Selection rules for quasibound states in the continuum

Photonic crystal slabs (PCSs) are a well-studied class of devices known to support optical Fano resonances for light normally incident to the slab, useful for narrow-band filters, modulators, and nonlinear photonic devices. In shallow-etched PCSs the linewidth of the resonances is easily controlled by tuning the etching depth. This design strength comes at the cost of large device footprints due to the poor in-plane localization of optical energy. In fully-etched PCSs realized in high-index-contrast material systems, the in-plane localization is greatly improved, but the command over linewidth suffers. This disadvantage in fully-etched PCSs, also known as high contrast gratings (HCGs), can be overcome by accessing symmetry-protected bound states in the continuum (BICs). By perturbing an HCG, the BIC may be excited from the free space with quality factor showing an inverse squared dependence on the magnitude of the perturbation, while inheriting the excellent in-plane localization of their unperturbed counterparts. Here, we report an exhaustive catalog of the selection rules (if and to which free space polarization coupling occurs) of symmetry-protected BICs controlled by in-plane symmetry breaking in six types of two-dimensional PCS lattices. The chosen lattices allow access to the three highest symmetry mode classes of unperturbed square and hexagonal PCSs. The restriction to in-plane symmetry breaking allows for manufacturing devices with simple lithographic fabrication techniques in comparison to out-of-plane symmetry breaking, useful for practical applications. The approach reported provides a high-level road map for designing PCSs supporting controllable sharp spectral features with minimal device footprints using a mature fabrication platform. To demonstrate the use of the resulting alphabet of structures, we numerically demonstrate nonlocal metasurface platforms for terahertz generation, mechanically tunable optical lifetimes, and wavefront shaping exclusively at resonance.