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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 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 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 Incident Pulse Process intrinsically phased locked for all harmonics! Zeptosecond pulses possible at keV 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) 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 Duration of attosecond pulses Extremely short pulses are possible by filtering the phase locked HHG nF (G. D. Tsakiris et al.,New J. Phys. 8, 19(2006) Dn=(21/p-1)nF Harmonic efficiency slope as n-p Atto pulse efficiency: ~n-p+1~n-1.5 Pulse duration (as) 1000 100 Few as pulses possible <1keV 10 1 10 100 1000 0.1 0.01 nF Zeptosecond@ >1keV 10000 Realistic experimental configuration (G. D. Tsakiris et al.,New J. Phys. 8, 19(2006) Filters (~0.1µm thick) have negligible dispersion Consequences from the oscillating mirror model Oscillating Mirror Flat, sharply defined critical density surface • Flatness results in specular reflection of the harmonics Surface denting/bowing in response to laser can change collimation. Surface roughness important for Ångstrom radiation. • Well defined mirror surface gives high conversion efficiency Phase locked harmonics – as pulses possible 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 Experimental Setup: Incident laser pulse: f3 cone Double plasma Mirror Setup Target position Grating spectrometer or von Hamos crystal spectrometer CCD or image plate detectors 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 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: 10131 photons 10231ph s-1mrad-2 (0.1%BW) Published: B. Dromey et al, Nature Physics, 2006 keV harmonics + the efficiency roll-over Intensity/ /arb. units Normalised at 1200th order 10 1.5.5x1020 Wcm-2 2.5 .5x1020 Wcm-2 ~n-2.55 ±.2 1 Intensity dependent roll-over 10-1 Harmonic efficiency n-2.55 Relativistic limit 10-2 1200 1414KeV Order, n Photon Energy First coherent, femtosecond, sub-nm source 3200 3767KeV I FWHM 1’ ~ 500fs t Roll over scaling confirmed as ~3 Roll-over measurements 83 Roll-over position (order n) 10000 42 1000 100 10 1 1 Vulcan 1996 highest observed 22 10 a0 (6 1020Wcm-2m2) 100 Roll over ~3 10 keV pulse @ a0~30 (1021Wcm-2m2) Standard contrast (~10-7) – Bright thermal emitters. Intensity/ arb. units 1 0.8 kT~3keV 0.6 2.5x1020Wcm-2 0.4 kT~1.5keV 0.2 2 7x1019Wcm-2 3 4 5 6 7 Wavelength /Å 8 Planckian Spectrum observed for standard contrast Signal brightness ~2x HHG signal Plasma mirrors are essential Absorption much higher for low contrast pulses. Beamed keV harmonic radiation - coherent keV radiation X-ray Signal > 1 keV 1 0.8 0.6 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 Surface denting Laser Ponderomotive pressure can deform surface. (under the current conditions some deformation is unavoidable Denting required to explain our results:~ 0.1m This would lead to the same divergence for all harmonics in agreement with results. Solution: use shorter pulses to prevent surface deformation 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 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 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) 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> 42 (Gordienko et al (PRL,93, 115002, 2004) Revised theory predicts rollover for n>81/23 (T. Baeva et al, PRE and talk after break) Very different predictions for reaching 10,000 harmonics: 42: a0=50 81/23: a0=22 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. 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 ) High Efficiency Assuming 1J,5fs (projected ELI front end) Spectral range Number of photons Pulse duration 20-70 eV (Al filter) ~7 *1015 84 as 80-200 eV (Zr filter) ~2*1014 38 as 400-1000 eV (Cu filter) ~2*1012 5 as Extremely powerful attosecond source Ultrahigh brightness may be possible with DL performance 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: ~7m Peak intensity (with PM) 2.5 1020Wcm-2 Attosecond pulses by spectral filtering Removing optical harmonics + fundamental changes wave from from saw-tooth to individual as-pulses and sub-as pulses from (G. D. Tsakiris et al.,New J. Phys. 8, 19(2006) PIC predicts asymptotic limit of pREL~2.5-3 Exact value of p is pulseshape dependent Gordienko et al. PRL 93, 115001, 2004 Orders > 1000, keV harmonics! Conversion efficiency Conversion efficiency into attosecond pulses 1.00E+00 1.00E-01 1 10 100 1000 10000 1.00E-02 1.00E-03 ~n-3/2 1.00E-04 1.00E-05 1.00E-06 1.00E-07 Centre frequency (n) Conv eff at filter peak: f|~(nf)-p Bandwidth: Dn~(21/p-1)nF Pulse efficiency: pulse~(21/p-1)nF-(p-1)~n-3/2 Laser contrast is the key to high efficiency. 1.3x104 1.2x104 1.1x104 Shot 1: Contrast 1011 (2 plasma mirrors) Signal (arb) 1x104 9x103 Reference Spectrum (arb.) Harmonic Spectrum (arb.) 8x103 ~ ~ 1200 ~ Strong harmonic signal. ~ b) No plasma mirror C-line @3.4nm Contrast ~10-8 1000 800 Shot 2: Contrast 107 (No plasma mirrors) C-line @4.01nm 600 Source Broadening increases linewidth in no PM case 400 200 0 Weak C-line emission 360 380 400 420 440 Pixel number 460 480 500 Harmonics >100x brighter than thermal source in water window