Quasi-Bound States in the Continuum Enabled Strong Terahertz Chiroptical Response in Bilayer Metallic Metasurfaces

Abstract

Bound state in the continuum (BIC) as a novel non-radiating state of light in the continuum of propagating modes has received great attention in photonics. Recently, chiral BICs have been introduced in the terahertz regime. However, strong chiroptical effects of transmitted waves remain challenging to achieve in metallic terahertz metasurfaces, especially for intrinsic chirality at normal incidences. Here, we propose a chiral quasi-BIC by simultaneously breaking the out-of-plane mirror and in-plane C₂ rotation symmetries in a bilayer metallic metasurface, in which spin-selective terahertz transmittance is successfully realized. Benefiting from the symmetry-protected nature of our proposed BIC, precise tuning of structural parameters can lead to anticipated chiroptical performance. As a degree of freedom, the rotation angle of the split ring gaps can fully determine the handedness, linewidth, and working frequency with strong circular dichroism. Besides, the sensing performance shows a surrounding refractive index sensitivity of 200 GHz/RIU, which is similar to those of previous works based on terahertz metasurfaces. Taking advantage exclusively of symmetry-protected BICs to realize transmitted terahertz chiroptical response provides fresh insights into the creation of novel BICs, which enables profound advancements in the surging field of novel terahertz devices.

1. Introduction

Terahertz polarization components are still lagged behind due to the lack of natural materials that possess significant terahertz–matter interactions [1,2,3]. Metasurfaces, which are the 2D counterparts of metamaterials, have superior abilities to manipulate the light of electromagnetic waves at subwavelength scales so that extraordinary phenomena not possible in natural materials can be achieved [4,5,6,7]. Such a paradigm has sparked the current surge in state-of-the-art materials. The metasurfaces resonated precisely with terahertz incident waves can provide an exceptional approach for the realization of numerous terahertz polarization components [8,9,10,11,12,13]. Among them, chiral 3D metamaterials [14,15,16,17] and 2D metasurfaces [18,19,20,21,22] have satisfied a certain set of requirements for targeted applications, such as biosensing [23,24,25,26], circular dichroic nonlinear generations [27], and spin-selective wavefront manipulations [28,29,30,31]. Recently, a number of related works employing metasurfaces to realize terahertz chirality have been reported [32,33,34,35,36]. Chirality is a ubiquitous phenomenon in nature, which refers to the property of an object that cannot be superimposed with its mirror image after rotations or translations [37]. Light interactions with geometries can include chiral-optical effects, including circular dichroism (CD) and optical activity, manifested by a difference in the intensity and phase responses between left/right circularly polarized (LCP/RCP) light illuminations. Although the chirality of metasurfaces is widely investigated, it is hard to achieve maximal chirality combined with an ultra-high quality factor (Q-factor) due to absorption and scattering loss, hindering many applications that rely on strong chiral light−matter interactions.

Photonic bound states in the continuum (BICs) are feasible to solve this problem of chiral photonics. Recently, because the radiative leakage rate is greatly suppressed to zero when photons are trapped in a particular way, BICs have attracted a lot of interest as one of the non-radiating electromagnetic states for light trapping [38,39]. In the context of quantum physics, this concept was first proposed by J. von Neumann and E. Wigner through destructive interference between two or more leaky modes [40,41]. Of greater importance is the quasi-BIC state that shows a narrow linewidth with a high Q-factor by breaking the structural symmetry or modifying the coupling strength between distinct resonance channels. BICs are identified as localized states coexisting with extend modes within the light cone and they have attracted tremendous attention due to their unbounded Q-factors. The Q-factor of the BICs in the three types, including bound states due to symmetry or separability, bound state through parameter tuning, and bound states from inverse construction, are theoretically infinite. It becomes finite but with an ultra-high value when BICs develop into quasi-BICs with conditions deviating from the requirements [39]. Such mechanisms to obtain quasi-BICs are generated from symmetry-protected and accidental BICs, respectively. Benefiting from the high-Q resonances of quasi-BICs, the metasurface can be designed to realize ultra-sharp transmission/reflection spectra with an ultra-high light−matter interaction strength [42,43,44]. Thus, BIC-based lasing [45,46,47], beam shifting [48,49], strong coupling [50,51], nonlinearity [52,53,54,55], modulation [56,57,58,59,60], imaging [61], displaying [59], and sensing [62,63,64,65] have all then been successfully achieved. As another stimulating aspect, quasi-BIC-induced chiroptical resonances have recently been established by using out-of-plane metasurfaces [66,67] and double layer metasurfaces [68] to generate geometrical perturbations. Unlike conventional metasurfaces, such chirality from quasi-BICs enables a significantly high Q-factor. Nevertheless, this cutting-edge field of novel chiral BICs in metasurfaces remains largely unexplored. Besides several dielectric BIC metasurfaces to realize high-Q chiroptical resonances, the metallic counterparts could also be a good candidate for spin-selective responses in the terahertz regime as a result of their strong light localization and more suitable for ultra-sensible modulators. Particularly, strong chiroptical effects of transmitted waves are challenging to achieve in metallic planar structures, especially for intrinsic chirality illuminated by normal incident waves. Various plasmonic devices have been designed to investigate the chirality of metallic metasurfaces; for instance, C. Yang et al. made great progress in the improvement of circular dichroism transmission by using a layer of plasmonic slanted nanoapertures with symmetry breaking [37], E. Plum et al. demonstrated optical activity in an intrinsically anisotropic planar metamaterial of a 2D array of metal split rings [69], C. Tong proposed a new paradigm to obtain a strong circular conversion dichroism based on extrinsic 2D chirality in a multilayer achiral Au square array [70], but the high circular dichroisms of most of the works are on the basis of the coupling process in the geometries with radiations. S. Zhonglei et al. have proposed a perfect chiral terahertz absorber with a 20-μm-thick gold structure [71]. However, such BIC-based chiral functionality can only operate for reflected waves and circular dichroism for the transmission of terahertz needs further exploration.

In this work, for the first of time, we have proposed a novel bilayer terahertz metallic metasurface to achieve quasi-BIC-based chiroptical transmittance. The metasurface can selectively transmit one circularly polarized terahertz wave but reflect its counterparts at the resonance frequency. Through systematical investigations, it is found that the working frequency, bandwidth, and handedness can all be flexibly controlled through the rotation angle of the split ring resonator (SRR) gaps via structure symmetry perturbation. Such an excellent property is tightly related to the symmetry-protected BIC eigenstate embedded in the metasurface. In addition, the near-field distributions reveal that the quasi-BIC state can sustain a highly enhanced local field at the SRR gaps. The large mode volume benefits the sensing performance with a surrounding refractive index as high as 200 GHz/RIU. Further theoretical analysis based on multipole calculations indicate that the selective excitation of magnetic dipole and electric quadrupole is the major reason to construct the chiroptical response. Additionally, we introduce more modulation depths of the circular dichroism by using a bilayer planar metallic metasurface without increasing the complexity of the geometry. Thus, the discovery not only directly manifests a viable approach to manipulate the chirality of transmitted terahertz, but also offers unique insights into the search for novel chiral BICs.

2. Results and Discussions

To realize the functionality of chiral-dependent terahertz responses by utilizing the BIC nature in a metallic metasurface, we propose bilayer coupled resonators consisting of two split rings (SRRs) within one unit cell. Figure 1a schematizes the working principle of the proposed terahertz chiral metasurface, in which a dielectric layer (i.e., quartz) is sandwiched by two layers of SRR arrays. The SRRs are made of 1-μm-thick gold which can be fabricated via the conventional planar microfabrication techniques [72], such as the ultraviolet lithography technique. For the convenience to discuss the physical origin of the chiral responses, we use a typical dielectric material (quartz) as the middle layer, which features a merit of low loss in the terahertz regime. A giant circular dichroism is generated, as shown in Figure 1a. As demonstrated in Figure 1b–d, the key geometric parameters determining the chiral chiroptical resonance include: the periods $P_x=P_y=100 \mathsf{\mu }\mathrm{m}$, the inner radius of SRRs $R_{in}=23 \mathsf{\mu }\mathrm{m}$, the outer radius of SRRs $R_{out}=30 \mathsf{\mu }\mathrm{m}$, the distance between two layers of SRRs $d=10 \mathsf{\mu }\mathrm{m}$, and the opening angle of gaps $\theta =2^{\circ }$. The rotation angle (${\beta }_1$ and ${\beta }_2$) of the gaps in one side plays an important role in evolving the ideal-BIC state into the quasi-BIC state with high chiral responses. To underpin the unique characteristics of the chiroptical performance of the quasi-BIC metasurface, its transmittance spectra at the normal incidence are calculated by leveraging the commercially available software CST Microwave Studio with a finite element method. Along the x/y-directions, the periodic boundary conditions are applied. To prevent interference between backscattering and the resonant modes, the bilayer metallic metasurface is placed in the middle of two z-directional boundaries with an open boundary condition. Two ports are applied at the interfaces of the open boundaries, so that the S-parameters will be obtained ($t_{xx}$, $t_{yx}$, $t_{yy}$, $t_{xy}$). Then, the transmission coefficients of circularly polarized waves are derived according to Equation (1). In order to fully attain high-Q resonance modes with ultranarrow linewidth, the solver accuracy is particularly set as −80 dB, which is much less than the default value of −40 dB. The convergence of the simulation is highly dependent on the mesh property. Typically, the convergence analysis should be performed to realize a required convergence. In this way, one can gradually decrease the mesh size until the transmission spectrum does not change anymore. In the xy plane, we have set the size of mesh in the gap as 0.1 μm and the size of mesh in the gold as 1 μm to ensure high accuracy. In the z-direction, we have set the mesh size of gold metasurfaces as 0.05 μm and dielectric layers as 1 μm. In this way, we have found no reduction of mesh size was needed since a further decrease would not influence the spectral response of the metasurface. Furthermore, the mesh view in the CST software is captured as shown in Figure S3. In the simulation, the permittivity of the dielectric layer is set as 4 and the conductivity of the gold is $4.75\times {10}^7 \mathrm{S}/\mathrm{m}$. Here, we introduce the rotation angle $\beta ={\beta }_1=-{\beta }_2$ to simultaneously break the out-of-plane mirror symmetry and in-plane C₂ rotational symmetry. To calculate the transmittance spectra $T_{RR}$, $T_{LR}$, $T_{LL}$, and $T_{RL}$ of circularly polarized waves, we can first obtain the co-polarization and cross-polarization transmission coefficients in simulations. According to the following equation [10], in order to derive the circular wave transmissions $t_{LL}$, $t_{LR}$, $t_{RR}$, and $t_{RL}$, the transmission coefficients of circularly polarized waves are:

$$\left(\begin{array}{cc}{t}_{RR}& t_{RL}\\ t_{LR}& t_{LL}\end{array}\right)=\frac{1}{2}\left(\begin{array}{cc}\left(t_{xx}+t_{yy}\right)+i\left(t_{xy}-t_{yx}\right)& \left(t_{xx}-t_{yy}\right)-i\left(t_{xy}+t_{yx}\right)\\ \left(t_{xx}-t_{yy}\right)+i\left(t_{xy}+t_{yx}\right)& \left(t_{xx}+t_{yy}\right)-i\left(t_{xy}-t_{yx}\right)\end{array}\right)$$

(1)

where the first and second subscripts represent the polarization state of the incident and transmitted waves. Here, ‘R’ and ‘L’ denote right and left circularly polarized waves. The letters ‘x’ and ‘y’ refer to the x-polarized and y-polarized waves. Then, the transmittance is the square of the transmission coefficient (for instance: $T_{RR}={\left|t_{RR}\right|}^2$). Figure 1e shows an achiral structure when $\beta =0^{\circ }$ as it has both types of symmetries. In this case, the resonators embed an ideal symmetry-protected BIC that does not radiate to the far field and the resonance responses of both right circular polarization (RCP) and left circular polarization (LCP) are totally degenerate. However, when $\beta \ne 0$, this geometrical perturbation will induce the disappearance of the ideal BIC. It is thus switched into a quasi-BIC that couple to the outgoing wave with significant chiroptical spectra, as shown in Figure 1f. Therefore, the gap rotation angle $\beta$ can serve as an efficient parameter to tune the chiroptical spectra.

To move further ahead in the comprehension of the BIC nature in the quasi-BIC chiral metasurface, the transmittance spectral mappings for LCP and RCP incidences are visibly shown in Figure 2a,b, respectively. It is noticeable that the transmittance of RCP waves is selectively resonantly blocked and LCP waves are resonant with a high transmittance when $\beta >0^{\circ }$, while the chiroptical responses can be completely reversible when $\beta <0^{\circ }$. By defining circular dichroism (CD) as $CD=T_{RCP}-T_{LCP}$, opposite CD is obtained as we change the gap rotation angle (Figure 2c), indicating two types of chiral enantiomers. It is gratifying to see that the resonant linewidth becomes narrower when the rotation angle decreases and it disappears when $\beta =0^{\circ }$. To quantitatively identify the quality factor evolution as a function of the asymmetry, the calculated radiative Q-factor of the perfect electric conductor (PEC) is plotted in Figure 2d. When the rotation angle of the gaps deviates from the zero point, the gap would have a left/right displacement $\Delta$. Thus, the asymmetry parameter can be defined as $\alpha =\Delta /R=sin\left(\beta \right)$. Since we use the ideal material without Ohmic loss, the simulated Q-factor can be well fitted by $Q_r=c{\alpha }^{-2}$, where c is the constant coefficient. It is noticeable that the inverse quadratic law $Q_r\propto {\alpha }^{-2}$ is elegantly reproduced in numerical simulations and its value diverges into infinity when $\alpha =0$. Such a phenomenon is a universal law for symmetry-protected BIC systems [73]. Therefore, we can safely conclude that the physical origination of spin-selective transmittance responses of the proposed chiral metasurface is from the symmetry-protected quasi-BIC resonance.

For practical implementation, noble metals are frequently used to construct metallic terahertz metasurface. To gain further insight into the influence of the rotation angle and the metal loss, Figure 3 gives the transmittance spectra with various rotation angles in the cases of PEC and Au, respectively. As Figure 3a shows, the slight perturbation ($\beta =0^{\circ }$) would result in a sharp resonant dip for the LCP incidence, whereas it is interesting to observe a sharp resonant transparent window for the RCP incidence. The chiral behaviour is completely reversed when the rotation angle changes its sign when compared with the results in Figure 3a,c. With the increment of asymmetry, the linewidths gradually broaden and the chiroptical response shows an obvious difference. The dependency of resonant frequency on the increasing of the asymmetry parameter demonstrates a significant red shift tendency. When it comes to the lossy metal case (Figure 3b,d), the high-contrast spin-selective response only occurs when the rotation angle is large enough ($\left|\beta \right|>{10}^{\circ }$). This is because the non-radiative loss of the gold results in the disappearance of high-Q resonance modes. From the results shown in Figure 3, we can conclude that by properly choosing the structural parameters with appliable materials, one can obtain a strong circular dichroism in the terahertz regime, implying great flexibility in practical applications.

As for the fabrication feasibility, please note that the quartz used in the proposed structure is very thin, for instance, less than 30 μm in our case. Owing to its fragility, it is very challenging to fabricate such a thin film. Fortunately, it has been recently noted in an experimental work [74] in which they have fabricated a terahertz metasurface on a 47-µm-thick SiO₂ substrate based on UV lithography. If a thin quartz substrate could be obtained, one can thus fabricate the proposed bilayer metallic structure by utilizing UV lithography in both sides. Therefore, the main difficulty of using quartz as the dielectric layer is due to the fact that it is too fragile to be destroyed. Alternatively, the fabrication processing could become more feasible when we choose other flexible materials, such as polydimethylsiloxane, polyimide, parylene, and cyclic olefin copolymer. As a typical example [8,75], polyimide has been widely used as a dielectric layer in the multilayer terahertz metasurfaces. However, polyimide has a considerably high intrinsic loss owing to its complex refractive index n = 2.96 + 0.27i [76]. Thus, the resonance strength would be strongly suppressed according to the results in Figure S2b in the supporting information of the revised manuscript. Fortunately, another type of flexible dielectric material, namely, cyclic olefin copolymers (COC) can be considered as a lossless dielectric layer in the terahertz regime whose complex refractive index is n = 1.53 + 0.001i [77,78]. According to the fabrication processing described in the reference [77], freestanding terahertz double layer metasurfaces can be feasibly fabricated without additional substrate. The sample can be prepared as follows: (i) A 10 nm titanium adhesion layer followed by a 1 $\mathsf{\mu }$m gold layer is deposited on both sides of the 10 μm COC (ZEONOR^®, Zeon Corp., Tokyo, Japan) by electron beam evaporation, (ii) the metasurface structures can be formed on both sides of the substrate using a femtosecond laser ablation process. The corresponding results are shown in Figure S1.

Besides, it is very necessary to describe the reason why the permittivity of the dielectric substrate is set as 4. As a matter of fact, we make an assumption in the manuscript that the dielectric layer is selected as quartz, which is typically used in the terahertz regime due to its low intrinsic loss. The refractive index of quartz substrate is approximately adopted as two according to previous experimental work [79]. The permittivity is the square of the refractive index and its value is about 4. Moreover, it is more practical to use a complex permittivity, when the loss of the dielectric material is taken into consideration. Then, according to the recent work [80], the refractive index of quartz at terahertz frequencies was comprehensively investigated. Based on their experimental measurements, the imaginary part of the refractive index of quartz should be carefully considered. In the frequency range of our interest, the refractive index is n = 2 − 0.0005i. Therefore, we have investigated the spectral responses when different imaginary parts of the permittivity are considered to represent the material loss in practice. As for the quartz we used here, the loss of the material would not influence the chiral spectra responses, as shown in Figure S2a. Admittedly, for other materials when the loss is high, the resonance strength is reduced, leading to a weak chiral response. Such a phenomenon can be solidly verified in Figure S2b.

It is important to discuss the structural and material parameter dependencies of the circular dichroism in the terahertz metasurface exhibiting a chiral quasi-BIC. Since the chiral quasi-BIC has great importance for chiral-based sensing, we investigate here the sensing performance by varying the surrounding refractive index of the resonance frequency, as shown in Figure 4a,b. It can be seen that the frequency shift of the chiral resonance is approximately proportional to the variation of the surrounding refractive index. According to the simulation results, when the surrounding refractive index changes from 1 to 1.3, the resonant frequency changes from 0.78 to 0.72 THz, as shown in Figure 4a. Generally, the sensitivity of the resonance can be defined as S = df⁄dn. Thus, the sensitivity of our proposed chiral quasi-BIC state is 200 GHz/RIU, which is similar to the previous works [81,82,83,84,85,86]. On the other hand, the distance between two layers of SRRs is much less than the working wavelength. To qualitatively explore the influence of the coupling effect between the two layers, we intentionally give the spectral responses with numerous thicknesses of the dielectric layer, as shown in Figure 4c,d. When the thickness increases from 5 μm to 30 μm, the resonance strength first increases and then decreases. According to the CD spectra, the maximal chiroptical response takes place when the thickness is 10 μm. Therefore, the coupling strength between the two layers of SRRs would greatly influence the chiroptical response and its value should be carefully optimized.

Please note the quasi-BIC state mentioned above is induced by rotating the gap angles for the upper and bottom layers at the same time. It is also of vital importance to investigate the contribution of each layer by separately rotating the gap angles of the upper layer and bottom layer. Figure 5a,b display the far-field spectra when the upper layer gap angle rotates from 10° to 50°. Compared with the results shown in Figure 3, the CD is strongly suppressed. However, the transmittance difference between LCP and RCP can reach its maximal value close to the results in Figure 3 when only the bottom layer gap angle rotates (Figure 5c,d). This observation manifests that the chiroptical response in quasi-BICs is mainly due to the symmetry breaking in the bottom SRR layer.

To further verify the origins of the two resonances induced by LCP and RCP, Figure 6 demonstrates the corresponding electromagnetic field distributions near the upper and bottom SRR layers, respectively. The frequency is selected at the resonance dip, indicating the frequency of the maximal chiroptical response of the metasurface. Figure 6a–d display the near-field enhancement of the quasi-BIC state when the gap rotation angle is 20°. It is visible that the electric field near the gaps can be strongly enhanced up to 150 fold when the metasurface is illuminated by the RCP incidence. Such a giant local field confinement is tightly associated with the relatively high Q-factor of quasi-BIC states and it can be very useful for its applications in sensors, switches, and modulators. Please note the corresponding spectrum is shown in Figure 3c. In this case, the RCP incidence would cause an obvious transmittance dip. For the LCP terahertz wave, a transparent transmittance window is formed. The near-field distributions shown in Figure 6c,d also exhibit a considerable enhancement up to 70 fold. The results mean that both RCP and LCP can excite the resonance of the metasurface, but they lead to totally different far-field radiation spectra. For comparison, the near-field distributions of the symmetry-protected structure ($\alpha =0^{\circ }$) are shown in Figure 6e–h, in which no field confinement is observed. Since ideal BICs are widely known to result from the destructive interference of numerous radiative channels, external access is not possible. By specifically perturbing the symmetry, quasi-BICs (q-BICs) with high-Q resonances can couple with the free-space radiation [73,87,88,89,90,91]. Please note the free-space radiation refers to the incoming incidence as well as the outgoing wave radiated from the metasurface. Since an ideal-BIC state is embedded in our proposed metasurface when the gap rotation angles are zeros, it would not couple with the incoming THz incidence. As a result, the metasurface with in-plane C₂ rotational and out-of-plane mirror symmetries cannot be excited by the THz incidence. Such an expectation can be clearly verified through Figure 6e–h that no near-field enhancement is observed. In comparison, the symmetry breaking results in high-Q quasi-BIC resonance couples with the incoming THz incidence. Such resonance can lead to a great field enhancement in the gaps due to the field localization, as shown in Figure 6a–d. This is because the structure simultaneously has the C₂ rotational and mirror symmetries. As a result, the eigenmode of the ideal BIC does not couple to the external far-field and does not exhibit chirality as well.

We use multipole analysis to extract the component for various multipoles in order to differentiate which moments contribute to such chiral quasi-BIC states. Through simulations, we first determined the current densities ($\overrightarrow{J}$) in the resonators. Then, using a Cartesian basis, the multipolar expansions are computed using the integral of the currents and the associated coordinates:

$${\overrightarrow{p}}_{\alpha }=\frac{1}{i\omega }\int J_{\alpha }{d}^{3}r$$

(2)

$${\overrightarrow{m}}_{\alpha }=\frac{1}{2c}{[\overrightarrow{r}\times \overrightarrow{J}]}_{\alpha }{d}^{3}r$$

(3)

$${\overrightarrow{t}}_{\alpha }=\frac{1}{10c}\int \left[(\overrightarrow{r}·\overrightarrow{J})r_{\alpha }-2r^2{J}_{\alpha }\right]d^{3}r$$

(4)

$${\overrightarrow{t}}_{\alpha }^{\left(\mathrm{1}\right)}=\frac{1}{28c}\int \left[3r^2{J}_{\alpha }-2r_{\alpha }(\overrightarrow{r}·\overrightarrow{J})\right]d^{3}r$$

(5)

$$Q_{\alpha \beta }^{\left(e\right)}=\frac{1}{i2\omega }\int \left[r_{\alpha }{J}_{\beta }+r_{\beta }{J}_{\alpha }-\frac{2}{3}{\delta }_{\alpha \beta }(\overrightarrow{r}·\overrightarrow{J})\right]d^{3}r$$

(6)

$$Q_{\alpha \beta }^{\left(m\right)}=\frac{1}{3c}\int \left[{[\overrightarrow{r}\times \overrightarrow{J}]}_{\alpha }{r}_{\beta }+r_{\alpha }{[\overrightarrow{r}\times \overrightarrow{J}]}_{\beta }\right]d^{3}rx$$

(7)

where $\overrightarrow{r}$ is the displacement vector from the origin to the specific point (x, y, z) and c is the speed of light. The charge density (q) in the dipoles and quadrupoles is replaced by the current density ($\overrightarrow{J}$) using the charge conservation equation. Since the post processing is a little hard to carry out in the CST, the software of COMSOL Multiphysics is used here as a tool to carry out the multipole decomposition. The multipole moments’ associated distributed powers are as follows:

$$I_p=\frac{2{\omega }^4}{3c^3}\sum _{\alpha }{\left|{\overrightarrow{p}}_{\alpha }\right|}^2$$

(8)

$$I_t=\frac{2{\omega }^6}{3c^5}\sum _{\alpha }{\left|{\overrightarrow{t}}_{\alpha }\right|}^2$$

(9)

$$I_M=\frac{2{\omega }^4}{3c^3}\sum _{\alpha }{\left|{\overrightarrow{m}}_{\alpha }\right|}^2$$

(10)

$$I_{Q^{\left(e\right)}}=\frac{{\omega }^6}{5c^5}\sum _{\alpha ,\beta }{\left|{\overrightarrow{Q}}_{\alpha \beta }^{\left(e\right)}\right|}^2$$

(11)

$$I_{Q^{\left(m\right)}}=\frac{{\omega }^6}{40c^5}\sum _{\alpha ,\beta }{\left|Q_{\alpha \beta }^{\left(m\right)}\right|}^2$$

(12)

In order to analyze the physical origins of these intriguing chirality features, detailed multipole decompositions of the scattered fields are performed for those whose gap rotation angle is $\beta ={20}^{\circ }$. The terms considered in the calculations that contribute to the emitted field include the electric dipole (ED), magnetic dipole (MD), toroidal dipole (TD), electric quadrupole (EQ), and magnetic quadrupole (MQ). Overall, the scattering of the electric dipole dominates the radiation so that the scattered spectrum of the electric dipole always occupies most of the scattering power. At the resonant frequency, the magnetic dipole as well as the electric quadrupole are dramatically enhanced. Although several multipoles are enhanced, the magnetic dipole dominates the radiation at the resonance frequency. Thus, the RCP incident wave can strongly excite both the upper and bottom SRRs. The surface currents rotate around the SRRs which thus leads to a magnetic dipole. However, such an enhancement of the magnetic dipole does not hold for the LCP incident wave, as shown in Figure 7b. We can note that even the electric field confinement also exists for the LCP wave (Figure 6c,d), the scatterings of the magnetic dipole and the electric quadrupole are dramatically suppressed. Therefore, the spin-selective excitation of the magnetic dipole and the electric quadrupole is the major reason to induce chiral quasi-BIC in our proposed metasurface.

3. Conclusions

In summary, we have shown that strong circular dichroism for a transmitted terahertz wave can be obtained in a bilayer quasi-BIC metasurface. The proposed metallic metasurface consists of a dielectric layer sandwiched by two layers of SRRs. The rotation angle of one-side gaps in SRRs could play a key role in breaking the out-of-plane mirror and in-plane C₂ rotation symmetries simultaneously. As a result, the non-radiative symmetry-protected BIC state evolves into a quasi-BIC state that exhibits a strong chiroptical response. Furthermore, the tunning mechanism of the asymmetric parameter and the distance between SRR arrays on the spin-selective terahertz transmittance have been thoroughly investigated. The coupling strength between the upper and bottom layers of SRRs has influenced the circular dichroism amplitude of the quasi-BIC to a great degree. Unlike an accidental BIC-based metasurface, the symmetry-protected nature of our proposed BIC enables us to select structural parameters to obtain the expected performance. The rotation angle can be used as an ideal degree of freedom to manipulate the handiness, linewidth, and working frequency of chiral responses. The sensing performance shows a surrounding refractive index sensitivity of 200 GHz/RIU, which is similar to previous works based on terahertz metasurfaces. The proposed chiral quasi-BIC metasurface can thus be an alternative method to fully exploit the polarization control of terahertz radiation and to potentially stimulate many terahertz applications.