Fig. 1. The concept and classification of BICs. (a) Schematic diagram for the positions of radiation resonance modes, BICs and ordinary bound states in the band structure of periodic optical systems, the symmetry-protected BIC is taken as an example, which is located at the high symmetry point (Γ point) of the wave vector space; (b) the diagram for the classification, far-field decoupling approaches and fundamentals of optics BICs in periodic systems

Fig. 2. Symmetry-protected BICs. (a) Even-symmetric modes when the constraint frequency of the circular-hole photonic crystal plate is below the diffraction limit, while odd-symmetric modes radiate out the circular-hole photonic crystal plate; (b) the common structures that support quasi-BIC due to C₂ symmetry is broken; (c) the quality factor decreases with increasing structural asymmetry, showing the relationship Q=Q₀α⁻²

Fig. 3. Resonance-coupled BICs. (a) Fabry–Pérot BIC supported by two identical highly reflective photonic crystal plates, and its mechanism is shown in (b): adjust the distance d of the two plate resonators to form a standing wave; (c) schematic diagram of the coupling of two modes in a periodic structure device, (d) the radiation spectrum coupled by the two modes with high-Q mode; (e) the frequency tuning spectrum, adjusting the structural parameters, the two eigenfrequencies move and cross, and the resonance damping of one frequency will disappear completely forming the Friedrich–Wintgen BIC near the crossover point, (f) the BIC point appears as a smooth line on the transmission spectrum.^[96] © 2020 Optical Society of America

Fig. 4. Single-resonance BICs. (a) Adjust the incident wave vector to enter the BIC again, and its Q factor changes as shown in (b); (c) schematic diagram of the coupled-wave theory explaining the source of the single-resonance BIC, which is considered to be derived from the destructive interference of all waves coupled into the open channel^[99]

Fig. 5. Electromagnetic multipole theory of BICs. (a) Electromagnetic multipole structures and its radiation images^[111]; (b) schematic diagram of multipole radiation in periodic structure, and (c) multipole interaction mechanism of symmetry-protected BIC and accidental BIC^[107]

Fig. 6. Radiation polarization characteristics of BICs and quasi-BICs in momentum space ^[116]. (a) The radiation polarization states in the momentum space with the symmetry-protected BIC as an example; (b) the schematic diagram for the change of the radiation polarization states in momentum space after breaking the C₂ symmetry; (c) radiation polarization states in momentum space of the quasi-BIC can cover the entire Poincaré sphere

Fig. 7. Construction for quasi-BICs with high Q factor and dynamic BICs. (a) Photonic crystal slab supporting several BICs, adjusting the period size, all BICs are gradually merged into one BIC; (b) the Q factor change diagram of the quasi-BIC before and after the merger, where the Q factor of the merged quasi-BIC is always greater than that of isolated quasi-BIC^[119]; (c) schematic diagram for the structure and function of dynamic BICs based on photo-doped rectangular and cylindrical silicon^[123] © 2019 Optical Society of America; (d) a patterned graphene-metal metasurface device by tuning the graphene Fermi-energy level realizes dynamic switching between BIC and quasi-BIC

Fig. 8. Advanced applications of BICs in periodic optical systems

Fig. 9. Applications of BICs in narrowband filtering and sensing. (a) Photonic crystal grating supporting quasi-BIC, quasi-BIC has narrow transmission peaks in the low background transmittance, and realizes the function of spatial narrow-band filtering^[71]; (b) high-sensitive molecular sensor based on all dielectric tetramer supporting quasi-BIC^[68]

Fig. 10. (a~b) Applications of BICs based on molecular spectral coding ^[65]. (c~d) The non-linear applications of BICs, where (c) shows a T-shaped quasi-BIC device for generating frequency doubling light, and (d) show the comparison of the third harmonic and second harmonic intensities with those of ordinary devices ^[130]. (e) The relationship between pump power and light emission intensity, for quasi-BIC metasurface used to generate micro laser, and (f) the relationship between period size and laser and output power^[119]

Fig. 11. (a) Schematic diagram for vortex beam generation in momentum space based on photonic crystal plate supporting BIC, the radiation polarization distribution in momentum space (left) and electric field phase and intensity distribution under circularly polarized incidence (right)^[78-79]; (b) schematic diagram of a concept proposed by our group by combining BIC photonic crystal slab with THz circularly polarized antenna to make THz vortex antenna with adjustable vortex topological charge. (c~f) Applications of BICs in the field of asymmetric transmission: (c) schematic diagram of the planar structure device supporting the chiral quasi-BIC, and its (d) circularly polarized transmission spectrum and circular dichroism spectrum^[137]; (e) schematic diagram for a metasurface supporting the chiral quasi-BIC, with in-plane C₂ symmetry and in-plane mirror symmetry breaking simultaneously (left), and its polarization distribution in momentum space (right), and (f) its circular dichroism spectrum containing multiple chiral quasi-BICs^[101]