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 results The 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 Reflected waveform is modified from sine to ~sawtooth Incident Pulse Reflected Pulse Process intrinsically phased locked for all harmonics! Zeptosecond pulses possible at keV  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 10 17 …10 19 Wcm -2 (a 0 =0.6.. 3) Very high orders become rapidly more efficient at high intensities e.g. 100 th harmonic~I 3 From Norreys, Zepf et al., PRL, 1832 (1996) What happens for much higher intensities >10 20 Wcm -2. (a 0 >10)? Is there a cut-off or can we generate arbitrarily high harmonics?

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

6. 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> 4  2 (Gordienko et al (PRL,93, 115002, 2004)  Revised theory predicts rollover for n>8 1/2  3 (T. Baeva et al, PRE and talk after break) Very different predictions for reaching 10,000 harmonics: 4  2 : a0=508 1/2  3 : a0=22

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

8. nFnF Duration of attosecond pulses  n=(2 1/p -1)n F Few as pulses possible <1keV Zeptosecond@ >1keV nFnF Extremely short pulses are possible Harmonic efficiency slope as n -p

9. Conversion efficiency into attosecond pulses Conv eff at filter peak:  f| ~(n f ) -p Bandwidth:  n~(2 1/p -1)n F Pulse efficiency:  pulse ~(2 1/p -1)n F -(p-1) ~n -3/2 ~n -3/2

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

11. Consequences from the oscillating mirror model Oscillating Mirror Flat, sharply defined critical density surface Flatness results in specular reflection of the harmonics Well defined mirror surface gives high conversion efficiency Phase locked harmonics – as pulses possible 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, high contrast pulses appear ideal. Single cycle pulses to generate atto pulses

12. Experimental Setup: CCD or image plate detectors Grating spectrometer or von Hamos crystal spectrometer Target position Double plasma Mirror Setup Incident laser pulse: f 3 cone

13. The issue of pulse contrast ASE contrast ns timescale Prepulses ns timescale Recompression errors ps timescale Plasma formation threshold If the contrast is not excellent (<10 -10 @ns, 10 -8 @ps) a plasma will form early and no steep gradient (mirror) will form.

14. Plasma Mirror - an ultra-fast optical switch A low reflectivity surface (i.e. a piece of glass with AR coating can operate as ~100fs rise time optical switch: - Illuminate with I max > plasma formation threshold - prepulse sees R cold <10 -2 -main pulse sees R plasma ~60-80% - contrast enhancement: R plasma /R cold ~ 100 Disadvantages: Energy loss, new PM required every shot. Plasma Mirror

15. 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)>10 7 :1 Contrast with PMs:>10 11 :1 Spot size:~7  m Peak intensity (with PM)2.5 10 20 Wcm -2

16. 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: 10 13  1 photons 10 23  1 ph s -1 mrad -2 (0.1%BW) Relativistic scaling p REL =2.5 Published : B. Dromey et al, Nature Physics, 2006

17. Pulse duration reduces with n:  ~n -1 Diffraction limited focus: w 0 ~n -2 Intensity increases: Theoretical max. intensity increases with harmonic order! (for p<3)

18. Laser contrast is the key to high efficiency. 360 380 400 420 440 460 480 500 Harmonic Spectrum (arb.) Reference Spectrum (arb.) Pixel number C-line @3.4nm C-line @4.01nm 9x10 3 1x10 4 1.1x10 4 1.3x10 4 0 1.2x10 4 ~ 200 ~ No plasma mirror Contrast ~10 -8 Source Broadening increases linewidth in no PM case Signal (arb) b) ~ ~ 8x10 3 400 600 800 1000 1200 Shot 1: Contrast 10 11 (2 plasma mirrors) Strong harmonic signal. Shot 2: Contrast 10 7 (No plasma mirrors) Weak C-line emission Harmonics >100x brighter than thermal source in water window

19. 10 1 10 -1 10 -2 Intensity/ /arb. units Normalised at 1200 th order Order, n 1200 3200 2.5 .5x10 20 Wcm -2 1.5 .5x10 20 Wcm -2 Harmonic efficiency  n -2.55  Relativistic limit  ~n -2.55 ±.2 Photon Energy 1.414KeV 3.767KeV Intensity dependent roll-over keV harmonics + the efficiency roll-over First coherent, femtosecond, sub-nm source I t FWHM 1’ ~ 500fs

20. Roll over scaling confirmed as ~  3  8  3 44 22 Roll-over measurements Vulcan 1996 highest observed (6 10 20 Wcm -2  m 2 ) Roll over ~  3  10 keV pulse @ a0~30 (10 21 Wcm -2  m 2 )

21. 1 0.8 0.6 0.4 0.2 7x10 19 Wcm -2 2.5x10 20 Wcm -2 Intensity/ arb. units Wavelength /Å 2 3 4 5 6 7 8 kT~1.5keV kT~3keV Standard contrast (~10 -7 ) – Bright thermal emitters. Planckian Spectrum observed for standard contrast Signal brightness ~2x HHG signal  Plasma mirrors are essential  Absorption much higher for low contrast pulses.

22. Beamed keV harmonic radiation - demonstrates coherent keV radiation X-ray emission above 1keV and 3  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 1 0.8 0.6 0.4 0.2 -100 50 0 50 100 150 Angle from target normal/deg (Specular reflection 45º, incident -45º) X-ray Signal > 1 keV 4º FWHM Gaussian fit to beamed HHG signal specular

23. What determines the angular distribution? 2)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  ) 1)What determines the angular distribution? Diffraction limited peformance would suggest  harmonic ~  Laser /n   harmonic ~10 -4 rad for keV harmonics.

24. Surface denting 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 Laser

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

26. Imprinted phase aberration Phase errors in fundamental beam are passed on to harmonics  n ~n  Laser Divergence of harmonics can be strongly affected (cf doubling of high power laser beams)

27. High Efficiency Spectral range Number of photons Pulse duration 20-70 eV (Al filter) ~7 *10 15 84 as 80-200 eV (Zr filter) ~2*10 14 38 as 400-1000 eV (Cu filter) ~2*10 12 5 as Assuming 1J,5fs (projected ELI front end) Extremely powerful attosecond source Ultrahigh brightness may be possible with DL performance For full ELI (4.5 kJ) 14 mJ in 1% BW @ 10 keV

28. 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: Beam quality at high harmonics remains an issue. Contrast requirements (>10 10 ) are a challenge for fs lasers Summary