22. Ultrashort x-ray pulses: High-Harmonic Generation

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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

Most of these slides kindly supplied by Margaret
Murnane, Henry Kapteyn, and Erik Zeek.
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High-Harmonic Generation
Amplified femtosecond laser pulse
gas jet
Coherent, ultrashort-pulse, low-divergence, x-ray
beam generated by focusing a femtosecond laser in
a gas jet Harmonic orders gt 300, photon energy gt
500 eV, observed to date Highest-order
nonlinear-optical processes observed to date
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The VUV, XUV, and soft x-ray regions
Soft x-rays 5 nm gt l gt 0.5 nm Strongly interacts
with core electrons in materials
Vacuum-ultraviolet (VUV) 180 nm gt l gt 50 nm
Absorbed by ltlt1 mm of air Ionizing to many
materials
Extreme-ultraviolet (XUV) 50 nm gt l gt 5
nm Ionizing radiation to all materials
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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)

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Application of x-rays lithography
Jorge J. Rocca
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Synchrotron X-ray source and uses at LBL
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X-ray wavelengths between 2.2 and 4.5 nm have
major biological applications.
Carbon absorbs these wavelengths, but water
doesnt. This is the water window.
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VUV, EUV, and Soft X-ray Issues

• Absorbed in lt1 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

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X-ray multilayer mirrors can reflect up to 70.
Jorge J. Rocca
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High Harmonic Generation in a gas
X-ray spectrometer
800 nm lt 1ps
detector
1015W/cm2
grating
Laser dump
HHG in neon

plateau
cutoff
Harmonic
31
7
10
15
Symmetry issues prevent HHG from occurring at
even harmonics. But it yields odd harmonics and
lots of them!
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10
Photons/pulse
65

5
10
4
10
50
40
30
20
Wavelength (nm)
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High Harmonic Generation with Ultra-intense Pulses
neon
helium
Kapteyn and Murnane, Phys. Rev. Lett., 79, 2967
(1997)
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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
nucleusa highly non-harmonic motion!
How do we know this? Circularly polarized light
(or even slightly elliptically polarized light)
yields no harmonics!
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Modeling high harmonics
The potential due to the nucleus in the absence
of the intense laser field
But the laser field is so intense that it highly
distorts the potential!
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High harmonics in both domains
Spectrum
A measured HHG spectrum And the field vs.
time from a high-intensity, non-perturbative
model
Possible E-field vs. time
t
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High harmonics exhibit a perturbative region, a
plateau region, and a cut-off.
For low-order harmonics, the intensity decreases
rapidly with harmonic number.
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.
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The cut-off wavelength depends on the medium.
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In He, its possible to generate x-rays in the
water window.
4 nm
5 nm
3.5 nm
Coherent lt 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)
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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.

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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.
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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.
This process yields electron energies
corresponding to the even harmonics!
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X-ray cross-correlation
Use a second gas jet to use LAPE to produce a
cross-correlation with the input pulse.
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)
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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.
Science 280, 1412 (1998)
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Pressure-tuned phase-matching of soft x-rays
29th harmonic at 27nm Created in a hollow fiber

• Phase-matched length in fiber 1-3 cm
• Output enhanced by 102-103
• Can phase-match harmonic orders 19 - 60 (or 28 -
  90 eV)
• Harmonic photon energy is limited by the presence
  of plasma

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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.
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Pulse-shaping (coherent control) in HHG
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.
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Feedback control in high-harmonic generation
Same idea as chemical control, but now were
optimizing x-rays.
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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 gt30 obtained to
date.
Bartels, R. et al., Nature, Vol. 406,164 (2000)
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Shaping the pulse rephases the harmonic light.
Optimized pulse has a nonlinear chirp on the
leading edge
Christov et al, PRL 86, 5458 (2001)
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Average brillianceHHG vs. other x-ray sources

• High harmonics are weaker, but theyre ultrafast
  and spatially coherent

(APS web page)