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Topologically protected bound states in photonic parity–time-symmetric crystals

Nature Materials volume 16, pages 433–438 (2017)Cite this article

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Abstract

Parity–time (PT)-symmetric crystals are a class of non-Hermitian systems that allow, for example, the existence of modes with real propagation constants, for self-orthogonality of propagating modes, and for uni-directional invisibility at defects. Photonic PT-symmetric systems that also support topological states could be useful for shaping and routing light waves. However, it is currently debated whether topological interface states can exist at all in PT-symmetric systems. Here, we show theoretically and demonstrate experimentally the existence of such states: states that are localized at the interface between two topologically distinct PT-symmetric photonic lattices. We find analytical closed form solutions of topological PT-symmetric interface states, and observe them through fluorescence microscopy in a passive PT-symmetric dimerized photonic lattice. Our results are relevant towards approaches to localize light on the interface between non-Hermitian crystals.

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Figure 1: The infinite dimer lattice and its dispersion relation.
Figure 2: Spectra of topological interface states in the dimer.
Figure 3: Realization of the PT-symmetric crystal interface.
Figure 4: Translation of the centre of mass (Δ s) of a broad Gaussian input beam whose phase front is tilted.
Figure 5: Loss of guided power in lattices with different dimerizations but fixed loss.
Figure 6: Fluorescence images of the light evolution after a single-waveguide excitation of the topological defect in different dimer configurations.

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Acknowledgements

The authors gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft (grants SZ 276/7-1, SZ 276/9-1, NO462/6-1, BL 574/13-1, GRK 2101/1) and the German Ministry for Science and Education (grant 03Z1HN31). K.G.M. is supported by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement number PIOF-GA-2011- 303228 (project NOLACOME), and by the European Union Seventh Framework Programme (FP7-REGPOT-2012-2013-1) under grant agreement 316165. M.C.R. acknowledges suport from the Alfred P. Sloan Foundation, the National Science Foundation under grant number ECCS-1509546, as well as the Penn State MRSEC, Center for Nanoscale Science, under the award NSF DMR-1420620. The authors acknowledge useful discussions with D. Leykam, Y. Chong, T. Hughes and H. Schomerus.

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Author notes

  1. S. Weimann and M. Kremer: These authors contributed equally to this work.

Authors and Affiliations

  1. Institut für Angewandte Physik, Abbe School of Photonics, Friedrich-Schiller-Universität Jena, Max-Wien Platz 1, 07743 Jena, Germany

    S. Weimann, M. Kremer, S. Nolte & A. Szameit

  2. Physics Department and Solid State Institute, Technion-Israel Institute of Technology, Haifa 32000, Israel

    Y. Plotnik, Y. Lumer & M. Segev

  3. Department of Physics, Crete Center for Quantum Complexity and Nanotechnology, University of Crete, PO Box 2208, 71003 Heraklion, Greece

    K. G. Makris

  4. Institute for Theoretical Physics, Vienna University of Technology, A-1040 Vienna, Austria, EU

    K. G. Makris

  5. Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16801, USA

    M. C. Rechtsman

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Contributions

S.W. and M.K. did the experimental work and data analysis. S.W., M.K., Y.P., Y.L., K.G.M. and M.C.R. did the theoretical work. K.G.M., M.S., M.C.R., A.S. and S.W. were responsible for the project planning. All authors contributed equally to the manuscript writing.

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Correspondence to A. Szameit.

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Weimann, S., Kremer, M., Plotnik, Y. et al. Topologically protected bound states in photonic parity–time-symmetric crystals. Nature Mater 16, 433–438 (2017). https://doi.org/10.1038/nmat4811

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