Fig. 1. Schematic illustration of the chiral quasi-BIC photonic crystal slab (PhCs) with perforating holes. The yellow and blue colors represent the RCP and LCP lights, respectively. The inset shows the in-plane unit cell.

Fig. 2. Bandstructures and Q-factors for TM mode of the PhC with parameters a=795  nm, h=430  nm, la=170  nm, wa=186.5  nm, lx=580  nm, and ly=560  nm. (a) Optical bands for TM mode of the PhC around Γ point. Insets show the normalized electric fields of the corresponding bands at the Γ point. (b) Q-factors for the three bands in (a) with the same color. The inset displays the far-field polarization diagram of the orange band in (a).

Fig. 3. Extrinsic and intrinsic chiroptical response of the quasi-BIC via pure TM mode. (a), (e) Schematics of the oblique and normal incidence at the PhC. (b) Extrinsic CD spectra with the variation of incident angle θ for fixed azimuthal angle φ=0°. (f) Intrinsic CD spectra as a function of the asymmetric parameter δ. (c), (g) The transmittance spectra TRR, TRL, TLL, TLR and CD were extracted from (b) and (f) for fixed incident angle (θ=9°) and asymmetric parameter (δ=60  nm), respectively. The Q-factors (red dots) and the corresponding fitting curves (black lines) with the variation of (d) illumination asymmetric parameter sin(θ) and (h) geometrical asymmetric parameter δ.

Fig. 4. Extrinsic chirality with parameters a=795  nm, h=650  nm, la=157  nm, wa=202  nm, lx=575  nm, ly=565  nm via the degeneration of TE and TM modes. (a) Three-dimensional (3D) optical bands of the TE (3D surfaces surrounded by the green line) and TM modes (3D surfaces surrounded by the red line). The two yellow lines indicate the interaction eigen-wavelength of the TE and TM modes. The blue and yellow dots are chosen from the yellow lines. (b) The absolute difference of the eigen-wavelength of TE and TM modes in (a), with the blue and purple dots corresponding to eigen-wavelength 1597.2 nm and 1598.6 nm, respectively. (c) and (d) are the optical CD spectra corresponding to the blue and purple dots for fixed azimuthal angle φ. (e) and (f) are the transmittance spectra TRR, TRL, TLL, TLR, and CD at oblique incidence angles corresponding to the blue and purple dots in (a) and (b).

Fig. 5. Intrinsic chirality of TE and TM coupling modes with parameters a=795  nm, h=685  nm, la=157  nm, wa=202  nm, lx=575  nm, ly=565  nm. (a) The black lines with circle/square shape are the eigen-wavelength of TM/TE mode at Γ point, respectively, as a function of δ, and the red lines are the corresponding Q-factors of the modes. (b) Bandstructure of the PhC with δ=90  nm near the vicinity of Γ point. (c) CD for different geometrical parameters δ. (d) Evolution of the TE and TM eigenmodes at the Γ point with the variation of the asymmetric parameter δ. (e) Electromagnetic (EM) field distribution under LCP excitation as a function of the asymmetric parameter δ.

Fig. 6. (a) Schematic of the CMT for extrinsic optical chirality along the positive k∥ direction. (b) Schematic of the TCMT for intrinsic optical chirality.

Fig. 7. (a)–(c) Fitting results of the CMT for extrinsic chirality utilizing Eq. (A14), corresponding to Fig. 3(c) in the main text at λ=1476.5  nm.

Fig. 8. Transmittance spectra TRR, TRL, TLL, TLR, and CD with small incident angle θ. The Q-factor and the maximum CD are 132,777/0.91, 5339/0.93, and 1379/0.94 for θ=0.4°, 2°, and 4°, respectively.

Fig. 9. CD spectra with the variation of azimuthal angle φ and wavelength at θ=9°.

Fig. 10. (a)–(c) Fitting results of the TCMT for intrinsic chirality utilizing Eq. (B13), corresponding to Fig. 3(g) in the main text.

Fig. 11. Transmittance spectra TRR, TRL, TLL, TLR, and CD with small asymmetric parameters δ. The Q-factor and the maximum CD are 986846/0.94, 39721/0.92, and 9147/0.92 for δ=2  nm, 10 nm, and 20 nm, respectively.

Fig. 12. Far-field polarization diagrams in momentum space with different δ. The red/blue color represents the right-handed/left-handed polarization states. The circular polarization states are marked with red/blue dots.

Fig. 13. Multipole contributions of the PhC (a) under oblique incidence (φ=0°, θ=9°, and δ=0  nm) and (d) normal incidence (φ=0°, θ=0°, and δ=60  nm) for TM eigenmode. The electromagnetic eigenmode for the (b) wave vector along Γ-X direction and (e) δ=60  nm at Γ point; here, the blue and red circles indicate the magnetic loops. (c), (f) Corresponding z component of electric field at 1476.5 nm and 1482.8 nm, respectively, under RCP excitation. The black vectors are magnetic fields (Hx, Hy). The electric field patterns are extracted from x-y plane at z=0  nm.

Fig. 14. Multipole contributions of the PhC under oblique incidence at (a) k1 and (d) k2 points in Fig. 4(a) under LCP and RCP excitation, respectively; the black dotted lines indicate the peak of the CD. Electric field distributions at the peak of CD are extracted from (b), (e) x-y plane for z=0 and (c), (f) y-z plane for x=−280  nm. The black vectors are magnetic fields (Hx, Hy); here, the blue and red circles indicate the magnetic loops.

Fig. 15. Multipole contributions of the PhC under LCP excitation with (a)–(d) δ=20  nm, 40 nm, 70 nm, and 90 nm, respectively.

Fig. 16. Normalized multipole contributions of the PhC under LCP excitation at the wavelength of the peak of the CD for δ=20  nm, 40 nm, 70 nm, and 90 nm, respectively.