High Harmonics from Overdense Plasma Surfaces The oscillating mirror model Gordienko´s power law scaling Harmonics cut-off Attosecond pulses Experimental results

Few-cycle pulse: Density variation aL=3 φ=π/2

Solid harmonics with 1ω from ATLAS M. Zepf, G. Tsakiris, G.Pretzler, I. Watts et al., Phys. Rev. E, 58, R5253(1998)

Oscillating mirror model, 1D-PIC simulation Bulanov et al. Phys. Plas.1 (1993), P. Gibbon, Phys. Rev. Lett. 76, 50 (1996), von der Linde et al. PRA 52, 25 (1996) R. Lichters, J. Meyer-ter-Vehn, A. Pukhov, Phys. Plasmas 3, 3425 (1996) ncrit n(x,t) x t a=3, a=45, ne/nc=27 1D PIC simulations 1019 W/cm2 a= 3 harmonics 3 Gbar light pressure electrons ions

1D-PIC simulation predicts harmonics up to 100 R. Lichters, J. Meyer-ter-Vehn, A. Pukhov, Phys. Plasmas 3, 3425 (1996) In 5 x 1019 W/cm2 harmonic number a=6, a=45, ne/nc=27

PIC simulation shows w-5/2 power law spectrum S. Gordienko et al., Phys. Rev. Lett., 93, 115002(2004) LPIC simulation

Doppler shift at relativistic mirror A. Einstein, Annalen der Physik 17, 891 (1905) observer time moving mirror 7

Gordienko theory: Phys.Rev.Lett 93, 115002 (2004) n-th Fourier component of reflected E-field stationary points with at t = tn = 0 saddle point integration

first derivative of for mirror velocity retarded mirror time t´ n-th harmonic appears only if (same as in Compton backscattering !)

Second derivative and n -5/2 scaling b t´ bmax tmax bn

17. Problem: Derive w-5/2 scaling of harmonic spectrum Evaluate the Fourier components of the light reflected from a plasma surface having position X(t‘) at surface time t‘ = t + 2X(t‘)/c + t0 Make use of the saddle point method by determining the stationary points tn of the phase function, dF(tn)/dt=0, and obtain Show that the harmonics spectrum decays with harmonic number n according to Verify that the largest stationary point in this approach corresponds to the largest g value at which the surface moves towards the incident light and to a largest harmonic number nmax =4 gmax2.

Electron motion at mirror interface T. Baeva, S. Gordienko, A. Pukhov, Phys. Rev. E74, 046404 (2006) q mirror

Mirror emits attosecond flash Attosecond Flash and Spectral Cutoff T. Baeva, S. Gordienko, A. Pukhov, PRE 74, 046404 (2006), arXiv:physics/0604228 Mirror emits attosecond flash at t=t0 when pt =0 ! t0 Flash length Flash duration Cutoff frequency

Harmonic oscillation as seen from observer cut-off X(t‘) X(t)

The spectrum of the reflected wave

Surface Harmonics observed in new VULCAN Experiment B.Dromey, M.Zepf et al., Queens Univ. Belfast, to appear in Nature Physics (2006): High Harmonic Generation in the Relativistic Limit contrast > 1011:1 achieved by double plasma mirror IL > 1020 W/cm2 aL > 10

High Harmonic Generation in the Relativistic Limit VULCAN data confirm 5/2 power law down to water window B.Dromey, M.Zepf et al., Queens University Belfast, to appear in Nature Physics (2006) High Harmonic Generation in the Relativistic Limit w-5/2 contributions up to 850th harmonic oberserved

High Harmonic Generation in the Relativistic Limit B.Dromey, M.Zepf et al., Queens University Belfast, to appear in Nature Physics (2006) High Harmonic Generation in the Relativistic Limit

keV harmonics + the efficiency roll-over 10 1.5.5x1020 Wcm-2 2.5 .5x1020 Wcm-2 h~n-2.55 ±.2 1 Intensity/ /arb. units Normalised at 1200th order Intensity dependent roll-over 10-1 Harmonic efficiency n-2.55  Relativistic limit 10-2 1200 Order, n 3200 1.414KeV Photon Energy 3.767KeV I t FWHM 1’ ~ 500fs It’s still a pulse train Smooth spectrum due to lack of resolution

Roll over scaling confirmed as ~g3 Roll-over measurements 8g3 4g2 Vulcan 1996 highest observed 22 (6 1020Wcm-2m2) Roll over ~g3  10 keV pulse @ a0~30 (1021Wcm-2m2)

Filters produce clean attosecond pulses G.D.Tsakiris, K.Eidmann, J.Meyer-ter-Vehn, F.Krausz, New J.Phys. 8, 19 (2006)

Efficiency variation with intensity efficiency at saturation

3D-PIC simulation of surface harmonics with far-fiels M. Geissler, S. Rykovanov, G. Tsakiris, J. Meyer-ter-Vehn, NJP submitted (2007) Ne I y,z x,z (pol) 5-10th harm 5-10th harm

3D-PIC simulation of surface harmonics with far-fiels M. Geissler, S. Rykovanov, G. Tsakiris, J. Meyer-ter-Vehn, NJP submitted (2007) Ne I Harmonics spectrum y,z x,z (pol) 5-10th harm 5-10th harm y (mm) x (mm) Far-field transverse distribution 200 mm from target

Selected publications: R.Lichters, J. Meyer-ter-Vehn, A.Pukhov, Phys.Plasmas 3, 3425 (1996). M. Zepf, G.D. Tsakiris, G. Pretzler, I. Watts, et al., Phys. Rev. E 58, 5253 (1998). I. Watts, M. Zepf, e.L. Clark, et al., Phys. Rev. Lett. 88, 155001 (2002). S.Gordienko, A.Pukhov, O.Shorokhov, T.Baeva, Phys. Rev. Lett.93, 115002 (2004): G.D.Tsakiris, K.Eidmann, J.Meyer-ter-Vehn, F.Krausz, New J.Phys. 8, 19 (2006): Route to Intense Single Attosecond Pulses Th.Baeva, S.Gordienko, A.Pukhov, PRE 74, 065401 (2006): Relativistic plasma control for single attosecond pulse generation Th.Baeva, S.Gordienko, A.Pukhov, PRE 74, 046404 (2006) (2006) Theory of high harmonic generation in relativistic laser interaction etc. B.Dromey, M.Zepf, A. Gopal, K. Lancaster, M.S. Wie, K. Krushelnik, M.Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, M. Tampo, C. Stoeckl, R. Clarke, H. Habara, D. Neely, S. Karsch, P. Norreys, Nature Physics, to appear (July 2006): High Harmonics Generation in the Relativistic Limit

Conclusions The mirror model and 1-D PIC simulations indicate that the plasma-vacuum interface constitutes an excellent medium for the generation of a harmonic comb at arbitrarily high intensities. At laser intensities of 1020 W/cm2 , 1-D PIC simulations predict a single attosecond pulse in the 20-70eV spectral range with duration of ~100as and few percent efficiency. Although no fundamental upper limit for the laser intensity is imposed by the non-linear process itself, technological limitations might be important.

Relativistic scaling pREL=2.5 Experimental data from Vulcan PW shows p=2.5.2 for a=10 HIGH EFFICIENCY 10-4@60 eV (17nm) 10-6@250eV (4nm) Extremely high photon numbers and brightness: 10131 photons 10231ph s-1mrad-2 (0.1%BW) Published: B. Dromey et al, Nature Physics, 2006

Angle from target normal/deg (Specular reflection 45º, incident -45º) Beamed keV harmonic radiation - demonstrates coherent keV radiation 1 0.8 0.6 X-ray Signal > 1 keV 4º FWHM Gaussian fit to beamed HHG signal 0.4 0.2 -100 50 0 50 100 150 specular Angle from target normal/deg (Specular reflection 45º, incident -45º) X-ray emission above 1keV and 3w is beamed into ~f/3 cone (laser also f/3) for nm rms roughness targets. No beaming observed for -shots with micron rms targets -shots without plasma mirrors

The efficiency for a power law spectrum Efficiency at saturation

Filtering different spectral ranges Plasma profile ramp l=0 time-domain frequency-domain filtered pulse

PW Field Synthesizer (PFS) project study (March 2005) 2 nJ seed 8 mJ amplified spectrum (OPCPA) 6.2 fs 1 TW pulse MPQ develops few-cycle pulses few J, < 10 fs, PW-range 2005 - 2008 F. Krausz, S. Karsch, et al. PW Field Synthesizer (PFS) project study (March 2005) 2 nJ seed

Filters produce clean attosecond pulses

The optimum filter for short pulses

Variation of the absolute phase

Surface Harmonics Literature R. Lichters, J. Meyer-ter-Vehn, A. Pukhov, Phys. Plasmas 3, 3425 (1996): Short-pulse laser harmonics from oscillating plasma surfaces driven at relativistic intensity S. Gordienko, A. Pukhov, O. Shorokhov, T. Baeva, PRL 93, 115002 (2004): Relativistic Doppler Effect: Universal Spectra and Zeptosecond Pulses S. Gordienko, A. Pukhov, O. Shorokhov, T. Baeva, PRL accepted (2005): Coherent Harmonic Focusing and the Light Extreme

measured harmonics spectrum critical surface motion (1D PIC) X(t´)

I ~ w -5/2 I ~ w -3 nmax = 4gmax2 long pulses discrete harmonics few-cycle pulses continuous spectrum cut-off harmonic nmax = 4gmax2 gmax peak mirror velocity