1. High Harmonics from Overdense Plasma Surfaces
The oscillating mirror model
Gordienko´s power law scaling
Harmonics cut-off
Attosecond pulses
Experimental results

2. Few-cycle pulse: Density variation
aL=3 φ=π/2

3. Solid harmonics with 1ω from ATLAS
M. Zepf, G. Tsakiris, G.Pretzler, I. Watts et al., Phys. Rev. E, 58, R5253(1998)

4. Oscillating mirror model, 1D-PIC simulation
Bulanov et al. Phys. Plas.1 (1993), P. Gibbon, Phys. Rev. Lett. 76, 50 (1996),
von der Linde et al. PRA 52, 25 (1996)
R. Lichters, J. Meyer-ter-Vehn, A. Pukhov, Phys. Plasmas 3, 3425 (1996)
ncrit
n(x,t) x t
a=3, a=45, ne/nc=27
1D PIC simulations
1019 W/cm2
a= 3
harmonics
3 Gbar
light
pressure
electrons
ions

5. 1D-PIC simulation predicts harmonics up to 100
R. Lichters, J. Meyer-ter-Vehn, A. Pukhov, Phys. Plasmas 3, 3425 (1996) In
5 x 1019 W/cm2
harmonic number
a=6, a=45, ne/nc=27

6. PIC simulation shows w-5/2 power law spectrum
S. Gordienko et al.,
Phys. Rev. Lett., 93, (2004)
LPIC simulation

7. Doppler shift at relativistic mirror
A. Einstein, Annalen der Physik 17, 891 (1905)
observer
time
moving mirror 7

8. Gordienko theory: Phys.Rev.Lett 93, 115002 (2004)
n-th Fourier component of reflected E-field
stationary points with at t = tn
= 0
saddle point integration

9. first derivative of for mirror velocity retarded mirror time t´
n-th harmonic appears only if
(same as in Compton backscattering !)

10. Second derivative and n -5/2 scalingb t´
bmax
tmax bn

11. 17. Problem: Derive w-5/2 scaling of harmonic spectrum
Evaluate the Fourier components of the light reflected from a plasma surface
having position X(t‘) at surface time t‘ = t + 2X(t‘)/c + t0
Make use of the saddle point method by determining the stationary points tn
of the phase function, dF(tn)/dt=0, and obtain
Show that the harmonics spectrum decays with harmonic number n
according to
Verify that the largest stationary point in this approach corresponds to the
largest g value at which the surface moves towards the incident light and
to a largest harmonic number nmax =4 gmax2.

12. Electron motion at mirror interface
T. Baeva, S. Gordienko, A. Pukhov, Phys. Rev. E74, (2006) q
mirror

13. Mirror emits attosecond flash
Attosecond Flash and Spectral Cutoff
T. Baeva, S. Gordienko, A. Pukhov, PRE 74, (2006), arXiv:physics/
Mirror emits attosecond flash
at t=t0 when pt =0 ! t0
Flash length
Flash duration
Cutoff frequency

14. Harmonic oscillation as seen from observer
cut-off
X(t‘)
X(t)

15. The spectrum of the reflected wave

16. Surface Harmonics observed in new VULCAN Experiment
B.Dromey, M.Zepf et al.,
Queens Univ. Belfast,
to appear in Nature Physics (2006):
High Harmonic Generation
in the Relativistic Limit
contrast > 1011:1 achieved
by double plasma mirror
IL > 1020 W/cm2
aL > 10

17. High Harmonic Generation in the Relativistic Limit
VULCAN data confirm 5/2 power law down to water window
B.Dromey, M.Zepf et al., Queens University Belfast, to appear in Nature Physics (2006)
High Harmonic Generation in the Relativistic Limit
w-5/2
contributions up to
850th harmonic
oberserved

18. High Harmonic Generation in the Relativistic Limit
B.Dromey, M.Zepf et al., Queens University Belfast, to appear in Nature Physics (2006)
High Harmonic Generation in the Relativistic Limit

19. keV harmonics + the efficiency roll-over10
1.5.5x1020 Wcm-2
2.5 .5x1020 Wcm-2
h~n-2.55 ±.2 1
Intensity/ /arb. units
Normalised at 1200th order
Intensity dependent roll-over
10-1
Harmonic efficiency n  Relativistic limit
10-2
1200
Order, n
3200
1.414KeV
Photon Energy
3.767KeV I t
FWHM 1’ ~ 500fs
It’s still a pulse train
Smooth spectrum due to lack of resolution

20. Roll over scaling confirmed as ~g3
Roll-over measurements
8g3
4g2
Vulcan 1996
highest observed 22
(6 1020Wcm-2m2)
Roll over ~g3  10 keV a0~30 (1021Wcm-2m2)

21. Filters produce clean attosecond pulses
G.D.Tsakiris, K.Eidmann, J.Meyer-ter-Vehn, F.Krausz, New J.Phys. 8, 19 (2006)

22. Efficiency variation with intensity
efficiency at saturation

23. 3D-PIC simulation of surface harmonics with far-fiels
M. Geissler, S. Rykovanov, G. Tsakiris, J. Meyer-ter-Vehn, NJP submitted (2007) Ne I
y,z
x,z (pol)
5-10th
harm
5-10th
harm

24. 3D-PIC simulation of surface harmonics with far-fiels
M. Geissler, S. Rykovanov, G. Tsakiris, J. Meyer-ter-Vehn, NJP submitted (2007) Ne I
Harmonics spectrum
y,z
x,z (pol)
5-10th
harm
5-10th
harm
y (mm)
x (mm)
Far-field
transverse distribution
200 mm from target

25. Selected publications:
R.Lichters, J. Meyer-ter-Vehn, A.Pukhov, Phys.Plasmas 3, 3425 (1996).
M. Zepf, G.D. Tsakiris, G. Pretzler, I. Watts, et al., Phys. Rev. E 58, 5253 (1998).
I. Watts, M. Zepf, e.L. Clark, et al., Phys. Rev. Lett. 88, (2002).
S.Gordienko, A.Pukhov, O.Shorokhov, T.Baeva, Phys. Rev. Lett.93, (2004):
G.D.Tsakiris, K.Eidmann, J.Meyer-ter-Vehn, F.Krausz, New J.Phys. 8, 19 (2006):
Route to Intense Single Attosecond Pulses
Th.Baeva, S.Gordienko, A.Pukhov, PRE 74, (2006):
Relativistic plasma control for single attosecond pulse generation
Th.Baeva, S.Gordienko, A.Pukhov, PRE 74, (2006) (2006)
Theory of high harmonic generation in relativistic laser interaction etc.
B.Dromey, M.Zepf, A. Gopal, K. Lancaster, M.S. Wie, K. Krushelnik, M.Tatarakis,
N. Vakakis, S. Moustaizis, R. Kodama, M. Tampo, C. Stoeckl, R. Clarke, H. Habara,
D. Neely, S. Karsch, P. Norreys, Nature Physics, to appear (July 2006):
High Harmonics Generation in the Relativistic Limit

26. Conclusions
The mirror model and 1-D PIC simulations indicate that the plasma-vacuum interface constitutes an excellent medium for the generation of a harmonic comb at arbitrarily high intensities.
At laser intensities of 1020 W/cm2 , 1-D PIC simulations predict a single attosecond pulse in the 20-70eV spectral range with duration of ~100as and few percent efficiency.
Although no fundamental upper limit for the laser intensity is imposed by the non-linear process itself, technological limitations might be important.

27. Relativistic scaling pREL=2.5
Experimental data from
Vulcan PW shows
p=2.5.2 for a=10
HIGH EFFICIENCY
eV (17nm)
(4nm)
Extremely high photon numbers
and brightness:
10131 photons
10231ph s-1mrad-2 (0.1%BW)
Published: B. Dromey et al, Nature Physics, 2006

28. Angle from target normal/deg (Specular reflection 45º, incident -45º)
Beamed keV harmonic radiation - demonstrates coherent keV radiation 1
0.8
0.6
X-ray Signal > 1 keV
4º FWHM Gaussian fit to beamed HHG signal
0.4
0.2
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

29. The efficiency for a power law spectrum
Efficiency at
saturation

30. Filtering different spectral ranges
Plasma profile ramp l=0
time-domain
frequency-domain
filtered pulse

31. PW Field Synthesizer (PFS) project study (March 2005) 2 nJ seed
8 mJ
amplified
spectrum
(OPCPA)
6.2 fs
1 TW
pulse
MPQ develops
few-cycle pulses
few J, < 10 fs,
PW-range
F. Krausz, S. Karsch, et al.
PW Field Synthesizer (PFS)
project study (March 2005)
2 nJ seed

32. Filters produce clean attosecond pulses

33. The optimum filter for short pulses

34. Variation of the absolute phase

35. Surface Harmonics Literature
R. Lichters, J. Meyer-ter-Vehn, A. Pukhov, Phys. Plasmas 3, 3425 (1996):
Short-pulse laser harmonics from oscillating plasma surfaces
driven at relativistic intensity
S. Gordienko, A. Pukhov, O. Shorokhov, T. Baeva, PRL 93, (2004):
Relativistic Doppler Effect: Universal Spectra and Zeptosecond Pulses
S. Gordienko, A. Pukhov, O. Shorokhov, T. Baeva, PRL accepted (2005):
Coherent Harmonic Focusing and the Light Extreme

36. measured harmonics spectrum
critical surface motion (1D PIC)
X(t´)

37. I ~ w -5/2 I ~ w -3 nmax = 4gmax2 long pulses discrete harmonics
few-cycle pulses
continuous spectrum
cut-off harmonic
nmax = 4gmax2
gmax peak mirror velocity