Two-dimensional solitons in triangular photonic lattices with parity-time symmetry

We report the existence and stability of two-dimensional (2D) fundamental, dipole-mode, vortex, and multipole solitons in parity-time (PT) symmetric triangular lattices with the Kerr self-focusing nonlinearity. It is demonstrated that the structure of such complex lattice potentials strongly affects the shape of the solitons, enabling the formation of stable out-of-phase dipole and multipole solitons, as well as vortices. The solitons of all these species have their stability regions in the semi-infinite gap. We also identify the point of the PT-symmetry-breaking phase transition in this lattice.