High Harmonic Generation from overdense plasma from ultra-relativistic spikes to single zeptosecond pulses Teodora Baeva, University of Dusseldorf, Germany

Motivation: HHG from Gases Short pulses from gas harmonics At moderate intensities HHG due to ionization and recombination Harmonic Spectrum Pulse duration Cut-off number of harmonics ~ ILaser T ≈ 100 as tbaeva@tp1.uni-duesseldorf.de

Higher harmonics from Gases Can we generate more harmonics if ILaser increases? New phenomenon needed at higher intensities Due to magnetic field the electrons miss the parent ion Atoms destroyed by the high intensity High harmonics from plasma tbaeva@tp1.uni-duesseldorf.de

Outline High harmonics from overdense plasma Theory of relativistic spikes Experimental confirmation Single sub-attosecond pulses Microscopic mechanism of HHG tbaeva@tp1.uni-duesseldorf.de

HHG from Overdense Plasma A short pulse of ultra-relativistic intensity irradiates a planar solid target, which turns into plasma Plasma is overdense – laser light cannot penetrate High harmonics in the reflected radiation tbaeva@tp1.uni-duesseldorf.de

Theory of Relativistic Spikes T. Baeva, S. Gordienko, A. Pukhov, PRE, 74, 046404 (2006) Explains the HHG phenomenon Universal spectrum power-law decay roll-over ωr ~ a03 In~n-8/3 a0=eA/mec2 dimensionless vector potential of the laser ωr ~ a03 tbaeva@tp1.uni-duesseldorf.de

Theory of Relativistic Spikes Motion of the electron fluid px/mec -1 -2 x/λ -20 -10 10 20 2 3 4 5 6 7 ωt/2π S. Gordienko, A. Pukhov, O. Shorokhov, T. Baeva, PRL, 93, 115002 (2004) tbaeva@tp1.uni-duesseldorf.de

Theory of Relativistic Spikes Motion of the plasma surface HHG at the time of a γ-spike only velocity: a smooth function of time approaching c γ-factor: has sharp spikes spikes appear exactly when tbaeva@tp1.uni-duesseldorf.de

Theory of Relativistic Spikes Universal harmonic spectrum vs resembles parabola around its maxima The high harmonic spectrum is universal, it does not depend on the details of the surface motion! tbaeva@tp1.uni-duesseldorf.de

The Universal Spectrum The spectrum always contains power-law decay with universal power -8/3 In ~ n-8/3 exponential decay roll-over position ωr ~ a03 ~ γ3max ωr ~ a03 T. Baeva, S. Gordienko, A. Pukhov, PRE, 74, 046404 (2006) tbaeva@tp1.uni-duesseldorf.de

Relativistic Spikes vs. Doppler Relativistic Doppler Effect Relativistic spikes Ideal mirror, moving with constant velocity and γ-factor, reflects laser light Maximal harmonic number ~ 4γ2 Accelerated plasma generates high harmonics only at very short moments of time Roll-over ~ √8γ3max tbaeva@tp1.uni-duesseldorf.de

Theory of Relativistic Spikes In ~ n-8/3 ωr ~ a03 The predictions of the relativistic spikes were confirmed experimentally! tbaeva@tp1.uni-duesseldorf.de

Power-law Spectrum Decay EXPERIMENT Experimental data from Vulcan PW shows p=2.5.2 for a=10 Extremely high photon numbers and brightness: 10131 photons 10231ph s-1mrad-2 Courtesy of M. Zepf Published: B. Dromey, M. Zepf et al, Nature Physics, 2006

First coherent, femtosecond, keV harmonics EXPERIMENT B. Dromey, M. Zepf et. al., PRL, 99, 085001, 2007 10 1.5.5x1020 Wcm-2 2.5 .5x1020 Wcm-2 h~n-2.55 ±.2 1 Intensity dependent roll-over Intensity/ /arb. units Normalised at 1200th order 10-1 Harmonic efficiency n-2.55  Relativistic limit 10-2 I FWHM 1’ ~ 500fs 1200 Order, n 3200 1.414KeV Photon Energy 3.767KeV First coherent, femtosecond, sub-nm source t Courtesy of M. Zepf

Roll-over scaling confirmed as ~γ3~a03 EXPERIMENT 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) Courtesy of M. Zepf B. Dromey, M. Zepf et. al., PRL, 99, 085001, 2007

Generation of sub-attosecond pulses Linearly polarized laser pulse produces a train of sub-attosecond pulses S. Gordienko, A. Pukhov, O. Shorokhov, T. Baeva, PRL, 93, 115002 (2004) tbaeva@tp1.uni-duesseldorf.de

Relativistic spikes and high harmonic generation High harmonics are generated only at the time of the γ-spikes (Aτ ≈ 0) When there are several spikes contributing – there is a train of sub-attosecond pulses. γs t´ tbaeva@tp1.uni-duesseldorf.de

Relativistic Plasma Control only one γ-spike once! Ay=0 and Az=0 at the same time! Shape ellipticity tbaeva@tp1.uni-duesseldorf.de

Relativistic Plasma Control Az ω0t Ay Vector potential of the polarization-managed pulse T. Baeva, S. Gordienko, A. Pukhov, PRE, 74, 065401 (2006) tbaeva@tp1.uni-duesseldorf.de

Relativistic Plasma Control Az ω0t Ay Az ω0t Ay T. Baeva, S. Gordienko, A. Pukhov, PRE, 74, 065401 (2006) tbaeva@tp1.uni-duesseldorf.de

Sub-attosecond pulse duration Relativistic spikes predict ωr ~ a03 ω0 Minimal pulse duration Example: In ~ n-8/3 ωr ~ a03 zepto-second (10-21s) pulse duration a0=20 tbaeva@tp1.uni-duesseldorf.de

Plasma gradient and roughness Two effects important for efficient generation of harmonics Plasma gradient Plasma surface roughness depends on pulse duration For what gradients is there efficient harmonic generation? λ4keV ~ Å How can such harmonics possibly be observed? tbaeva@tp1.uni-duesseldorf.de

Microscopic mechanism of HHG Distribution of Aτ inside the plasma is crucial for HHG Physical meaning R(aτ) aτ=eAτ /mec2 tangential vector potential aτ these regions decrease the γ-spike this region increases the γ-spike HHG by fast electrons moving towards the laser pulse tbaeva@tp1.uni-duesseldorf.de

Microscopic mechanism of high harmonic generation High harmonics are generated at times when Aτ small at the plasma surface (Aτ ≈ 0 γ-spike) Coherent electron dynamics in the relativistic skin layer leads to high harmonic generation by the whole bulk of the layer R(aτ) Aτ Aτ Aτ=mec2/e aτ this region increases γARP mec<pτ mec>pτ these regions decrease γARP px px tbaeva@tp1.uni-duesseldorf.de

Microscopic mechanism of high harmonic generation HHG for This condition is a mild one for short laser pulses Aτ Aτ=mec2/e tbaeva@tp1.uni-duesseldorf.de

Microscopic mechanism of high harmonic generation Roughness λ4keV ~ Å the harmonics are generated from the whole plasma skin layer surface roughness is irrelevant if smaller than LNe (≈ λ0/2π ≈ 150nm) Aτ Aτ=mec2/e tbaeva@tp1.uni-duesseldorf.de

Conclusions High harmonics are not a surface effect, they are generated coherently by the whole plasma skin layer HHG is not affected by plasma surface roughness Few oscillation laser pulses automatically provide necessary density gradients for efficient HHG No limiting laser intensity, harmonic number ~ ILaser3/2 HHG from overdense plasma: promising new tool for generation of single sub-attosecond pulses with state- of-the-art laser technology tbaeva@tp1.uni-duesseldorf.de