High Harmonic Generation from overdense plasma from ultrarelativistic

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 Cut-off number of harmonics ~ ILaser Pulse duration T ≈ 100 as tbaeva@tp 1. uni-duesseldorf. de

Higher harmonics from Gases Can we generate more harmonics if ILaser increases? Due to magnetic field the electrons miss the parent ion Atoms destroyed by the high intensity New phenomenon needed at higher intensities High harmonics from plasma tbaeva@tp 1. uni-duesseldorf. de

Outline High harmonics from overdense plasma Theory of relativistic spikes Experimental confirmation Single sub-attosecond pulses Microscopic mechanism of HHG tbaeva@tp 1. 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@tp 1. 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 In~n-8/3 roll-over ωr ~ a 03 a 0=e. A/mec 2 dimensionless vector potential of the laser ωr ~ a 03 tbaeva@tp 1. uni-duesseldorf. de

Theory of Relativistic Spikes Motion of the electron fluid px/mec -20 -10 0 x/λ 10 20 2 -2 -1 0 3 4 5 6 7 ωt/2π S. Gordienko, A. Pukhov, O. Shorokhov, T. Baeva, PRL, 93, 115002 (2004) tbaeva@tp 1. uni-duesseldorf. de

Theory of Relativistic Spikes Motion of the plasma surface velocity: a smooth function of time approaching c γ-factor: has sharp spikes appear exactly when HHG at the time of a γ-spike only tbaeva@tp 1. 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@tp 1. 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 ~ a 03 ~ γ 3 max ωr ~ a 03 T. Baeva, S. Gordienko, A. Pukhov, PRE, 74, 046404 (2006) tbaeva@tp 1. uni-duesseldorf. de

Relativistic Spikes vs. Doppler Relativistic Doppler Effect Ideal mirror, moving with constant velocity and γ-factor, reflects laser light Maximal harmonic number ~ 4γ 2 Relativistic spikes Accelerated plasma generates high harmonics only at very short moments of time Roll-over ~ √ 8γ 3 max tbaeva@tp 1. uni-duesseldorf. de

Theory of Relativistic Spikes In ~ n-8/3 ωr ~ a 03 The predictions of the relativistic spikes were confirmed experimentally! tbaeva@tp 1. uni-duesseldorf. de

T N E M I R E P EX Power-law Spectrum Decay Experimental data from Vulcan PW shows p=2. 5. 2 for a=10 Extremely high photon numbers and brightness: 1013 1 photons 1023 1 ph s-1 mrad-2 Courtesy of M. Zepf Published: B. Dromey, M. Zepf et al, Nature Physics, 2006

T N E M I R E P EX ke. V harmonics B. Dromey, M. Zepf et. al. , PRL, 99, 085001, 2007 Normalised at 1200 th order Intensity/ /arb. units 10 1. 5. 5 x 1020 Wcm-2 2. 5 . 5 x 1020 Wcm-2 h~n-2. 55 ±. 2 1 10 -1 Intensity dependent roll-over Harmonic efficiency n-2. 55 Relativistic limit 10 -2 1200 1. 414 Ke. V Order, n Photon Energy First coherent, femtosecond, sub-nm source Courtesy of M. Zepf 3200 3. 767 Ke. V I FWHM 1’ ~ 500 fs t

T N E M I R E P EX Roll-over scaling confirmed as ~γ 3~a 03 Roll-over measurements 8 g 3 Vulcan 1996 highest observed 4 g 2 22 (6 1020 Wcm-2 m 2) Roll over ~g 3 10 ke. V pulse @ a 0~30 (1021 Wcm-2 m 2) 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@tp 1. 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@tp 1. uni-duesseldorf. de

Relativistic Plasma Control only one γ-spike once! Ay=0 and Az=0 at the same time! Shape ellipticity tbaeva@tp 1. uni-duesseldorf. de

Relativistic Plasma Control Az ω0 t Ay Vector potential of the polarization-managed pulse T. Baeva, S. Gordienko, A. Pukhov, PRE, 74, 065401 (2006) tbaeva@tp 1. uni-duesseldorf. de

Relativistic Plasma Control Az ω0 t Ay T. Baeva, S. Gordienko, A. Pukhov, PRE, 74, 065401 (2006) tbaeva@tp 1. uni-duesseldorf. de

Sub-attosecond pulse duration Relativistic spikes predict In ~ n-8/3 ω r ~ a 03 ω 0 Minimal pulse duration ωr ~ a 03 Example: a 0=20 zepto-second (10 -21 s) pulse duration tbaeva@tp 1. uni-duesseldorf. de

Plasma gradient and roughness Two effects important for efficient generation of harmonics Plasma gradient depends on pulse duration For what gradients is there efficient harmonic generation? Plasma surface roughness λ 4 ke. V ~ Å How can such harmonics possibly be observed? tbaeva@tp 1. uni-duesseldorf. de

Microscopic mechanism of HHG aτ=e. Aτ /mec 2 tangential vector potential Distribution of Aτ inside the plasma is crucial for HHG R(aτ) aτ these regions decrease the γ-spike this region increases the γ-spike Physical HHG by fastmeaning electrons moving towards the laser pulse tbaeva@tp 1. 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) R(aτ) Aτ Aτ Aτ=mec 2/e aτ mec<pτ mec>pτ px px these regions decrease γARP this region increases γARP Coherent electron dynamics in the relativistic skin layer leads to high harmonic generation by the whole bulk of the layer tbaeva@tp 1. uni-duesseldorf. de

Microscopic mechanism of high harmonic generation HHG for Aτ Aτ=mec 2/e This condition is a mild one for short laser pulses tbaeva@tp 1. uni-duesseldorf. de

Microscopic mechanism of high harmonic generation Roughness λ 4 ke. V ~ Å Aτ the harmonics are generated from the whole plasma skin layer Aτ=mec 2/e surface roughness is irrelevant if smaller than LNe (≈ λ 0/2π ≈ 150 nm) tbaeva@tp 1. 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 ~ ILaser 3/2 HHG from overdense plasma: promising new tool for generation of single sub-attosecond pulses with stateof-the-art laser technology tbaeva@tp 1. uni-duesseldorf. de