Defect solitons in two-dimensional photonic lattices with parity-time symmetry

We report the existence and stability of defect solitons (DSs) in two-dimensional parity-time-symmetric photonic lattices with self-focusing Kerr nonlinearity. We analyze the effect of different values of the local defect strength parameter on stability properties of DSs. In the case of a positive defect, the DSs only exist in the semi-infinite gap and can propagate stably in their entire existence domain. For the uniform optical lattices (zero-defect lattices), the DSs also exist only in the semi-infinite gap, but they are unstable upon propagation only in a tiny domain of their existence region, near the edge of the first Bloch band. In the case of a negative defect, the DSs can exist in both the semi-infinite gap and in the first gap. In the first gap, they are stable only for moderate powers but are unstable for both high- and low-power regimes, near the edges of the first and the second Bloch bands. All DSs in the semi-infinite gap were found to be unstable. Thus the domains of stability can be effectively controlled by tuning the value and sign of the defect strength parameter.