The nonlinear (NL) diffraction of wave packets in honeycomb lattices near Dirac points is studied. Strong nonlinearity can significantly deform the diffraction patterns from conical to triangular structure. This is described by a mean field discrete NL Dirac system and in the continuous limit by a higher-order NL Dirac system, which, in turn, is consistent with the trigonal warping of the dispersion relation. The anticontinuous limit is also examined and similar properties are obtained.
© 2011 Optical Society of America
Original Manuscript: July 1, 2011
Manuscript Accepted: August 18, 2011
Published: September 20, 2011
Mark J. Ablowitz and Yi Zhu, "Nonlinear diffraction in photonic graphene," Opt. Lett. 36, 3762-3764 (2011)