  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, 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
extends 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 facilitate the development of a robust optical diode.
