1. 22. Ultrashort x-ray pulses: High-Harmonic Generation
Why generate high harmonics? Ultrashort X-ray pulses!
How to generate high harmonics
How to measure high-harmonic ultrashort pulses
Ion
electron
x-ray
Most of these slides kindly supplied by Margaret Murnane, Henry Kapteyn, and Erik Zeek.

2. High-Harmonic Generation
Amplified femtosecond laser pulse
x-rays
gas jet
Coherent, ultrashort-pulse, low-divergence, x-ray beam generated by focusing a femtosecond laser in a gas jet
Harmonic orders > 300, photon energy > 500 eV, observed to date
Highest-order nonlinear-optical processes observed to date

3. The VUV, XUV, and soft x-ray regions
Vacuum-ultraviolet (VUV)
180 nm > l > 50 nm
Absorbed by <<1 mm of air
Ionizing to many materials
Soft x-rays
5 nm > l > 0.5 nm
Strongly interacts with core electrons in materials
Extreme-ultraviolet (XUV)
50 nm > l > 5 nm
Ionizing radiation to all materials

4. Applications of Short-wavelength light
Applications in Molecular Dynamics
Charge transfer to solvent dynamics
Ultrafast dynamics of small molecules, coherent control
Ultrafast photoelectron spectroscopy (excited state dynamics, local order)
Electron-nuclear coupling (validity of Frank-Condon approximation)
Coherent phonon dynamics (short scalelength correlations, large k-vectors)
Time-resolved radiation chemistry
Efficient cross-linking of proteins to DNA
Applications in Materials Science
VUV lithography, x-ray nanoprobes
Ultrafast x-ray holography, x-ray microscopy
Laser-induced materials processing (micromachining and data storage)
Applications in Laser Physics
Coherent uv sources
Nonlinear optics at short wavelengths (quasi-phasematching, designer waveguides, clusters, nonadiabatic effects, attosecond pulses, coherent control)

5. Application of x-rays: lithography
Jorge J. Rocca

6. Synchrotron X-ray source and uses at LBL

7. X-ray wavelengths between 2. 2 and 4
X-ray wavelengths between 2.2 and 4.5 nm have major biological applications.
0.5 1 2 3 4 5 6 7 8 9 10
Transmission
Wavelength (nm)
Water
window
Carbon
Carbon absorbs these wavelengths, but water doesn’t.
This is the “water window.”

8. VUV, EUV, and Soft X-ray Issues
Absorbed in <1 mm of air
Needs vacuum
Sensitive to surface contamination
Surface-sensitive spectroscopies
Surface contaminants can “kill” an optical system
As few as 100 atomic layers of solid
Refractive optics (i.e. lenses) virtually impossible
Mirrors limited, but possible

9. X-ray multilayer mirrors can reflect up to 70%.
Jorge J. Rocca

10. High Harmonic Generation in a gas
X-ray spectrometer
800 nm
< 1ps
detector
1015W/cm2
grating
Laser dump
HHG in neon
plateau
cutoff
Harmonic 10 7 31 15
Symmetry issues prevent HHG from occurring at even harmonics. But it yields odd harmonics and lots of them! 10 6
Photons/pulse 65 10 5 10 4 50 40 30 20
Wavelength (nm)

11. High Harmonic Generation with Ultra-intense Pulses
neon
helium
Kapteyn and Murnane,
Phys. Rev. Lett., 79, 2967 (1997)

12. HHG is a highly nonlinear process resulting from highly nonharmonic motion of an electron in an intense field.
The strong field smashes the electron into the nucleus—a highly non-harmonic motion!
Ion
electron
x-ray
How do we know this? Circularly polarized light (or even slightly elliptically polarized light) yields no harmonics!

13. Modeling high harmonics
The potential due to the nucleus in the absence of the intense laser field:
electron
But the laser field is so intense that it highly distorts the potential!

14. High harmonics in both domains
Spectrum
A measured HHG spectrum:
And the field vs. time from a high-intensity, non-perturbative model: I ( w ) 2 n
<->
Possible E-field vs. time E
(t)
1/2 n
<-> t

15. High harmonics exhibit a perturbative region, a plateau region, and a cut-off.
For low-order harmonics, the intensity decreases rapidly with harmonic number.
Harmonic order
“Plateau”
“Cutoff”
“Perturbative”
Then the harmonics plateau for a while, until a “cut-off” wavelength is reached.
In the perturbative regime, frequencies couple to each other and compete for energy, and perturbation theory applies.

16. The cut-off wavelength depends on the medium.10
100
1000 30
Cut-off harmonic order
Ionization potential (eV)
o experimental results
calculated results (ADK model) Xe Kr Ar Ne He 20 h u
cutoff = I p + 3 . 2 U
ionization potential
of atom
Up  I l2
quiver energy of e-

17. In He, it’s possible to generate x-rays in the water window.
5 nm
4 nm
3.5 nm
Coherent < 10fs x-ray generation in He at 2.7 nm
Cutoff of Spectrometer
Z. Chang et al, Phys. Rev. Lett. 79, 2967 (1997)
C. Spielmann et al, Science 278, 661 (1997)

18. HHG works best with the shortest pulses.
argon
PRL 76,752 (1996)
PRL 77,1743 (1996)
PRL 78,1251 (1997)
Shorter pulses generate higher harmonics and do so more efficiently.

19. How do we measure VUV and x-ray pulses?
Autocorrelation using two-photon absorption is possible.
Autocorrelation trace of just the 9th harmonic
Even a single high harmonic pulse can be as short as (or shorter than) the initial pulse that generates it.
This measurement method lacks the bandwidth, however, to measure a pulse containing all the harmonics. Also, the x-rays are weak, and available nonlinear-optical effects are too weak.

20. A more broadband process is Laser-Assisted Photoelectron Emission
The original (intense) IR pulse in combination with the (weak) x-ray pulse will ionize atoms. This process is effectively sum- and difference-frequency generation.
Electron energy
X-ray
with laser
Photo-electron spectrum
(2n+1)st harmonic
2nth harmonic
(2n+2)nd harmonic
X-ray pulse h
uIR
IR pulse
This process yields electron energies corresponding to the even harmonics!

21. X-ray cross-correlation
Use a second gas jet to use LAPE to produce a cross-correlation with the input pulse.
Al Filter e -
TOF Electron
spectrometer
Gas jet
Laser pulse
x-ray
Energy-filter the photoelectrons to see only the sum or difference frequency.
J. M. Schins et al, JOSA B 13, 197 (1996)
T. E. Glover et al, Physical Review Letters, 76, 2468 (1996)

22. femtosecond light pulse
HHG in a hollow fiber yields a longer interaction length and “phase-matching.”
By propagating the laser light in a hollow fiber, its phase velocity can be “phase-matched” to that of the generated x-rays, increasing the conversion efficiency.
The wave-guide refractive index depends on the pressure (as usual), but also the size of the wave-guide and the cladding material.
coherent EUV light
femtosecond light pulse
hollow fiber filled with noble gas
Science 280, 1412 (1998)

23. Pressure-tuned phase-matching of soft x-rays1 20 40 60 80
100 H 2 Ar Kr Xe
Pressure (Torr)
Relative energy of 29th harmonic
29th harmonic at 27nm
Created in a hollow fiber
Phase-matched length in fiber: 1-3 cm
Output enhanced by
Can phase-match harmonic orders (or eV)
Harmonic photon energy is limited by the presence of plasma

24. X-rays produced from hollow fibers are spatially coherent.
The hollow fiber yields a high-quality spatial intensity and phase.
X-ray beam spatial profile
Double-slit interference
These x-ray beams are temporally and spatially coherent, with a sub-5fs duration.

25. Pulse-shaping (coherent control) in HHG
X-Ray CCD
X-Ray
Spectrometer
lens
filter
27fs laser
gas
fibers
iris
Pulse Control
Input
~27 fs, 1.4 mJ, 800 nm pulse at 1kHz
Coupled into a hollow core fiber
Ar gas pressure 2.5 Torr.
Not phase-matched.
Detector
X-ray CCD coupled to an X-ray Spectrometer.
Allow detection of multiple harmonics simultaneously.
Erik Zeek

26. Feedback control in high-harmonic generation
Same idea as chemical control, but now we’re optimizing x-rays.

27. The excitation pulse can be shaped to select one EUV harmonic.
Controls phase and shape of electron wave-function using light
Coherence of EUV beam can be adjusted to generate transform-limited x-ray pulses
Enhancements of >30 obtained to date.
Bartels, R. et al., Nature, Vol. 406,164 (2000)

28. Shaping the pulse rephases the harmonic light.
Optimized pulse has a nonlinear chirp on the leading edge
Christov et al, PRL 86, 5458 (2001)

29. Average brilliance: HHG vs. other x-ray sources
Harmonics
Average brilliance: HHG vs. other x-ray sources
High harmonics are weaker, but they’re ultrafast and spatially coherent
(APS web page)