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Observation of intrinsic chiral bound states in the continuum

Photons with spin angular momentum possess intrinsic chirality which underpins many phenomena including nonlinear optics1, quantum optics2, topological photonics3 and chiroptics4. Intrinsic chirality is weak in natural materials, and recent theoretical proposals5-7 aimed to enlarge circular dichroism by resonant metasurfaces supporting bound states in the continuum that enhance substantially chiral light-matter interaction. Those insightful works resort to three-dimensional sophisticated geometries, which are too challenging to be realized for optical frequencies8. Therefore, most of the experimental attempts9-11 showing strong circular dichroism rely on false/extrinsic chirality by employing either oblique incidence9, 10 or structural anisotropy11. Here, we report on the experimental realization of true/intrinsic chiral response with resonant metasurfaces where the engineered slant geometry breaks both in-plane and out-of-plane symmetries. Our result marks the first observation of intrinsic chiral bound states in the continuum with near-unity chiral dichroism of 0.93 and record-high quality factor exceeding 2663 for visible frequencies. Our chiral metasurfaces promise a plethora of applications in chiral light sources and detectors, chiral sensing, valleytronics and asymmetric photocatalysis.

achieve and engineer high-Q resonances [22][23][24][25] . When BIC acquires intrinsic chirality, the resulting chiral BIC can simultaneously generate high Q-factors and strong CDs without involving false chirality. As pointed out by previous theoretical works, the key to enabling chiral BIC is to break all the mirror symmetries of the structure [5][6][7] , which, however, has hindered its experimental realization. We have witnessed numerous approaches to break either the in-plane 24,26 or the out-of-plane 27 mirror symmetry, but the remaining symmetry planes still prevent the generation of intrinsic chiral BIC. The measured high-Q CD resonances are inevitably attributed to the false chirality of oblique incidence 9, 10 or polarization conversion 11 .
Here, we report the first optical realization of intrinsic/true chiral BIC based on a new paradigm of slant-perturbation metasurfaces. The metasurface is composed of a square array of slanted trapezoid nanoholes in a TiO2 film, which is placed on a glass substrate and covered with PMMA ( Fig. 1a). This structure is evolved from vertical square nanoholes by introducing two types of perturbations, an in-plane deformation angle α and an out-of-plane slant angle φ, so that all the mirror symmetries are broken. A series of Bloch modes are supported by the metasurface (Fig.   1b), whose mode profiles are shown in Supplementary Fig. 1. Without loss of generality, we first consider the fundamental TM1 mode. When no perturbations are involved (α = 0, φ = 0), it supports a symmetry-protected BIC at the Γ point of Brillouin Zone because of the C 2 z symmetry of the structure. Due to time-reversal symmetry, the electromagnetic near fields are always linearly polarized for BIC and their distributions cancel each other to prohibit far-field radiation (see Supplementary Section 3).
Once an in-plane geometric perturbation is introduced to break the C 2 z symmetry, e.g., the square nanohole is cut into a trapezoid (α ≠ 0, φ = 0), the BIC is evolved to a quasi-BIC possessing circular polarizations in the near field, whose chirality can be evaluated by optical chirality density 28, 29 : Since OCD is a parity-odd scalar 30 , the existence of a mirror symmetry forces it to have opposite values on the two sides of the mirror as shown in Fig. 1c. In the far field, the Stokes parameter S3 of radiation is related to the optical chirality flux ℱ by the equation: where is the power flux and ℱ is defined as: In analogy to Poynting's theorem, optical chirality is also bounded by the conservation law. Thus, optical chirality flux ℱ is directly related to the near-field OCD of the associated resonance by the equation: Here, the antisymmetric OCD distributions cancel each other in the near field of the metasurface and hence generate no chiral flux in the far field. This is protected by out-of-plane mirror symmetry and is immune from in-plane geometries. One of the most convenient methods to break the out-of-plane mirror symmetry is to slant the nanohole in x-direction. Then the variation of OCD is written as: ∆ = (∆ / ) • , where (∆ / ) denotes the change of permittivity divided by its original value. As highlighted in Fig. 1c (see the middle panel), Δε and OCD have opposite signs in all perturbed areas and hence the volume-integrated ΔOCD is negative. The unbalanced OCD distributions in the near field of the slant-perturbation metasurface will induce non-zero optical chirality flux in the far field, corresponding to circularly polarized radiation (Fig. 1c).
The origin of slant-induced chirality can also be analyzed by examining the near-field electromagnetic distributions at the central x-y plane. As shown in Fig. 1d, when no slant perturbation is introduced, the magnetic fields of quasi-BIC are predominantly x-polarized while the electric fields are out-of-plane. According to the generalized theory of chiroptics 12,15 , the optical chirality of an object in the dipole approximation is controlled by the dot product p ⊥ ·m ⊥ , where p ⊥ and m ⊥ are the projections of the associated electric dipole p and magnetic dipole m on the plane perpendicular to the k-vector of incident light. Here, p is parallel to k, resulting in no optical chirality. To break such parallel configuration, the nanohole can be slanted towards negative x-direction so that the associated electric field vectors are tilted towards the same direction, while the magnetic fields approximately remain x-polarized ( Fig. 1d), leading to non-zero p ⊥ ·m ⊥ and optical chirality.
In Fig. 2a, we calculate the unbalanced OCD that is equal to ∫ as a function of the slant angle for different quasi-BICs. It can now be seen that an optimal slant angle exists for attaining the maximal unbalanced OCD, where the largest degree of circular polarization of far-field radiation is anticipated. Besides, we can see that the amplitude of unbalanced OCD cannot reach unity through the slant operation alone for TM2 and TE2 modes. For TE1 mode, the slant angle needs to be larger in order to obtain large unbalanced OCD, and inevitably leads to a much smaller Q-factor. Thus, TM1 mode is found to be the best candidate for achieving intrinsic chiral BIC with large Q-factor.
The evolution of the momentum-space eigenpolarization map of TM1 along with geometric perturbations is presented in Fig. 2b.  Fig. 2d. It is observed that the C+ point represented by the diminishing point in the TM1 band of LCP incidence appears at normal direction, i.e., Γ point. But for the RCP incidence case, the TM1 mode can be excited at normal incidence, and the C-point is observed at the incidence angle of -0.04 rad. The experimental results agree well with simulations, where the measured C+ and C-points are present at the incidence angles of 0 and -0.044 rad (Fig. 2d). The details of the optical experimental setup are provided in Supplementary Fig. 7.
To study the evolution of C points with the slant angle, we have fabricated a serious of metasurfaces with a fixed α but variable φ. As retrieved from transmission spectra, the incident angles that C+ and C-points occur approximately follow linear relationships with φ, which is consistent with simulations results (Fig. 3a). Apparently, the key point for achieving chiral BIC is to cooperatively modulate α and φ, so that one C points is generated and then moved back to Γ point. To reveal such inherent linkage between α and φ, the generalized model based on electric and magnetic dipoles shown in Fig. 1d is revisited. When the associated perturbations α and φ are small, the Q-factor of quasi-BIC roughly scales with the inversely quadratic square of all the perturbations 24 : Q ~ 1/(α 2 + Aφ 2 ), where A expresses the different sensitivities of Q to α and φ.
Meanwhile, the amplitudes of electric dipole p and magnetic dipole m are proportional to the square root of the Q-factor: |p| ~ Q 1/2 and |m| ~ Q 1/2 . Then, the intrinsic chirality of quasi-BIC, manifested by CD, can be estimated by: As predicted by Eq. 2, if φ is raised from zero while α is fixed, CD will first rapidly increase to the maximum and then gradually decrease. This is well reproduced by simulations results (Fig.   3b). The experimental results also follow a similar dependence except that the measured CDs are smaller than the simulated ones (see detailed spectra data in Supplementary Fig. 8). Such deviation is mainly attributed to the fabrication tolerance and the undesired scattering from surface roughness. Further, by calculating the derivative of CD versus φ, the condition for maximizing CD is deduced as: = √ • . This offers a straightforward recipe to select a suitable set of φ and α for achieving chiral BIC. The slope √ is related to the mode profile and could take different values for different chiral BICs. For TM1 mode, the slope is theoretically predicted to be 1.066 (see Supplementary Section 9), which agrees well with the simulation results (Fig. 3c). The experimental data also follow a linear relationship and the fitted slope of 1.197 is slightly deviated from the predicted one. Accordingly, as long as φ and α are cooperatively decreased, the Q-factor of chiral BIC can be continuously boosted while maintaining a unity CD (see details in Supplementary Section 10). In our experiments, φ and α are set as 0.1 and 0.12 due to fabrication capacity. We notice that the slant direction of the nanohole can also be rotated with an azimuthal angle θ, whose impact is discussed in Supplementary Section 11.
Another way to raise the Q-factor of chiral BIC is to enlarge the metasurface size, so that both in-plane and out-of-plane leakage are suppressed 31 . We have fabricated a group of metasurface samples with different sizes. The highest Q-factor of 2663 is obtained for the largest sample of 200 μm, while the maximum CD is also reached to be 0.93 (Fig. 4a). Here, CD is defined as: CD = (RR -RL) / (RR + RL), where RR(L) is the normalized reflection spectra under RCP (LCP) illumination. Their differential near-field distributions are presented in Supplementary Fig. 12.
To exclude the possible impact of structural anisotropy, we have measured the normalized reflection matrix R = [RRR, RRL; RLR, RLL] in circular basis, where the notation RRL refers to the reflection of RCP light under LCP incidence. As shown in Fig. 4b, the cross-polarized components, RRL and RLR, possess negligible intensities, suggesting the absence of polarization conversion. It is thus concluded that the observed CD signal is attributed to the intrinsic chirality of quasi-BIC. The measured transmission spectra are included in Supplementary Fig. 13 In Fig. 4c, we have summarized the experimental Q-factors and CDs from some typical works about chiral metamaterials/metasurfaces 11,14,[32][33][34][35][36][37][38][39][40] . These works are divided into two categories according to the origin of CD signals: one purely relies on the true chirality of associated resonance and the other also has false chirality involved. Clearly, most approaches achieving high CDs rely on false chirality effects 11,35,37,38 and their Q-factors are still much smaller than ours. Besides, it is noted that the previous works exhibiting relatively large Q-factors are inevitably conducted in the infrared spectra 11,38,39 , highlighting the great difficulty and significance in achieving intrinsic chiral BIC in the visible. In