Fig. 1. (a) Scheme of a triangular-lattice PCS. (b) Schematic illustration of first Brillouin zone of the PCSs. (c) Calculated band structure of PCSs. BIC-1, BIC-2, BIC-3, and BIC-4 at the Γ point are indicated by the red, pink, blue, and light blue lines, respectively. (d) Cross section of the PCSs. The radius of the circle hole is b. The semi-long axis and semi-short axis radii of the ellipse are a and b, respectively. (e)–(h) Eigen field profiles of BIC-1, BIC-2, BIC-3, and BIC-4. (i)–(l) Q-factors of BIC-1, BIC-2, BIC-3, and BIC-4 in the Γ-K direction.

Fig. 2. Simulated polarization vectors around the BICs with the log10Q as the background color. (a)–(d) Correspond respectively to BIC-1, 2, 3, and 4. Left: for triangular-lattice PCSs with circular holes. Right: for triangular-lattice PCSs with elliptical holes (R=1.2).

Fig. 3. (a)–(c) Schematics of triangular-lattice PCSs slab with circular holes (θ=0°,45°,90°). (d)–(f) Q-factors versus α=a−bb at Γ point in the mode 1 (θ=0°,45°,90°). (g)–(i) Q-factors versus α=a−bb at Γ point in the mode 3 (θ=0°,45°,90°).

Fig. 4. (a)–(c) Q-factors versus α=a−bb at Γ point in the mode 2 (θ=0°,45°,90°). (d)–(f) Q-factors versus α=a−bb at Γ point in the mode 4 (θ=0°,45°,90°).

Fig. 5. Schematic illustration of experimental setup based on cross-polarization measurement.

Fig. 6. (a) Schematic illustration of a photonic crystal slab under plane wave illumination. (b) SEM image of a PCS. The scale is 400 nm. (c) Scattering spectra of PCSs with Δ=a−b=20  nm. (d) Scattering spectra of PCSs while a quasi-BIC based on BIC-1 is excited in this wavelength window. (e), (f) Retrieved resonance wavelengths (e) and Q-factors (f) of resonance based on mode 1 at different Δ=a−b. (g) Scattering spectra of PCS while a quasi-BIC based on BIC-3 is excited in this wavelength window. (h), (i) Retrieved resonance wavelengths (h) and Q-factors (i) of resonance based on mode 3 at different Δ=a−b.

Fig. 7. (a) Scattering spectra of PCSs while a quasi-BIC based on BIC-2 is excited in this wavelength window. (b) Scattering spectra of PCSs while a quasi-BIC based on BIC-4 is excited in this wavelength window. (c), (d) Retrieved resonance wavelengths (c) and Q-factors (d) of resonance based on mode 2 and mode 4 at different Δ=a−b. In the legends of (c) and (d), 0.01 and 0.02 represent (kx,ky)=(0.012πp,0.012πp) and (kx,ky)=(0.022πp,0.022πp), which correspond to angles of approximately 1° and 3°, respectively.