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keV Harmonics from Solid Targets - The Relatvisitic Limit and Attosecond pulses

keV Harmonics from Solid Targets - The Relatvisitic Limit and Attosecond pulses. Matt Zepf Queens University Belfast. B.Dromey et al. Queen’s University Belfast K. Krushelnick et al, Imperial College P. Norreys et al, RAL. Outline. High Harmonic Generation from Solid Targets

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keV Harmonics from Solid Targets - The Relatvisitic Limit and Attosecond pulses

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  1. keV Harmonics from Solid Targets - The Relatvisitic Limit and Attosecond pulses Matt Zepf Queens University Belfast B.Dromey et al. Queen’s University Belfast K. Krushelnick et al, Imperial College P. Norreys et al, RAL

  2. Outline High Harmonic Generation from Solid Targets Harmonics from solid targets – Background Experimental resultsThe relativistic limit – high conversion efficiencies keV harmonics – coherent fs radiation Angular distribution- beamed keV radiation Potential for very bright attosecond pulse generation

  3. Ultra High Harmonic Generation - the principle • High power pulse tightly focused onto a solid target • Critical surface oscillates with v approaching c Relativistically oscillating mirror  = (1+(a0)2/2)1/2 Process intrinsically phased locked for all harmonics! Zeptosecond pulses possible at keV Incident Pulse Reflected Pulse • Reflected waveform is modified from sine to ~sawtooth Harmonic efficiency is FT of reflected waveform Train of as pulses (analogous to mode-locking)

  4. Typical spectra – Conversion efficiency follows power law scaling Conversion efficiency scales q~n-p With p=5.5…3.3 for I=5 1017…1019Wcm-2 (a0=0.6 .. 3) From Norreys, Zepf et al., PRL, 1832 (1996) Very high orders become rapidly more efficient at high intensities e.g. 100th harmonic~I3 PIC predicts q~n-2.5 >1020Wcm-2. (a0>10) and 1000s of orders

  5. Duration of attosecond pulses Few as pulses possible <1keV Zeptosecond@>1keV nF Extremely short pulses are possible by filtering the phase locked HHG (G. D. Tsakiris et al.,New J. Phys. 8, 19(2006) nF Dn=(21/p-1)nF Harmonic efficiency slope as n-p Atto pulse efficiency: h~n-p+1~n-1.5

  6. Realistic experimental configuration (G. D. Tsakiris et al.,New J. Phys. 8, 19(2006) Filters (~0.1µm thick) have negligible dispersion

  7. Consequences from the oscillating mirror model • Flatness results in specular • Well defined mirror surface gives high conversion efficiency Phase locked harmonics – as pulses possible reflection of the harmonics Surface denting/bowing in response to laser can change collimation.Surface roughness important for Ångstrom radiation. Harmonic efficiency depends strongly on plasma scale length, L L/  0.1-0.2 Short, highcontrast pulses appear ideal. Single cycle pulses to generate atto pulses Oscillating Mirror Flat, sharply defined critical density surface

  8. Experimental Setup: Double plasma Mirror Setup Incident laser pulse: f3 cone Target position Pulse Energy: up to 500J Pulse energy with PM:up to 150 J Pulse duration: 500-600fs Contrast (no PM) >107:1 Contrast with PMs: >1011:1 Peak intensity (with PM) 2.5 1020Wcm-2 Grating spectrometer or von Hamos crystal spectrometer CCD or image plate detectors

  9. 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

  10. Intensity dependent roll-over I FWHM 1’ ~ 500fs 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 3767KeV 1414KeV Photon Energy First coherent, femtosecond, sub-nm source

  11. 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)

  12. Standard contrast (~10-7) – Bright thermal emitters. 1 0.8 kT~3keV 0.6 Intensity/ arb. units 2.5x1020Wcm-2 0.4 kT~1.5keV 0.2 7x1019Wcm-2 2 3 4 5 6 7 8 Wavelength /Å Planckian Spectrum observed for standard contrast Signal brightness ~2x HHG signal Plasma mirrors are essential Absorption much higher for low contrast pulses.

  13. Beamed keV harmonic radiation - 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

  14. Surface denting Laser Ponderomotive pressure can deform surface. (under the current conditions some deformation is unavoidable Denting required to explain our results:~ 0.1m This would lead to the same divergence for all harmonics in agreement with results.  Solution: use shorter pulses to prevent surface deformation

  15. Summary • Harmonics from solids are efficient way of producing as pulses up to keV photon energies. • Ideal for converting ultra high power pulses (100’s of TW) • HHG in the relativistic limit has been demonstrated. • Simple geometry for as-pulse production (surface harmonics, phase locked with flat phase, dispersion free system) • Two possible schemes: polarisation switching or single cycle pulses • Angular divergence limit remains a question mark: have we reached DL performance? • Contrast requirements (>1010) are a challenge for fs lasers

  16. Surface roughness Laser • Surface roughness would impact on the highest orders only • Unlikely to be a major factor in this experiment • Solution: highly polished targets

  17. Imprinted phase aberration • Phase errors in fundamental beam are passed on to harmonics Dfn~n DfLaser Divergence of harmonics can be strongly affected (cf doubling of high power laser beams)

  18. The cut-off question. Until recently no firm theoretical basis for a cut-off • Should one expect a cut-off? • Harmonic spectrum is simply FT of reflected waveform • no cut-off infinitely fast risetime components (unphysical) • Recently: Rollover for n> 4g2 (Gordienko et al (PRL,93, 115002, 2004) • Revised theory predicts rollover for n>81/2g3 (T. Baeva et al, PRE and talk after break) Very different predictions for reaching 10,000 harmonics: 4g2: a0=50 81/2g3: a0=22

  19. What determines the angular distribution? 1) What determines the angular distribution? Diffraction limited peformance would suggest qharmonic~qLaser/n  qharmonic~10-4 rad for keV harmonics. • Why do keV harmonics beam at all?Surface roughness should prevent beaming(Wavelength<< initial surface roughness for keV harmonics) • what reduces the surface roughness • a) smoothing in the expansion phase? • b) Relativistic length contraction (highest harmonics are only generatedat max. surface g)

  20. High Efficiency Assuming 1J,5fs(projected ELI front end) Extremely powerful attosecond source Ultrahigh brightness may be possible with DL performance

  21. Experimental paramters Pulse Energy (No Plasma Mirror):up to 500J Pulse energy with PM: up to 150 J Pulse duration: 500-600fs Contrast (no PM) >107:1 Contrast with PMs: >1011:1 Spot size: ~7m Peak intensity (with PM) 2.5 1020Wcm-2

  22. Attosecond pulses by spectral filtering Removing optical harmonics + fundamental changes wave from from saw-tooth to individual as-pulses and sub-as pulsesfrom (G. D. Tsakiris et al.,New J. Phys. 8, 19(2006)

  23. PIC predicts asymptotic limit of pREL~2.5-3 Exact value of p is pulseshape dependent Orders > 1000, keV harmonics! Gordienko et al. PRL 93, 115001, 2004

  24. Conversion efficiency into attosecond pulses ~n-3/2 Conv eff at filter peak: hf|~(nf)-p Bandwidth: Dn~(21/p-1)nF Pulse efficiency: hpulse~(21/p-1)nF-(p-1)~n-3/2

  25. Laser contrast is the key to high efficiency. 1.3x104 1.2x104 1.1x104 1x104 9x103 Reference Spectrum (arb.) Harmonic Spectrum (arb.) Signal (arb) 8x103 ~ ~ ~ ~ No plasma mirrorContrast ~10-8 1200 b) C-line @3.4nm 1000 800 C-line @4.01nm 600 Source Broadening increases linewidth in no PM case 400 200 0 360 380 400 420 440 460 480 500 Pixel number Shot 1: Contrast 1011(2 plasma mirrors) Strong harmonic signal. Shot 2: Contrast 107(No plasma mirrors) Weak C-line emission Harmonics >100x brighter than thermal source in water window

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