Fig. 1. (a) Simulated Q factor and resonant wavelength as a function of θ (top) and l (bottom), respectively. Inset: the schematic view of the model (a square block with l=0.4 μm). (b) Simulated transmission spectrum as a function of the angle and wavelength. Inset: the magnetic field profiles under the normal incidence condition, where white arrows correspond to electric field vectors and the black wireframe outlines the single unit. (c) Modeled the Q factor as a function of a for a broken-symmetry square block (l=0.4 μm). Bottom inset: the schematic image of the concave Si block. The top two insets show the magnetic field distributions at around a=0 μm and a=0.4 μm, respectively. (d) Simulated Q factor and resonant wavelength as a function of θ (top) and l (bottom) for the BIC mode at a=0.4 μm. The top inset: simulated Q factor as a function of l at θ=19°. The bottom left inset: the schematic view of the model (a rectangle block with l₁=0.3 μm). The bottom right inset: the magnetic field profile at θ=0°. The scaling parameter is set as 1.2 in (a−d).

Fig. 2. (a) Dependence of the Q factor on asymmetry parameter β for both designs (log-log scale). Inset: two definitions of the asymmetry parameter. (b) Simulated Q in momentum space at a=0 μm (left) and a=0.4 μm (right). Inset: the designed patterns shown in the xy plane for both cases. (c) Schematic image of a period metasurface with concave nanopillars. Inset: device fabrication process. (d) SEM image of the fabricated metasurface.

Fig. 3. (a) Measured transmission spectrum at different s (20×20 array). Inset: The magnetic field distribution in the yz plane for the metasurface with the substrate. (b) Polarization dependence measurements of the transmission (T_exp) and reflection (R_exp) spectra at a wavelength of 1.55 μm and their corresponding calculations (i.e. T_sim and R_sim). The arrow indicates the direction of the x-axis. (c) Top: Modeled the calculated and measured Q factor as a function of a (s=1.2 and b=0.1 μm). Inset: SEM image of the single unit at a=0.02 μm and a=0.32 μm, respectively. Bottom: The evolution of Q factor at different α for two definitions (log-log scale). (d) Numerically simulated dependence of the resonant wavelength and Q factor on t_sub (t_sub=0 μm means that there is no substrate). The top inset shows the comparison of the measured Q factor for different dimensions and array sizes. Structure 1: l=0.4 μm, a=0.15 μm, b=0.1 μm, and s=1.15. Structure 2: l=0.5 μm, a=0.1 μm, b=0.1 μm, and s=1.02. The bottom inset shows the SEM images of the prepared structures before and after the process optimization.

Fig. 4. Magnitude plots of the on-resonance magnetic field for the isolated resonator and 3×3, 5×5, 7×7, and 9×9 arrays. The magnetic field distributions are obtained at the vertical mid-plane of the blocks and the magnitude is indicated by the height. The structural parameters are l =0.4 μm, a=0.15 μm, b=0.1 μm, s=1.2. The table on the right shows the corresponding Q factors.

Fig. 5. (a) Measured transmission spectrum of the proposed metasurface (200×200 array) and its fitting of Fano function. Optimized structural parameters are p=0.6 μm, l=0.5 μm, a=0.1 μm, b=0.1 μm, s=1.05. (b) Comparison of THG in the proposed structure (red line) and a flat Si film with the same thickness (black line). The intensity of the THG in the flat Si film is amplified 100 times. (c) The electric field profiles at the resonance (left) and the off-resonance (right), respectively. (d) The corresponding polarization dependence measurements (normalized to the peak value of the resonance).