  Topological edge states are the core of topological photonics. Here we
introduce the antihelical edge states of time-reversal symmetric topological
metals and propose a photonic realization in an anisotropic square lattice of
coupled ring resonators, where the clockwise and counterclockwise modes play
the role of pseudospins. The antihelical edge states robustly propagate across
the corners toward the diagonal of the square lattice: The same (opposite)
pseudospins copropagate in the same (opposite) direction on the parallel
lattice boundaries; the different pseudospins separate and converge at the
opposite corners. The antihelical edge states in the topological metallic phase
alter to the helical edge states in the topological insulating phase under a
metal-insulator phase transition. The antihelical edge states provide a unique
manner of topologically-protected robust light transport applicable for
topological purification. Our findings create new opportunities for topological
photonics and metamaterials.
