Generation of multiple bound states in the continuum through doubly degenerate quasi-guided modes

We present a detailed theoretical analysis of a peculiar generation of multiple bound states in the continuum (BICs) in two-dimensional periodic arrays of dielectric spheres. They emerge in high-symmetry lattices with the C₆ᵥ and C₄ᵥ point groups and involve doubly degenerate quasi-guided modes at the Γ point that can couple to external radiation. By tuning a system parameter, the doubly degenerate modes can exhibit accidental BICs at a critical parameter. In the vicinity of the critical parameter, the two bands originating from the degenerate mode exhibit multiple off-Γ BICs. They move and annihilate across the two bands by changing the parameter around the critical one. A ring-like high Q channel pinned with multiple BICs emerges particularly for the C₆ᵥ case. Across the critical coupling, the total vorticity of the multiple BICs is conserved. The *k·*p perturbation theory explains some features of the phenomena reasonably well.