Defect solitons in parity-time symmetric optical lattices with self-defocusing nonlinearity

The existence and stability of defect solitons in parity-time (PT) symmetric optical lattices with self-defocusing nonlinearity are reported. It is found that various solitons can exist in different gaps for different defects. All of the solitons have real and imaginary parts of opposite parities. For positive defects, fundamental and multipole solitons can exist stably in the semi-infinite gap and the first gap, respectively. For zero or negative defects, fundamental and multipole solitons can exist stably in the first gap and the second gap, respectively. For solitons with positive and negative defects, there exists a cutoff point of the propagation constant above which the defect solitons vanish. The relation with the cutoff point and the depth of PT potentials is studied. The influence of the imaginary part of the PT-symmetric potentials on soliton stability is given.