Fig. 1. (a) Schematic representation of the unit cells of the metasurface. The unit cell period is defined as p=22μm. The rectangular rings are characterized by their outer and inner dimensions: the outer rectangle has a length of l1=20μm and a width of w1=10μm, while the inner rectangle has a length of l2=11.50μm and a width of w2=5.75μm. (b) Eigenmode analysis of the metasurface with a rectangular ring in the absence of perturbation (g=0μm), illustrating the transition of a symmetry-protected BIC (SP-BIC at λBIC=29.35μm) to a quasi-BIC. Error bars indicate the linewidth of the eigenmodes. (c) Schematic diagram of spawning an EP from a quasi-BIC. Based on the quasi-BIC of the quadrupole mode, high-Q characteristics are imparted to the EP. The white arrow denotes the mode schematic. The inset illustrates the LCP and RCP responses at the EP, where the metasurface completely suppresses the scattering channel from RCP to LCP.

Fig. 2. Quasi-BIC supported by the metasurface with broken in-plane symmetry. (a) Transmission characteristics for different chiral incidences as the asymmetry parameter increases. The response modes indicated by black arrows within the dashed box correspond to the structure’s behavior under LCP and RCP incidence, at an asymmetry value of α=18.26%. (b) Q-factors extracted from the spectrum in (a). An inverse quadratic fit, represented by the solid gray line, is characteristic of quasi-BICs with broken symmetry. (c) Distribution of surface currents and the z-component of the electric field for the modes corresponding to black arrows in (a). Both configurations exhibit behavior indicative of a magnetic quadrupole mode.

Fig. 3. Transmission coefficients tlr and trl for circular polarization conversion in the parameter space. The maximum asymmetry of the polarization conversion is detected at (λEP,gEP)=(29.25μm,2.10μm). The colormap of tlr indicates a vortex phase profile adjacent to the vanishing polarization conversion.

Fig. 4. Theoretical analysis of eigenvalue and eigenstate dynamics in the parameter space of non-Hermitian systems. Amplitude (a) and phase (b) distribution of the eigenvalues in the parameter space, where the blue and red denote the two distinct eigenvalues of the non-Hermitian system. The yellow pentagram indicates the locations of the EPs. The representative evolution of eigenstate in the parameter space: encircling EP (c), evolution with g for fixed λ (d), and evolution with λ for fixed g (e). (c) Extracted eigenvalue trajectories encircling the EP on Riemann surfaces with corresponding eigenstate tracking. “A”–“G”: selected characteristic states along the trajectory for illustrative demonstration. The black scatter in the Poincaré sphere is RCP. (d), (e) Eigenstate responses under parameter variations with fixed EP-corresponding wavelength (d) or geometry (e). Extended parameter ranges from (a) and (b) used for comprehensive understanding.

Fig. 5. (a) Framework for EP emergence from quasi-BIC modes via Fano resonance. The incident CP light excites a quadrupole quasi-BIC mode (|ψq⟩) coupled with a dipole broad mode (|ψd⟩), forming a Fano lineshape. Red/blue represents RCP/LCP-induced responses, with the gray dashed line marking quasi-BIC spectral positions. The yellow arrows indicate symmetry-breaking-induced spectral shifts. (b) EP-specific transmission spectra analysis: (left) total transmittance under chiral illumination; (middle) co-polarized component conversion efficiency; (right) cross-polarized conversion efficiency. Gray dashed lines denote EP resonance positions.

Fig. 6. Construction of an alternative parameter space with tunable Fermi energy of BDS. (a) As Fermi energy increases, the real part of the permittivity of BDS increases. (b) Concurrently, the imaginary part of the permittivity decreases. (c) The CP conversion coefficients tlr vary with distinct Fermi energies. The blue solid line, indicating complete suppression of the polarization conversion, corresponds to a Fermi energy EF=0.15eV, which is the EP discussed previously. (d) The eigenvalues of the system evolve with growing Fermi energy, with the gray dashed line illustrating the resonance positions on the upper and lower Riemann surfaces.

Fig. 7. Integrated chiral detection-display platform on a metasurface utilizing maximum spin transmission asymmetry induced by EP. (a) Schematic of the metasurface design process. The designed 2-bit grayscale image is mapped to a numerical matrix, and by matching unit structures, a metasurface achieving near-field display functionality is obtained. The symbol “1” represents the unit cell that exhibits strong resonance response in RCP→LCP conversion, while “0” corresponds to the unit cell that shows strong resonance in LCP→RCP conversion. The platform’s dual functionality is demonstrated in (b)–(e): (b), (c) chiral detection via total field analysis and (d), (e) high-contrast chiral display through polarization-filtered field display.

Fig. 8. Evolution of the CP conversion coefficient with wavelength for fixed geometry in the complex plane of (a) tlr and (b) trl. The black spot in the center of the plane is EP, and the yellow line is the case g=gEP.

Fig. 9. Polarization eigenstate evolution of distinct paths modulated. (a) Evolution of the eigenstates with increasing geometrical defect g for a fixed wavelength λ, where λ=λEP corresponds to the process in Fig. 4(d). (b) Evolution of the eigenstates with increasing λ for a fixed g, where g=gEP corresponds to the process in Fig. 4(e). Blue and red denote the two eigenstates. The color gradient indicates the running direction of the parameter, as shown by the direction of the colored arrows. The g along the black dashed arrows in (a) represent 1 μm, 2 μm, 2.10 μm (gEP), 2.25 μm, and 3.10 μm, while the black dashed arrows in (b) relate to λ of 29 μm, 29.18 μm, 29.25 μm (λEP), 29.31 μm, and 29.50 μm.

Fig. 10. (a) Evolution trajectory of NR-FPC in the parameter space when both incident angle and geometric perturbation are varied simultaneously. The subscripts L/R indicate the corresponding chiral incidence that yields NR-FPC. Inset: configuration of oblique incidence in the xz plane, with the incident angle θ defined as positive on the positive x-direction side. (b1)–(b8) Jones matrix transmission coefficients at the inflection points of the trajectory.

Fig. 11. The chirality of the system in the parameter space in the vicinity of the EP.

Fig. 12. (a) Evolution of transmission coefficient |tlr| versus unit cell connection width w0. (b)–(e) Surface current distributions for (b), (d) RCP incidence and for (c), (e) LCP illumination in (b), (c) original and (d), (e) x-axis mirror-symmetric configurations.

Fig. 13. (a) Transmission under varying incident angles for CP incidences in the symmetric structure (g=0). (b) Structural perturbation-dependent transmission under normal incidence. (c) Phase of the tlr corresponding to (b). (d) Transmission evolution along the four trajectories in Fig. 10(a). Yellow markers denote the quadrupole mode of interest (mode 1), with blue/purple representing two other modes. Arrows indicate parametric mode migration.