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Self-hybridization within non-Hermitian localized plasmonic systems

Nature Physics volume 14, pages 360–364 (2018)Cite this article

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Abstract

The orthogonal eigenmodes are well-defined solutions of Hermitian equations describing many physical situations from quantum mechanics to acoustics. However, a large variety of non-Hermitian problems, including gravitational waves close to black holes or leaky electromagnetic cavities, require the use of a bi-orthogonal eigenbasis with consequences challenging our physical understanding1,2,3,4. The need to compensate for energy losses made the few successful attempts5,6,7,8 to experimentally probe non-Hermiticity extremely complicated. We overcome this problem by considering localized plasmonic systems. As the non-Hermiticity in these systems does not stem from temporal invariance breaking but from spatial symmetry breaking, its consequences can be observed more easily. We report on the theoretical and experimental evidence for non-Hermiticity-induced strong coupling between surface plasmon modes of different orders within silver nanodaggers. The symmetry conditions for triggering this counter-intuitive self-hybridization phenomenon are provided. Similar observable effects are expected to exist in any system exhibiting bi-orthogonal eigenmodes.

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Fig. 1: Symmetry-driven bi-orthogonality in LSP systems.
Fig. 2: Self-hybridization principle.
Fig. 3: Experimental observation of self-hybridization in nanodaggers.

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Acknowledgements

We thank O. Stéphan and M. Walls for in-depth reading of the manuscript. This work has received support from the French state managed by the National Agency for Research under the programme of future investment EQUIPEX TEMPOS-CHROMATEM with the reference ANR-10-EQPX-50.

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  1. H. Lourenço-Martins and P. Das contributed equally to this work.

Authors and Affiliations

  1. Laboratoire de Physique des Solides, Univ. Paris-Sud, CNRS UMR 8502, Orsay, France

    Hugo Lourenço-Martins, Pabitra Das, Luiz H. G. Tizei, Raphaël Weil & Mathieu Kociak

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  1. Hugo Lourenço-Martins
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Contributions

P.D., H.L.-M. and M.K. designed the experiments. H.L.-M., P.D., L.H.G.T. and M.K. performed the EELS experiments. R.W., P.D. and H.L.-M. prepared the samples. H.L.-M., P.D. and L.H.G.T. analysed the data. H.L.-M. and M.K. performed the theoretical analysis. H.L.-M. performed simulations. H.L.-M. and M.K. wrote the manuscript. H.L.-M., P.D., L.H.G.T. and M.K. discussed experimental and theoretical results, and participated in improvement of the manuscript.

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Correspondence to Mathieu Kociak.

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Supplementary information

Supplementary Information

1. Physical Origin of Plasmonic Bi-Orthogonality, 2. LSP versus Electromagnetic Wave in Open Systems, 3. Phase Diagram, 4. Coupling Constant, 5. The Overlap Matrices, 6. Determination of the F-Symmetric Geometrical Configurations, 7. Experimental.

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Lourenço-Martins, H., Das, P., Tizei, L.H.G. et al. Self-hybridization within non-Hermitian localized plasmonic systems. Nature Phys 14, 360–364 (2018). https://doi.org/10.1038/s41567-017-0023-6

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