Optical Solitons inPTPeriodic Potentials

We investigate the effect of nonlinearity on beam dynamics in parity-time ($\mathcal{P}\mathcal{T}$) symmetric potentials. We show that a novel class of one- and two-dimensional nonlinear self-trapped modes can exist in optical $\mathcal{P}\mathcal{T}$ synthetic lattices. These solitons are shown to be stable over a wide range of potential parameters. The transverse power flow within these complex solitons is also examined.