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

2. 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

3. 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

4. Outline High harmonics from overdense plasma
Theory of relativistic spikes
Experimental confirmation
Single sub-attosecond pulses
Microscopic mechanism of HHG

5. 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

6. Theory of Relativistic Spikes
T. Baeva, S. Gordienko, A. Pukhov, PRE, 74, (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

7. 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, (2004)

8. 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

9. 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!

10. 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, (2006)

11. 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

12. Theory of Relativistic Spikes
In ~ n-8/3
ωr ~ a03
The predictions of the relativistic spikes were confirmed experimentally!

13. 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

14. First coherent, femtosecond,
keV harmonics
EXPERIMENT
B. Dromey, M. Zepf et. al., PRL, 99, , 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  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

15. 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 a0~30 (1021Wcm-2m2)
Courtesy of M. Zepf
B. Dromey, M. Zepf et. al., PRL, 99, , 2007

16. 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, (2004)

17. 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´

18. Relativistic Plasma Control
only one γ-spike
once!
Ay=0 and Az=0 at the same time!
Shape ellipticity

19. Relativistic Plasma ControlAz
ω0t Ay
Vector potential of the polarization-managed pulse
T. Baeva, S. Gordienko, A. Pukhov, PRE, 74, (2006)

20. Relativistic Plasma ControlAz
ω0t Ay Az
ω0t Ay
T. Baeva, S. Gordienko, A. Pukhov, PRE, 74, (2006)

21. 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

22. 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?

23. 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

24. Microscopic mechanism of high harmonic generation
High harmonics are generated at times when Aτ small at the plasma surface (Aτ ≈ 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

25. Microscopic mechanism of high harmonic generation
HHG for
This condition is a mild one for short laser pulses Aτ
Aτ=mec2/e

26. 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

27. 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