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Parity-Time Symmetry in Scattering Problems

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Parity-time Symmetry and Its Applications

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

Abstract

The realization that non-Hermitian parity-time (PT) symmetric Hamiltonians can exhibit entirely real spectra has raised considerable interest in the physics and engineering communities. In the context of optics and photonics, in particular, mathematical analogies with quantum mechanical problem have enabled several breakthrough in terms of observing and utilizing PT-symmetry in closed guided-wave systems. On the other hand, less attention has been paid to the scattering behavior of open PT-symmetric systems. In this chapter, we consider canonical PT-symmetric open systems and explore some of the scattering characteristics of coupled waveguide cavity arrangements. In this regard, we show how an open PT-symmetric configuration can be compared to a closed system, and how the scattering properties are related to the spectral properties of the PT-symmetric system and the associated phase transitions. Afterwards, different scattering geometries are explored in one, two and three dimensions. In addition, we review recent investigations on this topic and highlight opportunities for future research.

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Acknowledgments

This work was partially supported by the Office of Naval Research.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX, USA

    Mohammad-Ali Miri, Robert S. Duggan & Andrea Alù

  2. Photonics Initiative, Advanced Science Research Center, City University of New York, New York, NY, USA

    Andrea Alù

  3. Physics Program, Graduate Center, City University of New York, New York, NY, USA

    Andrea Alù

  4. Department of Electrical Engineering, City College of The City University of New York, New York, NY, USA

    Andrea Alù

  5. Department of Physics, Queens College of the City University of New York, Queens, New York City, NY, USA

    Mohammad-Ali Miri

Authors
  1. Mohammad-Ali Miri
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  2. Robert S. Duggan
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Corresponding author

Correspondence to Andrea Alù .

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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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Miri, MA., Duggan, R.S., Alù, A. (2018). Parity-Time Symmetry in Scattering Problems. 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_3

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  • DOI: https://doi.org/10.1007/978-981-13-1247-2_3

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-1246-5

  • Online ISBN: 978-981-13-1247-2

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