  Here, the frequency 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-dependent edge states are
demonstrated and a broadband photonic detouring is proposed. Our findings
provide the guidance for designing the frequency-dependent property of
topological structures and show its potential applications in wavelength
division multiplexers.
