Two-dimensional gap solitons supported by a parity-time-symmetric optical lattice with saturable nonlinearity and fractional-order diffraction

The existence and stability of fundamental and in-phase dipole solitons supported by a two-dimensional (2D) parity-time (PT)-symmetric optical lattice with defocusing saturable nonlinearity and fractional-order diffraction are carefully investigated. It is found that both fundamental and dipole solitons can exist in the first finite gap and are stable within a moderate power region. The fundamental solitons can bifurcate from the lower edge of the first Bloch band, but the dipole solitons cannot. With the decrease of the Le<acute accent>vy index, the stability regions of both the fundamental and dipole solitons become smaller. The saturation parameter significantly influences the existence and stability of both types of solitons. In addition, we also discuss the transverse energy flow vector in these fundamental and dipole gap solitons.