1. HHG and attosecond pulses in the relativistic regime Talk by T. Baeva University of Düsseldorf, Germany Based on the work by T. Baeva, S. Gordienko, A. Pukhov

2. Outline High harmonic generation from plasma Theory of Relativistic Spikes Generation of sub-attosecond pulses PIC simulations The role of roughness and density gradient Conclusion tbaeva@tp1.uni-duesseldorf.de

3. Harmonics from overdense plasma 1981: Harmonics first observed with a CO 2 laser: R. L. Carman, D. W. Forslund, J. M. Kindel, Phys. Rev. Lett. 46, 29 (1981) mid 80’s: CPA – more intense pulses 2006: HHG observed in the ultra-relativistic regime B. Dromey, M. Zepf et. al., Nature Physics, 2, 456 (2006) tbaeva@tp1.uni-duesseldorf.de

4. Harmonics from overdense plasma A short pulse of ultra-relativistic intensity irradiates a planar solid target High harmonics in the reflected radiation tbaeva@tp1.uni-duesseldorf.de

5. I n ~ n -8/3 ω r ~ a 0 3 Theory of Relativistic Spikes Explains the HHG phenomenon Universal spectrum power-law decay roll-over ω r ~ a 0 3 tbaeva@tp1.uni-duesseldorf.de a 0 =eA/m e c 2 dimensionless vector potential of the laser T. Baeva, S. Gordienko, A. Pukhov, PRE, 74, 046404 (2006)

6. Theory of Relativistic Spikes The plasma surface γ-factor has spikes. The spikes appear at times such that High harmonics are generated at these times. The predictions of the theory of relativistic spikes were confirmed experimentally γsγs t´ T. Baeva, S. Gordienko, A. Pukhov, PRE, 74, 046404 (2006) tbaeva@tp1.uni-duesseldorf.de

7. Relativistic scaling p REL =2.5 Experimental data from Vulcan PW shows p=2.5 .2 for a=10 Extremely high photon numbers and brightness: 10 13  1 photons 10 23  1 ph s -1 mrad -2 Published : B. Dromey, M. Zepf et al, Nature Physics, 2006 Courtesy of M. Zepf

8. 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 First coherent, femtosecond, sub-nm source I t FWHM 1’ ~ 500fs Courtesy of M. Zepf B. Dromey, M. Zepf et. al. (submitted, 2007)

9. Roll-over measurements  8  3 44 22 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 ) (γ ~ a 0 ) Roll-over scaling confirmed as ~γ 3 Courtesy of M. Zepf B. Dromey, M. Zepf et. al. (in press, 2007)

10. High harmonics from overdense plasma Applications of the high harmonics Coherent Harmonic Focusing allows breaking the Schwinger limit I max ~ I 0 3 S. Gordienko, A. Pukhov, O. Shorokhov, T. Baeva Phys. Rev. Lett., 94, 103903 (2005) generation of (single) sub-attosecond pulses T pulse ~ 1/a 0 3 T. Baeva, S. Gordienko, A. Pukhov Phys. Rev. E, 74, 046404 (2006) tbaeva@tp1.uni-duesseldorf.de

11. After filtering we can obtain a train of sub-attosecond pulses S. Gordienko, A. Pukhov, O. Shorokhov, T. Baeva, PRL, 93, 115002 (2004) tbaeva@thphy.uni-duesseldorf.de Generation of sub-attosecond pulses

12. Ultra-short pulse structure T. Baeva, S. Gordienko, A. Pukhov, PRE, 74, 046404 (2006) tbaeva@thphy.uni-duesseldorf.de Depends on the filter position

13. Pulse Applications tbaeva@thphy.uni-duesseldorf.de Empty pulse: study atom excitation by a single strong kick Filled pulse: study the resonance excitation of ion and atom levels T. Baeva, S. Gordienko, A. Pukhov, PRE, 74, 046404 (2006)

14. Relativistic Plasma Control once! tbaeva@thphy.uni-duesseldorf.de A y =0 and A z =0 at the same time! Shape ellipticity

15. Relativistic Plasma Control Vector potential of the polarization-managed pulse ω0tω0t AzAz AyAy T. Baeva, S. Gordienko, A. Pukhov, Phys. Rev. E, 74, 065401(R) (2006) tbaeva@tp1.uni-duesseldorf.de

16. Relativistic Plasma Control T. Baeva, S. Gordienko, A. Pukhov, Phys. Rev. E, 74, 065401 (2006) AzAz AyAy ω0tω0t ω0tω0t AzAz AyAy tbaeva@tp1.uni-duesseldorf.de

17. Ramp effect and Roughness? Plasma boundary steepness It depends on laser amplitude, prepulse, duration How easy is to perform a successful experiment? Plasma surface roughness For the 3keV harmonics observed λ 3keV ~1Å What is the effect of surface roughness? In order to answer these questions: microscopic description of the plasma tbaeva@tp1.uni-duesseldorf.de M. Zepf, G. Tsakiris et al, Phys. Rev. E, 58, R5253 (1998)

18. Results from Microscopic Description of Plasma High harmonics are generated at times when A τ small at the plasma surface Coherent electron dynamics in the relativistic skin layer leads to high harmonic generation by the whole bulk of the layer tbaeva@tp1.uni-duesseldorf.de pxpx m e c<p τ pxpx mec>pτmec>pτ AτAτ AτAτ A τ =m e c 2 /e p τ = eA τ / c

19. Effect of Plasma Gradient HHG for This condition is a mild one for short laser pulses First microscopical demonstration of spectrum universality tbaeva@tp1.uni-duesseldorf.de AτAτ A τ =m e c 2 /e

20. Effect of Plasma Roughness Roughness the harmonics are generated from the whole plasma skin layer surface roughness is irrelevant if smaller than L n tbaeva@tp1.uni-duesseldorf.de AτAτ A τ =m e c 2 /e

21. 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 provided the roughness is much less than skin layer Few oscillation laser pulses automatically provide necessary density gradients for efficient HHG HHG from plasma makes feasible the generation of single sub-attosecond pulses and reaching ultra-intense electric fields (Schwinger limit) with state-of-the-art laser technology tbaeva@tp1.uni-duesseldorf.de