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.

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

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

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)

Application of x-rays: lithography Jorge J. Rocca

Synchrotron X-ray source and uses at LBL

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.”

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

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

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)

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

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!

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!

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

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. 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-

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)

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.

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.

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!

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)

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)

Pressure-tuned phase-matching of soft x-rays 1 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 102-103 Can phase-match harmonic orders 19 - 60 (or 28 - 90 eV) Harmonic photon energy is limited by the presence of plasma

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.

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

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

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)

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

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)