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High Harmonics from Overdense Plasma Surfaces

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. a L =3 φ = π /2. Solid harmonics with 1 ω from ATLAS. a = 3.

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High Harmonics from Overdense Plasma Surfaces

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

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

  3. Solid harmonics with 1ω from ATLAS a = 3 M. Zepf, G. Tsakiris, G.Pretzler, I. Watts et al., Phys. Rev. E, 58, R5253(1998)

  4. t harmonics ncrit 1D PIC simulations n(x,t) 3 Gbar light pressure x 1019 W/cm2 a= 3 a=3, a=45, ne/nc=27 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) electrons ions

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

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

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

  8. = 0 Gordienko theory: Phys.Rev.Lett 93, 115002 (2004) n-th Fourier component of reflected E-field stationary points with at t = tn saddle point integration

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

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

  11. 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. 17. Problem: Derive w-5/2 scaling of harmonic spectrum

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

  13. t0 Flash length Flash duration Cutoff frequency 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 !

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

  15. w-5/2 The spectrum of the reflected wave

  16. IL > 1020 W/cm2 aL > 10 contrast > 1011:1 achieved by double plasma mirror 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

  17. w-5/2 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 contributions up to 850th harmonic oberserved

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

  19. Intensity dependent roll-over I FWHM 1’ ~ 500fs It’s still a pulse train Smooth spectrum due to lack of resolution t 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 10-1 Harmonic efficiencyn-2.55Relativistic limit 10-2 1200 3200 Order, n 3.767KeV 1.414KeV Photon Energy

  20. 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)

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

  22. Efficiency variation with intensity efficiency at saturation

  23. 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

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

  25. 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

  26. 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.

  27. 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

  28. 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

  29. The efficiency for a power law spectrum Efficiency at saturation

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

  31. p.567 8 mJ amplified spectrum (OPCPA) 6.2 fs 1 TW pulse MPQ develops few-cycle pulses few J, < 10 fs, PW-range 2005 - 2008 2 nJ seed F. Krausz, S. Karsch, et al. PW Field Synthesizer (PFS) project study (March 2005)

  32. Filters produce clean attosecond pulses

  33. The optimum filter for short pulses

  34. Variation of the absolute phase

  35. 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

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

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

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