  The discovery of a new type of solitons occuring in periodic systems without
photonic bandgaps is reported. Solitons are nonlinear self-trapped wave
packets. They have been extensively studied in many branches of physics.
Solitons in periodic systems, which have become the mainstream of soliton
research in the past decade, are localized states supported by photonic
bandgaps. In this Letter, we report the discovery of a new type of solitons
located at the Dirac point beyond photonic bandgaps. The Dirac point is a
conical singularity of a photonic band structure where wave motion obeys the
famous Dirac equation. These new solitons are sustained by the Dirac point
rather than photonic bandgaps, thus provides a sort of advance in conceptual
understanding over the traditional gap solitons. Apart from their theoretical
impact within soliton theory, they have many potential uses because such
solitons have dramatic stability characteristics and are possible in both Kerr
material and photorefractive crystals that possess self-focusing and
self-defocusing nonlinearities. The new results elegantly reveal that
traditional photonic bandgaps are not required when Dirac points are
accessible. The findings enrich the soliton family and provide valuable
information for studies of nonlinear waves in many branches of physics,
including hydrodynamics, plasma physics, and Bose Einstein condensates.
