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

x-ray. Ion. electron. 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.

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

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  1. x-ray Ion electron 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.

  2. x-rays 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 > 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. 1 Water window Carbon Transmission 0.5 Water 10 9 8 7 6 5 4 3 2 Wavelength (nm) X-ray wavelengths between 2.2 and 4.5 nm have major biological applications. 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 31 7 10 15 Symmetry issues prevent HHG from occurring at even harmonics. But it yields odd harmonics and lots of them! 6 10 Photons/pulse 65 5 10 4 10 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. x-ray Ion electron 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! How do we know this? Circularly polarized light (or even slightly elliptically polarized light) yields no harmonics!

  13. electron 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!

  14. 1/2 n <-> E (t) I ( ) w 2 n <-> w 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

  15. “Perturbative” “Plateau” “Cutoff” 45 39 29 25 17 Harmonic order 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.

  16. Up Il2 quiver energy of e- 1000 o experimental results D calculated results (ADK model) I 3 . 2 U u = + D h o cutoff p p He D o ionization potential of atom Cut-off harmonic order Ne 100 o D Ar D o Kr D o Xe 10 10 30 20 Ionization potential (eV) The cut-off wavelength depends on the medium.

  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. • Shorter pulses generate higher harmonics and do so more efficiently. argon PRL 76,752 (1996) PRL 77,1743 (1996) PRL 78,1251 (1997)

  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. uIR uIR Photo-electron spectrum h h IR pulse (2n+1)st harmonic X-ray pulse 2nth harmonic (2n+2)nd harmonic X-ray Electron energy withlaser 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!

  21. x-ray Gas jet Laser pulse Al Filter Gas jet TOF Electron spectrometer e - 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)

  22. femtosecond light pulse coherent EUV light hollow fiber filled with noble gas 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)

  23. H Xe Kr Ar 2 1 Relative energy of 29th harmonic 0 0 20 40 60 80 100 Pressure (Torr) 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

  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. X-Ray gas X-Ray CCD Spectrometer iris filter 27fs laser lens fibers Pulse Control 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.

  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, PRL86, 5458 (2001)

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

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