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Effects of Exceptional Points in PT-Symmetric Waveguides

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Parity-time Symmetry and Its Applications

Part of the book series: Springer Tracts in Modern Physics ((STMP,volume 280))

Abstract

We start with a general theoretical introduction to \(\mathcal {PT}\)-symmetric systems. Quantum systems with gain and loss can be modeled by non-Hermitian Hamiltonians, and \(\mathcal {PT}\)-symmetry is a property that can be achieved, e.g. by a coupling with the laser field. The resulting \(\mathcal {PT}\)-symmetric Hamiltonians possess a real spectrum (when the gain and loss are not too strong) and can be considered as a special case of pseudo-Hermitian Hamiltonians. The transition from a real to a complex spectrum occurs at the exceptional point (EP), where two eigenmodes coalesce both in eigenvalue and eigenvector. The \(\mathcal {PT}\)-symmetric Hamiltonian can be realized experimentally in a system of two coupled waveguides with loss and gain. We describe in detail two physical effects related to the EPs in such a system. First, we show that light oscillations between two waveguides are suppressed by approaching the EP condition. Second, we prove that the group velocity of a light pulse decreases to zero as the system is tuned to be at the EP.

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Acknowledgements

The authors thank Adi Pick for most helpful comments. N.M. acknowledges the financial support of I-Core: The Israeli Excellence Center “Circle of Light”, and of the Israel Science Foundation Grant No. 1530/15. A.A.M. was supported by the CNPq Grant No. 302351/2015-9.

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Authors and Affiliations

  1. Schulich Faculty of Chemistry and Faculty of Physics, Technion – Israel Institute of Technology, Haifa, Israel

    Nimrod Moiseyev

  2. Instituto Nacional de Matemática Pura e Aplicada – IMPA, Rio de Janeiro, Brazil

    Alexei A. Mailybaev

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  1. Nimrod Moiseyev
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  2. Alexei A. Mailybaev
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Correspondence to Nimrod Moiseyev .

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Editors and Affiliations

  1. College of Optics and Photonics, University of Central Florida, Orlando, FL, USA

    Demetrios Christodoulides

  2. Department of Mathematics and Statistics, University of Vermont, Burlington, VT, USA

    Jianke Yang

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Moiseyev, N., Mailybaev, A.A. (2018). Effects of Exceptional Points in PT-Symmetric Waveguides. In: Christodoulides, D., Yang, J. (eds) Parity-time Symmetry and Its Applications. Springer Tracts in Modern Physics, vol 280. Springer, Singapore. https://doi.org/10.1007/978-981-13-1247-2_9

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  • DOI: https://doi.org/10.1007/978-981-13-1247-2_9

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  • Print ISBN: 978-981-13-1246-5

  • Online ISBN: 978-981-13-1247-2

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