Defect solitons in parity-time symmetric superlattices with focusing saturable nonlinearity

•Defect solitons exist in 1D PT-symmetric superlattices with saturable nonlinearity.•High-power defect superlattice solitons are unstable.•Stable regions become narrow with a decrease of defect strength.•The power of solitons may change rapidly in saturable nonlinearity media.•We give a qualitatively explanation for the change of power of defect solitons.

In this paper, we find that defect superlattice solitons (DSSs) exist at the defect site in one-dimensional optical superlattices with a parity-time (PT) symmetric potential and focusing saturable nonlinearity. We discuss the existence and stability of DSSs numerically and find that both the saturation parameter s and the defect strength ε can affect the power, the existence and stable regions of solitons significantly. For given saturation parameter s and defect strength ε (propagation constant μ), the power of DSSs increases with the increase (decrease) of μ (ε). For positive and zero defects, DSSs only exist in the semi-infinite band gap, whereas for negative defects, DSSs exist not only in the semi-infinite band gap but also in the first finite band gap. Besides, our numerical calculations show that when the saturation nonlinearity increases up to some level, the increasing rate of soliton power with μ is very fast and the stable regions of DSSs will become obviously narrow and eventually disappear with a decrease of ε for negative defects.