Abstract
Recent demonstrations of high-harmonic generation (HHG) at very high repetition frequencies (∼100 MHz) may allow for the revolutionary transfer of frequency combs to the vacuum-ultraviolet range. This advance necessitates unifying optical frequency-comb technology with strong-field atomic physics. Whereas strong-field studies of HHG have often focused on above-threshold harmonic generation (photon energy above the ionization potential), for vacuum-ultraviolet frequency combs an understanding of below-threshold harmonic orders and their generation process is crucial. Here, we present a new and quantitative study of the harmonics 7–13 generated below and near the ionization threshold in xenon gas with an intense 1,070 nm driving field. We show multiple generation pathways for these harmonics that are manifested as on-axis interference in the harmonic yield. This discovery provides a new understanding of the strong-field, below-threshold dynamics under the influence of an atomic potential and allows us to quantitatively assess the achievable coherence of a vacuum-ultraviolet frequency comb generated through below-threshold harmonics. We find that under reasonable experimental conditions, temporal coherence is maintained. As evidence, we present the first explicit vacuum-ultraviolet frequency-comb structure beyond the third harmonic.
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References
Jones, R. J., Moll, K. D., Thorpe, M. J. & Ye, J. Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity. Phys. Rev. Lett. 94, 193201 (2005).
Gohle, C. et al. A frequency comb in the extreme ultraviolet. Nature 436, 234–237 (2005).
Cundiff, S. T. & Ye, J. Femtosecond optical frequency combs. Rev. Mod. Phys. 75, 325–342 (2003).
Udem, T., Holzwarth, R. & Hänsch, T. W. Optical frequency metrology. Nature 416, 233–237 (2002).
Marian, A., Stowe, M. C., Lawall, J. R., Felinto, D. & Ye, J. United time-frequency spectroscopy for dynamics and global structure. Science 306, 2063–2068 (2004).
Witte, S., Zinkstok, R. Th., Ubachs, W., Hogervorst, W. & Eikema, K. S. E. Deep-ultraviolet quantum interference metrology with ultrashort laser pulses. Science 307, 400–403 (2005).
Zinkstok, R. Th., Witte, S., Ubachs, W., Hogervorst, W. & Eikema, K. S. E. Frequency comb laser spectroscopy in the vacuum-ultraviolet region. Phys. Rev. A 73, 061801 (2006).
Lewenstein, M., Balcou, Ph., Ivanov, M. Y., L’Hullier, A. & Corkum, P. B. Theory of high-harmonic generation by low-frequency laser fields. Phys. Rev. A 49, 2117–2132 (1994).
Meckel, M. et al. Laser-induced electron tunneling and diffraction. Science 320, 1478–1482 (2008).
Hentschel, M. et al. Attosecond metrology. Nature 414, 509–513 (2001).
Sansone, G. et al. Isolated single-cycle attosecond pulses. Science 314, 443–446 (2006).
Lyngå, C. et al. Temporal coherence of high-order harmonics. Phys. Rev. A 60, 4823–4830 (1999).
Cavalieri, S., Eramo, R., Materazzi, M., Corsi, C. & Bellini, M. Ramsey-type spectroscopy with high-order harmonics. Phys. Rev. Lett. 89, 133002 (2002).
Gaarde, M. B., Tate, J. L. & Schafer, K. J. Macroscopic aspects of attosecond pulse generation. J. Phys. B 41, 132001 (2008).
Schafer, K. J. & Kulander, K. C. High harmonic generation from ultrafast pump lasers. Phys. Rev. Lett. 78, 638–641 (1997).
Balcou, Ph., Dederichs, A. S., Gaarde, M. B. & L’Huillier, A. Quantum-path analysis and phase matching of high-order harmonic generation and high-order frequency mixing processes in strong laser fields. J. Phys. B 32, 2973–2989 (1999).
Gaarde, M. B. & Schafer, K. J. Quantum path distributions for high-order harmonics in rare gas atoms. Phys. Rev. A 65, 031406(R) (2002).
Lewenstein, M., Salières, P. & L’Huillier, A. Phase of the atomic polarization in high-order harmonic generation. Phys. Rev. A 52, 4747–4754 (1995).
Bellini, M. et al. Temporal coherence of ultrashort high-order harmonic pulses. Phys. Rev. Lett. 81, 297–300 (1998).
Peatross, J. & Meyerhofer, D. Angular distribution of high-order harmonics emitted from rare gases at low density. Phys. Rev. A 51, R906–R909 (1995).
Balcou, Ph. & L’Huillier, A. Phase matching effects in strong-field harmonic generation. Phys. Rev. A 47, 1447–1459 (1993).
Ho, P. J. & Eberly, J. H. Different rescattering trajectories related to different total electron momenta in nonsequential double ionization. Opt. Express 11, 2826–2831 (2003).
Nubbemeyer, T., Gorling, K., Saenz, A., Eichmann, U. & Sandner, W. Strong-field tunneling without ionization. Phys. Rev. Lett. 101, 233001 (2008).
Shuman, E. S., Jones, R. R. & Gallagher, T. F. Multiphoton assisted recombination. Phys. Rev. Lett. 101, 263001 (2008).
Zhu, M. & Hall, J. L. Stabilization of optical phase/frequency of a laser system: Application to a commercial dye laser with an external stabilizer. J. Opt. Soc. Am. B 10, 802–816 (1993).
Xu, L. et al. Route to phase control of ultrashort light pulses. Opt. Lett. 21, 2008–2010 (1996).
Hartl, I. et al. Cavity-enhanced similariton Yb-fiber laser frequency comb: 3×1014 W cm−2 peak intensity at 136 MHz. Opt. Lett. 32, 2870–2872 (2007).
Schibli, T. R. et al. Optical frequency comb with submillihertz linewidth and more than 10 W average power. Nature Photon. 2, 355–359 (2008).
Yost, D. C., Schibli, T. R. & Ye, J. Efficient output coupling of intracavity high-harmonic generation. Opt. Lett. 33, 1099–1101 (2008).
He, X. et al. Spatial and spectral properties of the high-order harmonic emission in argon for seeding applications. Phys. Rev. A 79, 063829 (2009).
Zaïr, A. et al. Quantum path interferences in high-order harmonic generation. Phys. Rev. Lett. 100, 143902 (2008).
Acknowledgements
We gratefully thank I. Hartl, A. Marcinkevičius and M. Fermann at IMRA America, for the design and construction of the high-power Yb-fibre laser system. Funding at JILA is provided by DARPA, NIST and NSF. Funding at LSU is provided by the NSF through grant numbers PHY-0449235 and PHY-0701372, and by the CCT at LSU. K.J.S. acknowledges support from the Ball Family Professorship. Portions of this research were conducted with high-performance computational resources provided by the Louisiana Optical Network Initiative (http://www.loni.org).
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The experimental work was carried out by the team at JILA: D.C.Y., T.R.S. and J.Y. The theoretical work was carried out by the team at LSU: J.L.T., J.H., M.B.G. and K.J.S. Manuscript preparation was completed by D.C.Y, J.Y., M.B.G. and K.J.S.
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Yost, D., Schibli, T., Ye, J. et al. Vacuum-ultraviolet frequency combs from below-threshold harmonics. Nature Phys 5, 815–820 (2009). https://doi.org/10.1038/nphys1398
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DOI: https://doi.org/10.1038/nphys1398
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