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 electronx-ray

Most of these slides kindly supplied by Margaret Murnane, Henry Kapteyn, and Erik Zeek.

High-Harmonic Generation

gas jet

x-raysAmplified femtosecond laser pulse

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

The VUV, XUV, and soft x-ray regions

Soft x-rays5 nm > > 0.5 nm

Strongly interacts with core electrons in materials

Vacuum-ultraviolet (VUV)

180 nm > > 50 nm Absorbed by <<1 mm of air

Ionizing to many materials

Extreme-ultraviolet (XUV)50 nm > > 5 nm

Ionizing radiation to all materials

Applications of Short-wavelength light

Applications in Molecular DynamicsCharge transfer to solvent dynamicsUltrafast dynamics of small molecules, coherent controlUltrafast 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 chemistryEfficient cross-linking of proteins to DNA

Applications in Materials Science VUV lithography, x-ray nanoprobesUltrafast x-ray holography, x-ray microscopyLaser-induced materials processing (micromachining and data storage)

Applications in Laser PhysicsCoherent uv sourcesNonlinear optics at short wavelengths (quasi-phasematching, designer

waveguides, clusters, nonadiabatic effects, attosecond pulses, coherent control)

Application of x-rays: lithography

Jorge J. Rocca

Synchrotron X-ray source and uses at LBL

X-ray wavelengths between 2.2 and 4.5 nm have major biological applications.

0.5

1

2345678910

Tra

nsm

issi

on

Wavelength (nm)

Waterwindow

Carbon

Water

Carbon absorbs these wavelengths, but water doesn’t. This is the “water window.”

VUV, EUV, and Soft X-ray Issues

Absorbed in <1 mm of airNeeds vacuum

Sensitive to surface contaminationSurface-sensitive spectroscopies

Surface contaminants can “kill” an optical system

As few as 100 atomic layers of solidRefractive optics (i.e. lenses) virtually impossible

Mirrors limited, but possible

Jorge J. Rocca

X-ray multilayer mirrors can reflect up to 70%.

High Harmonic Generation in a gas

grating

detector

Laser dump

800 nm

< 1ps

1015W/cm2

plateau cutoff

HHG in neon

50 40 30 20

104

105

106

107

Pho

tons

/pul

se 1531

65

Wavelength (nm)

X-ray spectrometer

Harmonic

Symmetry issues prevent HHG from occurring at even harmonics. But it yields odd harmonics and lots of them!

High Harmonic Generation with Ultra-intense Pulses

Kapteyn and Murnane, Phys. Rev. Lett., 79, 2967 (1997)

neon

helium

HHG is a highly nonlinear process resulting from highly nonharmonic motion of an electron in an intense field.

Ion electronx-ray

The strong field smashes the electron into the nucleus—a highly non-harmonic motion!

How do we know this? Circularly polarized light (or even slightly elliptically polarized light) yields no harmonics!

Modeling high harmonics electron

laser field

electron

laser field

electron

laser field

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!

U x e2

4o x eEx

High harmonics in both domains

E(t)

1/2

I() 2

Possible E-field vs. time

Spectrum

t

A measured HHG spectrum:

And the field vs. time from a high-intensity, non-perturbative model:

High harmonics exhibit a perturbative region, a plateau region, and a cut-off.

For low-order harmonics, the intensity decreases rapidly with harmonic number.

45 39 29 25 17

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.

The cut-off wavelength depends on the medium.

o

10

100

1000

10 30

Cu

t-o

ff h

arm

on

ic o

rder

Ionization potential (eV)

o experimental results calculated results (ADK model)

Xe

Kr

Ar

Ne

He

20

o

o

o

o hcutoff Ip 3.2Up

ionization potentialof atom

Up I 2

quiver energy of e-

In He, it’s possible to generate x-rays in the water window.

Z. Chang et al, Phys. Rev. Lett. 79, 2967 (1997)

C. Spielmann et al, Science 278, 661 (1997)

Cutoff of Spectrometer

Inte

nsity

(ar

bitr

ary

units

)

199163 211 221

water window

C edge

Harmonic order

179

Coherent < 10fs x-ray generation in He at 2.7 nm

4 nm5 nm 3.5 nm

HHG works best with the shortest pulses.

Shorter pulses generate higher harmonics and do so more efficiently.

PRL 76,752 (1996)PRL 77,1743 (1996)PRL 78,1251 (1997)

Harmonic Order

Num

ber

of P

hoto

ns

100 fs pulse

50 fs pulse (2x)

25 fs pulse (4x)

2723 31 35 39 43 47 51 55 59

argon

How do we measure VUV and x-ray pulses?

Autocorrelation using two-photon absorption is possible.

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.

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.

A more broadband process is Laser-Assisted Photoelectron Emission

X-ray pulse

hIRIR pulse

hIR

This process yields electron energies corresponding to the even harmonics!

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 cross-correlation

J. M. Schins et al, JOSA B 13, 197 (1996)

T. E. Glover et al, Physical Review Letters, 76, 2468 (1996)

Use a second gas jet to use LAPE to produce a cross-correlation with the input pulse.

Al Filter

e-TOF Electronspectrometer

Gas jet

Gas jetLaser pulse x-ray

Energy-filter the photoelectrons to see only the sum or difference frequency.

( ) ( ) ( )e X IRU I t I t dt

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)

coherent EUV lightfemtosecond light pulse

hollow fiber filled with noble gas

Pressure-tuned phase-matching of soft x-rays

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

29th harmonic at 27nm

Created in a hollow fiber

0

1

0 20 40 60 80 100

H2ArKrXe

Pressure (Torr)

Rel

ativ

e en

ergy

of

29th

harm

onic

X-rays produced from hollow fibers are spatially coherent.

X-ray beam spatial profile

Double-slit interference

These x-ray beams are temporally and spatially coherent, with a sub-5fs duration.

The hollow fiber yields a high-quality spatial intensity and phase.

Pulse-shaping (coherent control) in HHG

X-Ray CCDX-Ray

Spectrometer

lensfilter

27fs laser

gas

fibers

iris

Pulse Control

Input~27 fs, 1.4 mJ, 800 nm pulse at 1kHz

Coupled into a hollow core fiberAr gas pressure 2.5 Torr.

Not phase-matched.

DetectorX-ray CCD coupled to an X-ray Spectrometer.

Allow detection of multiple harmonics simultaneously.

Feedback control in high-harmonic generation

Same idea as chemical control, but now we’re optimizing x-rays.

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.

The excitation pulse can be shaped to select one EUV harmonic.

Bartels, R. et al., Nature, Vol. 406,164 (2000)

Shaping the pulse rephases the harmonic light.

Christov et al, PRL 86, 5458 (2001)

Optimized pulse has a nonlinear chirp on the leading edge

Average brilliance:HHG vs.

other x-ray sources

Harmonics

High harmonics are weaker, but they’re ultrafast and spatially coherent

(APS web page)