Asymptotically circularly polarized bound states in the continuum

We study a class of bound states in the continuum (BICs) in all-dielectric periodic structures, near which resonant states approach ideal circularly polarized states (CPSs). We term these BICs {\em asymptotically circularly polarized BICs} ({\em acp}-BICs) and identify two types: single-angle and all-angle. Single-angle {\em acp}-BICs permit convergence to left- or right-handed CPSs only along a single momentum-space direction, whereas all-angle {\em acp}-BICs exhibit convergence to CPSs of a single handedness throughout the entire momentum space, rendering them exceptionally promising for chiral optical applications. We reveal that the existence of {\em acp}-BICs is underpinned by total reflection of circularly polarized waves. Moreover, all-angle {\em acp}-BICs qualify as super-BICs, with uniform nearby polarization being an intrinsic property. In addition, a bifurcation theory is developed to analyze the emergence of genuine CPSs from {\em acp}-BICs under $C_{2}$-symmetric structural perturbations. Our results suggest {\em acp}-BICs as a platform for singular and chiral optical responses in all-dielectric systems.