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Discrete nonlinear topological photonics

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Abstract

Topological materials, whether in solid state, photonic or acoustic systems, or other domains, are characterized by bulk topological invariants that remain unchanged as long as the relevant spectral gaps remain open. Through the bulk–edge correspondence principle, these invariants predict the presence of robust states that are localized at the termination of the material. A key example is a Chern insulator, which supports backscatter-free edge states that lead to sharply quantized conductance in the electronic case, and allows for robustness against fabrication imperfections in photonic devices. There has been a great deal of research into the linear properties of topological photonic structures, but it has been only recently that interest in the nonlinear domain has bloomed. Nonlinearity has been of particular interest because it is only in nonlinear and interacting systems that the true bosonic character of photons emerges, giving rise to physics with no direct correspondence in solid-state materials. In this Perspective, we discuss recent results concerning nonlinearity in topological photonics—with an emphasis on laser-written waveguide arrays as a model discrete system.

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Fig. 1: Schematic of the driving protocol for a unit cell of an anomalous Floquet topological insulator lattice.
Fig. 2: Experimentally observed wavefunction profiles of solitons in an anomalous Floquet topological insulator.
Fig. 3: Operation of a nonlinearity-induced topological insulator.
Fig. 4: Nonlinear Thouless pum**.

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Acknowledgements

M.C.R. acknowledges the support of the Office of Naval Research under grant numbers N00014-20-1-2325, N00014-23-1-2102 and N00014-18-1-2595, the Air Force Office of Scientific Research under grant number FA9550-22-1-0339, as well as the Packard Foundation under fellowship number 2017-66821. A.S. acknowledges funding from Deutsche Forschungsgemeinschaft (SFB 1477 “Light-Matter Interactions at Interfaces”, project no. 441234705, and IRTG 2676/1-2023 ‘Imaging of Quantum Systems’, project no. 437567992), the FET Open Grant EPIQUS (grant no. 899368) within the framework of the European H2020 programme for Excellent Science, as well as the Krupp von Bohlen and Halbach foundation.

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  1. University of Rostock, Institute for Physics, Rostock, Germany

    Alexander Szameit

  2. The Pennsylvania State University, Department of Physics, University Park, PA, USA

    Mikael C. Rechtsman

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Szameit, A., Rechtsman, M.C. Discrete nonlinear topological photonics. Nat. Phys. 20, 905–912 (2024). https://doi.org/10.1038/s41567-024-02454-8

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