PT-symmetric phase in kagome photonic lattices

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. Here we propose a complex photonic lattice by placing $\mathcal{PT}$-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 $\mathcal{PT}$-symmetric phase for finite gain/loss parameter up to a critical value. The 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.