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Guiding Trojan light beams via Lagrange points

Nature Physics volume 20, pages 95–100 (2024)Cite this article

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Abstract

The guided transmission of optical waves is critical for light-based applications in modern communication, information processing and energy generation systems. Traditionally, the guiding of light waves in structures such as optical fibres has been predominantly achieved through the use of total internal reflection. In periodic platforms, a variety of other physical mechanisms can also be deployed to transport optical waves. However, transversely confining light in fully dielectric, non-periodic and passive configurations remains a challenge in situations where total internal reflection is not supported. Here we present an approach to trapping light that utilizes the exotic features of Lagrange points—a special class of equilibrium positions akin to those responsible for capturing Trojan asteroids in celestial mechanics. This is achieved in twisted arrangements in which optical Coriolis forces induce guiding channels even at locations where the refractive index landscape is defocusing or entirely unremarkable. These findings may have implications beyond standard optical waveguiding schemes and could also apply to other physical systems such as acoustics, electron beams and ultracold atoms.

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Fig. 1: Celestial and optical beam dynamics in the vicinity of a stable Lagrange point.
Fig. 2: Light propagation dynamics around a stable Lagrange point.
Fig. 3: Trojan beam guiding in the index potential produced by a single helical heat source.
Fig. 4: Trojan beam trapping in the index landscape produced by a double-helix current source.

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Data availability

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

Code availability

The used numerical codes are based upon MATLAB and COMSOL and are available upon reasonable request to the corresponding authors.

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Acknowledgements

This work was supported by the Air Force Office of Scientific Research (AFOSR) Multidisciplinary University Research Initiative (MURI) award on Novel light-matter interactions in topologically non-trivial Weyl semimetal structures and systems (award no. FA9550-20-1-0322) (M.K., D.N.C., H.L., Y.W., F.O.W. and G.G.P.), AFOSR MURI award on Programmable systems with non-Hermitian quantum dynamics (award no. FA9550-21-1-0202) (M.K., D.N.C., H.L., Y.W., F.O.W. and G.G.P.), ONR MURI award on the classical entanglement of light (award no. N00014-20-1-2789) (M.K., D.N.C., H.L., Y.W., F.O.W. and G.G.P.), AFRL – Applied Research Solutions (S03015) (FA8650-19-C-1692) (M.K.), W.M. Keck Foundation (D.N.C.), MPS Simons collaboration (Simons grant no. 733682) (D.N.C.) and US Air Force Research Laboratory (FA86511820019) (D.N.C.).

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Author notes

  1. These authors contributed equally: Haokun Luo, Yunxuan Wei.

Authors and Affiliations

  1. Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, California, CA, USA

    Haokun Luo, Yunxuan Wei, Georgios G. Pyrialakos, Demetrios N. Christodoulides & Mercedeh Khajavikhan

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

    Fan O. Wu & Georgios G. Pyrialakos

  3. School of Applied and Engineering Physics, Cornell University, Ithaca, NY, USA

    Fan O. Wu

  4. Department of Physics and Astronomy, University of Southern California, California, CA, USA

    Demetrios N. Christodoulides & Mercedeh Khajavikhan

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  1. Haokun Luo
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Contributions

D.N.C. and M.K. conceived the idea. H.L., Y.W., F.O.W. and G.G.P. developed the theory. H.L. and Y.W. conducted the simulations, data analysis and the experiments. All the authors contributed to the writing of the original draft, reviewing and editing.

Corresponding authors

Correspondence to Demetrios N. Christodoulides or Mercedeh Khajavikhan.

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All authors acknowledge the Global Research Code on the development, implementation and communication of this research. For the purpose of transparency, we have included this statement on inclusion and ethics. This work cites a comprehensive list of research from around the world on related topics.

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The authors declare no competing interests.

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Nature Physics thanks Ulf Leonhardt and Tomáš Tyc for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Sections 1–9, Figs. 1–6 and Table 1.

Source data

Source Data Fig. 3c

Variation of the beam’s mean spot size as a function of distance for current I = 4.0 A.

Source Data Fig. 3d

Dependence of the Trojan mode’s output mean spot size and ellipticity versus square of current.

Source Data Fig. 4e

Variation of the beam’s mean spot size as a function of distance for I = 3.5 A.

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Luo, H., Wei, Y., Wu, F.O. et al. Guiding Trojan light beams via Lagrange points. Nat. Phys. 20, 95–100 (2024). https://doi.org/10.1038/s41567-023-02270-6

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