Anomalous refraction of optical spacetime wave packets

Abstract

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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

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.

References

  1. 1.

    Saleh, B. E. A. & Teich, M. C. Principles of Photonics (Wiley, 2007).

  2. 2.

    Donnelly, R. & Ziolkowski, R. Designing localized waves. Proc. R. Soc. Lond. A 440, 541–565 (1993).

    ADS  Article  Google Scholar 

  3. 3.

    Longhi, S. Gaussian pulsed beams with arbitrary speed. Opt. Express 12, 935–940 (2004).

    ADS  Article  Google Scholar 

  4. 4.

    Saari, P. & Reivelt, K. Generation and classification of localized waves by Lorentz transformations in Fourier space. Phys. Rev. E 69, 036612 (2004).

    ADS  Article  Google Scholar 

  5. 5.

    Kondakci, H. E. & Abouraddy, A. F. Diffraction-free pulsed optical beams via space-time correlations. Opt. Express 24, 28659–28668 (2016).

    ADS  Article  Google Scholar 

  6. 6.

    Parker, K. J. & Alonso, M. A. The longitudinal iso-phase condition and needle pulses. Opt. Express 24, 28669–28677 (2016).

    ADS  Article  Google Scholar 

  7. 7.

    Wong, L. J. & Kaminer, I. Ultrashort tilted-pulsefront pulses and nonparaxial tilted-phase-front beams. ACS Photon. 4, 2257–2264 (2017).

    Article  Google Scholar 

  8. 8.

    Porras, M. A. Gaussian beams diffracting in time. Opt. Lett. 42, 4679–4682 (2017).

    ADS  Article  Google Scholar 

  9. 9.

    Kondakci, H. E. & Abouraddy, A. F. Diffraction-free space-time beams. Nat. Photon. 11, 733–740 (2017).

    ADS  Article  Google Scholar 

  10. 10.

    Kondakci, H. E. & Abouraddy, A. F. Optical space-time wave packets of arbitrary group velocity in free space. Nat. Commun. 10, 929 (2019).

    ADS  Article  Google Scholar 

  11. 11.

    Sabra, A. I. Theories of Light from Descartes to Newton (Cambridge University Press, 1981).

  12. 12.

    Koenderink, A. F., Alú, A. & Polman, A. Nanophotonics: shrinking light-based technology. Science 348, 516–521 (2015).

    ADS  Article  Google Scholar 

  13. 13.

    Yessenov, M., Bhaduri, B., Kondakci, H. E. & Abouraddy, A. F. Classification of propagation-invariant space-time light-sheets in free space: theory and experiments. Phys. Rev. A 99, 023856 (2019).

    ADS  Article  Google Scholar 

  14. 14.

    Saari, P. Reexamination of group velocities of structured light pulses. Phys. Rev. A 97, 063824 (2018).

    ADS  Article  Google Scholar 

  15. 15.

    Besieris, I. M., Shaarawi, A. M. & Ziolkowski, R. W. A bidirectional travelling plane representation of exact solutions of the scalar wave equation. J. Math. Phys. 30, 1254–1269 (1989).

    ADS  MathSciNet  Article  Google Scholar 

  16. 16.

    Saari, P. & Reivelt, K. Evidence of X-shaped propagation-invariant localized light waves. Phys. Rev. Lett. 79, 4135–4138 (1997).

    ADS  Article  Google Scholar 

  17. 17.

    Salo, J. & Salomaa, M. M. Diffraction-free pulses at arbitrary speeds. J. Opt. A 3, 366–373 (2001).

    ADS  Article  Google Scholar 

  18. 18.

    Turunen, J. & Friberg, A. T. Propagation-invariant optical fields. Prog. Opt. 54, 1–88 (2010).

    ADS  Article  Google Scholar 

  19. 19.

    Hernández-Figueroa, H. E., Recami, E. & Zamboni-Rached, M. (eds) Non-diffracting Waves (Wiley-VCH, 2014).

  20. 20.

    Efremidis, N. K. Spatiotemporal diffraction-free pulsed beams in free-space of the Airy and Bessel type. Opt. Lett. 42, 5038–5041 (2017).

    ADS  Article  Google Scholar 

  21. 21.

    Bhaduri, B., Yessenov, M. & Abouraddy, A. F. Space–time wave packets that travel in optical materials at the speed of light in vacuum. Optica 6, 139–146 (2019).

    ADS  Article  Google Scholar 

  22. 22.

    Faccio, D. et al. Spatio-temporal reshaping and X wave dynamics in optical filaments. Opt. Express 15, 13077–13095 (2007).

    ADS  Article  Google Scholar 

  23. 23.

    Hillion, P. How do focus wave modes propagate across a discontinuity in a medium? Optik 93, 67–72 (1993).

    Google Scholar 

  24. 24.

    Donnelly, R. & Power, D. The behavior of electromagnetic localized waves at a planar interface. IEEE Trans. Antennas Propag. 45, 580–591 (1997).

    ADS  MathSciNet  Article  Google Scholar 

  25. 25.

    Attiya, A. M., El-Diwany, E., Shaarawi, A. M. & Besieris, I. M. Reflection and transmission of X-waves in the presence of planarly layered media: the pulsed plane wave representation. Prog. Electromagn. Res. 30, 191–211 (2001).

    Article  Google Scholar 

  26. 26.

    Salem, M. A. & Bağcí, H. Reflection and transmission of normally incident full-vector X waves on planar interfaces. J. Opt. Soc. Am. A 29, 139–152 (2012).

    ADS  Article  Google Scholar 

  27. 27.

    Bhaduri, B. et al. Broadband space-time wave packets propagating 70 m. Opt. Lett. 44, 2073–2076 (2019).

    ADS  Article  Google Scholar 

  28. 28.

    Yessenov, M. et al. What is the maximum differential group delay achievable by a space-time wave packet in free space? Opt. Express 27, 12443–12457 (2019).

    ADS  Article  Google Scholar 

  29. 29.

    Liberal, I. & Engheta, N. Near-zero refractive index photonics. Nat. Photon. 11, 149–158 (2017).

    ADS  Article  Google Scholar 

  30. 30.

    Yu, N. et al. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science 334, 333–337 (2011).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

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.

Author information

Affiliations

Authors

Contributions

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.

Corresponding author

Correspondence to Ayman F. Abouraddy.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

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

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Bhaduri, B., Yessenov, M. & Abouraddy, A.F. Anomalous refraction of optical spacetime wave packets. Nat. Photonics 14, 416–421 (2020). https://doi.org/10.1038/s41566-020-0645-6

Download citation

Further reading

Search

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing