Symmetrical and anti-symmetrical topological edge states based on two-dimensional magneto-optical photonic crystals

We report our design of a topological waveguide at the boundary of two adjacent magneto-optical photonic crystals with opposite magnetic biases which can simultaneously support symmetrical and anti-symmetrical topological edge states. In this non-reciprocal topological photonic model, the symmetrical and anti-symmetrical topological edge states possess the same direction of backscattering-immune chiral energy propagation. However, their directions of phase propagation are opposite, i.e., forward phase propagation for the symmetrical state while backward for the anti-symmetrical one. Using a finite-size structure, we can selectively couple one topological edge state to free space via oblique incidence to realize one-way transmission and reflection in a compact configuration. Furthermore, we design an all-photonic tunable splitter by hybridizing these two topological states. Based on manipulating the phase propagation of topological edge states, our work may offer promising applications in tunable topological photonics and extend the scope of topological photonics.