Topological phases and edge states in a non-Hermitian trimerized optical lattice

Topologically engineered optical materials support robust light transport. Herein, the investigated non-Hermitian lattice is trimerized and inhomogeneously coupled using uniform intracell coupling. The topological properties of the coupled waveguide lattice are evaluated and we find that the PT-symmetric phase of a PT-symmetric lattice can have different topologies; the edge states depend on the lattice size, boundary configuration, and competition between the coupling and degree of non-Hermiticity. The topologically nontrivial region is extended in the presence of periodic gain and loss. The nonzero geometric phases accumulated by the Bloch bands indicate the existence of topologically protected edge states between the band gaps. The unidirectional amplification and attenuation zero modes appear above a threshold degree of non-Hermiticity, which facilitates the development of a robust optical diode.