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Anomalous refraction of optical spacetime wave packets


Refraction at the interface between two materials is fundamental to the interaction of light with photonic devices and to the propagation of light through the atmosphere at large1. Underpinning the traditional rules for the refraction of an optical field is the tacit presumption of the separability of its spatial and temporal degrees of freedom. We show here that endowing a pulsed beam with precise spatiotemporal spectral correlations2,3,4 unveils remarkable refractory phenomena, such as group-velocity invariance with respect to the refractive index, group-delay cancellation, anomalous group-velocity increase in higher-index materials, and tunable group velocity by varying the angle of incidence. A law of refraction for ‘spacetime’ (ST) wave packets5,6,7,8,9,10 encompassing these effects is verified experimentally in a variety of optical materials. Spacetime refraction defies our expectations derived from Fermat’s principle and offers new opportunities for moulding the flow of light and other wave phenomena.

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Fig. 1: Dynamical refraction of ST wave packets.
Fig. 2: Experimental verification of the law of refraction for ST wave packets at normal incidence.
Fig. 3: Confirmation of the law of refraction for ST wave packets at normal incidence.
Fig. 4: Refraction of ST wave packets at oblique incidence.

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.


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We thank D. N. Christodoulides, A. Dogariu and K. L. Schepler for useful discussions. This work was supported by the US Office of Naval Research (ONR) under contracts N00014-17-1-2458 and N00014-19-1-2192.

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Authors and Affiliations



A.F.A. developed the concept and supervised the research. B.B. designed the experiments, carried out the measurements, and analysed the data, with assistance from M.Y. The Supplementary information was prepared by M.Y. with assistance from B.B. All the authors contributed to writing the paper.

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Correspondence to Ayman F. Abouraddy.

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Supplementary Information

Supplementary Figs. 1–15 and discussion (including derivations, details of the experimental set-up and measurement procedure).

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Bhaduri, B., Yessenov, M. & Abouraddy, A.F. Anomalous refraction of optical spacetime wave packets. Nat. Photonics 14, 416–421 (2020).

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