Fig. 1. Representative examples of different types of BICs in periodic photonic systems. (a) Original FW BICs and symmetry-protected BICs in one-dimensional plasmonic gratings. The original FW BICs appear at the avoided crossing points and symmetry-protected BICs appear at the Γ point^[32]. (b) Accidental BIC supported by a PhC slab. It is located at the off-Γ point with the infinite Q factor and confined field profile^[15]. (c) General descriptions of BICs in periodic photonic structures from the mechanism of FW BICs. Both the symmetry-protected BICs and accidental BICs have similar FW origins from the couplings of modes^[44].

Fig. 2. Understandings of BICs from different bases: plane waves and Bloch waves. (a) Plane-wave perspective of BICs in PhC slabs^[45]. Left: schematic view of a PhC slab with C4v and up-down mirror symmetries. Right: participating channels of symmetry-protected BIC at the Γ point and accidental BICs along the Γ−X and Γ−M directions. (b) Mechanisms of BICs based on the total internal reflection of Bloch waves^[48]. Upper left: schematic view of the TIR at the interface between the PhC slab and free space. Upper right: BIC in a PhC slab when both the TIR and phase accumulation conditions are satisfied. Lower: BICs and the generalized conditions for waveguide modes.

Fig. 3. Understandings of BICs from the perspective of multipolars. (a) Upper panel: radiation patterns and the dominant multipolar components of the symmetry-protected BICs in square and hexagonal PhCs. Lower panel: Q factor, far-field radiation patterns, and the major multipolar compositions of the accidental BICs^[50]. (b) Schematic view of the multipolar origin of symmetry-protected and accidental BICs^[51]. (c) Radiation patterns and multipolar components of the polarization vortices in photonic quasicrystals^[53].

Fig. 4. Topological nature of BICs. (a) Topological nature of BICs^[22]. First panel: schematic view of the far-field radiations of guided resonances in PhC slabs. Second panel: undefined far-field polarization of a BIC and the polarization vortex around it. Last two panels: distribution of Q factor and polarization vector in momentum space. (b), (c) Experimental observation of the polarization vortices around BICs in a C4v photonic crystal slab^[23] and a one-dimensional grating^[24], respectively. (d) Left: polarization graph in momentum space. Right: merging of two general BICs and an off-Γ BIC with the variation of geometrical parameters^[55].

Fig. 5. BICs with multi-radiation channels. (a) BICs with two different radiation channels and the evolutions of the far-field polarization. Each radiation channel has a different behavior with the variation of structural parameters^[48]. (b) Left: honeycomb-lattice photonic crystal slab and its first Brillouin zone. Right: distribution of the Q factor around a BIC at the K1-point. The BIC has a divergent Q factor^[59].

Fig. 6. Momentum-space evolution of BICs. (a) Merging process of multiple BICs by tuning the periodicity a of the structures^[39]. As a increases, multiple BICs merge close to Γ point and BICs with opposite charges finally annihilate each other. (b) Merging process of two BICs with opposite charges by tuning the thickness t of the structures^[33]. (c) Experimental observation of BIC merging at off-Γ point by tuning the etching depth hg of the 1D PhC slab^[44]. (d) Evolution of BICs in the kx−h space^[44]. By continuously tuning the thickness h, the accidental BICs can continuously move along the photonic bands.

Fig. 7. Momentum-space evolution of BICs by symmetry breaking. (a) Left: schematic view of how an at-Γ BIC splits into a pair of C points. Right: experimentally measured transmittance along the band under LCP and RCP incidence^[66]. L(R)CP: left (right)-handed circular polarization. (b) Schematic view of how a high-order BIC with topological charge −2 evolutes under different symmetry breaking^[57]. (c) Evolution from off-Γ BIC to unidirectional guided resonance (UGR) by breaking the up-down mirror symmetry^[60]. (d) Right: evolution of polarization singularities in momentum space. Left: schematic view of the 1D PhC slab constructed by two superimposed gratings and the realized UGRs^[61].

Fig. 8. Various types of quasi-BICs. (a) Quasi-BICs realized by tilted silicon-bar pairs^[25]. The Q factor can be modulated by the symmetry-breaking factor. (b) Quasi-BICs in photonic quasicrystals^[53]. Unfolded dispersions and polarization maps show this quasi-BIC can also carry polarization vortices in momentum space. (c) Quasi-BIC in a moiré structure composed of twisted bilayer graphene PhC slabs^[78]. The vortex configuration can be found in the zero-order diffraction. (d) Miniaturized BICs constructed by laterally combined structures^[79]. The miniaturized BICs can confine the in-plane light field by adding a surrounding PhC slab with an overlapped photonic bandgap. (e) Chiral quasi-BIC in perturbed structures, whose unit cells are composed of two pairs of twisted elliptical pillars^[80]. The magnetic field distributions show that the chiral quasi-BIC leaks to circularly polarized light. (f) Chiral quasi-BIC in a slant-perturbation structure composed of a square array of slanted trapezoid nanoholes^[71]. The momentum-space polarization distributions of different slant perturbations exhibit the generation process of this chiral quasi-BIC.

Fig. 9. Modulating the flow of light via the high Q factors of BICs. (a) Zero-index propagation effect enabled by symmetry-protected BICs in a C6v PhC slab^[102]. (b) Negative refraction mediated by BICs^[106]. (c) Optofluidic transport and assembly of nanoparticles by utilizing strong electromagnetic field enhancement of the quasi-BIC resonance^[111]. (d) Saturated reds by quasi-BICs^[112]. (e) Steering spatiotemporal spectra by actively tailoring BICs^[77]. (f) Giant enhancement Goos-Hänchen shift by quasi-BICs^[113].

Fig. 10. Manipulating light by utilizing the topological vortex configurations around BICs. (a) Generating optical vortices via momentum-space polarization vortices around BICs^[121]. LCP and RCP denote the left- and right-handed circularly polarized lights. When an RCP Gaussian beam shines normally on the PhC slab, the converted LCP light beam will obtain a spiral phase wavefront via resonant responses with the polarization vortex around the BIC. (b) Spin Hall shifts of light via momentum-space polarization vortices around BICs^[126]. When a circularly polarized light beam obliquely shines on the PhC slab, the cross-polarized light beam will have a spin-dependent lateral light beam shift due to the momentum-space phase gradients enabled by polarization vortex around the BIC. (c) Polarization control around BICs with two phase-controlled inputs^[127]; a and b correspond to two input waves. In the presence of multiple input beams, the topological features of BICs enable full polarization control on the entire Poincaré sphere. (d) Topological features of optical force distribution around BICs^[128]. In contrast with untwisted PhC slabs, twisted PhC slabs can trap nanoparticles with a spinning pattern.

Fig. 11. Researches of photonic BIC combined with strong coupling and photonic BEC. (a) Sketch of the BIC-strong coupling system with a PMMA grating fabricated on the top of a DBR-WS2-SiO2 structure^[148]. (b) Fitting of the PL dispersion at the anticrossing leading to a 70 meV Rabi splitting by (a)’s structure^[148]. (c) Schematic of the electrically driven perovskite metasurface with tunable polaritonic emission leading to strong coupling of photonic modes and electrically injected excitons^[149]. (d) Experimental angle-dependent reflection spectra of the active perovskite metasurface under TE illumination, showing the Rabi splitting^[149]. (e) Sketch of the polariton waveguide with partially etched 1D lattice combining BIC and polariton BEC^[147](f) Left panel: angle-resolved photoluminescence emission showing the dark spot on the lower polaritonbranch from the BIC. Right panel: on increasing the pumping power, the measured polariton dispersionshows a two-lobe emission, which is the characteristic of polariton BEC^[147].

Fig. 12. Light–matter interaction enhancement and nonlinear optics. (a) Diagram of second harmonic generation (SHG) in a metal antenna (left), and the measured SH intensity versus nano-resonator diameter at different pump polarizations (right). The SH intensity is normalized on the square of the pump power^[194]. (b) Diagram of enhanced SHG in a doubly resonant cavity (left) and the measured SHG intensity (right). The red and blue lobes represent the far-field intensities of the first-harmonic (FH) and SH modes, respectively^[195]. (c) Conceptual diagram (left) and typical distribution of the photon arrival time difference for two detectors (right), of multiplexed entangled photon generation by spontaneous parametric downconversion utilizing BIC in a metasurface. The photon arrival time difference demonstrates photon pair generation^[196]. (d) Conceptual diagram (left) and measured SHG intensity (right) of an enhanced SHG with a 2D GaSe flake on a metasurface with a BIC state^[197]. The GaSe flake was laid on the surface of a Si metasurface consisting of a periodic square lattice of T-shaped pillars.

Fig. 13. Applications of BIC in lasers. (a) Schematic structure of the first lasing PCSEL based on the wafer fusion technique. The inset shows the SEM photograph of the triangular-lattice structure^[201]. (b) Dually modulated on-chip beam scanning lasers. Each unit can be selectively operated by driving the corresponding line electrodes^[211]. (c) Directional lasing in resonant GaAs nanopillar array^[213]. (d) Left: schematic of mini-BIC laser device consisting of a suspended GaAs thin membrane with periodically etched airholes. Right: microphotoluminescence (μ-PL) spectrum of the cavity modes^[90]. (e) Merging of the BICs in super-BIC laser^[214]. (f) All-optical switching from the vortex microlaser. Insets show the far-field emission patterns at different pumping densities^[76].

Fig. 14. Applications of BIC in sensors. (a) Topological charge evolution and refractive index sensing of merging BICs based on a BIC PhC slab^[246]. (b) Hyperspectral imaging and biodetection enabled by BIC metasurfaces^[253]. (c) Hybrid BICs-enhanced senor with a plasmonic component enables strong field confinement^[254]. (d) Chiral layer-enhanced sensing applications enabled by BIC metasurfaces^[241].