Abstract

Precise knowledge of the behaviour of the phase of light in a focused beam is fundamental to understanding and controlling laser-driven processes. More than a hundred years ago, an axial phase anomaly for focused monochromatic light beams was discovered and is now commonly known as the Gouy phase1,2,3,4. Recent theoretical work has brought into question the validity of applying this monochromatic phase formulation to the broadband pulses becoming ubiquitous today5,6. Based on electron backscattering at sharp nanometre-scale metal tips, a method is available to measure light fields with sub-wavelength spatial resolution and sub-optical-cycle time resolution7,8,9. Here we report such a direct, three-dimensional measurement of the spatial dependence of the optical phase of a focused, 4-fs, near-infrared pulsed laser beam. The observed optical phase deviates substantially from the monochromatic Gouy phase—exhibiting a much more complex spatial dependence, both along the propagation axis and in the radial direction. In our measurements, these significant deviations are the rule and not the exception for focused, broadband laser pulses. Therefore, we expect wide ramifications for all broadband laser–matter interactions, such as in high-harmonic and attosecond pulse generation, femtochemistry10, ophthalmological optical coherence tomography11,12 and light-wave electronics13.

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Acknowledgements

We gratefully acknowledge M. Förster for supplying nanotips, and P. Dombi and S. Thomas for support in the measurement campaign. This work has been supported by the DFG Grants PA 730/5 and SPP-1840 QUTIF, Laserlab-Europe EU-H2020 654148, ERC Grant NearFieldAtto, and the DFG Cluster of Excellence Munich Center for Advanced Photonics. D.H. acknowledges the Helmholtz Association for financial support. M.K. acknowledges the Minerva Foundation and the Koshland Foundation for financial support.

Author information

Author notes

    • Dominik Hoff
    •  & Michael Krüger

    These authors contributed equally to this work.

Affiliations

  1. Helmholtz-Institut Jena and Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, D-07743 Jena, Germany

    • Dominik Hoff
    • , A. M. Sayler
    •  & Gerhard G. Paulus
  2. Department Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstr. 1, D-91058 Erlangen, Germany

    • Michael Krüger
    •  & Peter Hommelhoff
  3. Department of Physics of Complex Systems, Weizmann Institute of Science, 234 Herzl St., Rehovot 76100, Israel

    • Michael Krüger
  4. Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany

    • Lothar Maisenbacher
    •  & Peter Hommelhoff
  5. Max-Planck-Institut für die Physik des Lichts, Staudtstr. 2, D-91058 Erlangen, Germany

    • Peter Hommelhoff

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All authors contributed to all parts of the experiment including the final version of the manuscript.

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The authors declare no competing financial interests.

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Correspondence to Dominik Hoff or Peter Hommelhoff.

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https://doi.org/10.1038/nphys4185

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