Degenerate high-order hybrid bound states in the continuum beyond diffraction limit

We demonstrate the existence of at-$Γ$ degenerate hybrid bound-states in the continuum (BICs) with high-order topological charges and quadratic band degeneracy in periodic photonic structures with $C_{6v}$ symmetry above the diffraction limit. The degenerate BICs are realized by combining symmetry protection, which suppresses radiation into zeroth-order diffraction channel, with quadratic band degeneracy and parameter tuning to eliminate radiation into first-order diffraction channels. An effective Hamiltonian is used to investigate the band structure around the degeneracy point, and the topological dynamics in all diffraction channels are characterized. This work reveals a novel mechanism for realizing degenerate BICs above the diffraction limit, opening up opportunities for new physics and applications.