 % transverse FWHM reduced: 44 μm 10 μm need high intensity to excite plasma grating centre amplified at expense of wings increase energy-transfer with super-gaussian profiles some relativistic self-focusing but not dominant effect

14 Simulation results: high-energy-transfer-efficiency 80 fs seed pulse is amplified down a plasma ramp high energy extraction efficiency of 53% but low final intensity of 4 x W/cm 2 ramp profile: affects SRS strongly but SBS very little (robustness of SBS) pump & seed meet at high-density edge of ramp where coupling is strong from beginning such profiles can be easily generated from gas jets increase final intensity by optimizing plasma profile

15 Transition from sc-sbs to new modes τ s =210 fs > ϒ sc -1 τ s =80 fs <~ ϒ sc -1 τ s =13 fs < ϒ sc -1 Transition from sc-sbs to mixed/new modes monochromatic 2 carrier frequencies continuum

16 Spectral properties of amplified seed as amplification evolves frequency of seed is downshifted far beyond Δω sc high-intensity amplification starts to mix SBS and SRS

17 Ion mobility issue Mixed Pure sc-sbs spectrum IMMOBILE IONS versus MOBILE IONS creation of a pure sc-sbs tail, as predicted by Lehmann et al. PoP 20, (2013)

18 The logical step CARRYING OVER TO EXPERIMENT Pump Laser Plasmas

19 We did the first demonstration of the possibility to use ion waves for CPA pulse amplification in 2010 We used a non-colliding geometry to protect the diagnostics and ease of set-up

20 Result: amplification factor 32 was achieved Ar 0.1nc W/O pump no pump (X5) no seed (X5) polar. crossed (X5) with pump Crossed polarization No amplification Electro-magnetic coupling is the key 34µm 10 34µm 2D autocorrelator wavelength (nm) 1 3 L. Lancia et al., PRL (2010)

21 Important: Pump beam was depleted Without seed interaction Focal spot With seed Log scale Log scale Typical shot. Ar 50 bar 3.5 ps pump Seed/pump coincident Same conditions, same colorbar Total signal 6 times less

22 Dependence of amplification on plasma density 3 sc n e

23 Dependence of amplification on plasma density Less energy is available for transfer due to low pump transmission at high densities role of plasma inhomogeneities

24 Amplification peaks at zero pump / seed delay Ar 50 bar (pump 3.5 ps)

25 Next steps: toward the Joule level & beyond Limit of first experiment due to plasma inhomogeneities & limited overlapping region Need to have a more homogeneous plasma to avoid pump loss of transmission and fragmentation Use of He or H to have full ionization of the gas jet Longer overlapping region Head-on interaction Need to control undesired instabilities (SRS, filamentation) Allow for inhomogeneous plasma (to control SRS) and limit the maximum value of n e (to control filamentation)

26 We thus moved in June 2013 to a counter-propagation setup 10J 3ps ~ W/cm 2 50J 2ns ~10 13 W/cm 2 15mJ 400 fs W/cm 2 H cc

27 And developed asymetric gas jets for extended interactions while minimizing the transverse dimension Horizontal map 700µm above the nozzle Measurement of the density for a rectangular Nozzle : (0.6x2.0mm / throat : 0.3mm ) Argon gas jet, 80bar Reconstruction with 10 angles. Vertical maps. Density in the y=0 and x=0 planes.

28 Design of profiles is made using simulations with OpenFoam Exemple of mesh for a 2D axisymmetric nozzle. OpenFoam is an open source 3D eulerian code. It helps us design nozzle for specific density profile. It can simulate cylindrical, rectangular and asymetric nozzle (work in progress). Exemple of output

29 Example of absolute amplification

30 Perspective: asymmetric gas jet profiles for optimum amplification Density in cm -3 for 100 bars By tilting a rectangular nozzle in the vertical plan we can get a density profile with different gradients. Exemple of density map in the horizontal plan if the nozzle is turned by x2.0mm nozzle / 0.3mm throat. Argon at 80bar. Density in cm -3 /bar. 4E+19 3,5E+19 3E+19 2,5E+19 2E+19 1,5E+19 1E+19 Advantages: *reproducible *tuneable 5E+18 0 Space (mm) 0 0,5 1 1,5 2 2,5 3 3,5

31 After producing high-power pulses, one also needs to focus them plasma-based mirror compact, free from damaging Plasma mirror Focusing plasma plasma Debris Compact ~ 4.4mm (FWHM) ~ 0.9mm (FWHM) f/ Hz images l L ~0.5mm 3mm 1/5 spot 3mm M. Nakatsutsumi, et. al., Opt. Lett (2010)

32 Perspective: combine plasma optics take advantage of existing kj laser facilities to convert them to extreme intensities (QED physics, pair production, )

33 CONCLUSION & PERSPECTIVES High-energy density plasmas offer possibilities to create devices for control of high-power light pulses (focusing, contrast enhancement, guiding, amplification, compression) on the theory/simulation side: effect of magnetic fields much more analysis (1D simulation & analytical) for mixing modes intelligent use of plasma profiles for short pulses distinction between SBS and SRS gets blurred on the experimental side: transition from relative to absolute amplification is encouraging need experiments with more energy and shorter seed pulses Continuation to large-scale facilities (GSI, PETAL) and also part of the ELI-R5 research program