Geometric-anisotropy-controlled degeneracy lifting and vortex singularity splitting with dominant +2 orbital angular momentum.

Abstract

Bound states in the continuum (BICs) enable the support of spatially confined electromagnetic fields within the radiation continuum, exhibiting high-quality factors and nontrivial topology in the far field. This paper investigates a silicon nitride (Si₃N₄) photonic crystal incorporating rotated elliptical holes. This geometric anisotropy reduces the in-plane symmetry, lifts the original mode degeneracy, and redistributes coupling to the radiation channels. The Γ-point states remain radiative, whereas the two branches formed after degeneracy lifting separately support off-Γ BICs at nonzero in-plane wave vectors. The selected target branch retains a narrowband resonance, while the same perturbation splits a higher-order vortex singularity into two spatially separated first-order singularities, producing two dark regions. As the anisotropy increases, the spectral shifting and singularity splitting evolve in a correlated manner. Propagation analysis shows that the orbital angular momentum (OAM) component with l =  + 2 remains dominant over a representative propagation range, while its mode purity varies with propagation distance. The proposed structure therefore provides a compact route to narrowband vortex-beam generation and a potential field platform for structured-light control and multiparticle optical manipulation.