Terahertz (THz, 1THz=1012Hz) waves, typically covering 0.1–10 THz, occupy the transitional region of the electromagnetic spectrum between electronics and photonics [1]. THz technology has garnered significant attention due to its unique characteristics and potential applications in imaging, non-destructive testing, biomedicine, and next-generation wireless communications [2–5]. The burgeoning development of THz technology is impossible without the breakthrough of THz functional devices, such as THz modulators [6,7], polarization converters [8,9], isolators [10,11], filters [12,13], and switches [14,15]. The performance of these devices commonly depends on the strength of light-matter interactions, which manifest as a high-quality (Q) factor resonance. However, natural materials usually enable a relatively weak interaction with THz radiations, and the devices are severely limited by the large volume and losses.

The concept of bound states in the continuum (BICs) has attracted considerable attention in optics and photonics, owing to their infinite photon lifetime and Q-factors in theory [16–24]. BICs show great promise for enhancing light-matter interactions, and they have been widely studied in optical sensing, nonlinear optics, and filters [25–29]. However, BIC is a state whose energy is completely bound to the resonant system and thus uncouples to free space. There are two typical categories of BIC, one is symmetry-protected BIC and the other is accidental BIC [30,31]. By breaking the symmetry of the structure, the symmetry-protected BIC shifts to a leaky mode with limited Q-factor and resonant bandwidth, which is called a quasi-BIC [32–34]. Metamaterials provide a reliable platform for the study of quasi-BIC, and different types of unit cells have been found to support quasi-BIC, such as circular and square split ring resonators [17,35], tilted elliptic strip pairs [36,37], and nanodisks with holes [38]. In our previous work, Cong and Singh [39] demonstrated dual BICs in a symmetry-protected square split ring metamaterial, and the quasi-BIC is experimentally observed in the THz spectrum by slightly breaking the C2 symmetry with large Q-factors. Nevertheless, once the structural parameters of these BICs or quasi-BICs are determined, it is difficult to realize the active control of the device.

Recently, active control of optical resonances has been highly desired in various THz application scenarios, such as THz sensing, switching, and wireless communications. The incorporation of the tunable materials with metamaterial or metasurfaces provides an efficient approach for achieving active THz quasi-BIC devices. The active control mechanism is mainly attributed to perturbations induced by phase transition, change of electrical conductivity, or refractive index, which are induced by external stimuli. Tunable functional materials can fill in gaps of resonators or be designed directly as metamaterials, including graphene [21,40,41], phase-transition materials [42,43], and semiconductors [44–48]. For example, Hu et al. [49] reported a BIC-mediated reconfigurable metamaterial for spatiotemporal lineshape tailoring, and the symmetry of the structure was broken by introducing VO2 into the split ring resonators. Dynamic control of the device was realized under optical pumping. In particular, the LC possesses large birefringence and low absorption loss in the THz regime, and its orientation can be actively controlled by the external electric field, magnetic field, or light field, which is a very promising active material in the THz band. Nowadays, the LC-based metasurface has attracted extensive attention for its superiority in flexible control of electromagnetic waves [50–52].

In this work, we experimentally demonstrate an LC-integrated metasurface for THz quasi-BIC modulation and asymmetric transmission induced by polarization conversion. The quasi-BIC resonance is supported by an asymmetric double-gap split ring resonator, but behaves as a non-resonant state in the orthogonal polarization excitation. Therefore, we could switch on and off the quasi-BIC by manipulating the incident polarization of THz waves. Here, we propose a configuration of an LC-integrated metasurface, where dynamic polarization rotation is realized by the LC layer actuated by an external voltage. Furthermore, our proposed LC-integrated metasurface is capable of asymmetric transmission with the active isolation degree by changing the external field. This work provides a new paradigm for active quasi-BIC devices, which could be applied to THz communication, switching, and sensing systems.

The radiation properties of BIC have been thoroughly studied in recent works from symmetry and reciprocal space of the unit cells. It is indeed helpful to understand the intrinsic properties of BIC or quasi-BIC; however, the radiation will be fixed once the structure is fabricated. An effective strategy is thus necessary to tune the mode properties, and polarization offers an external freedom. We propose an LC-integrated metasurface supporting quasi-BIC where LC layers play the role of polarization controller. Figure 1(a) shows the schematic diagram of the configuration where the LC layer is actuated by two graphite electrodes. A constant magnetic field (M-field) is applied along the u-axis to anchor the LC molecules, so that the orientation control of LC molecules is possible in the u–z plane with the electric field along the z-axis.

The working principles of the LC layer and tunable quasi-BIC are shown in Figs. 1(b) and 1(c). LC molecules will be driven by an external electric field along the z-axis when the actuation voltage is higher than the threshold, and gradually shifted back to the x-y plane along the M-field direction with an intermediate state when the actuation voltage decreases. The shift of LC molecule orientation will lead to the modulation of the polarization state of light transmitting through the layer. With a high voltage, incident polarization conserves due to the isotropic response of the LC layer, while the polarization state is rotated by 90° without external electrical actuation. The polarization rotation will lead to the switch ON and OFF states of quasi-BIC whose response is polarization dependent. As manifested from the schematic diagram of the transmission spectra, the quasi-BIC resonances will experience the modulation in Fig. 1(c).

Figure 2(a) shows a unit cell of the proposed metallic metasurface, which is a typical subwavelength double-gap split ring resonator (DSRR). Here, DSRR was fabricated by traditional photolithography, and it has a uniform period of p=73μm; the inside diameter of the circular ring is r=25μm, the width is d=5μm, and the gap is g=3μm. In particular, we define an angle α representing the degree of asymmetry, and α=0° means the open ring is located in the middle of the DSRR, in which case the BIC mode of symmetry protection is supported. The photonic band and analysis of the BIC mode can be found in Appendix A. The transition from BIC to quasi-BIC resonance is realized by breaking the C2 symmetry of the structure with the increased α. Under y-polarization excitation, the BIC to quasi-BIC responses of DSRR with different α were obtained, and the experimental and simulated THz transmission spectra are shown in Fig. 2(b) and Fig. 2(c), respectively. In order to observe quasi-BIC more easily in experiments, we chose a relatively large asymmetric breaking angle here. An obvious Fano resonance in the THz spectra was observed with α of 15°, 30°, and 45°, while the resonance cannot be captured for symmetric structure with α=0°. The experimental results match well with the simulations. A standard THz time-domain spectral (THz-TDS) system was employed to conduct the THz experiments. The detailed experiments and device fabrication procedures can be found in Appendix B and Appendix C. The numerical simulations were carried out based on the finite element method using commercially available software (COMSOL Multiphysics). In simulations, the silicon substrate was modeled as a lossless material with a permittivity of 11.7. The metallic part of DSRR was set as a perfect electrical conductor (PEC) to calculate the eigenmode and radiative Q-factors, and modeled as aluminum with a conductivity of 3.56×107S/m for the frequency-domain solver. Periodic boundary conditions were set in the x- and y-directions, while the z-direction was set as a perfectly matched layer (PML).

Based on the analysis of the eigenmode in the simulations, the Q-factors of the quasi-BIC were extracted in Fig. 2(d). According to Ref. [53], the total Qtot can be decomposed into the radiative Qrad and resistive Qres, which follows as Qtot (1/Qtot=1/Qrad+1/Qres). Here, the total Qtot equals Qres for the DSRR modeled as PEC without the resistive loss, and it shows a clear diverging trend to infinity at α=0°. The extracted Q-factors have a good match with the theoretical fitting of the inverse square equation. According to the Fano lineshape equation, the experimental Qtot can be obtained from the transmission spectra in Fig. 2(b), but the experimental value of Q-factors is lower than the simulations due to the extra contribution of both radiative and non-radiative losses. In addition, we show the surface current distributions of DSRR with different asymmetry degrees in Figs. 2(e)–2(g). Under the y-linear polarization excitations, the current distribution of the two arms of DSRR (α=0°) is symmetrical with equal intensity and reversed direction, and then it is an obvious dipole resonance mode [36]. For the DSRR with α=30°, a Fano resonance appears at 0.56 THz with annular current distribution and symmetry-broken intensity [Fig. 2(f)], which allows a channel to couple with the incident radiation (quasi-BIC). In addition, the current distribution at 0.8 THz presents an inverted but asymmetric intensity distribution, as shown in Fig. 2(g). As a result, the quasi-BIC mode was achieved by the symmetry breaking in DSRR, and the evolution can be clarified from the surface current distributions.

The birefringence characteristics of the independent LC layer were experimentally probed with external actuation of electric and magnetic fields [54], as illustrated in Fig. 3(a). Here, we adopted the LC named NC-M-LC-LDn03 (Nanjing Ningcui Optical Technology Co., Ltd.) with a thickness of 1 mm. The adjustable voltage is applied through graphite electrodes. The graphite layer has a thickness of 2.4 μm, and it has a high transmission of nearly 90% [52], so the graphite electrode has little impact on the overall transmittance of the device. A constant M-field of 0.17 T is applied to uniformly orient the LC molecules. We measured the THz time-domain spectra when LC is oriented along the y-axis or z-axis, and the effective refractive index of ne and no can be achieved under the y-linear polarization incidence. Figure 3(b) shows the time-domain spectra with different LC orientations, and the LC-y signal lags significantly behind that of LC-z. Based on the Fourier transform of the time-domain signal, we obtain the refractive index of no=1.53 and ne=1.81, as well as the phase difference spectrum as shown in Fig. 3(c). A specific phase difference of Δφ=π was realized at 0.56 THz.

Due to the limitations of the experimental THz testing system, it is difficult to capture the BIC modes with extremely high Q-factors; therefore we choose the symmetry-broken DSRR with α=30° as the basic quasi-BIC structure in the following discussion. The microscope image of DSRR is presented in Fig. 3(d). To illustrate the effect of polarization conversion in the LC-integrated metasurface, the transmittance spectra of DSRR under two orthogonal polarizations are given in Figs. 3(e) and 3(f). Different from the Fano resonance that occurs at 0.56 THz and supports a quasi-BIC mode, DSRR under x-polarization behaves as a non-resonant spectrum at this frequency (0.56 THz), which brings the possibility of switching quasi-BIC induced by the LC polarization conversion.

To analyze the polarization-induced THz quasi-BIC modulation in an LC-integrated metasurface, the experimental setup was designed with two polarizers, as shown in Fig. 4(a). The first polarizer P1 was fixed to ensure that the incident light is linear polarization along the x-axis, while the second polarizer P2 can be rotated to detect the parallel polarization component (Txx) and the crossed polarization component (Tyx). Here, Tij stands for the polarization components of the i-polarized output induced by j-polarized incidence (i,j=x,y). Figures 4(b) and 4(c) illustrate the working principle of polarization state conversion and induced resonance in the decomposed structure of an LC-integrated metasurface. In the case when LC is along the z-axis driven by the high voltage, LC has no polarization conversion effect on the incident light, and the device appears as a non-resonant state (at 0.56 THz) output from DSRR in Fig. 4(b), which is consistent with the red line in Fig. 3(e). When an external voltage is switched off, LC is bound to the M-field along the u-axis direction with an angle of 45° relative to incident polarization. Based on classical polarization optics, the polarization state will be converted to y-linear polarization when Δφ=π. If the frequency of polarization rotation matches with the quasi-BIC, the quasi-BIC resonance will be excited, which is depicted in Fig. 4(c).

Based on the polarization testing setup, the experimentally measured Txx and Tyx under different actuation voltages were obtained as shown in Figs. 4(d)–4(g). At forward incidence [+z direction, expressed as →LC-DSRR→, the same configuration as shown in Fig. 4(a)], the unconverted Txx component first appears as a flat non-resonant state at a high voltage of 170 V, and then drops off with the decreased voltage, finally forming a transmittance valley, as shown in Fig. 4(d). On the contrary, the transformed Tyx component gradually increases with the decreased voltage, and it results from the polarization conversion during the LC-orientation changes from the z-axis to the u-axis. Notably, the resonance valley (quasi-BIC state) is still retained in the transmittance spectra, which is consistent with the diagram in Fig. 4(c). Therefore, the active modulation of quasi-BIC is achieved in the LC-integrated metasurface. In addition, we studied the Txx and Tyx in the situation of backward incidence (−z direction, expressed as ←LC-DSRR←) in Figs. 4(f) and 4(g). We can observe that the unconverted Txx component in Fig. 4(f) basically coincides with Fig. 4(d), but the transformed Tyx component differs greatly compared with Figs. 4(e) and 4(g). Based on the difference of the converted Tyx component in forward and backward incidence, the LC-integrated metasurface is expected to achieve asymmetric transmission. The perturbation in the transmittance spectrum is primarily influenced by the dispersion of the introduced LC material and the machining accuracy of the DSRR metasurface.

As mentioned above, the LC-integrated metasurface exhibits completely different Tyx transmission spectra between the forward incidence and backward incidence. To clearly illustrate the physical mechanism of asymmetric transmission in the LC-integrated metasurface, here we show the transmission schematic diagram of the device in Figs. 5(a) and 5(b). For the forward incidence, a linear polarization incident along the x-axis will be converted to the cross-polarization along the y-axis at the frequency of Δφ=π, and then induces Fano resonance by DSRR, which is shown as the quasi-BIC state in Fig. 5(a). As to the backward incidence, the linear polarization along the x-axis first excites DSRR and appears as a non-resonant state, and then is transmitted through the LC layer, but the polarization conversion of the LC layer does not change the resonance state, only the amplitude modulation. Therefore, a non-resonant spectrum was observed from backward incidence, as shown in Fig. 5(b). The measured transmittance spectra from forward and backward incidence with different voltages are depicted in Figs. 5(c)–5(f). In our design, a voltage equal to zero indicates the strongest polarization conversion ability of the LC layer, and the maximal isolation of 9.8 dB is achieved at 0.56 THz when no voltage is applied to the device, as shown in Fig. 5(c). Here, the isolation of asymmetric transmission is defined: ΔTisolation=Tforward−Tbackward. With the increase of voltage, the device gradually loses the polarization conversion effect, which then results in the decrease of asymmetric transmission. The isolation of 1.9 dB is realized when the voltage is 150 V, which could be regarded as symmetric transmission at this state. Therefore, the active control of asymmetric transmission was achieved by adjusting LC orientation under the external field in the LC-integrated metasurface. In this work, the insertion loss of the device primarily originates from the LC layer, and reducing the thickness of the LC layer may result in a decrease in insertion loss. It is possible to adjust the structural parameter of DSRR to a smaller scale to match the thinner LC layer. In addition, the isolation of asymmetric transmission is correlated with the Q-value of the symmetric broken DSRR; therefore, employing a smaller symmetry broken angle with a higher Q-value can effectively enhance device isolation.

In conclusion, active modulation of quasi-BIC resonance has been experimentally demonstrated through polarization rotation without reconfiguring the structural parameters of resonators. An LC-integrated metasurface was proposed where the LC layer behaves as the polarization conversion and a DSRR metasurface supports a symmetry-broken quasi-BIC resonance. Due to the anisotropic properties of the metasurface, orthogonal polarization of incident light will induce contrasting transmitting responses that form the basis of active modulation via electrically and magnetically actuated LC layers. The combination of polarization rotation and quasi-BIC resonance also enables the asymmetry transmission with a maximal isolation of 9.8 dB between forward and backward incidence, which is also adjustable by external voltage. The isolation of asymmetric transmission of the device can be further improved if a high-Q structure with smaller perturbations is used. Moreover, the metallic metasurface in the composite device also can be substituted by other asymmetry-broken structures. The proposed LC-integrated metasurface configuration offers a powerful platform to study the functional devices in THz applications, which would benefit the next-generation wireless communications and single-pixel imaging.