PT -symmetry in kagome photonic lattices
Photonic lattices composed of balanced gain and loss waveguides have attracted considerable attention due of their potential applications in optical beam engineering and image processing. These photonic lattices belong to a larger class of intriguing active metamaterials that exhibit the parity-time ( PT ) symmetry. Kagome lattice is a two-dimensional network of corner-sharing triangles and is often associated with geometrical frustration. In particular, the frustrated coupling between waveguide modes in a kagome array leads to a dispersionless flat band consisting of spatially localized modes. Recently, a PT -symmetric photonics lattice based on the kagome structure has been proposed by placing PT -symmetric dimers at the kagome lattice points. Each dimer corresponds to a pair of strongly coupled waveguides. With balanced arrangement of gain and loss on individual dimers, the system exhibits a PT -symmetric phase for finite gain/loss parameter up to a critical value. Here we discuss the linear and nonlinear optical beam propagations in this novel PT -symmetric kagome system. The linear beam evolution in this complex kagome waveguide array exhibits a novel oscillatory rotation of optical power along the propagation distance. Long-lived local chiral structures originating from the nearly flat bands of the kagome structure are observed when the lattice is subject to a narrow beam excitation. We further show that inclusion of Kerr-type nonlinearity leads to novel optical solitons.