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Observation of optical de Broglie–Mackinnon wave packets

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05 June 2024 Editor’s Note: Readers are alerted that there is an error in Equation (2) in this paper. Editorial action is being taken to correct this.

Abstract

de Broglie wave packets accompanying moving particles are dispersive and lack an intrinsic length scale solely dictated by the particle mass and velocity. Mackinnon proposed a localized non-dispersive wave packet constructed out of dispersive de Broglie phase waves that possess an intrinsic length scale via an inversion of the roles of particle and observer. So far, the de Broglie–Mackinnon wave packet has remained a theoretical proposal. Here we report the observation of optical de Broglie–Mackinnon wave packets using paraxial space–time-coupled pulsed laser fields in the presence of anomalous group-velocity dispersion. Crucially, the bandwidth of de Broglie–Mackinnon wave packets has an upper limit that is compatible with the wave-packet group velocity and equivalent mass. In contrast to previously observed linear-propagation-invariant wave packets whose spatio-temporal profiles at any axial plane are X-shaped, those for de Broglie–Mackinnon wave packets are uniquely O-shaped (circularly symmetric with respect to space and time). By sculpting their spatio-temporal spectral structure, we produce dispersion-free de Broglie–Mackinnon wave packets in the dispersive medium, observe their circularly symmetric spatio-temporal intensity profiles and closed-trajectory spectra, and tune the field parameters that uniquely determine the wave-packet length scale.

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Fig. 1: de Broglie phase waves and wave packets, and dBM wave packets.
Fig. 2: Optical dBM wave packets.
Fig. 3: Synthesizing and characterizing optical dBM wave packets.
Fig. 4: Observation of optical dBM wave packets in the presence of anomalous GVD and tuning their group velocity.
Fig. 5: Tuning the equivalent rest mass of an optical dBM wave packet.
Fig. 6: Changing the spatio-temporal structure of optical dBM wave packets.

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Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Change history

  • 05 June 2024

    Editor’s Note: Readers are alerted that there is an error in Equation (2) in this paper. Editorial action is being taken to correct this.

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Acknowledgements

We thank M. Yessenov, K. L. Schepler, D. N. Christidoulides and A. Dogariu for helpful discussions. This work was supported by the US Office of Naval Research (ONR) under contracts N00014-17-1-2458 and N00014-20-1-2789.

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  1. CREOL, The College of Optics and Photonics, University of Central Florida, Orlando, FL, USA

    Layton A. Hall & Ayman F. Abouraddy

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Contributions

L.A.H. and A.F.A. conceived the idea and designed the experimental approach. L.A.H. carried out the experiment. L.A.H. and A.F.A. analysed the data and wrote the manuscript.

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Correspondence to Ayman F. Abouraddy.

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Hall, L.A., Abouraddy, A.F. Observation of optical de Broglie–Mackinnon wave packets. Nat. Phys. 19, 435–444 (2023). https://doi.org/10.1038/s41567-022-01876-6

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