In the nonlinear optics regime, photonic devices that have topologically nontrivial photonic bandstructures are predicted to support a novel class of "topological solitons", which inherit exotic features of linear topological edge states such as unidirectional edge propagation. We present a detailed theoretical study of the conditions under which topological solitons can arise, and how they can be used to implement nonlinear optical isolators. Such isolators can achieve large isolation ratios, while being robust to lattice defects. Our results are based on theoretical analysis backed by numerical simulations of coupled-waveguide lattice and ring resonator lattice structures.
Unpaired Dirac cones are bandstructures with two bands crossing at a single point in the Brillouin zone. It is known that photonic bandstructures can exhibit pairs of Dirac cones, similar to graphene; unpaired cones, however, have not observed in photonics, and have been observed in condensed-matter systems only among topological insulator surface states. We show that unpaired Dirac cones occur in a 2D photonic lattice that is not the surface of a 3D system. These modes have unusual properties, including conical diffraction and antilocalization immune to short-range disorder, due to the absence of "intervalley" scattering between Dirac cones.