Square-root topological insulator for a dual-band photonic waveguide

•A square-root topological photonic waveguide is presented.•The topological valley transport occurs in two frequency bands.•Unidirectional propagation is numerically observed. We show that square-root topological insulators can be utilized as a platform for dual-band topological waveguides in 2-dimensional photonic crystals. Valley states for each of two frequency band gaps in differently perturbed decorated honeycomb lattices have opposite directions of the phase rotations, revealing opportunities for dual-band unidirectional topological valley transport. The topological valley edge states exist at the boundary between differently perturbed photonic crystals in the two frequency bands. In addition, unidirectional, and robust propagation of electromagnetic waves along the boundary in the two frequency bands are numerically performed. Our work provides extensions of square-root topological insulators to robust, unidirectional, and dual-band photonic waveguides.