Selection rules for quasibound states in the continuum

Wavefront-selective Fano resonant metasurfaces

“…The degree of lateral localization and the optical lifetime of the q-BIC, therefore, constrain the range of spatial frequencies an eigenwave can carry if nearunity diffraction efficiency is desired in a compact device. 14,35 Achieving flatter bands or using lower Q will improve the efficiency of the device within a finite range of spatial frequencies. q-BICs in high-contrast systems have been shown to enable flat bands with high Q-factor resonance, 35,36 offering precisely the needed degrees of freedom.…”

“…10,11 When this suppression of coupling to radiation is due to symmetry-protection, 12 applying a perturbation that breaks the relevant symmetry introduces radiative coupling, yielding a quasi-bound state in the continuum (q-BIC) responsible for a Fano resonance whose linewidth is directly controlled by the perturbation. 13,14 Due to their origin lying in symmetries, q-BICs are broadly applicable across many geometries and material systems and have been rapidly emerging as a powerful rationally designed platform leveraging enhanced-light-matter interactions 15 to advance planarized optical modulators, 16 biological sensors, 17 and compact non-linear optical devices. 18,19 As with other Fano resonant systems, q-BICs have been commonly studied in infinitely periodic photonic crystal slabs with subwavelength periodicity, affording two notable simplifications: (i) the presence of a single diffraction order, into which the supported dark and bright modes may interfere, and (ii) a natural description in momentum-frequency space.…”

“…In such systems, the peak reflectance is unity in the absence of optical loss, 20 a marker of complete interference between the bright and dark modes, and the Fano resonance can be observed only for incident plane waves matching the underlying band structure in both momentum (angular selectivity) and frequency (spectral selectivity). The polarization properties are governed by selection rules 14 that specify whether the excitation of a q-BIC may be forbidden or allowed according to the space group of the perturbed symmetry. Notably, a metasurface patterned in a way to retain only twofold rotation symmetries after perturbation, i.e., having a p2 space group, may couple a q-BIC to any designer linear polarization angle with arbitrary lifetime.…”

“…Notably, a metasurface patterned in a way to retain only twofold rotation symmetries after perturbation, i.e., having a p2 space group, may couple a q-BIC to any designer linear polarization angle with arbitrary lifetime. 14,21 By introducing suitable out-of-plane symmetry-breaking perturbations, q-BICs can also extend circularly dichroic Fano resonances [22][23][24][25] to exhibit arbitrary elliptical dichroism. 26 These systems thereby exhibit rationally tailorable selectivity to polarization, momentum, and frequency rooted in symmetry breaking.…”

“…Recently, Fano resonant metasurfaces capable of shaping the wavefront of light at resonance have been demonstrated based on the symmetry features of q-BICs. 14,21,[26][27][28] In Ref. 21, it was demonstrated that the orientable linear dichroism afforded by the p2 space group can carry a geometric phase when excited by circular polarization.…”