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

an emphasis on laser-written waveguide arrays as a model discrete system. Access through your institution Buy or subscribe This is a preview of subscription content, access via your

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subscriptions * Read our FAQs * Contact customer support SIMILAR CONTENT BEING VIEWED BY OTHERS NONTRIVIAL COUPLING OF LIGHT INTO A DEFECT: THE INTERPLAY OF NONLINEARITY AND TOPOLOGY Article

Open access 19 August 2020 NON-HERMITIAN TOPOLOGICAL PHASE TRANSITIONS CONTROLLED BY NONLINEARITY Article 23 October 2023 NONLINEAR CONTROL OF PHOTONIC HIGHER-ORDER TOPOLOGICAL BOUND STATES

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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. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS *

University of Rostock, Institute for Physics, Rostock, Germany Alexander Szameit * The Pennsylvania State University, Department of Physics, University Park, PA, USA Mikael C. Rechtsman

Authors * Alexander Szameit View author publications You can also search for this author inPubMed Google Scholar * Mikael C. Rechtsman View author publications You can also search for this

author inPubMed Google Scholar CONTRIBUTIONS The authors contributed equally to the writing. CORRESPONDING AUTHORS Correspondence to Alexander Szameit or Mikael C. Rechtsman. ETHICS

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permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Szameit, A., Rechtsman, M.C. Discrete nonlinear topological photonics. _Nat. Phys._ 20, 905–912 (2024).

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