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Gap solitons in partially parity-time-symmetric optical lattices

The existence and stability of gap solitons are investigated in the semi-infinite gap of a partially parity-timesymmetric two-dimensional periodic potential (optical lattice), which is invariant under complex conjugation and reflection in a single spatial direction. Firstly we study the Bloch bands and band gaps of this partially parity-time-symmetric optical lattice. We find the partially parity-time-symmetric optical lattice can still possess all-real spectra and the phase transition point remains unchangeable. Secondly, we investigate the fundamental solitons in the semi-infinite gap of the partially parity-time-symmetric optical lattice. We get the continuous families of fundamental solitons, which own the same partial parity-time-symmetry as the partially parity-timesymmetric optical lattice. Thirdly, we study the linear stability of the fundamental solitons we have got. We also investigate nonlinear evolution of the partially parity-time solitons under perturbation. It has been found that the stable domains of fundamental solitons in the partially parity-time-symmetric optical lattices are bigger than those in parity-time-symmetric optical lattices.