High quality (Q) factor toroidal dipole (TD) resonances have played an increasingly important role in enhancing light–matter interactions. Interestingly, TDs share a similar far-field distribution as the conventional electric/magnetic dipoles but have distinct near-field profiles from them. While most reported works focused on the electric TD, magnetic TDs (MTDs), particularly high-Q MTD, have not been fully explored yet. Here, we successfully realized a high-Q MTD by effectively harnessing the ultrahigh Q-factor guided mode resonances supported in an all-dielectric metasurface, that is, changing the interspacing between silicon nanobar dimers. Other salient properties include the stable resonance wavelength but a precisely tailored Q-factor by interspacing distance. A multipole decomposition analysis indicates that this mode is dominated by the MTD, where the electric fields are mainly confined within the dielectric nanostructures, while the induced magnetic dipole loops are connected head-to-tail. Finally, we experimentally demonstrated such high-Q MTD resonance by fabricating a series of silicon metasurfaces and measuring their transmission spectra. The MTD resonance is characterized by a sharp Fano resonance in the transmission spectrum. The maximum measured Q-factor is up to 5079. Our results provide useful guidance for realizing high-Q MTD and may find exciting applications in boosting light–matter interactions.

All-dielectric metasystems have been widely used as a versatile platform to manipulate the propagation of electromagnetic waves with unprecedented flexibility.1–3 Similar to the plasmonic resonances provided by metallic nanostructures, dielectric metasystems support electric and magnetic multipolar Mie resonances, providing abundant freedom of tailoring near-fields and far-fields.4–6 On the other hand, they have much lower losses compared to noble metals,7 thus significantly improving the performance of dielectric-metasurface-based photonic and optoelectronic devices. In addition, all-dielectric metasurfaces are compatible with the complementary metal–oxide semiconductor (CMOS) process.

Recently, toroidal dipole (TD) resonances have received increasing attention in both fundamental physics and practical applications.8–10 They have the same far-field distributions as those of the electric dipole (ED) or magnetic dipole (MD), but have distinct near-field profiles. The role of toroidal dipole resonances has been neglected for a long time because the response of TD is much weaker than those of ED and MD. Thanks to the emergence of metamaterials, TD resonance was experimentally realized in the microwave frequency range by embedding four metallic split-ring resonators in the dielectric plate.10 Later, another group demonstrated the TD response with all-dielectric metamaterials.11 Except for TD, toroidal multipoles were found in a single dielectric nanosphere.12 The appearance of toroidal multipoles significantly enriches multipolar physics. For instance, the interaction between the electric TD (ETD) and ED can give rise to an anapole state, which shows enhanced near-field distribution but has a quenched far-field scattering.13–15 

More recently, TD resonances with high quality (Q) factors have gained increasing interest because they can significantly boost light–matter interactions. High-Q resonances supported by all-dielectric metasurfaces usually originate from quasi-bound states in the continuum (BICs).16–25 BICs correspond to dark states with an infinite Q-factor and lifetimes that coexist in the continuum spectrum.26–30 To make it become accessible to external excitations, BICs must be transformed into quasi-BICs by introducing perturbations. Typically, BICs can be categorized according to the formation mechanisms, including symmetry-protected (SP) BICs,3,31–34 accidental BICs,35,36 Friedrich–Wintgen BICs,37–39 and Fabry–Perot BICs.40 Based on BICs, the high Q-factor TD resonance has been successfully demonstrated in hollow cuboid metasurfaces41,42 and dimer nanodisk metasurfaces.24,43,44 However, most published TD modes belong to ETD, where the electric field is located within the air gap or air hole. Only a few works reported magnetic TD (MTD) with limited Q-factors,45–47 and high Q-factor MTD resonances are seldom realized, as shown in Table I. Compared to ETD, MTD shows better electric field confinement within the dielectric structure. Therefore, they are ideal candidates for realizing lasing and nonlinear harmonic generation based on semiconductor-based metasurfaces.

TABLE I.

Comparison of the experimental Q-factor for resonance type. SP-BIC: symmetry-protected bound state in the continuum; EIT: electromagnetically induced transparency.

Wavelength/
Resonance typeNanostructuresMeasured QfrequencyReferences
TD resonance ETD Metallic metamaterial 240 ∼15.4 GHz 10  
ETD Metallic metasurface 42.5 0.4 THz 48  
ETD Dielectric metasurface 728 1505 nm 41  
ETD Dielectric metasurface 160 ∼700 nm 41  
ETD Photonic crystal slabs 1373 1275 nm 49  
ETD Dielectric metasurface 584 1500 nm 50  
ETD Dielectric metasurface 206 756 nm 42  
ETD Dielectric metasurface 261 1498 nm 51  
ETD Dielectric metasurface 4990 1479 nm 52  
ETD Dielectric metasurface 3142 1480 nm 44  
MTD Dielectric metasurface ∼120 ∼1423 nm 53  
MTD Dielectric nanodisk clusters ∼20 630 nm 54  
MTD Dielectric metasurface 5079 1474.5 nm This work 
Other resonance SP-BIC Dielectric metasurface 1 946 1430 nm 55  
SP-BIC Dielectric metasurface 3 571 1548 nm 56  
SP-BIC Dielectric metasurface 18 511 1588 nm 19  
SP-BIC Dielectric metasurface 36 964 1552.5 nm 18  
EIT Dielectric metasurface 483 1371 nm 57  
EIT Dielectric metasurface 2 750 1183.4 nm 58  
Wavelength/
Resonance typeNanostructuresMeasured QfrequencyReferences
TD resonance ETD Metallic metamaterial 240 ∼15.4 GHz 10  
ETD Metallic metasurface 42.5 0.4 THz 48  
ETD Dielectric metasurface 728 1505 nm 41  
ETD Dielectric metasurface 160 ∼700 nm 41  
ETD Photonic crystal slabs 1373 1275 nm 49  
ETD Dielectric metasurface 584 1500 nm 50  
ETD Dielectric metasurface 206 756 nm 42  
ETD Dielectric metasurface 261 1498 nm 51  
ETD Dielectric metasurface 4990 1479 nm 52  
ETD Dielectric metasurface 3142 1480 nm 44  
MTD Dielectric metasurface ∼120 ∼1423 nm 53  
MTD Dielectric nanodisk clusters ∼20 630 nm 54  
MTD Dielectric metasurface 5079 1474.5 nm This work 
Other resonance SP-BIC Dielectric metasurface 1 946 1430 nm 55  
SP-BIC Dielectric metasurface 3 571 1548 nm 56  
SP-BIC Dielectric metasurface 18 511 1588 nm 19  
SP-BIC Dielectric metasurface 36 964 1552.5 nm 18  
EIT Dielectric metasurface 483 1371 nm 57  
EIT Dielectric metasurface 2 750 1183.4 nm 58  

In this article, we theoretically propose and experimentally demonstrate the high-Q factor MTD mode based on a guided mode resonance (GMR) in a dielectric metasurface. The designed metasurface consists of silicon nanobar dimers, and when the spacing between the nanobars is adjusted, the translational symmetry of the device is broken, successfully exciting a high-Q factor MTD GMR. The strong MTD resonance characteristic is confirmed by multipole decomposition and near-field analysis. In addition, we show that such a high-Q MTD resonance is more stable in momentum space, which is insensitive to the incident light angle. Furthermore, the perturbation parameters of the structure can be easily controlled in real fabrication. In addition, we confirm that the MTD resonance is able to trap the electric field inside the device and is accompanied by a significant magnetic field enhancement effect. Finally, we fabricate a series of silicon-dimer metasurfaces and experimentally demonstrate the existence of MTD resonance by measuring their transmission spectra with the experimentally measured Q-factor as high as 5 × 103. Our results are promising for applications in photonic devices based on the MTD mode with a high Q-factor.

The designed metasurface is composed of an array of Si nanobar dimers sitting on the SiO2 substrate, which supports a significant MTD response, as shown in Fig. 1(a). The excitation mechanism of MTD is shown in Fig. 1(b). The two nanobars support the magnetic field distributions of the reverse vortex, which in turn generates the head-to-tail electric dipole and ultimately excites the MTD mode along the direction between the two nanobars. Figure 1(c) shows the structural parameters of the unit cell with period Px = Py = 940 nm, length of the nanobars l = 650 nm, width w = 210 nm, and thickness of the Si nanobars 340 nm. The refractive index of Si and SiO2 is nSi = 3.48 and nSiO2 = 1.46, respectively. The interspacing between two nanobars is denoted as L, while the original center-to-center spacing is denoted as L0 = 470 nm, which is equal to half of the lattice period. The offset distance is denoted as ΔL = LL0. When two nanobars are far away from each other (ΔL > 0) or close to each other (ΔL < 0), the high Q-factor MTD mode will be realized due to the breaking of the translational symmetry of the metasurface. In addition, when fixing the high symmetry position of the dimer nanobars, we add a bump shaped like a square to one side of the dimer nanobars, and the focused mode can still be excited, while the field local distribution evolves due to the increase in the length of the square side of the bumps, and it is difficult to obtain a high Q-factor for such a gap-breaking approach in the experiment (see Fig. S1 of the supplementary material). Therefore, we mainly focus on introducing the offset distance to excite the MTD modes. Compared to single nanobar arrays, the guide mode under the light cone is folded to the Γ-point due to the reduction of the first Brillouin region for the dimer metasurface, resulting in the appearance of an ultrahigh Q-factor GMR at the Γ-point. We calculate the optical response characteristics of the devices such as the band structure, Q-factor, and field distribution with the COMSOL Multiphysics and finite-difference time-domain method (FDTD Solutions). Figure 1(d) shows the band structure of the metasurface. In this work, we mainly focus on mode B with normalized eigenfrequency around 0.636, which corresponds to the MTD mode. In addition, the characteristics and eigenfield distributions of modes A and C are shown in Fig. S2. Since the Q-factors of these two modes almost remain above 108 with the change of offset distance, they cannot be excited by changing the spatial distance of the nanobars, and they are not TD-dominated modes in terms of the eigenfield distribution. Figure 1(e) shows that the Q-factor is fairly stable as k-vector changes, so the mode is robust in momentum space. However, the Q-factor decreases rapidly as the nanobar’s spacing changes. It suggests that this mode is not coupled to the oblique incidence but can be excited by tuning the interspacing between nanobar dimers.

FIG. 1.

Excitation of high-Q MTD GMRs. (a) A square array of silicon nanobars containing the MTD resonance principle. (b) A schematic illustration of MTD excitation in the unit cell. (c) Geometric parameter of the unit cell; P is the period of the unit cell, l is the length of the Si nanobars, w is the width, and L0 is the distance between the centers of the 2 nbars. (d) Band structure for nanobar arrays. (e) The simulated Q-factor evolution for mode B along the X′–Γ–X direction for different offset distance ΔL.

FIG. 1.

Excitation of high-Q MTD GMRs. (a) A square array of silicon nanobars containing the MTD resonance principle. (b) A schematic illustration of MTD excitation in the unit cell. (c) Geometric parameter of the unit cell; P is the period of the unit cell, l is the length of the Si nanobars, w is the width, and L0 is the distance between the centers of the 2 nbars. (d) Band structure for nanobar arrays. (e) The simulated Q-factor evolution for mode B along the X′–Γ–X direction for different offset distance ΔL.

Close modal

Next, we adjust the distance between two nanobars in geometric space to achieve a high Q-factor GMR. Figure 2(a) shows the Q-factor and the resonance wavelength of mode B as a function of the offset distance (ΔL) of the silicon metasurface, where the red triangles denote the resonance wavelength with different ΔL, the dark blue five-pointed stars represent the calculated Q-factors, and the black solid line is the fitting result, which shows the inverse quadratic dependence of ΔL. It is clearly seen that the Q-factor decreases with the increase of the |ΔL|, while the resonance wavelength of the GMR is almost stable around 1474.5 nm at different ΔL. To further confirm the existence of such an ultrahigh Q-factors GMR, we calculate the transmission mapping of the metasurface vs ΔL and resonance wavelength under x-polarized light, as shown in Fig. 2(b). Since the ultrahigh Q-factor GMR mode is almost not coupled with the incident light, it can be seen that the resonance peak in the transmission spectrum has the vanished linewidth at ΔL = 0 nm, and the resonance peak becomes broad gradually as |ΔL| increases, suggesting a decreased Q-factor. To better visualize the trend of Q-factors, we extract three sets of transmission spectra with different ΔL plotted in Fig. 2(c); it can be clearly observed that a sharp Fano resonance peak appears near 1474.5 nm, and the linewidth of the spectral line gradually becomes narrower as ΔL decreases; finally, the resonance peak disappears at ΔL = 0 nm.

FIG. 2.

Confirmation of high Q-factor MTD resonance. (a) Dependence of the Q-factor and resonance wavelength (ƛ) of the MTD mode on different offset distance (ΔL); the dark blue stars represent the calculated Q-factor, and the black solid line shows the inverse quadratic dependence of ΔL. The red triangles correspond to ƛ. (b) The transmission mapping vs both ΔL and ƛ. (c) Transmission spectra at ΔL = 0, 15, and 40 nm. (d) Total scattered power and contributions of different multipoles. (e) and (f) The normalized magnetic field vector distribution in the xy plane and electric field vector distribution in the xz plane, respectively.

FIG. 2.

Confirmation of high Q-factor MTD resonance. (a) Dependence of the Q-factor and resonance wavelength (ƛ) of the MTD mode on different offset distance (ΔL); the dark blue stars represent the calculated Q-factor, and the black solid line shows the inverse quadratic dependence of ΔL. The red triangles correspond to ƛ. (b) The transmission mapping vs both ΔL and ƛ. (c) Transmission spectra at ΔL = 0, 15, and 40 nm. (d) Total scattered power and contributions of different multipoles. (e) and (f) The normalized magnetic field vector distribution in the xy plane and electric field vector distribution in the xz plane, respectively.

Close modal

To reveal the nature of this resonant mode, we perform multipole decompositions on the structure with ΔL = 15 nm (see details from Sec. I of the supplementary material). From Fig. 2(d), it can be observed that the MTD dominates this resonance, which accounts for 72.2% of the total scattered power, and it is along the y-direction (see Fig. S3 of the supplementary material). In addition, the dominant response of the MTD is also validated by checking the near-field distributions of the magnetic and electric field vectors in Figs. 2(e) and 2(f). Figure 2(e) illustrates that the magnetic vectors exhibit two opposite circular distributions in the xy plane, which can generate head-to-tail electric dipole moments in the xz plane, as shown in Fig. 2(f), and ultimately excites the MTD in the y-direction. Therefore, both near-field distribution and far-field radiation confirm that the resonance mode is dominated by the MTD response. It is noted that the MTD resonance is universal in a dimer metasurface, given that this folded mode is always present regardless of the shape of the nanobar (i.e., elliptical or circular nanodisk; see Fig. S4 of the supplementary material).

As discussed above, the focused resonant mode is mainly governed by MTD, and the MTD resonance can generate a huge local field enhancement inside the two nanobars structures, which has great potential applications in enhancing the interaction between light and matter. Next, we evaluate the ability of the MTD resonance metasurface to trap electric and magnetic fields within nanostructures. Figures 3(a) and 3(b) demonstrate the electric and magnetic field distributions in the xy plane at the resonance wavelength at ΔL = 15 nm and the one-dimensional line plots of the field enhancement in the y = 0 axis. The different colors in Figs. 3(a) and 3(b) indicate the magnitude of the field intensity, where bright color denotes a strong field and dark color indicates a weak field. It can be easily found that the electric field of the mode is mainly confined inside the two silicon nanobars, while the magnetic field is mainly distributed in the air gap near the edge of the nanobars. Moreover, we find that the trapping capability of the magnetic field is stronger than the electric field by the interior of the nanobar device for this resonant mode, and the field localization by the metasurface gradually increases as ΔL decreases (see Fig. S5 of the supplementary material). In addition, to quantitatively indicate the field enhancement, we defined the average enhancement factor of the electric field intensity (EFE) and the magnetic field intensity (EFH) through integration within the nanostructures, respectively, which takes the following expressions:
EFE=E2dVE02V,
(1a)
EFH=H2dVH02V,
(1b)
where V is the total volume of a unit cell except substrate and E0, E (H0, H) are the electric (magnetic) field intensities of the incident light and the electric (magnetic) field intensities of the resonant metasurface device, respectively. As shown in Figs. 3(c) and 3(d), the maximum value of the average field enhancement at different ΔL is located at the resonance wavelength of 1474.5 nm, and they are fairly stable. Meanwhile, it can be found that as ΔL increases, the values of both EFE and EFH decrease rapidly. To provide a more intuitive comparison of the maximum values for different ΔL, we plot the histograms in Figs. 3(e) and 3(f), when the minimum offset distance ΔL = 5 nm and the maximum average enhancement factor of the electric and magnetic field intensities reaches 4723 and 23 990, respectively. The enhancement of the localized field can effectively facilitate the enhancing of the light–matter interactions at the nanoscale.
FIG. 3.

Local characteristics of the electromagnetic field of a high Q-factor MTD resonance mode. (a) and (b) Distribution of the electric and magnetic fields in the xy plane at the resonance wavelength at ΔL = 15 nm. (c) and (d) The average enhancement factor of the electric and magnetic field intensities vs wavelength at different ΔL. (e) and (f) The maximum value of the average enhancement factor for different ΔL.

FIG. 3.

Local characteristics of the electromagnetic field of a high Q-factor MTD resonance mode. (a) and (b) Distribution of the electric and magnetic fields in the xy plane at the resonance wavelength at ΔL = 15 nm. (c) and (d) The average enhancement factor of the electric and magnetic field intensities vs wavelength at different ΔL. (e) and (f) The maximum value of the average enhancement factor for different ΔL.

Close modal

Finally, we present the experimental demonstrations of the excitation of a high Q-factor MTD mode with stable resonance wavelength. The optical transmission spectra of the fabricated sample are measured using a home-built setup, as shown in Fig. 4(a). The light source from a broadband picosecond pulsing laser (YSL Photonics SC-5-FC) is incident onto the fabricated metasurface with a fiber collimator and then is collected by using an optical spectrometer optical spectrum analyzer (YOKOGAWA AQ-6370B). Since the nanobar dimer metasurface we studied is polarization dependent, we add a linear polarizer between the collimator and the samples to adjust the polarization of the light. We fabricate a series of silicon dimer metasurfaces based on the commercial wafer-340 nm silicon-on-insulator (SOI) platform. The fabrication processes mainly include electron-beam lithography (EBL) and inductively coupled plasma (ICP) etching techniques (see Sec. V). Ten samples with offset distance ΔL in steps of 2 nm are fabricated, and the oblique angle image of a scanning electron microscope (SEM) of the fabricated samples is shown in Fig. 4(b). Figures 4(c) and 4(d) show the measured and simulated transmission spectra, respectively. From the experimental transmission spectra, one can observe that there is an obvious Fano resonance peak around 1474.5 nm, and the peak position remains quite stable with the change of ΔL. The resonance peak becomes narrower, and the extinction ratio drops gradually with the decrease of ΔL. This is understandable because the coupling efficiency of the incident light to the device is usually lower for devices with a high Q factor, which can be extracted by using the Fano fitting (see Sec. II and Fig. S6 of the supplementary material). Figure 4(d) shows the transmission spectra of the corresponding simulation, which exhibit stable wavelengths that match well with the experimental results. Compared to the experimental transmission spectra, the simulated transmission spectra are sharper. Figure 4(e) demonstrates the variation of experimental and simulated Q-factor with ΔL, both of which decrease with the increase of the offset distance ΔL, with the maximum experimental Q-factor reaching 5079. The overall experimental Q-factor is lower than the theoretical values. This can be mainly attributed to the non-uniformity and roughness of the nanobars in the whole device, resulting in partial light scattering into free space. It should be noted that the device we designed is polarization-dependent. Thus, rotating the polarizer could result in different transmission spectra (see Fig. S7 of the supplementary material). We shall expect even higher Q-factor values after the fabrication process and testing system are further optimized. In Table I, we list the experimental Q-factor of the ETD and MTD resonances. The MTD is relatively understudied in the experiment, and the Q-factors obtained in our experiments are the recorded values of the MTD resonance.

FIG. 4.

Experimental confirmation of high Q-factor MTD resonance excitation. (a) Measurement system. (b) The scanning electron microscope image from an oblique view; the scale bar in white is 200 nm. (c) Experimental transmission spectra at different ΔL. (d) Transmission spectra corresponding to the simulation. (e) Comparison of experimental and theoretical Q-factors at different ΔL.

FIG. 4.

Experimental confirmation of high Q-factor MTD resonance excitation. (a) Measurement system. (b) The scanning electron microscope image from an oblique view; the scale bar in white is 200 nm. (c) Experimental transmission spectra at different ΔL. (d) Transmission spectra corresponding to the simulation. (e) Comparison of experimental and theoretical Q-factors at different ΔL.

Close modal

In summary, we demonstrate the high Q-factor MTD mode in dielectric metasurfaces through theoretical predictions as well as experimental validation. The designed metasurface consists of an array of silicon nanobar dimers, and the Q-factor of the mode shows weak dependence on the wave vector in the momentum space. By changing the spacing of the nanobar dimers, the high Q-factor GMR with stable resonance wavelength can be achieved. In addition, both the multipole decomposition and the near-field distribution confirm that MTD dominates in this mode. In addition, we calculate the local field enhancement and the average field enhancement factor of the MTD mode, whose magnetic field enhancement is larger than the electric field enhancement attributed to significant MTD response, and the field enhancement is effectively regulated when the spacing of the nanobars is regulated. Finally, we experimentally demonstrate the existence of the MTD mode, and the experimental measurements and simulated results are in good agreement, and a high Q-factor of 5079 for the MTD mode in the experiment is obtained. This MTD resonator with a high-Q factor and stable resonance wavelength may facilitate the realization of a high-quality nonlinear light source and low-threshold laser.

The finite difference-time-domain method (FDTD Solution) is employed to calculate the transmission spectrum, field distribution, and multipole decomposition of the metasurface, and the finite element method (COMSOL Multiphysics) is used to calculate the Q-factor and eigenfields. In the simulation, periodic boundary conditions are set in the x- and y-directions, and perfectly matched layers (PMLs) are set in the z-direction. An x-polarized plane wave is normally incident on metasurfaces to excite this high-Q mode.

The metasurface is fabricated on silicon on insulator (SOI) wafers with a top layer of silicon 340 nm thick and a silicon substrate ∼700 µm thick. First, a resist layer (ZEP520) is applied to a clean SOI wafer. Then, the metasurface pattern was defined into the photoresist by electron beam lithography (EBL), followed by development and fixation. The silicon metasurface was etched by inductively coupled plasma (ICP). Finally, the remaining resist was removed with N-methyl-2-pyrrolidone liquor. Note that the metasurfaces are fabricated in Tianjin H-Chip Technology Group Corporation.

The samples are measured by a piece of homemade equipment. Applying a supercontinuum light source (YSL Photonics SC-5-FC, 400–2200 nm), the light is normally incident on the fabricated metasurface and then is collected by using an optical spectrum analyzer (YOKOGAWA AQ-6370B, 600–1700 nm).

Multipole decomposition, Fano fitting, characterization of the non-radiation modes, the far-field scattering power ratio of multipoles, magnetic toroidal dipole modes with different shapes, the enhanced electric field for different ΔL, and experimentally measured transmission mapping vs the different polarization angle and wavelength can be found in the supplementary material.

C. Zhou and J. Huang were supported by the National Natural Science Foundation of China (Nos. 12164008 and 12004084), the Science and Technology Innovation Team Project of Guizhou Colleges and Universities (No. [2023]060), the Guizhou Provincial Science and Technology Projects (Nos. ZK[2024]504 and ZK[2021]030), and the Natural Science Foundation of Guizhou Minzu University (Nos. GZMUZK[2022]YB04, GZMUZK[2024]QD29, and GZMUZK[2023]CXTD06). L. Huang and A. E. Miroshnichenko were supported by the Australian Research Council Discovery Project (No. DP200101353) and the UNSW Scientia Fellowship program. L. Huang was also sponsored by the Shanghai Pujiang Program (No. 22PJ1402900).

The authors declare no conflict of interest.

Ying Zhang and Lulu Wang contributed equally to this work.

Ying Zhang: Investigation (equal); Methodology (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Lulu Wang: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Visualization (equal). Haoxuan He: Investigation (equal); Methodology (equal); Validation (equal); Writing – original draft (equal). Hong Duan: Supervision (equal). Jing Huang: Investigation (equal). Chenggui Gao: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Visualization (equal). Shaojun You: Investigation (equal). Lujun Huang: Validation (equal). Andrey E. Miroshnichenko: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Visualization (equal). Chaobiao Zhou: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Visualization (equal).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

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