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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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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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.
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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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DOI: https://doi.org/10.1038/s41567-023-02270-6
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