Breakdown of Dirac Dynamics in Honeycomb Lattices due to Nonlinear Interactions

TL;DR

This paper demonstrates that nonlinear interactions in honeycomb lattices disrupt Dirac dynamics, significantly altering wave evolution and symmetry, with implications for optics and Bose-Einstein condensates.

Contribution

It reveals how even weak nonlinearity breaks down Dirac dynamics and modifies conical diffraction in honeycomb lattices, a novel insight into nonlinear wave behavior.

Findings

Weak nonlinearity causes triangular symmetry in diffraction patterns.

Nonlinearity populates Bloch modes outside the Dirac cone.

Dirac dynamics are fundamentally altered by nonlinear effects.

Abstract

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.