Multi-topological state via the Brillouin zone overlap for nonlinear frequency conversion.

Multiband topological edge states (TESs) or topological corner states (TCSs) in photonic crystals provide effective ways to manipulate the nonlinear frequency conversions. However, the deliberate design and the limited number of multibands lead to the difficulty of experimental realization of the topological nonlinear frequency conversion or higher harmonic generation. Here, we propose an effective method to achieve multiple TESs and TCSs by combining the Brillouin zones of multiple different systems. It is shown that the spectra of the subsystems disperse into different energy levels due to the inter-system hopping. Based on this approach, we construct a topological photonic crystal based on the Brillouin zone overlapped SSH model, which enables the overlapped TCSs to participate in nonlinear frequency conversion. Our scheme can provide a significant way to realize the topological nonlinear frequency conversion with double resonances or multiple resonances.