Localized surface modes in parity–time-symmetric potentials

We investigate light-beam propagation along the interface between linear and nonlinear media with parity–time symmetry. A novel class of two-dimensional localized surface modes (LSMs) is found analytically and numerically. If the potential is parity–time invariant along the direction parallel to the interface between the two media, stable LSMs can exist. Otherwise, if the potential is parity–time invariant along the direction perpendicular to the interface between the two media, there are no stable LSMs.