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Generalized angle–orbital angular momentum Talbot effect and modulo mode sorting

Nature Photonics volume 19, pages 392–399 (2025)Cite this article

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Abstract

The Talbot effect describes the periodic revivals of field patterns, and is ubiquitous across wave systems. In optics, it is mostly known for its manifestations in space and time, but it is also observed in the wavevector and frequency spectra owing to the Fourier duality. Recently, the Talbot self-imaging has been shown separately in the azimuthal angle and orbital angular momentum (OAM) domains. Here we reveal the missing link between them and demonstrate the generalized angle–OAM Talbot effect. Versatile transformations of petal fields and OAM spectra are experimentally demonstrated, based on the synergy of angular Talbot phase modulation and light propagation in a ring-core fibre. Moreover, the generalized self-imaging concept leads to new realizations in mode sorting, which separate OAM modes in a modulo manner, theoretically free from any crosstalk within the congruence classes of OAM modes. We design and experimentally construct various mode sorters with excellent performance, and show the unconventional behaviour of Talbot-based sorters where neighbouring OAM modes can be mapped to positions that are far apart. Besides its fundamental interest, our work has applications in OAM-based information processing, and implies that the physical phenomena in time–frequency and angle–OAM domains are broadly connected and that their processing techniques may be borrowed interchangeably.

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Fig. 1: Schematic diagram of the generalized angle–OAM Talbot effect and modulo OAM mode sorting.
Fig. 2: Experimental demonstration of the generalized angle–OAM Talbot effect.
Fig. 3: Versatile angular petal transformations based on the generalized Talbot effect.
Fig. 4: Talbot-based modulo 3 and modulo 4 OAM mode sorting.
Fig. 5: Unconventional modulo 12 OAM mode sorting and enhanced sorting of five consecutive OAM modes.

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Data availability

The data used to produce the plots within this article are available via Zenodo at https://doi.org/10.5281/zenodo.13921431 (ref. 62).

Code availability

The code used to produce the plots within this article is available via Zenodo at https://doi.org/10.5281/zenodo.13921431 (ref. 62).

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Acknowledgements

J.H. acknowledges the Swiss National Science Foundation fellowship (P2ELP2_199825). S.G. is a member of the Institut Universitaire de France. M.E. acknowledges the Research Council of Finland Flagship Programme, Photonics Research and Innovation (PREIN), 320165. R.F. acknowledges the Research Council of Finland through the Academy Research Fellowship (Decision 332399). M.E. and R.F. acknowledge the European Research Council (TWISTION, 101042368).

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  1. These authors contributed equally: Jianqi Hu, Matias Eriksson.

Authors and Affiliations

  1. Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, Paris, France

    Jianqi Hu & Sylvain Gigan

  2. Physics Unit, Photonics Laboratory, Tampere University, Tampere, Finland

    Matias Eriksson & Robert Fickler

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  1. Jianqi Hu
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  2. Matias Eriksson
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J.H. conceived the idea and led the project. M.E. and J.H. performed the experiments and numerical simulations, and analysed the results. J.H. and M.E. carried out the theoretical analysis and wrote the paper with contributions from all authors. R.F., S.G. and J.H. supervised the project.

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Correspondence to Jianqi Hu.

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Hu, J., Eriksson, M., Gigan, S. et al. Generalized angle–orbital angular momentum Talbot effect and modulo mode sorting. Nat. Photon. 19, 392–399 (2025). https://doi.org/10.1038/s41566-025-01622-3

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