Breakdown of Dirac Dynamics in Honeycomb Lattices due to Nonlinear Interactions

Details Breakdown of Dirac Dynamics in Honeycomb Lattices due to Nonlinear Interactions Breakdown of Dirac Dynamics in Honeycomb Lattices due to Nonlinear Interactions

2010-04-12

arxiv.org/abs/1004.1913v2

Physics

Optics

Scientific paper

We study the dynamics of coherent waves in nonlinear honeycomb lattices and show that nonlinearity breaks down the Dirac dynamics. As an example, we demonstrate that even a weak nonlinearity has major qualitative effects one of the hallmarks of honeycomb lattices: conical diffraction. Under linear conditions, a circular input wave-packet associated with the Dirac point evolves into a ring, but even a weak nonlinearity alters the evolution such that the emerging beam possesses triangular symmetry, and populates Bloch modes outside of the Dirac cone region. Our results are presented in the context of optics, but we propose a scheme to observe equivalent phenomena in Bose-Einstein condensates.

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