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Nonlinear Dynamics of Bloch Wave Packets in Honeycomb Lattices

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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

Nonlinear waves in deformed optical honeycomb lattices are investigated. Discrete couple mode equations are used to find higher order continuous nonlinear Dirac systems which are employed to describe key underlying phenomena. For weak deformation and nonlinearity the wave propagation is circular–ellliptical. At strong nonlinearity the diffraction pattern becomes triangular in structure which is traced to appropriate nonequal energy propagation in momentum space. At suitably large deformation the dispersion structure can have nearby Dirac points or small gaps. The effective dynamics of the wave packets is described by two maximally balanced nonlocal nonlinear Schrödinger type equations.

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Acknowledgments

Mark J. Ablowitz was partially supported by the U.S. Air Force Office of Scientific Research, under grant FA9550-12-0207 and by NSF under grants DMS-0905779, CHE 1125935. Yi Zhu was partially supported by the NSFC under grant 11204155.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Colorado, 526 UCB, Boulder, CO, 80309-0526, USA

    Mark J. Ablowitz

  2. Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing, 100084, China

    Yi Zhu

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  1. Mark J. Ablowitz
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  2. Yi Zhu
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Correspondence to Yi Zhu .

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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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Ablowitz, M.J., Zhu, Y. (2013). Nonlinear Dynamics of Bloch Wave Packets in Honeycomb Lattices. 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_27

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  • DOI: https://doi.org/10.1007/10091_2012_27

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