Fig. 1. Symmetry-protected BIC^[12]. (a) Schematic of optical waveguide structure; (b) light intensity at the output plane; (c) relationship between normalized optical power coupled into continuum states and applied thermal gradient across the structure; (d) refractive index symmetry of waveguide array is broken, resulting in light leakage into the waveguide array

Fig. 2. Accidental BIC. (a)(b) Schematic of the generation of Fabry-Pérot BIC^[58]; (c) Fabry-Pérot BIC realized by using semi-infinite waveguides with a side-coupled waveguide^[63]; (d) near-field image of the output field by fluorescence microscopy^[63]; (e)(f) illustration of Friedrich-Wintgen BIC by single nanorod^[68]; (g) single layer photonic crystal plate supporting single-resonance BIC^[69]; (h) band structure of this photonic crystal plate, BIC mode is the red circle position on the TM mode^[69]; (i) radiation lifetime in momentum space of TM mode^[69]; (j) radiation lifetime of TM1 mode along Γ‑X direction^[69]; (k) electric-field profile of BIC mode corresponding to extreme radiation lifetime of non-Γ points ^[69]

Fig. 3. Theoretical models of BIC. (a) Band diagram used to analyze BIC in a hybrid plasmonic-photonic structure^[66]; (b) temporal coupled mode theory with a resonator system with n ports^[78]; (c) multipole decomposition of a metasurface with a square unit cell and the formation mechanism of symmetry protected BIC and accidental BIC by multipole decomposition method^[80]

Fig. 4. Application of BIC in nonlinear optics. (a) (b) Schematic and experiment of perovskite metasurface with BIC mode to produce vortex beam^［29］; (c) (d) multi-beams, multi-wavelength BIC laser and the spectra at different angles and different wavelengths^［32］; (e) second harmonic intensity generated by single nanocolumn pumped by different pump light^［103］; (f) symmetry-broken quasi-BIC Si metasurface realizes the generation of second and third harmonics^［100］

Fig. 5. Application of BIC in polarization control and chirality enhancement. (a)(b) Intrinsic chiral BIC generated by inclined disturbance^[104]; (c) production of bilayer chiral quasi-BIC metasurface^［105］; (d) geometric phase is introduced into the bilayer structure to realize the oblique emergence of the intrinsic circular polarization state^[105]; (e) DSS structure is used to realize extrinsic and intrinsic chirality^[106]; (f) plasma dimer structure realizes the decoupling of CD and quality factor^[107]

Fig. 6. Application of BICs in filtering, sensing, and imaging. (a) Measurement sensitivity curve of top refractive index n^[120];(b) molecular fingerprint retrieval and spatial absorption^[45]; (c) principle of hyperspectral imaging-based biomolecule detection^[34]

Fig. 7. Application of BIC in waveguide. (a)(b) Low refractive index structure on a high refractive index substrate and diagram of the generation of bound states^［73］; (c) coupling strength g20 and propagation length L against waveguide width w^[73]; (d) BIC-based photonic integrated circuit and experiment results of microring cavity and MZI electro-optic modulator^[123]