Defect gap solitons in real linear periodic optical lattices with parity-time-symmetric nonlinear potentials

We report on the existence and stability of defect gap solitons in real linear periodic optical lattices with parity-time (PT)-symmetric nonlinear potentials. For uniform real periodic optical lattices and for a positive defect, the fundamental solitons exist in the semi-infinite gaps, and they are stable in wide regions. For a negative defect, solitons can exist in the semi-infinite gap and in the first gap. In the semi-infinite gap, solitons are also stable in a wide region, but are unstable in the region near the Bloch band. In the first gap, solitons are stable. With an increase of the amplitude of the imaginary part of the PT-symmetric nonlinear optical potentials, the stable region in the semi-infinite gap is shrunk; solitons are only stable in the moderate power region. In the first gap, solitons are unstable in the high-power region; they are only stable in the low-power region.