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Spatial Solitons in Parity-Time-Symmetric Photonic Lattices: Recent Theoretical Results

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Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations

Part of the book series: Progress in Optical Science and Photonics ((POSP,volume 1))

Abstract

In 1998, seminal work [1] had demonstrated that non-Hermitian Hamiltonians (\( \hat{H}^{\dag } \ne \hat{H} \)) can give rise to entirely real eigenvalue spectra (thus being appropriate for physical applications), provided that they obey the condition of the parity-time (PT) symmetry, i.e., \( \hat{H}( - {\mathbf{r}}) = \hat{H}^{\dag } ({\mathbf{r}}) \). This condition implies that the Hermitian and anti-Hermitian parts of the Hamiltonian are spatially even and odd, respectively. Such a Hamiltonian usually features spontaneous breaking of the PT-symmetry at a critical value of the coefficient accounting for its anti-Hermitian part. Above the critical point, the spectrum is no longer completely real [2–6].

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 11174061) and the Guangdong Province Natural Science Foundation of China (Grant No. S2011010005471).

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Authors and Affiliations

  1. School of Electronics and Information, Guangdong Polytechnic Normal University, Guangzhou, 510665, China

    Ying-Ji He

  2. Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, 69978, Tel Aviv, Israel

    Boris A. Malomed

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  1. Ying-Ji He
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  2. Boris A. Malomed
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Correspondence to Ying-Ji He .

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Editors and Affiliations

  1. Faculty of Engineering The Iby and Aladar Fleischman, Tel Aviv University, Ramat Aviv, Israel

    Boris A. Malomed

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He, YJ., Malomed, B.A. (2012). Spatial Solitons in Parity-Time-Symmetric Photonic Lattices: Recent Theoretical Results. In: Malomed, B. (eds) Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations. Progress in Optical Science and Photonics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10091_2012_24

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  • DOI: https://doi.org/10.1007/10091_2012_24

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