High-Quality Leaky Modes with the Polarization States Fully Covering the Shell of the Poincaré Sphere

In the momentum space of a photonic crystal slab, merging multiple bound states in the continuum (BICs) into an at-Γ BIC is the typical topological configuration of polarizations to achieve high-quality (Q) leaky modes in a broad region. However, the robust high-quality leaky modes in the configuration are predominantly linearly polarized, which restricts their applicability. Here, we theoretically demonstrated that polarization states of the robust high-quality leaky modes on one band of the C3V-symmetry photonic crystal slabs can fully cover the shell of the Poincaré sphere. It occurs in the topological configuration consisting of pairs of C points with the opposite handedness located on two adjacent circles, which contract toward an at-Γ BIC along the reflection-time-symmetry axes. Merging quasi-BICs between the pairs of C points with the at-Γ BIC enables leaky modes near them with simultaneously high Q factors and diverse polarization states. Remarkably, the generations and evolutions of C points in the topological configuration are simply manipulated by a single C6V-symmetry-breaking parameter. Accidental BICs with zero charge are found in the photonic crystal slab. Our work unveils a profound connection among polarization singularities and unlocks a paradigm for not only coengineering polarization states and Q factors of leaky modes but also reconstructing the band structures of photonic crystal slabs.