Fig. 1. Hybrid BIC lattices. (a–c) Schematic diagram of a symmetry-protected BIC lattice without radiation channel (a), a uniform quasi-BIC lattice with radiation channel open by breaking symmetry of all the resonators (b), and a hybrid quasi-BIC lattice with C₂ symmetry preserved in the neighboring resonators along x-axis in a supercell (c). (d) A double gap split ring resonator as the unit cell of the metasurface. (e, f) Simulated (e) and experimental (f) transmission amplitude spectra for the three-type lattices. The same asymmetry degree (α = 4.95%) was applied for U-qBIC and H_x-BIC metasurfaces.

Fig. 2. Interpretation of hybrid BIC from reciprocal space. (a, b) Brillouin zones of monoatomic and diatomic supercells at α = 0 when the periods were chosen with a and 2a in the x direction. (c) Illustration of Brillouin zones for monoatomic and diatomic supercells showing the band folding operation where X and M points in the BZ of a monoatomic supercell are folded to X′ and M′ points in the BZ of a diatomic supercell, and Г(Г′) point is fixed. (d) Band diagrams of monoatomic (black circles) and diatomic (orange lines) supercells showing the folding behavior where all the modes of a monoatomic supercell in unshaded region are reflected into the shaded region representing modes of a diatomic supercell. (e) Radiative quality factors of monoatomic and diatomic supercells. The same folding behavior of Q is inherited from the eigenmodes. (f) Comparison of radiative Q versus k between monoatomic and diatomic supercells. Circles are simulated values and solid lines are fitting curves with Eq. (2) whose coefficient is 4-times larger in a diatomic supercell than that of a monoatomic supercell. Here, p_x is period of supercell along x direction. Perfect electric conductor (PEC) was used for DSRRs in simulations to calculate eigenvalues and quality factors.

Fig. 3. Experimental demonstration of the high-Q hybrid BIC. (a, b) Microscopic images of U-qBIC and H_x-BIC metasurfaces. Supercells of U-qBIC and H_x-BIC metasurfaces are shown in the inset. Scale bar, 20 μm. (c) Simulated transmission amplitude spectra of U-qBIC (left) and H_x-BIC (right) metasurfaces at an asymmetry degree of 2.97% with excitation electric field polarized along y-axis. Band diagrams of U-qBIC and H_x-BIC supercells are shown in the middle. (d) Simulated radiative Q (circles) versus asymmetry degree (α) with inverse quadratic fitting curves (solid lines) of U-qBIC (black) and H_x-BIC (orange) supercells. Here, an additional constant of β is necessary to account for the nonuniform asymmetry in the hybrid lattice. (e) Experimental transmission amplitude spectra of U-qBIC and H_x-BIC metasurfaces at an asymmetry degree of 7.42% with excitation electric field polarized along y-axis. The linewidth of Fano resonances is larger than that of simulations due to Ohmic loss in metallic resonators (aluminum) and finite number of supercells.

Fig. 4. Generalized high-order hybrid BICs. (a, b) Microscopic images of H_t-BIC and H_q-BIC metasurfaces with three and one asymmetric resonators out of four in a 2×2 supercell, respectively, and the period is 2a along both x and y axes. Scale bar, 20 μm. (c) Schematic diagram of band folding from U-qBIC lattice (black) to H_t-BIC/H_q-BIC (red) in the Brillouin zone. (d) Simulated transmission amplitude spectra of the H_t-BIC (left) and H_q-BIC (right) metasurfaces at an asymmetry degree of 2.97%. The band structure of H_t-BIC/H_q-BIC is shown in the middle, and the modes at the Г point marked with different colored circles are folded from X (red), Y (orange), and M (blue) points in the Brillouin zone of U-qBIC lattice, respectively. The highlighted resonances show the original modes inherited from U-qBIC lattice. (e) Experimental (orange) and simulated (black) transmission amplitude spectra of H_t-BIC and H_q-BIC metasurfaces at an asymmetry degree of 7.42%. The overall linewidth of Fano resonances is larger than that of simulations due to Ohmic loss in metallic resonators (aluminum) and finite number of supercells.

Fig. 5. Significant Q improvement in hybrid BIC supercells and robustness against fabrication imperfections. (a) Evolution of radiative Q versus AD for U-qBIC, H_t-BIC, H_x-BIC, and H_q-BIC supercells. The overall quality factors are improved in hybrid supercells with a lower radiation density. (b) Influences of fabrication imperfection on quality factors in the four scenarios. Imperfection is introduced by adjusting the sharp right-angle of square in the resonators to rounded angles indicated by radius r. Q and Q' indicate radiative quality factors for lattices with right-angle and rounded-angle resonators, respectively.