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Abstract
In this paper, a highly sensitive sensor consisting of a silicon nanorod and symmetric rings (SNSR) is presented. Theoretically, three Fano resonances with high Q-factors are excited in the near-infrared range by breaking the symmetry structure based on quasi-bound states in the continuum (Q-BICs). The electromagnetic near-field analysis confirms that the resonances are mainly controlled by toroidal dipole (TD) resonance. The structure is optimized by adjusting different geometrical parameters, and the maximum Q-factor of the Fano resonances can reach 7427. To evaluate the sensing performance of the structure, the sensitivity and the figure of merit (FOM) are calculated by adjusting the environmental refractive index: the maximum sensitivity of 474 nm/RIU and the maximum FOM of 3306 RIU-1. The SNSR can be fabricated by semiconductor-compatible processes, which is experimentally evaluated for changes in transmission spectra at different solution concentrations. The results show that the sensitivity and the Q-factor of the designed metasurface can reach 295 nm/RIU and 850, while the FOM can reach 235 RIU-1. Therefore, the metasurface of SNSR is characterized by high sensitivity and multi-wavelength sensing, which are current research hotspots in the field of optics and can be applied to biomedical sensing and multi-target detection.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurface with high Q-factor resonances can be used to evaluate the performance of micro/nano devices [1–4] that have been applied in nonlinear optics [5,6], optical switches [7–9], and optical sensors [10–13]. Because of the characteristic of solving the ohmic loss, all-dielectric materials are used to create the metasurface, which is favorable for the excitation of Fano resonance with high Q-factor [14–16]. The Q-factor is a key parameter for evaluating the performance of Fano resonance, which is a special mode of a photonic system with an asymmetric linear shape. The interference between the wide bright mode and the narrow dark mode [17,18] leads to the Fano resonance [19]. The high Q-factor Fano resonance can be used to realize high-performance sensors. Therefore, the sensor with high Q-factor Fano resonance based on the all-dielectric metasurface has gradually become a research hotspot.
Researchers have found that the quasi-bound states in the continuum (Q-BICs) [20–22] are an effective method for realizing high Q-factor Fano resonance on all-dielectric metasurface. BICs are concepts derived from quantum mechanics, including symmetry-protected BICs [23] and accidental BICs [24,25]. The energy leakage in the radiation channel can be caused by breaking the structural symmetry [26], thus transforming the bound states in the continuum (BICs) under symmetric with an infinite Q-factor into asymmetric with a finite Q-factor. The Q-factor of the Fano resonance under asymmetric can be adjusted by controlling the linewidth. Therefore, the theory is often applied to analyze the excitation of new Fano resonance with high Q-factor.
The multipolar resonance modes of Fano resonances excited by BICs under the all-dielectric mainly include magnetic dipole (MD), toroidal dipole (TD) [27,28], electric dipole (ED), and other multipoles [29,30]. MD is defined as a dynamic recirculating loop formed by an electric current. ED is defined as the excitation of a charged particle. TD is equivalent to MD arranged along the head and tail, which is generated by currents flowing along the ring surface. And TD is closely related to resonances with high Q-factor [31,32], which plays an important role in sensing. However, TD is often masked by MD, ED in metallic metasurface. Excitation of TD resonance by all-dielectric metasurface structures has been widely discussed nowadays. It has been realized that the TD resonance can be enhanced and high Q-factor can be achieved in all-dielectric metasurface by tuning the structural design. For example, Li et al. proposed a metasurface composed of asymmetric nanorods based on toroidal resonance with Q-factor up to 7253.3 in 2023 [33]. Huang et al. presented hollow cylindrical tetramer metasurface structure with Q-factor up to 5653.4 in 2022 [34].
In this paper, refractive index sensor utilizing an asymmetric all-dielectric metasurface with high performance is presented. The structural unit consists of a nanorod and symmetric rings with the same opening angle, abbreviated as SNSR. The Q-BICs are excited by changing the length of the nanorod, which achieves three sharp TD Fano resonances. The existence of Q-BICs are demonstrated by calculating the inverse quadratic trend relationship between the Q-factors and the asymmetric parameters. The potential resonance mechanism is further analyzed using the multiple decomposition method and the near-field mode. The transmission spectra of the structure at different polarization angles are also analyzed, demonstrating the potential application of the structure in optical switching. Then the sensing performance of the structure under different refractive index conditions and its practical application value are evaluated by subjecting the structure to different environments through simulation and experiment, respectively.
2. Design and simulation of SNSR structure
2.1 Simulation under symmetry and asymmetry
SNSR is composed of arrays arranged periodically along the x direction and y direction, illustrated in Fig. 1. The proposed metasurface consisting of a silicon nanorod and symmetric open rings are deposited on a silicon dioxide substrate. And the whole structure in this design is placed in the liquid environment with ${RI\; = \; 1}\textrm{.33}$. Each unit period is Px and Py along the x direction and y direction, and ${{P}_{x}}{\; = \; }{{P}_{y}}{\; = \; 800\; \textrm{nm}}\textrm{.}$ The length (L), width (w), and thickness of the nanorod are 690 nm, 100 nm, and 140 nm, respectively. The distance (δ1) between the nanorod and the left boundary is 50 nm. And the inner (r) and outer radii (R) of the rings are 70 nm and 150 nm. In this design, the left ring and the right ring opening angle are set to $\mathrm{\theta \;\ =\ \;\ 35^\circ }$. After the structural design is completed, the way of finite difference time domain (FDTD) is used to simulate the transmission spectrum and electric field distribution of the structure. During the simulation process, an appropriate grid size needs to be selected to accommodate the rapid changes in the transmission spectrum that occur during the simulation. Therefore, the grid size is set to 8 nm × 8 nm × 8 nm.The plane wave is incident vertically on the surface of the structure in the negative direction of the z-axis, which is polarized along the y-axis. Periodic boundary condition is set in the x direction and y direction, while the perfectly matched layer (PML) is set in the z direction.
In addition to the metasurface parameters mentioned above, other structural parameters such as the center coordinates of the left circle is ${{x}_\textrm{1}}{\; = \; 200\; \textrm{nm}}$ and ${{y}_\textrm{1}}{\; = \; 250\; \textrm{nm}}$, and the center coordinates of the right circle is ${{x}_\textrm{2}}{ = \; 600\; \textrm{nm}}$ and ${{y}_\textrm{2}}{ = \; 250\; \textrm{nm}}$. The symmetry is broken by changing the value of δ2, new radiation channels are established and new resonance peak with better performance is generated as shown in Fig. 2(a). When δ2 = 60 nm, the blue solid line indicates the transmission spectrum curve in the case of structural asymmetry, and three resonance peaks appear at 1114 nm, 1136 nm and 1142 nm. When the structure is symmetric (δ2 = 50 nm), the purple dashed line shows the two resonance peaks at ${\mathrm{\lambda} \;\ =\ \;\ 1113\;\ \textrm{nm}\;\ }$and ${\mathrm{\lambda} \;\ =\ \;\ 1121\;\ \textrm{nm}}$.
Fig. 2. (a) Transmission spectral curves of metastructure in symmetric and asymmetric cases (the blue line), and (b) the plot of fitting results at $\mathrm{\lambda \;\ =\ \;\ 1114\;\ nm}$ and $\mathrm{\lambda \;\ =\ \;\ 1136\;\ nm}$ when δ2 = 60 nm (the red dashed indicates the fitting curve of mode I and the black dashed indicates the fitting curve of mode II;).
The Q-factor and modulation depth indicate the characteristics of the response transmission spectral curve. The spectral contrast of the transmission spectrum is calculated to be close to 100%, and the calculation formula is as follows
The excitation of the Fano resonance peak can be calculated by equation [35]
In Eq. (2), a1, a2 and a3 are real numbers, w0 is the resonant frequency, and γ is the damping factor. The fitting results at ${\mathrm{\lambda} \;\ =\ \;\ 1114\;\ \textrm{nm}}$ and ${\mathrm{\lambda} \;\ =\ \;\ 1136\;\ \textrm{nm}\;\ }$are shown in Fig. 2(b). It shows that the simulation curve (solid blue line) is basically consistent with the fitting result (red dotted line and black dotted line).
In order to calculate the Q-factor of the Fano resonance, it can be calculated by the following equation
The Q-factor of the Fano resonances can reach 7427, 5738 and 36.7. To know the trend of the transmission spectral as the δ2 changes, the transmission spectral curves are obtained by the simulation, which is shown in Fig. 3(a). With the increasing of δ2, the mode II peak appears gradually, which has Fano resonance properties. Meanwhile, the transmission peaks are slightly red-shifted, and the mode II transmission gradually increases. The relationship between the Q-factor and the degree of structural asymmetry is shown in Fig. 3(b). ΔS/S is the degree of asymmetry (α), where ΔS is the change of the area in structure and S is the total area of silicon in the symmetric structure. It is concluded that the Q-factor is quadratically inversely related to the degree of asymmetry (α) through the analysis.
Fig. 3. (a)Transmission spectral curves for different geometrical parameters δ2, and (b) the Q-factor is quadratically inversely related to the degree of asymmetry (α) at $\mathrm{\lambda \;\ =\ \;\ 1136\;\ nm}$.
The effect of geometric parameters on the performance of Fano resonance is investigated by varying the inner diameter of the ring and the size of the ring opening angle. Figure 4(a) displays the transmission curve from ${r\; = \; 60\; \textrm{nm}}$ to ${r\; = \; 80\; \textrm{nm}}$ in 5 nm steps. As can be seen from the figure, three resonance peaks are blue-shifted, with slight variations in line width and much variation in modulation depth. In addition, Fig. 4(b) displays the transmission curves from ${\theta \;\ =\ \;\ 25^\circ }$ to ${\theta \;\ =\ \;\ 45^\circ }$ in 5° steps. It can be seen that the resonance curve is slightly blue-shifted, while the change in the opening angle will have a large effect on the modulation depth and line width. Different geometric parameter values can be selected according to different requirements to obtain refractive index sensors for various applications, reflecting the controllability of the Q-factor.
Fig. 4. (a) The transmission spectrum diagram of ${n\; = \; 40\; \textrm{nm}\; - \; 80\; \textrm{nm}}$, (b) the transmission spectrum diagram of $\mathrm{\theta \;\ =\ \;\ 25^\circ \;\ -\ \;\ 45^\circ }\textrm{.}$
2.2 Electromagnetic field analysis
The electromagnetic field distribution is evaluated at different wavelengths to study the resonance mechanism of three Fano resonance peaks in a more intuitive way. As shown in Fig. 5(a), the xoy plane forms two magnetic fields along the x axis at $\mathrm{\lambda \;\ =\ \;\ 1114\;\ nm}$. And two current loops in opposite directions are formed in the yoz plane in Fig. 5(b), indicating that the resonance mode I is TD resonance consisting of two magnetic dipole resonances in the x-positive direction and x-negative direction. At mode II, the xoy plane forms two magnetic fields in opposite directions along the y axis at $\mathrm{\lambda \;\ =\ \;\ 1136\;\ nm}$ in Fig. 5(d). And two current loops in opposite directions are formed in the xoz plane in Fig. 5(e), indicating that the resonance mode II is TD resonance along the y-direction, which consists of two magnetic dipole resonances in the y-positive direction and y-negative direction. At mode III, the xoy plane forms two magnetic fields in opposite directions along the z axis in Fig. 5(g). And two currents in opposite directions are formed in the xoz plane in Fig. 5(h), indicating that the resonance mode III is a TD resonance along the z-direction, which consists of two magnetic dipole resonances in the z-positive direction and z-negative direction.
Fig. 5. Normalized electromagnetic field distributions of the asymmetric structure at the resonance wavelength. (a)-(b) Xoy plane magnetic field distribution (black arrows), yoz plane electric field distribution (white arrows) at $\mathrm{\lambda \;\ =\ \;\ 1114\;\ }$nm and toroidal dipole diagram, (d)-(e) xoy plane electric field distribution (white arrows), xoz plane magnetic field distribution (black arrows) at $\mathrm{\lambda \;\ =\ \;\ 1136\;\ nm}$ and toroidal dipole diagram, and (g)-(h) xoy plane electric field distribution, xoz plane magnetic field distribution at $\mathrm{\lambda \;\ =\ \;\ 1142\;\ nm}$ and toroidal dipole diagram.
2.3 Influence of refractive index and polarization angle on SNSR
The Fano resonance has the property of being extremely sensitive to the ambient refractive index. To investigate the effect of background refractive index on sensor performance, the refractive index varies from 1.31-1.35 in steps of 0.01 in Fig. 6(a)-(c). Three Fano resonances are showed in the transmission spectra and the position of the resonance peaks appear red-shift, respectively. The key parameters to measure the excellent performance of refractive index sensors are sensitivity (S) and the figure of merit (FOM). The S is defined as
where Δn is the change of environmental refractive index and Δλ is the offset of resonance peak. Refractive index unit (RIU) represents the ratio of the speed of light as it travels through a medium relative to the speed of light as it travels through a vacuum, which determines the change in direction and speed of light propagating in different mediums. The calculated sensitivities for the three resonance peaks are 474 nm/RIU, 442 nm/RIU, and 496 nm/RIU. The FOM is defined as [36] where FWHM is the full width at half maxima. The calculated FOM for the three resonance peaks are 3160, 2232, and 15.9. It can be seen that the sensitivity and FOM values of the three Fano resonances as shown in Fig. 6(d). The simulation results are compared with the existing results and the Q-factor, sensitivity and FOM values are shown in Table 1. It is worth noting that the Q-factor in this paper is calculated under the condition that the modulation depth is close to 100%. It can be concluded that our results have valuable reference in sensing.Fig. 6. (a-b) The transmission spectrum of mode I, mode II and mode III when ${\textrm{n}\; = \; 1}{.31\; - \; 1}{.35}$ in steps of 0.01, (c) the variation of three resonances wavelength positions at different refractive index, and (d) comparison of S and FOM for the three resonance peaks.
Table 1. Comparative Analysis of Refractive Index Sensor Performance.
The effect of the extinction coefficient on the transmission spectrum in symmetric and asymmetric cases is discussed in Fig. 7(a)-(b). It can be seen that the resonance peak increases the line width and decreases the modulation depth as increasing of extinction coefficient (k). And the extinction coefficient affects the transmission peak differently in symmetric and asymmetric structures. Compared to other resonance peaks, mode I is more sensitive to change in extinction coefficient. In the liquid environment, the metasurface is subject to inherent absorption, which attenuates the transmission spectral profile. In addition, the transmission curves and transmission spectra of asymmetric structures at different polarization angles are calculated in Fig. 8. Here, the angle between the light source and the x-axis is defined as the polarization angle. Figure 8(a) shows the variation of the transmission curve with increasing angle of incidence of the light source for φ from 0° to 90°. Opening and closing of multiple Fano resonances can be controlled by changing the polarization angle of the incident light. As the increasing of the polarization angle, the resonance in the green-shaded portion turns off gradually, and the resonance in the purple-dashed portion turns on gradually. It can be seen that the structure has good optical polarizability, which can be used as an optical switch.
Fig. 7. (a) The effect of extinction coefficients on transmission spectra in symmetric structure, and (b) the effect of extinction coefficients on transmission spectra in asymmetric structure.
Fig. 8. (a) When δ2 = 60 nm, the transmission peak of the transmission spectrum increases with the incident angle from 0° to 90°, and (b) The transmittance magnitude and position are identical corresponding to transmission curves.
3. Experimental results
The proposed structure is tested experimentally and the parameters of the structure are set as ${{P}_{x}}{\; = \; }{{P}_{y}}{\; = \; 800\; \textrm{nm}}$, ${h\; = \; 140\; \textrm{nm}}$, ${L\; = \; 690\; \textrm{nm}}$, ${m\; = \; 100\; \textrm{nm}}$, ${R\; = \; 150\; \textrm{nm}}$, ${r\; = \; 70\; \textrm{nm}}$, ${{\delta }_\textrm{1}}{\; = \; 50\; \textrm{nm}}$ and ${{\delta }_\textrm{2}}{\; = \; 60\; \textrm{nm}}{.\; }$The process flow diagram of the structure is shown in Fig. 9. The manufacturing process flow mainly consists of depositing silicon film onto the oxide layer (SiO2) by low-pressure chemical vapor deposition (LPCVD) as shown in Fig. 9(b). Then ZEP520 is spin-coated on the sample in Fig. 9(c). Next, the metasurface is obtained with the help of the inductively coupled plasma (ICP) technique in Fig. 9(d) and the electron beam lithography (EBL) technique in Fig. 9(e). Finally, the structure is cleaned by plasma after removal of ZEP520 as shown in Fig. 9(f).
The SEM image of the SNSR is shown in Fig. 10(a), through which it can be seen that the array consists of periodic nanorod and symmetric open rings. It can also be seen that the internal structural array of the device is uniformly distributed. To test the performance of the device, a measurement system is shown in Fig. 10(b), which is set up to test the sensing performance of the device. A laser (800 nm-2400 nm) is used as the light source, and the incident light passes sequentially through a collimating lens and a polarizer to the sample surface. The light source passes through the sample to be received and collected by the fiber optic collimator. The sample has been placed in a container filled with diluted ethylene glycol solution using pure water. The final transmission spectrum is displayed by a spectrometer.
Fig. 10. (a) The SEM picture of the experimental sample, and (b) measuring system of the metasurface.
Different concentrations of ethylene glycol solutions measured experimentally have important biological applications. Specific concentrations of ethylene glycol solutions can be used to preserve biological samples as an important component of cryoprotectant solutions, which have significant environmental and biological applications [41,42]. Different concentration of ethylene glycol solutions are configured, and the transmission spectral curves are measured experimentally to determine the changes in the refractive index of the ethylene glycol solutions, thus realizing the measurement of the content of the ethylene glycol solutions. After several measurements with an Abbe refractometer, the refractive index concentrations of the ethylene glycol solutions are 3.5%, 10%, 18%, 28% and 39%, corresponding to refractive indexes of 1.3346, 1.3425, 1.3510, 1.3605, and 1.3710, respectively. The final transmission spectra obtained in different backgrounds are shown in Fig. 11(a)-(b), and the maximum sensitivity of the experimental data is calculated to be 295 nm/RIU. And the Q-factor of 850 and FOM of 235 RIU-1 are calculated. Figure 11(c) shows the comparison curve between the simulation result and the experimental result when the refractive index is 1.3346, and it can be seen that there are certain inaccuracies between the experimental and theoretical values. The transmission and performance of the experimental results are lower due to the external environment and the manufacturing error of the samples.
Fig. 11. (a-b) The plot of transmission spectra obtained by experiment, and (c) comparison of FDTD simulation result with measured result plotted for the asymmetric case.
4. Conclusion
In summary, an all-dielectric structure (SNSR) with multiple Fano resonances excited by an asymmetric nanorod is presented. Three resonance peaks are acquired by asymmetrical structure, the second of which is a new resonance with high Q-factor, narrow line width, and near 100% modulation depth performance. The maximum Q-factor of the resonances is simulated and measured to 7427. The electromagnetic sources of modes I, II and III are proved to be TD resonances by electromagnetic field analysis. Then the effect of RI on the sensing performance is discussed, showing that the maximum sensitivity and FOM values are 474 nm/RIU and 3306 RIU-1, respectively. In addition, the modulation of the Fano resonance peaks by varying the polarization angle of the incident light from the source is explored, which can be used to optical switching. Finally, SNSR with the maximum sensitivity of 295 nm/RIU when the variation between refractive index and concentration of the ethylene glycol solution is experimentally measured. And the Q-factor of 850 and FOM of 235 RIU-1 are calculated. The external environment and manufacturing process contribute to the error between experimental and theoretical values. The high Q-factor, high sensitivity, and multiple Fano resonance properties are embodied in SNSR, which have a large potential for applications in optical switching, biosensing, and multi-target detection.
Funding
Youth Innovation Team Project for Talent Introduction and Cultivation in Universities of Shandong Province (2021RC085); Natural Science Foundation of Shandong Province (ZR2021MF053, ZR2021MF070, ZR2022MF253, ZR2022MF305).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. X. Luo, X. Li, T. Lang, et al., “Excitation of High Q toroidal dipole resonance in an all-dielectric metasurface,” Opt. Mater. Express 10(2), 358–368 (2020). [CrossRef]
2. X. Long, M. Zhang, Z. Xie, et al., “Sharp Fano resonance induced by all-dielectric asymmetric metasurface,” Opt. Commun 459, 124942 (2020). [CrossRef]
3. C. Peng, C. Feng, J. Xia, et al., “Near-infrared Fano resonance in asymmetric silicon metagratings,” J. Opt 22(9), 095102 (2020). [CrossRef]
4. Z. Gao, P. Wang, Z. Xu, et al., “Chiral metasurface absorber with near-infrared excitation-induced dual circular dichroism,” Opt. Laser Technol 175, 110826 (2024). [CrossRef]
5. A. Krasnok, M. Tymchenko, and A. Alù, “Nonlinear metasurfaces: a paradigm shift in nonlinear optics,” Mater. Today 21(1), 8–21 (2018). [CrossRef]
6. X. Shuyuan, Q. Meibao, D. Junyi, et al., “Robust enhancement of high-harmonic generation from all-dielectric metasurfaces enabled by polarization-insensitive bound states in the continuum,” Opt. Express 30(18), 32590–32599 (2022). [CrossRef]
7. L. Yang, S. Yu, H. Li, et al., “Multiple Fano resonances excitation on all-dielectric nanohole arrays metasurfaces,” Opt. Express 29(10), 14905–14916 (2021). [CrossRef]
8. Z. Han and J. Yang, “All-optical self-switching with ultralow incident laser intensity assisted by Bound state in the continuum,” Opt. Lett. 46(3), 524–527 (2021). [CrossRef]
9. J. Yu, J. Zhu, S. Ye, et al., “Ultra-wide sensing range plasmonic refractive index sensor based on a two-dimensional circular-hole grating engraved on a gold film,” Results Phys 26(7), 104396 (2021). [CrossRef]
10. S. A. Khan, N. Z. Khan, Y. Xie, et al., “Optical sensing by metamaterials and metasurfaces: from physics to biomolecule detection,” Adv. Opt. Mater 10(18), 1 (2022). [CrossRef]
11. J. Qin, S. Jiang, Z. Wang, et al., “Metasurface micro/nano-optical sensors: principles and applications,” ACS Nano 16(8), 11598–11618 (2022). [CrossRef]
12. R. Wang, L. Xu, L. Huang, et al., “Ultrasensitive terahertz biodetection enabled by quasi-bic-based metasensors,” Small 19(35), 2301165 (2023). [CrossRef]
13. J. Li and L. Ye, “Dielectric dual-dimer metasurface for enhanced mid-infrared chiral sensing under both excitation modes,” Nanophotonics 12(12), 2189–2197 (2023). [CrossRef]
14. I. Staude and J. Schilling, “Metamaterial-inspired silicon nanophotonics,” Nat. Photonics 11(5), 274–284 (2017). [CrossRef]
15. S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol 11(1), 23–36 (2016). [CrossRef]
16. Z.-J. Yang, R. Jiang, X. Zhuo, et al., “Dielectric nanoresonators for light manipulation,” Phys. Rep 701, 1–50 (2017). [CrossRef]
17. V. A. Fedotov, M. Rose, S. L. Prosvirnin, et al., “Sharp dark-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett 99(14), 147401 (2007). [CrossRef]
18. K. Wang, Y. Wang, X. Wang, et al., “All-dielectric refractive index sensor based on multiple fano resonance with high sensitivity in the long-wave infrared region,” Coatings 12(7), 970 (2022). [CrossRef]
19. Z. Rukhsar, N Sarfaraz, S Ghanshyam, et al., “Plasmonics-based refractive index sensor for detection of hemoglobin concentration,” IEEE Sensors J. 18(11), 4372–4377 (2018). [CrossRef]
20. Y. He, G. Guo, T. Feng, et al., “Toroidal dipole bound states in the continuum,” Phys. Rev. B 98(16), 161112 (2018). [CrossRef]
21. S. Garmon, K. Noba, G. Ordonez, et al., “Non-Markovian dynamics revealed at a bound state in the continuum,” Phys. Rev. A 99(1), 010102 (2019). [CrossRef]
22. K. M. Mustafizur Rahman, M. Shah Alam, M. Asiful Islam, et al., “Highly sensitive surface plasmon resonance refractive index multi-channel sensor for multi-analyte sensing,” IEEE Sensors J. 21(24), 27422–27432 (2021). [CrossRef]
23. K. Ashok, L. Thomas, G. Qing, et al., “Lasing action from photonic bound states in continuum,” Nature 541(7636), 196–199 (2017). [CrossRef]
24. T. Shi, Z. D. Deng, Q. T. An, et al., “Displacement-mediated bound states in the continuum in all-dielectric superlattice metasurfaces,” PhotoniX 2(1), 7 (2021). [CrossRef]
25. Z. Gao, P. Wang, S. Yu, et al., “High circular dichroism optical chiral metasurfaces based on bound states in the continuum,” Symmetry 15(7), 1444 (2023). [CrossRef]
26. K Kirill, L Sergey, L Mingkai, et al., “Asymmetric metasurfaces with high-Q resonances governed by bound states in the continuum,” Phys. Rev. Lett. 121(19), 193903 (2018). [CrossRef]
27. A. Sayanskiy, M. Danaeifar, P. Kapitanova, et al., “All-dielectric metalattice with enhanced toroidal dipole response,” Adv. Opt. Mater 6(19), 1800302.1 (2018). [CrossRef]
28. S. Tu, S. Tu, X. Liu, et al., “An ultra-high figure of merit refractive index sensor with Mie lattice resonance of a toroidal dipole in an all-dielectric metasurface array in the near-infrared,” J. Phys. D: Appl. Phys. 56(11), 115101 (2023). [CrossRef]
29. L. Cong, Y. S. Kumar, and S. Ranjan, “Tailoring the multipoles in THz toroidal metamaterials,” Appl. Phys. Lett 111(8), 081108 (2017). [CrossRef]
30. G. Manoj, Y. S. Kumar, and S. Ranjan, “A toroidal metamaterial switch,” Adv. Mater 30(30), 1 (2018). [CrossRef]
31. J. F. Algorri, D. C. Zografopoulos, A. Ferraro, et al., “Ultrahigh-quality factor resonant dielectric metasurfaces based on hollow nanocuboids,” Opt. express 27(5), 6320–6330 (2019). [CrossRef]
32. S. Liu, Z. Wang, W. Wang, et al., “High Q-factor with the excitation of anapole modes in dielectric split nanodisk arrays,” Opt. Express 25(19), 22375–22387 (2017). [CrossRef]
33. H. Li, J. Xing, Y. Shi, et al., “Performance analysis and optimization of high Q-factor toroidal resonance refractive index sensor based on all-dielectric metasurface,” Opt. Laser. Technol 157, 108752 (2023). [CrossRef]
34. L. Huang and H. Li, “Analogue of electromagnetically induced transparency inspired by bound states in the continuum and toroidal dipolar response in all-dielectric metasurfaces,” Photonic. Nanostruct 51, 101041 (2022). [CrossRef]
35. Y. Yuanmu, Ivan I. Kravchenko, Dayrl P. Briggs, et al., “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun 5(1), 5753 (2014). [CrossRef]
36. H. Hao, S. Yu, L. Yang, et al., “High Q-factor multi-Fano resonances in all-dielectric double square hollow metamaterials,” Opt. Laser. Technol 140(107072), 107072 (2021). [CrossRef]
37. S. Romano, G. Zito, S. Torino, et al., “Label-free sensing of ultralow-weight molecules with all-dielectric metasurfaces supporting bound states in the continuum,” Photon. Res. 6(7), 726–733 (2018). [CrossRef]
38. J. Xing, S. Yu, Y. Shi, et al., “Multiple Fano resonances driven by bound states in the continuum in an all-dielectric nanoarrays system,” Aip. Adv 13(3), 1 (2023). [CrossRef]
39. Y. Huo, X. Zhang, M. Yan, et al., “Highly-sensitive sensor based on toroidal dipole governed by bound state in the continuum in dielectric non-coaxial core-shell cylinder,” Opt. Express 30(11), 19030–19041 (2022). [CrossRef]
40. S. K. Modi, J. Kaur, P. S. Singh, et al., “Extremely high figure of merit in all-dielectric split asymmetric arc metasurface for refractive index sensing,” Opt. Commun 462, 125327 (2020). [CrossRef]
41. R. A. G. Raju, G.B. Haranath, K. M. Krishna, et al., “Vitrification of human 8-cell embryos, a modified protocol for better pregnancy rates,” Reprod. Biomed. Online 11(4), 434–437 (2005). [CrossRef]
42. K. Takahashi, T. Mukaida, T. Goto, et al., “Perinatal outcome of blastocyst transfer with vitrification using cryoloop: A 4-year follow-up study,” Fertil. Steril 84(1), 88–92 (2005). [CrossRef]
