Attosecond pulses are created (by Fourier synthesis) from a comb of odd-order high harmonics resulting from the non-perturbative interaction of intense near-visible laser light with an atomic gas1,2,3. When produced by a mid-infrared laser, harmonics can have simultaneously high order, visible wavelength, and photon energy below the ionization threshold, Ip, of the generating atom. Methods requiring photon energies greater than Ip have been developed4 that measure the spectral amplitude and phase necessary for temporal reconstruction of the harmonic radiation. Here we report the temporal characterization of below-threshold harmonics using sum frequency generation cross-correlation frequency resolved optical gating5 (SFG XFROG), a technique sensitive to the relative delay between orders6, coupled with a novel approach that makes use of the Keldysh scaling7 in strong-field physics. The results surprisingly suggest non-perturbative generation of below threshold harmonics, providing a potential alternative to existing vacuum–ultraviolet frequency comb generation methods8,9.
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McPherson, A. et al. Studies of multiphoton production of vacuum–ultraviolet radiation in the rare gases. J. Opt. Soc. Am. B 4, 595–601 (1987).
Ferray, M. et al. Multiple-harmonic conversion of 1064 nm radiation in rare gases. J. Phys. B 21, L31–L35 (1988).
Agostini, P. & DiMauro, L. F. The physics of attosecond light pulses. Rep. Prog. Phys. 67, 813–855 (2004).
Quéré, F., Mairesse, Y. & Itatani, J. Temporal characterization of attosecond XUV Fields. J. Mod. Opt. 52, 339–360 (2005).
Linden, S., Giessen, H. & Kuhl, J. XFROG—a new method for amplitude and phase characterization of weak ultrashort pulses. Phys. Stat. Sol. B 206, 119–124 (1998).
Keusters, D. et al. Relative-phase ambiguities in measurements of ultrashort pulses with well-separated multiple frequency components. J. Opt. Soc. Am. B 20, 2226–2237 (2003).
Keldysh, L. V. Ionization in the field of a strong electromagnetic wave. Sov. Phys. JETP 20, 1307–1314 (1965).
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).
Zinkstok, R. T., Witte, S., Ubachs, W., Hogervorst, W. & Eikema, K. S. Frequency comb laser spectroscopy in the vacuum–ultraviolet region. Phys. Rev. A 73, 061801 (2006).
Schafer, K. J., Yang, B., DiMauro, L. F. & Kulander, K. C. Above threshold ionization beyond the high harmonic cutoff. Phys. Rev. Lett. 70, 1599–1602 (1993).
Corkum, P. B. Plasma perspective on strong field multiphoton ionization. Phys. Rev. Lett. 71, 1994–1997 (1993).
L'Huillier, A., Schafer, K. J. & Kulander, K. C. Theoretical aspects of intense field harmonic generation. J. Phys. B 24, 3315–3341 (1991).
Paul, P. M. et al. Observation of a train of attosecond pulses from high harmonic generation. Science 292, 1689–1692 (2001).
Mauritsson, J. et al. Measurement and control of the frequency chirp rate of high-order harmonic pulses. Phys. Rev. A 70, 021801 (2004).
Mairesse, Y. & Quéré, F. Frequency-resolved optical gating for complete reconstruction of attosecond bursts. Phys. Rev. A 71, 011401 (2005).
Agostini, P. & DiMauro, L. F. Atoms in high intensity mid-infrared pulses. Contemp. Phys. 49, 179–197 (2008).
DeLong, K. W., Fittinghoff, D. N., Trebino, R., Kohler, B. & Wilson, K. Pulse retrieval in frequency-resolved optical gating based on the method of generalized projections. Opt. Lett. 19, 2152–2154 (1994).
Trebino, R. & Kane, D. J. Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating. J. Opt. Soc. Am. A 10, 1101–1111 (1993).
Wang, Z., Zeek, E. & Trebino, R. Determining error bars in measurements of ultrashort laser pulses. J. Opt. Soc. Am. B 20, 2400–2405 (2003).
Su, Q. & Eberly, J. H. Model atom for multiphoton physics. Phys. Rev. A 44, 5997–6008 (1991).
Schafer, K. J. & Kulander, K. C. High harmonic generation from ultrafast pump lasers. Phys. Rev. Lett. 78, 638–641 (1997).
Börzsönyi, A., Heiner, Z., Kalashnikov, M. P., Kovács, A. P. & Osvay, K. Dispersion measurement of inert gases and gas mixtures at 800 nm. Appl. Opt. 47, 4856–4863 (2008).
Miles, R. B. & Harris, S. E. Optical third-harmonic generation in alkali metal vapors. IEEE J. Quantum Electron. 9, 470–484 (1973).
Yost, D. C. et al. Vacuum-ultraviolet frequency combs from below-threshold harmonics. Nature Phys. 5, 815–820 (2009).
Balcou, P., 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).
Clatterbuck, T. O. et al. Yield and temporal characterization of high-order harmonics from intense midinfrared excitation of a cesium vapor. Phys. Rev. A 69, 033807 (2004).
This work was supported by the United States Department of Energy/Basic Energy Sciences contract no. DE-FG02-04ER15614. L.F.D. acknowledges support from the Hagenlocker Chair at OSU. We are grateful to L. Van Woerkom (Ohio State University) for the loan of the vacuum chamber and J. Tate (Louisiana State University) for useful discussions.
The authors declare no competing financial interests.
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Power, E., March, A., Catoire, F. et al. XFROG phase measurement of threshold harmonics in a Keldysh-scaled system. Nature Photon 4, 352–356 (2010). https://doi.org/10.1038/nphoton.2010.38
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