The existence of localized modes supported by the $\mathcal{PT}$-symmetric nonlinear lattices is reported. The system considered reveals unusual properties: unlike other typical dissipative systems, it possesses families (branches) of solutions, which can be parametrized by the propagation constant; relatively narrow localized modes appear to be stable, even when the conservative nonlinear lattice potential is absent; and finally, the system supports stable multipole solutions.

• Received 9 February 2011

DOI:https://doi.org/10.1103/PhysRevA.83.041805