Frequency range dependent topological phases and photonic detouring in valley photonic crystals

The recent exploration of the valley degree of freedom in photonic systems has enriched the topological phases of light and brought the robust transport of edge states around sharp bends. The two and more simultaneous band gaps in valley-Hall systems have attracted researchers' attention for enlarging the working bandwidth. However, band gaps with frequency range dependent topology were not reported and the demonstrated flow of electromagnetic waves is limited to the robust transport of edge states. Here, the frequency range degree of freedom is introduced into valley photonic crystals with dual band gaps. Based on the high-order plane-wave expansion model, we derive an effective Hamiltonian which characterizes dual band gaps. Metallic valley photonic crystals are demonstrated as examples in which all four topological phases are found. At the domain walls between topologically distinct valley photonic crystals, frequency range dependent edge states are demonstrated and a broadband photonic detouring is proposed. Our findings provide the guidance for designing the frequency range dependent property of topological structures and show its potential applications in wavelength division multiplexers.