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Abstract
The exceptional resonances excited by symmetry-protected quasi-bound states in the continuum (QBICs) have provided significant potential in high-sensitive sensing applications. Herein, we have proposed a type of metal-insulator-metal (MIM) absorbers supported by QBIC-induced resonances, and the ideal Q-factors of QBIC-induced resonances can be enhanced up to 105 in the THz regime. The coupled mode theory and the multipole scattering theory are employed to thoroughly interpret the QBIC-induced absorption mechanism. Furthermore, the refractive index sensing capacities of the as-presented absorbers have been investigated, where the maximum values of the sensing sensitivity and figure of merit (FOM) can reach up to 187 GHz per refractive index unit and 286, respectively. Therefore, it is believed that the proposed absorbers enabled by QBIC-induced resonances hold promising potential in a broad range of highly demanding sensing applications.
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1. Introduction
Engineering metamaterials/metasurfaces with high quality-factors (Q-factors) has recently drawn considerable attention in the fields of modulators [1], refractive index sensors [2–8], and other optical devices [9–12]. Among all varieties of optical applications, the refractive index sensors with high Q-factors could significantly enhance the light-matter interaction and thus realize high sensing sensitivity and figure of merit (FOM) [13]. Thus, numerous strategies have been proposed to obtain high Q-factors, such as toroidal dipolar excitation [10,14], and electromagnetically induced transparency (EIT) [15–17]. For instance, Yang et al. [16] have experimentally elucidated that a Si-based metasurface possessed sharp EIT-like resonances with a Q-factor over 483, which is attributed to the low absorption loss and coherent interaction of neighboring meta-atoms. Leng et al. [18] have reported that an all-dielectric metamaterial reached a high Q-factor of more than 270 by the efficient modulation of Fano resonance. Nonetheless, many of the abovementioned approaches generally focus on all-dielectric metamaterials based on Fano-like resonances and do not utilize metallic materials due to their inevitable intrinsic ohmic losses. It can be seen that the Q-factors remain in the order of hundreds and far away from the alluring upper limit thus new strategies are highly desirable to effectively ameliorate the Q-factors owing to ohmic losses.
The concept of bound states in the continuum (BICs) originated from quantum mechanics [19], has gained enormous attraction in recent years due to its simpleness and effectiveness to excite ultra-sharp resonances. Ideal BICs are non-radiating eigenmodes embedded in the radiation continuum and featured with infinite Q-factors and vanishing bandwidth, which can only occur in the lossless infinite cavities or structures with zero or infinite permittivity. Fortunately, by creating a leakage channel through symmetry-breaking perturbations, ideal symmetry-protected BICs can be transformed into quasi-BICs (QBICs) that generate QBIC-induced resonances with finite but nontrivially high Q-factors. Inspired by this physical mechanism, a bunch of QBIC-induced metamaterial with high Q-factors involving not only all-dielectric [14,20–32] configurations but also all-metal [33–40] and metal-dielectric [41–45] configurations have been widely explored. However, the metal-dielectric-metal (MIM)-based metamaterial absorbers with ultrahigh Q-factors remain less explored.
In this work, an MIM-based terahertz (THz) absorber empowered by QBIC-induced resonance has been proposed, where the resonance is excited by the third fundamental family of electromagnetic multipoles, i.e., the toroidal dipoles. By breaking the C2-symmetry of proposed meta-molecules that consist of a pair of bar-like meta-atoms, an extremely sharp resonant peak can be obtained. Two variants consisting of all-metal and four bar-like configurations have been further explored, respectively. Comprehensive methods including the multipole extension theory and coupled mode theory are employed to unveil the underlying mechanism of QBIC-induced resonances. Finally, the refractive index sensing capacities of proposed MIM absorbers are numerically investigated, where the sensitivity and FOM are quantified by divergent analytes. It is believed that this work might provide an alternative pathway to engineering high-sensitive sensors and hold promising potential in biosensing applications.
2. Structure design
The schematic in Fig. 1 illustrates the geometrical dimension of the designed MIM THz absorber. It consists of a periodic array of meta-molecules (Fig. 1(a)), which are composed of a pair of bar-like meta-atoms as shown in Fig. 1(b), where Px = 4Sx = 350 µm, Py = 4Sy = 320 µm, H = 25 µm, L = 100 µm, W = 35 µm, and Δx is the adjustable asymmetry parameter. A gold layer with the conductivity of 5.61 × 107 S/m is deposited on the silicon substrate, and the bar-like meta-atom is formed by a resin cuboid with the relative permittivity of ɛr = 2.85(1-0.08j) at 1 THz [46] and covered by another gold layer on the top. With a thickness (200 nm) higher than the skin depth in the frequency range of interest, the downward gold layer serves as a back-reflector to prohibit the THz transmission, therefore, the absorption A(ω) can be simply derived from the reflection R(ω) as A(ω) = 1 - R(ω). In this work, the absorbers are investigated under normal incidence by the y-polarized THz waves unless otherwise specified. The unit-cell boundary condition is applied to the x- and y-directions while the open boundary condition is utilized to the z-direction in the CST Studio Suite software. The meta-atom in the bottom-left corner remains fixed while the meta-atom in the top-right corner varies its position along the x-axis by Δx to break the C2-symmetry in which case the meta-molecule can no longer overlap with the original structure after a π rotation along any axis in the x-y surface plane.
Fig. 1. Schematics of the (a) absorber on the silicon substrate and (b) its meta-molecules consisting of a pair of bar-like meta-atoms, where Px = 4Sx = 350 µm, Py = 4Sy = 320 µm, H = 25 µm, L = 100 µm, W = 35 µm, and Δx is the adjustable asymmetry parameter.
3. Results and discussions
To unveil the phenomenon of QBICs, the absorption spectra of the absorber for divergent Δx under normal incidence are evaluated as depicted in Fig. 2(a). It can be observed that a resonant peak around 0.9-1.0 THz remains rather robust when Δx changes, while another sharp resonant peak induced by QBICs emerges at 1.2 THz. The frequency range (1.20-1.30 THz) of interest is individually extracted for a clear illustration. In Fig. 2(b), when Δx = 0 under which the meta-molecules possess C2-symmetry, there is no resonance at all, which agrees well with the common attribute of symmetry-protected BICs. However, when |Δx| gradually increases, the resonant peak gradually arises with expanded linewidth and experiences an incremental blueshift in the absorption spectra. In addition, further destroying the symmetry promotes the emergence of a high-order resonant peak governed by QBICs at 1.265 THz with extremely narrow bandwidth. As a comparison, the ideal absorber is analyzed by replacing the real gold layer with the lossless perfect electrical conductor (PEC), and its absorption spectra supported by QBICs are depicted in Fig. 2(d). The ideal PEC absorber and the real golden absorber have trivial differences except for the shrunk bandwidths of the PEC absorber. Next, their respective radiative quality factors (Qr) are calculated by (see Supplement 1 for detailed derivations):
Fig. 2. (a) The absorption spectra of the THz absorber for different Δx. The zoom-in absorption spectra at the QBICs-based resonance of the absorbers for (b) the real golden case and (d) lossless PEC case, respectively, where the stars highlight the BICs with a vanishing resonance. (c) The radiative quality factors (Qr) of two absorbers for various Δx, where the cyan curve represents the fitted results for the PEC case.
Next, the underlying physical mechanism of the phenomenon can be interpreted by the temporal coupled mode theory (CMT) model [49]. The absorber can be seen as a one-port single-mode system since the transmission is prohibited, which can be consequently described as:
To gain further insight into the properties of QBIC-supported resonances, the underlying mechanism of the resonance is also investigated through a comprehensive method. Here Δx = 30 µm is selected as an instance. The near field distributions of the meta-molecule at the resonant frequency ω0 = 1.22 THz, including electric fields and surface currents, are illustrated in Fig. 4(a). Enormous charges with opposite signs accumulate at two ends of each meta-atom, which implies the excitation of electric dipoles. Meanwhile, as the arrows indicate, surface currents loop clockwise and anticlockwise on the top of two meta-atoms, respectively, which forms a pair of anti-parallel magnetic dipoles. Previous studies have reported that such anti-parallel magnetic dipoles can further excite toroidal dipolar resonance [50]. Afterward, magnetic vectors are monitored at the resonant frequency in the x-z plane in Fig. 4(b). A clear magnetic loop can be noticed, which suggests the toroidal dipole is exactly excited. In general, multiple dipoles can be observed, but it is difficult to distinguish major components that excite the resonance merely through near-field analysis. To quantitatively evaluate the domain contributions of the QBIC-induced resonance, multipole scattering theory [51–53] that reflects the scattered power for various multipole moments is employed. We extract the current density of meta-atoms in the frequency range of 1.175 to 1.250 THz from CST simulations, then calculate the normalized scattered power magnitudes of electric dipole (P), magnetic dipole (M), toroidal dipole (T), electric quadrupole (Qe), and magnetic quadrupole (Qm) as shown in Fig. 4(c). (More details about scattered power calculation are summarized in Supplement 1.) The location of the maximum strength is consistent with the resonant frequency (1.22 THz). In addition, the electric dipole is suppressed near the resonant frequency while the toroidal dipole, in particular the subcomponent Ty displayed in the inset, primarily dominates the resonance, which further corroborates that the sharp resonance mainly originates from the toroidal dipolar excitation.
Fig. 3. The (a) amplitudes of absorption and (b) phase variation at ω0 concerning γr and γd. The (c) absorption and (d) phase spectra comparison of the simulated (solid lines) and calculated (dots) results. The inset in panel (c) is the enlarged view at the resonant frequency. The calculated γr and γd corresponding to Δx from 15 to 40 µm extracted from the spectra through CST are marked in panels (a) and (b).
Fig. 4. (a) The distributions of the electric field of the meta-molecule and the surface currents on the top of meta-atoms at the resonant frequency ω0 = 1.22 THz. (b) The arrows show the magnetic vectors in the x-z plane. (c) Calculated normalized scattered powers of electric dipole (P), magnetic dipole (M), toroidal dipole (T), electric quadrupole (${\textrm{Q}_\textrm{e}}$), and magnetic quadrupole (${\textrm{Q}_\textrm{m}}$), where the inset portrays the specific subcomponents of the toroidal dipole. The asymmetry coefficient Δx is 30 µm.
Aiming at expanding the functionality of the QBIC-supported THz absorber, a variant absorber (variant-I) is proposed by supplementing another pair of meta-atoms but orientated along the x-axis while other parameters remain unchanged. As depicted in Fig. 5(a), the meta-atom in the top-left corner keeps fixed as the meta-atom in the bottom-right corner moves along the y-axis by Δx. It should be noted that the right two meta-atoms vary their location simultaneously. Except for the abovementioned y-polarized incidence, variant-I is also capable of resonating under x-polarized illumination. As displayed in Fig. 5(b), the left (right) half of the panel denotes the QBIC-supported absorption spectra at various Δx from −30 to 30 under y-polarized (x-polarized) THz waves. Consistent trends can be observed even though the resonant frequency under x-polarized incidence is higher, which can be ascribed to the nearer distance between the new pair of meta-atoms. Similarly, the radiative quality factors are also calculated under both polarized incidences for the real gold and the ideal PEC absorbers. As shown in Fig. 5(c) and 5(d), the ideal PEC absorber possesses a higher Qr than the gold absorber under either x- or y-polarized waves and coincides well with the inverse quadratic law with Qr = 7.10 × 105Δx−2 + 96.89 and Qr = 4.59 × 105Δx−2 + 298.15, respectively. To provide deep insight into the mechanism of the resonances, the normalized scattered powers are calculated through multipole scattering theory under x- (Fig. 5(e)) and y-polarized (Fig. 5(f)) incidence. Here the asymmetry parameter Δx is set as 30 µm. The scattered power analysis in Fig. 5(f) has great accordance with that in Fig. 4(c) and the little difference can be attributed to the surface currents on the newly added metamorphic meta-atoms. Under x-polarized incidence as portrayed in Fig. 5(e), magnetic quadrupole (Qm) dominates the resonance. The multipole scattering provides a powerful platform for not only distinguishing the contributions from multiple types of dipoles but also elucidating the radiative patterns that may not be explicitly observed by near-field analysis in complicated scenarios.
Fig. 5. Variant-I. (a) The schematic of its meta-molecule. (b) The QBIC-exerted absorption spectra at various Δx under y-polarized (left panel) and x-polarized (right panel) incidence, respectively. Radiative quality factors of the real gold case and ideal PEC case under (c) x-polarized and (d) y-polarized illumination as Δx = 30. The normalized scattered power magnitudes of multipoles under (e) x-polarized and (f) y-polarized THz incidence, and the insets indicate the subcomponents of the toroidal dipole.
Another variant absorber (variant-II) shares the same geometric parameters as the first proposed MIM absorber, whereas the meta-molecule becomes all-metallic as portrayed in Fig. 6(a). It can be observed that the low order resonance around 0.9-1.0 THz in Fig. 2(a) disappears, and only the QBIC-induced absorption can be observed in Fig. 6(b). As |Δx| decreases from 60 to 30 µm, the absorption amplitude, and the resonance bandwidth incrementally diminish until Δx = 0 where no resonance can be found in this frequency range. Hence, the QBICs are turned back into the BIC with the rebuilt C2-symmetry. In Fig. 6(c), substantial enhancements for radiative Q-factors are noticed compared to the MIM absorber, which is owing to the small dissipative losses through the removal of dielectric resin. The scattered power of variant-II at Δx = 30 µm follows a similar law as the MIM absorber as shown in Fig. 6(d).
Fig. 6. Variant-II. (a) The schematic of the meta-molecule of variant-II. (b) The absorption amplitude and (c) radiative Q-factors at various $\mathrm{\Delta x}$. (d) The scattered power of variant-II when Δx = 30 µm; and the inset shows the subcomponent of power of the toroidal dipole.
Ultimately, the abovementioned MIM absorber and its two variants are employed as refractive index sensors to further explore their potential application. Herein Δx = 30 is chosen to make a general demo, and it may not be the most optimal for the sensing performance. The working principle for the sensing application is schematically plotted in Fig. 7(a), where a thin dielectric analyte film covers the sensor. In general, temperature variations, biological reactions, and ingredient types all contribute to the changes in the refractive index (n) of analyte samples. Initially, the thickness of the analyte film is set as 20 µm, while its n varies from 1.0 to 2.0. All resonant peaks undergo noticeable redshifts and the frequency shifts as a function of n for these sensors are depicted in Fig. 7(b), where the variant-I is analyzed under both x- (red) and y-polarized (blue) incidence. The frequency shifts can be well fitted by the linear lines, hence, the sensitivity S can be calculated as:
where f and f0 represent the resonant frequency for each refractive index and n = 1. The inset illustrates four groups of sensitivity of three sensors, incorporating the MIM sensor and variant-II under y-incidence as well as variant-I under both x- and y-polarized incidence. Around 142.7 GHz/RIU at least (MIM sensor) can be achieved while the maximum sensitivity (variant-II) can reach up to 187.1 GHz/RIU. Moreover, we adjust the thickness of the analyte with its refractive index fixed at 1.5 to investigate the sensitivity (S = df/dt) of sensors at various thicknesses t. As shown in Fig. 7(c), the sensitivity follows clear linearity with respect to the thickness of the analyte. Little difference in sensitivity can be found from the minimum of 6.86 GHz/μm to the maximum of 7.01 GHz/μm, which suggests that the sensors keep robust in sensing the analyte with the thickness variation. The figure of merit (FOM) is an essential metric that can be calculated as:Fig. 7. (a) The schematic of the sensing application setup where the sensor is covered by a layer of thin analyte film. The frequency shift and sensitivity of the sensors at various (b) refractive indices and (c) thicknesses. (d) The FOM of sensors with the thickness of analyte set as 20 µm.
For all sensors as shown in Fig. 7(d), when the refractive index of the analyte increases, the bandwidth of the resonance gets wider, thus leading to the decrease of FOM. Variant-II has the largest FOM than that of other sensors, which is similar to the observation of the radiative Q-factors and can be attributed to the narrow bandwidth at the resonance. The appealing FOMs with an average of 10, 26, 13, and 286 are achieved and the sensing performance can be further enhanced by choosing the optimal Δx. Finally, several key parameters of recently proposed THz sensors, including the structures, materials, operating frequencies, and sensing performance, have been intuitively listed in Table 1 to briefly compare their sensing capabilities. In Table 1, Ref. [54] shows an ultra-high sensitivity of 1900 GHz/RIU and a high FOM value of 229, due to the natural advantages of metal surface plasmons that are sensitive to the changes in the dielectric medium. However resonant amplitudes dramatically decrease to less than a half, which suggests the robustness needs to be further enhanced. Overall, our suggested sensors simultaneously exhibit great competence and palpable superiority in the sensitivity and FOM among recent THz sensors, which renders QBIC-supported absorbers featuring high Q-factors pave an effective avenue to engineer high-performance sensors.
Table 1. Comparison of several terahertz absorbers for sensing applications.
4. Conclusion
In summary, we have theoretically demonstrated that the QBIC-induced phenomenon promotes high Q-factors which is attractive to develop exhilarating THz absorbers. We thoroughly investigate the Q-factors of the MIM absorber and its two variants at various Δx, and the Qr at the order of 105 can be achieved by tuning the asymmetry parameters. The underlying physical mechanisms have been investigated by employing the coupled mode theory, near-field analysis, and the multipole scattering theory. Benefiting from the highly enhanced light-matter interaction, the absorbers can achieve ultrahigh sensing ability with a maximum sensitivity of 187.1 GHz/RIU and FOM of 285.8, respectively. Our proposed design provides great advantages and it can be estimated that the proposed QBICs-induced absorbers might boost promising development in highly sensitive THz sensing.
Funding
Natural Science Foundation of Zhejiang Province (LZ19A020002); National Natural Science Foundation of China (51805414, 52175115).
Disclosures
The authors declare no conflicts of interest.
Data availability
Date underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. K. Liu, C. R. Ye, S. Khan, and V. J. Sorger, “Review and perspective on ultrafast wavelength-size electro-optic modulators,” Laser Photonics Rev. 9(2), 172–194 (2015). [CrossRef]
2. A. H. Aly and Z. A. Zaky, “Ultra-sensitive photonic crystal cancer cells sensor with a high-quality factor,” Cryogenics 104, 102991 (2019). [CrossRef]
3. M. Askari, H. Pakarzadeh, and F. Shokrgozar, “High Q-factor terahertz metamaterial for superior refractive index sensing,” J. Opt. Soc. Am. B 38(12), 3929 (2021). [CrossRef]
4. J. Chen, W. Fan, T. Zhang, C. Tang, X. Chen, J. Wu, D. Li, and Y. Yu, “Engineering the magnetic plasmon resonances of metamaterials for high-quality sensing,” Opt. Express 25(4), 3675–3681 (2017). [CrossRef]
5. Y. Zhang, W. Liu, Z. Li, Z. Li, H. Cheng, S. Chen, and J. Tian, “High-quality-factor multiple Fano resonances for refractive index sensing,” Opt. Lett. 43(8), 1842–1845 (2018). [CrossRef]
6. W. Xiao, Y. Ou, S. Wang, S. Wang, Y. Meng, X. Zhai, S. Xia, and L. Wang, “Ultra-high sensitivity terahertz sensor based on a five-band absorber,” J. Opt. 24(5), 055102 (2022). [CrossRef]
7. Z. Shen, L. Zhang, and X. Chen, “Monolayer crumpled graphene-based mechanically and electrically tunable infrared absorbers for high-sensitivity sensing,” Opt. Laser Technol. 153, 108265 (2022). [CrossRef]
8. S. Li, L. Zhang, and X. Chen, “3D-printed terahertz metamaterial absorber based on vertical split-ring resonator,” J. Appl. Phys. 130(3), 034504 (2021). [CrossRef]
9. X. Fang, L. Xiong, J. Shi, and G. Li, “High-Q quadrupolar plasmonic lattice resonances in horizontal metal-insulator-metal gratings,” Opt. Lett. 46(7), 1546–1549 (2021). [CrossRef]
10. Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-Quality-Factor Mid-Infrared Toroidal Excitation in Folded 3D Metamaterials,” Adv. Mater. 29(17), 1606298 (2017). [CrossRef]
11. X. Ji, S. Roberts, M. Corato-Zanarella, and M. Lipson, “Methods to achieve ultra-high quality factor silicon nitride resonators,” APL Photonics 6(7), 071101 (2021). [CrossRef]
12. B. Zhang, J. Hendrickson, N. Nader, H.-T. Chen, and J. Guo, “Metasurface optical antireflection coating,” APL Photonics 105, 241113 (2014). [CrossRef]
13. A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6(1), 8069 (2015). [CrossRef]
14. H. Li, S. Yu, L. Yang, and T. Zhao, “High Q-factor multi-Fano resonances in all-dielectric double square hollow metamaterials,” Opt. Laser Technol. 140, 107072 (2021). [CrossRef]
15. T. Chen, T. Xiang, J. Wang, T. Lei, and F. Lu, “Double E-shaped toroidal metasurface with high Q-factor Fano resonance and electromagnetically induced transparency,” AIP Adv. 11(9), 095011 (2021). [CrossRef]
16. Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5(1), 5753 (2014). [CrossRef]
17. W. He, X. A. Cheng, M. Tong, and Y. Hu, “Molecularization of meta-atoms for electromagnetically induced transparency resonance and quality-factor switching,” Opt. Express 29(26), 42607–42620 (2021). [CrossRef]
18. J. Leng, J. Peng, A. Jin, D. Cao, D. Liu, X. He, F. Lin, and F. Liu, “Investigation of terahertz high Q-factor of all-dielectric metamaterials,” Opt. Laser Technol. 146, 107570 (2022). [CrossRef]
19. H. Friedrich and D. Wintgen, “Interfering resonances and bound states in the continuum,” Phys. Rev. A 32(6), 3231–3242 (1985). [CrossRef]
20. S. Han, L. Cong, Y. K. Srivastava, B. Qiang, M. V. Rybin, A. Kumar, R. Jain, W. X. Lim, V. G. Achanta, S. S. Prabhu, Q. J. Wang, Y. S. Kivshar, and R. Singh, “All-Dielectric Active Terahertz Photonics Driven by Bound States in the Continuum,” Adv. Mater. 31(37), 1901921 (2019). [CrossRef]
21. W. Cen, T. Lang, J. Wang, and M. Xiao, “High-Q Fano Terahertz resonance based on bound states in the continuum in All-dielectric metasurface,” Appl. Surf. Sci. 575, 151723 (2022). [CrossRef]
22. X. Chen and W. Fan, “Tunable Bound States in the Continuum in All-Dielectric Terahertz Metasurfaces,” Nanomaterials 10(4), 623 (2020). [CrossRef]
23. Y. Wang, Z. Han, Y. Du, and J. Qin, “Ultrasensitive terahertz sensing with high-Q toroidal dipole resonance governed by bound states in the continuum in all-dielectric metasurface,” Nanophotonics 10(4), 1295–1307 (2021). [CrossRef]
24. K. Koshelev and Y. Kivshar, “Dielectric Resonant Metaphotonics,” ACS Photonics 8(1), 102–112 (2021). [CrossRef]
25. Q. Wang, J.-X. Jiang, L. Wang, X.-Y. Yin, X. Yan, A. Zhu, F. Qiu, and K.-K. Zhang, “An asymmetric grating refractive index sensor generating quasi-bound states in the continuum with high figure of merit and temperature self-compensation,” J. Phys. D: Appl. Phys. 55(15), 155103 (2022). [CrossRef]
26. S. Xiao, X. Wang, J. Duan, T. Liu, and T. Yu, “Engineering light absorption at critical coupling via bound states in the continuum,” J. Opt. Soc. Am. B 38(4), 1325–1330 (2021). [CrossRef]
27. A. Ndao, L. Hsu, W. Cai, J. Ha, J. Park, R. Contractor, Y. Lo, and B. Kanté, “Differentiating and quantifying exosome secretion from a single cell using quasi-bound states in the continuum,” Nanophotonics 9(5), 1081–1086 (2020). [CrossRef]
28. W. Shi, J. Gu, X. Zhang, Q. Xu, J. Han, Q. Yang, L. Cong, and W. Zhang, “Terahertz bound states in the continuum with incident angle robustness induced by a dual period metagrating,” Photonics Res. 10(3), 810–819 (2022). [CrossRef]
29. W. Liu, Z. Liang, Z. Qin, X. Shi, F. Yang, and D. Meng, “Polarization-insensitive dual-band response governed by quasi bound states in the continuum for high-performance refractive index sensing,” Results Phys. 32, 105125 (2022). [CrossRef]
30. S. Lee, J. Song, and S. Kim, “Graphene perfect absorber with loss adaptive Q-factor control function enabled by quasi-bound states in the continuum,” Sci Rep 11(1), 22819 (2021). [CrossRef]
31. F. Yesilkoy, E. R. Arvelo, Y. Jahani, M. Liu, A. Tittl, V. Cevher, Y. Kivshar, and H. Altug, “Ultrasensitive hyperspectral imaging and biodetection enabled by dielectric metasurfaces,” Nat. Photonics 13(6), 390–396 (2019). [CrossRef]
32. C. Liu, Y. Bai, J. Zhou, J. Chen, and L. Qiao, “Refractive index sensing by asymmetric dielectric gratings with both bound states in the continuum and guided mode resonances,” Opt. Express 29(26), 42978–42988 (2021). [CrossRef]
33. T. C. W. Tan, E. Plum, and R. Singh, “Lattice-Enhanced Fano Resonances from Bound States in the Continuum Metasurfaces,” Adv. Opt. Mater. 8(6), 1901572 (2020). [CrossRef]
34. J. Li, J. Li, C. Zheng, Z. Yue, S. Wang, M. Li, H. Zhao, Y. Zhang, and J. Yao, “Free switch between bound states in the continuum (BIC) and quasi-BIC supported by graphene-metal terahertz metasurfaces,” Carbon 182, 506–515 (2021). [CrossRef]
35. Y. Liang, K. Koshelev, F. Zhang, H. Lin, S. Lin, J. Wu, B. Jia, and Y. Kivshar, “Bound States in the Continuum in Anisotropic Plasmonic Metasurfaces,” Nano Lett. 20(9), 6351–6356 (2020). [CrossRef]
36. W. Zhang, A. Charous, M. Nagai, D. M. Mittleman, and R. Mendis, “Extraordinary optical reflection resonances and bound states in the continuum from a periodic array of thin metal plates,” Opt. Express 26(10), 13195–13204 (2018). [CrossRef]
37. D. Liu, F. Wu, R. Yang, L. Chen, X. He, and F. Liu, “Quasi-bound states in the continuum in metal complementary periodic cross-shaped resonators at terahertz frequencies,” Opt. Lett. 46(17), 4370–4373 (2021). [CrossRef]
38. J. Niu, Y. Zhai, Q. Han, J. Liu, and B. Yang, “Resonance-trapped bound states in the continuum in metallic THz metasurfaces,” Opt. Lett. 46(2), 162–165 (2021). [CrossRef]
39. X. Zhao, C. Chen, K. Kaj, I. Hammock, Y. Huang, R. D. Averitt, and X. Zhang, “Terahertz investigation of bound states in the continuum of metallic metasurfaces,” Optica 7(11), 1548–1554 (2020). [CrossRef]
40. Z. Shen, X. Fang, S. Li, W. Yin, L. Zhang, and X. Chen, “Terahertz spin-selective perfect absorption enabled by quasi-bound states in the continuum,” Opt. Lett. 47(3), 505–508 (2022). [CrossRef]
41. G. Yang, M. S. Allen, J. W. Allen, and H. Harutyunyan, “Bound States in the Continuum-assisted High-Q Optical Absorption using Resonant Dielectric Metasurfaces on Metal,” (2021).
42. Y. K. Srivastava, R. T. Ako, M. Gupta, M. Bhaskaran, S. Sriram, and R. Singh, “Terahertz sensing of 7 nm dielectric film with bound states in the continuum metasurfaces,” Appl. Phys. Lett. 115(15), 151105 (2019). [CrossRef]
43. R. Wang, L. Xu, J. Wang, L. Sun, Y. Jiao, Y. Meng, S. Chen, C. Chang, and C. Fan, “Electric Fano resonance-based terahertz metasensors,” Nanoscale 13(44), 18467–18472 (2021). [CrossRef]
44. Q. Ren, F. Feng, X. Yao, Q. Xu, M. Xin, Z. Lan, J. You, X. Xiao, and W. E. I. Sha, “Multiplexing-oriented plasmon-MoS2 hybrid metasurfaces driven by nonlinear quasi bound states in the continuum,” Opt. Express 29(4), 5384–5396 (2021). [CrossRef]
45. X. Liu, F. Li, Y. Li, T. Tang, Y. Liao, Y. Lu, and Q. Wen, “Terahertz metasurfaces based on bound states in the continuum (BIC) for high-sensitivity refractive index sensing,” Optik 261, 169248 (2022). [CrossRef]
46. Z. Shen, S. Li, Y. Xu, W. Yin, L. Zhang, and X. Chen, “Three-Dimensional Printed Ultrabroadband Terahertz Metamaterial Absorbers,” Phys. Rev. Appl. 16(1), 014066 (2021). [CrossRef]
47. K. Koshelev, S. Lepeshov, M. Liu, A. Bogdanov, and Y. Kivshar, “Asymmetric Metasurfaces with High-Q Resonances Governed by Bound States in the Continuum,” Phys. Rev. Lett. 121(19), 193903 (2018). [CrossRef]
48. J. Wang, J. Yang, H. Zhao, and M. Chen, “Quasi-BIC-governed light absorption of monolayer transition-metal dichalcogenide-based absorber and its sensing performance,” J. Phys. D: Appl. Phys. 54(48), 485106 (2021). [CrossRef]
49. Q. Li, T. Wang, Y. Su, M. Yan, and M. Qiu, “Coupled mode theory analysis of mode-splitting in coupled cavity system,” Opt. Express 18(8), 8367–8382 (2010). [CrossRef]
50. X. Chen, W. Fan, and H. Yan, “Toroidal dipole bound states in the continuum metasurfaces for terahertz nanofilm sensing,” Opt. Express 28(11), 17102–17112 (2020). [CrossRef]
51. T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510 (2010). [CrossRef]
52. A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric Metamaterials with Toroidal Dipolar Response,” Phys. Rev. X 5(1), 011036 (2015). [CrossRef]
53. V. Savinov, V. A. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Physical Review B 89 (2014).
54. B. X. Wang, Y. H. He, P. C. Lou, and W. H. Xing, “Design of a dual-band terahertz metamaterial absorber using two identical square patches for sensing application,” Nanoscale Adv. 2(2), 763–769 (2020). [CrossRef]
55. Z. Li, Y. Xiang, S. Xu, and X. Dai, “Ultrasensitive terahertz sensing in all-dielectric asymmetric metasurfaces based on quasi-BIC,” J. Opt. Soc. Am. B 39(1), 286–291 (2022). [CrossRef]
56. Y. P. Qi, Y. Zhang, C. Q. Liu, T. Zhang, B. H. Zhang, L. Y. Wang, X. Y. Deng, Y. L. Bai, and X. X. Wang, “A tunable terahertz metamaterial absorber composed of elliptical ring graphene arrays with refractive index sensing application,” Results Phys. 16, 103012 (2020). [CrossRef]
57. A. Veeraselvam, G. N. A. Mohammed, K. Savarimuthu, J. Anguera, J. C. Paul, and R. K. Krishnan, “Refractive Index-Based Terahertz Sensor Using Graphene for Material Characterization,” Sensors 21(23), 8151 (2021). [CrossRef]
58. H. Ge, L. Li, Y. Jiang, G. Li, F. Wang, M. Lv, and Y. Zhang, “Design of High-performance Terahertz Sensor Based on Metamaterials,” J. Phys.: Conf. Ser. 2174(1), 012001 (2022). [CrossRef]
59. Z. Xiong, L. Shang, J. Yang, L. Chen, J. Guo, Q. Liu, S. A. Danso, and G. Li, “Terahertz Sensor With Resonance Enhancement Based on Square Split-Ring Resonators,” IEEE Access 9, 59211–59221 (2021). [CrossRef]
60. W. Yin, Z. Shen, S. Li, L. Zhang, and X. Chen, “A Three-Dimensional Dual-Band Terahertz Perfect Absorber as a Highly Sensitive Sensor,” Front. Phys. 9, 665280 (2021). [CrossRef]
