Ultra-compact and tunable devices for terahertz (THz) beam manipulation are highly desired in wireless communication and radar scanning. Although the appearance of the Pancharatnam-Berry (PB) metasurface has provided strategies for THz beam scanning, active output power distribution is still difficult to achieve, and the flexibility of beam manipulation is limited by a single metasurface. In this work, we demonstrated an all-dielectric cascaded metasurface consisting of a spin-decoupled metasurface and a PB metasurface. The conjugated characteristic of the PB phase for two photonic spin states is broken with highly efficient high-order diffractions of wave vector superposition through the cascaded metasurfaces, and both spin-symmetric and spin-asymmetric transmissions are obtained by designing the differences in metasurface bandwidth. Moreover, the output power between the deflection beams can be actively tuned by changing the incident polarization state, achieving power modulation ratios of 99.3% and 95.1% for the two conjugated spin beams, respectively. Therefore, this work realizes controllable wave division multiplexing and power distribution and opens new avenues for the design of ultra-compact multifunctional devices.

## I. INTRODUCTION

Electromagnetic waves in the frequency band of 0.1–10 THz (1 THz = 10^{12} Hz) are defined as Terahertz (THz) waves. Due to its important applications in wireless communication,^{1,2} radar monitoring,^{3} imaging,^{4} and sensing,^{5,6} THz technology has attracted considerable attention recently. In addition to the vital THz sources^{7} and detectors,^{8,9} efficient THz manipulation technologies, including beam focusing, deflection, steering, and polarization conversion, are also highly desired in these applications.^{10–12} For conventional THz deflection devices, active angle scanning and energy distribution are hard to realize, which limits the degree of freedom of beam control. Moreover, their bulky size and low efficiency also cannot meet the needs of ultra-compact devices.^{13}

The rapid development of metasurfaces provides an effective solution for ultra-compact and high-efficiency THz wavefront manipulation devices.^{14–16} Metasurfaces are constituted of prearranged artificial unit cells or so-called meta-atoms with sub-wavelength size, the meta-atoms are capable of generating abrupt phase changes over the scale of the wavelength.^{17–19} By constructing meta-atoms to form certain predesigned phase profiles, versatile beam manipulation effects can be demonstrated, such as anomalous deflection,^{20–22} polarization manipulation,^{23,24} and holograms.^{25–27}

Pancharatnam–Berry (PB) metasurfaces, which are composed of half-wave-plate (HWP) meta-atoms with the spatial rotation axis, exhibit interesting properties in manipulating right-handed circularly polarized (RCP) states and left-handed circularly polarized (LCP) states with conjugated spatial phase distribution.^{28–30} PB metasurfaces have been proposed for various functions, such as special beam generation,^{31–33} metalens,^{34} hologram,^{35,36} and anomalous reflection.^{37–39} To break the spin-conjugated symmetry of the geometric phase, a strategy is proposed to manipulate independent phase profiles by introducing additional dynamic phases. This kind of metasurface is also known as a spin-decoupled metasurface.^{40–42} For example, Li *et al.*^{43} proposed a metasurface with these two types of phases, broke the conjugated characteristic of the PB phase simultaneously, and achieved the longitudinal focusing and transverse shifting of different spin states.

However, the fixed structure cannot meet the requirements of dynamic manipulation of THz beam deflection, and the active control of power distribution is also difficult to achieve for the traditional PB or decoupled metasurfaces. Therefore, different kinds of fabrication processes and materials have been introduced into the metasurface devices for efficient diffraction and active functions. For example, PB metasurfaces integrated with magneto-optical materials,^{44} graphene,^{45} and liquid crystals^{46} have been demonstrated recently. Kim *et al.*^{45} proposed a gate-controlled THz PB metasurface that combined graphene to modulate the intensity of anomalous refracted waves, but the modulation depth was limited to 28%. Moreover, the rise of semiconductor materials has effectively improved the speed of beam modulation.^{47,48} For example, Lan *et al.*^{47} recently demonstrated a reconfigurable metasurface based on GaN technology, achieving wide-angle beam scanning with a high speed of 100 MHz. However, an active THz beam deflection device with high modulation depth is still a challenge, and the flexibility in high-order diffraction, large-angle deflection, spin conversion, and order transformation is limited by a single metasurface. Cascading two or more metasurfaces may greatly enrich the function of beam manipulation.

In this work, we propose an all-dielectric cascaded metasurface that integrates a decoupled metasurface and a PB metasurface. The conjugated characteristic of the PB phase for two photonic spin states is broken by efficient high-order diffractions through the wave vector superposition of the cascaded metasurfaces. Moreover, the spin-asymmetric transmission for spin-locked states (*RR* state and *LL* state) and the spin-symmetric transmission for spin–flip states (*RL* state and *LR* state) are obtained in different frequency bands based on the differences in metasurface bandwidth designing. By changing the incident polarization state, the active power distribution between the deflection beams has been confirmed. The unique method of manipulating the deflection of spin photons may have a significant impact on the design of ultra-compact multifunctional devices and spin photonics devices.

## II. METHODS

### A. Metasurface design and fabrication

The cascaded metasurface is composed of a decoupled metasurface and a PB metasurface. Both the two metasurfaces were fabricated by a photolithography process and reactive ion beam etching on a high-resistance Si substrate of >10 kΩ cm with a thickness of 1 mm. The detailed fabrication process and geometric parameters can be found in Sec. A of the supplementary material. As shown in Fig. 1(a), the THz wave passes through the decoupled metasurface first. A supercell of decoupled metasurface consists of three rectangular silicon column meta-atoms with different lengths (*l*), widths (*w*), and orientations (*θ*). Different from the decoupled metasurface, a PB supercell is composed of four meta-atoms with the same length and width but different orientation angles with a step of Δ*θ*_{PB} = 45° along the *x*-axis. The scanning electron microscope (SEM) photographs of two metasurfaces are shown in the inset in Fig. 1(a). The two metasurface layers are tightly attached with no separated air gap, and only a layer of Si substrate is separated between the spin-decoupled microstructures and the PB microstructures. The size of both metasurfaces is 1.5 × 1.5 cm^{2}, so there are 17 supercells in the *x*-direction for the PB metasurface and 26 supercells in the *x*-direction for the decoupled metasurface.

*t*

_{x}=

*t*

_{y}= 1 is satisfied, for the normal incidence of two conjugate photonic spin states, the output beam will be transformed with the form as follows:

^{44}

*iθ*and −2

*iθ*are introduced into LCP and RCP states, respectively, and the spin states will be converted to their spin–flip states. Consequently, the spatial phases introduced by PB meta-atoms are merely determined by their orientation angle

*θ*, and the PB phase has spin symmetry. The simulation results for the transmission property of each meta-atom are shown in Sec. B of the supplementary material.

*θ*. It should be noted that decoupled meta-atoms also have the function of HWP. With the combination of the PB phase and dynamic phase, the metasurface can realize the asymmetric transmission of different spin states. In the ideal case of

*t*

_{x}=

*t*

_{y}= 1, for the normal incidence of two conjugate photonic spin states, the output beam will be transformed as follows:

^{43}

*ϕ*

_{x}is the phase of the meta-atoms in the

*x*-direction and it is related to the dynamic phase. The spin states will also be converted to their spin–flip states, and their spatial phases are determined by both geometry and the orientation angle of the meta-atoms. Consequently, with a reasonable design of the meta-atoms, asymmetrical spatial phase gradients for conjugated photonic spin states can be introduced, thus breaking the spin symmetry of the PB phase.

### B. Transmission matrix and wave vector matching of cascaded metasurface

The working frequency band in which the metasurface has good spin state conversion and beam deflection performance is worthy of our attention. In the simulation, we get the frequency-dependent far-field diffraction distribution of two metasurfaces as shown in Fig. 1(b). For incident conjugated spin states, a decoupled metasurface can achieve asymmetric transmission. This means when an RCP state is incident, the beam will deflect toward the negative angle side in the range of Δ*f*_{DC} = 0.6–0.85 THz, while the beam will not deflect when an LCP state is incident. However, outside this frequency range, there are still plenty of directly transmitted components that exist at 0° when the RCP state is incident, indicating that the spin-decoupling effect fails. In contrast, the PB metasurface can realize symmetrical deflection transmission with high diffraction efficiency in a broader frequency range of over 0.5–1.05 THz than the decoupled metasurface in the simulation.

Whereas, outside the frequency range Δ*f*_{DC}, there are plenty of directly transmitted components with *φ*_{1} = 0° after the THz beam passes through the decoupled metasurface. In this case, the spin conversion and spatial phase of the decoupled meta-atoms will disappear, so the transmission matrix of the cascaded metasurface is consistent with that of the PB meta-atoms as shown in Eq. (1).

*m*th order diffraction wave meets the conditions in the

*K*space as follows:

*k*

_{in}=

*k*

_{out}= 2

*πf*/

*c*,

*c*is the speed of light in vacuum,

*f*is the frequency of a THz wave,

*φ*

_{in}and

*φ*

_{out}are the incident and output angles, respectively. The diffraction angle, which is equivalent to the deflection angle in this work, can be directly obtained by substituting the additional vector

*K*= 2

*π*/

*A*of the periodical structures of the metasurface, where

*A*is the period of one supercell in the metasurface. We define that the sign of the

*K*vector is “−” when the phase delay of meta-atoms on the left side is larger than that of the right side, and “+” is for the opposite case.

*K*vectors of the decoupled metasurface and the PB metasurface as

*K*

_{DC}and

*K*

_{PB}, respectively. They correspond to the supercell periods of

*A*

_{DC}= 540

*µ*m and

*A*= 800

_{PB}*µ*m, respectively. Since the THz wave is vertically incident, the incidence angle

*φ*

_{in}= 0°. Therefore, the final diffraction angle of the cascaded metasurface satisfies the equations as follows:

*m*

_{1}and

*m*

_{2}represent the diffraction order of THz waves passing through the decoupled metasurface and the PB metasurface, respectively. It reveals that the metasurface vectors

*K*

_{DC}and

*K*

_{PB}determine the final diffraction angle.

### C. Experimental methods

We utilized an angle-resolved THz time-domain polarization spectroscopy (AR-THz-TDPS) system as shown in Fig 1(c). The femtosecond laser used is a fiber-based femtosecond laser (CFL-10RFF from Carmel Laser Company). It works at 780 nm with a repetition rate of 80 MHz and a pulse width of 86 fs. All experiments were carried out at room temperature (20 ± 2 °C) and relative humidity <30%. The laser beam is divided into two optical paths by a beam splitter, and both laser beams illuminate on THz GaAs photoconductive antenna (PCA), respectively. One is used to excite the THz wave, and the other is used to detect the THz signal.

The excited THz wave polarizes along the *y*-axis direction, and the parabolic mirror collimates the THz wave into a parallel beam with a diameter of 2 cm. The metasurface is placed at the center of a rotating table. As shown in Fig. 1(d), after the beam passes through the first polarizer and the metasurface, it is deflected with a diffraction angle *φ* and incident into the detector after passing through the second rotatable polarizer. The deflected parallel beam is focused on the PCA probe by a silicon lens located at the front of the detector. The angle-adjustable module has an angle resolution of 0.25°. Compared with the traditional THz-TDS system, we add a pair of THz polarizers before and after the metasurface for the generation and detection of orthogonal linearly polarized (LP) states. The THz polarizers are composed of double-layer metallic wire grids. The polarizers have more than 99.7% polarization degree in a range of 0.3 to 2.0 THz.

*A*

_{±45°}and phase

*δ*

_{±45°}of the orthogonal signal can be obtained by Fourier transform. The amplitude transmission of RCP and LCP components can be given by

*RR*,

*LR*,

*RL*, and

*LL*) can be obtained as follows:

^{49,50}

*t*

_{++45°},

*t*

_{+−45°},

*t*

_{−+45°}, and

*t*

_{−−45°}are obtained by rotating two THz polarizers.

## III. RESULTS AND DISCUSSION

### A. Spin-asymmetric transmission

When the decoupled metasurface realizes good performance in spin conversion and beam deflection, it exhibits decoupled transmission properties for different photonic spin states as shown in Fig. 2(a). At this point, both metasurfaces can achieve the conversion of spin states. Therefore, the beam will retain its initial spin state after passing through the cascaded metasurface, that is, the spin-locked states *RR* and *LL*.

Next, we discuss the wave vector matching process of the spin-asymmetric transmission as shown in Fig. 2(b). As discussed in Sec. II B, the decoupled metasurface forms a negative phase gradient profile only for the incident RCP state, so the metasurface vector *K*_{DC} = 2*π*/*A*_{DC} is negative along the *x*-axis for the incident RCP state, and *K*_{DC} = 0 for the incident LCP state. Consequently, the RCP state can be converted to the LCP state and diffracted to −1st order (*m*_{1} = 1) with the diffraction angle *φ*_{1} = arcsin(−*λ*/*A*_{DC}) calculated by Eq. (4). While the LCP state is converted to the RCP state and still stays at 0°. Since the PB metasurface forms conjugated gradient phases for different spin states, the vectors *K*_{PB} = 2*π*/*A*_{PB} have opposite directions along the *x*-axis for the two spin states, respectively. For the above outgoing wave vector *k*_{1} along the *z*-axis direction, when it is superposed with the vector *K*_{PB}, +1st order (*m*_{2} = 1) diffraction can be obtained, and the RCP state is converted to the LCP state.

*k*

_{1}is incident on the PB metasurface with the incident angle

*φ*

_{1},

*k*

_{1x}and

*K*

_{PB}has the same direction along the

*x*-axis, which results in a cut-off frequency

*f*

_{c}of −1st order diffraction satisfying the following conditions:

*f*

_{c}= 0.93 THz is obtained, which means −1st order diffraction exists only for

*f*> 0.93 THz. Therefore, in the frequency band Δ

*f*

_{DC}, the beam cannot meet the wave vector matching condition of −1st order diffraction, and the energy of the beam will be diffracted to a higher order. At this point, the direction of

*K*

_{PB}is no longer in the negative direction of the

*x*-axis. When

*m*

_{2}= 3,

*k*

_{1}can be well matched with

*k*

_{2}to obtain +3rd order diffraction, and the LCP state will be converted to the RCP state.

In this case, according to Eq. (5), the diffraction angle of the cascaded metasurface is *φ*_{LL} = arcsin[+*c*/(*fA*_{PB})] when the RCP state is incident, and *φ*_{RR} = arcsin[−*c*/(*fA*_{DC}) + 3*c*/(*fA*_{PB})] when the LCP state is incident. The results show that the two spin-locked states *RR* and *LL* are deflected to the same side with different diffraction angles. We use the beam diffraction order: +1st and +3rd orders through the PB metasurface to distinguish the two deflected beams.

In the simulation, we get the frequency-dependent diffraction distribution of two spin-locked states as shown in Fig. 2(c). The results show that both spin-locked states *LL* and *RR* are diffracted to a positive angle with different diffraction orders. The diffraction angles *φ*_{LL} and *φ*_{RR} satisfy the frequency-angle correspondence of the +1st order and +3rd order, respectively. The diffraction frequency range of the +1st order is wider than that of the +3rd order, which is related to the critical angle for total internal reflection. The diffraction intensity of the +1st order is also stronger than that of the +3rd order.

We scanned the diffraction angles in the experiment and obtained the diffraction efficiency of the cascaded metasurface as shown in Fig. 2(d). For the *LL* state, the +1st diffraction order covers the frequency range over 0.52–1 THz, corresponding to the diffraction angle range over 22°–46°. While for the *RR* state, the +3rd order covers the frequency range over 0.6–0.87 THz, corresponding to a larger diffraction angle over 41°–72°. The intensity of both diffraction orders reaches its maximum at 0.72 THz, and the diffraction intensity of the +1st order is also stronger than that of the +3rd order in the experiment. As a consequence, the spin-asymmetric transmission between the two spin-locked states *RR* and *LL* can be achieved by the cascaded metasurface in the frequency band 0.6–0.87 THz.

### B. Spin-symmetric transmission

When the beam frequency is outside the operating frequency band Δ*f*_{DC} of the decoupled metasurface, there are plenty of directly transmitted components that maintain the original spin states at *φ*_{1} = 0° after the THz beam passes through the decoupled metasurface as shown in Fig. 3(a). At this point, the vectors *K*_{DC} for the two spin states are always equal to 0, resulting in the outgoing wave vector *k*_{1} remaining in the *z*-axis direction without deflection as shown in Fig. 3(b). The vectors *K*_{PB} = 2*π*/*A*_{PB} still have opposite directions along the *x*-axis for the two spin states, respectively. In this case, the cascaded metasurface will degenerate into a PB metasurface with the functions of spin conversion and spin-symmetric transmission. When the outgoing wave vector *k*_{1} is superposed with the vector *K*_{PB}, +1st order and −1st order diffraction (*m*_{2} = 1) can be obtained for the two spin states, respectively. The diffraction angle of the cascaded metasurface becomes *φ*_{LR} = arcsin[+*c*/(*fA*_{PB})] when the RCP state is incident, and *φ*_{RL} = arcsin[−*c*/(*fA*_{PB})] when the LCP state is incident. Consequently, the two spin–flip states RL and LR are deflected to different sides in the *x*-direction with the same diffraction angles.

Similarly, we verified the theory in the simulation and experiment, and the frequency-dependent diffraction distributions of two spin–flip states are shown in Figs. 3(c) and 3(d). The simulated results reveal that the diffraction distributions of the two spin–flip states *RL* and *LR* are symmetric to 0°, and the beams have essentially equal power at ±1st order. In the experiment, we scanned the diffraction angles and obtained a symmetric diffraction distribution for *RL* and *LR* states in a frequency band of 0.42–0.67 and 0.85–1.05 THz, corresponding to a diffraction angle of 34°–63° and 21°–26°. There are some deviations between the simulation and experimental results in terms of diffraction efficiency and bandwidth, which are mainly caused by the imperfections in the actual fabrication process. Fortunately, a larger bandwidth was obtained in the experiments. Therefore, the spin-symmetric transmission between the two spin–flip states *RL* and *LR* can be achieved by the cascaded metasurface in the frequency bands 0.42–0.67 and 0.85–1.05 THz.

### C. Active power distribution

*y*axis. The fast axis of the QWP forms an angle of

*α*relative to the

*y*axis, the LP state will be converted into an RCP state when

*α*= 45° and into an LCP state when

*α*= 135° with different spatial phases, and the ratio of LCP and RCP components can be tuned by rotating the QWP. When the cascaded metasurface achieves asymmetric transmission, the beam transmission matrix after the introduction of QWP can be obtained as follows:

*f*

_{DC}of the decoupled metasurface, the transmission matrix is simplified as the PB metasurface,

In the simulation, the QWP is modeled as a medium with uniaxial anisotropy, a detailed simulation of the QWP can be found in Sec. D of the supplementary material. We selected the incident wave sources with frequencies of 0.7 and 0.45 THz, respectively, and obtained far-field transmittance spectra to verify the power distribution function as shown in Figs. 4(b) and 4(c). When the wave is incident with a frequency of 0.7 THz, the beam can be diffracted to +32.5° and +54.5° diffraction angles, respectively, corresponding to the diffraction angles of the +1st and +3rd orders in the frequency band Δ*f*_{DC}. It can be seen that the beam power can be actively distributed from +3rd order to +1st order with the increase of the rotation angle *α*. Whereas, when the wave is incident with a frequency of 0.45 THz, the beam can be diffracted to ±56.5° diffraction angles symmetrically, corresponding to the diffraction angles of the ±1st orders outside the frequency range Δ*f*_{DC}, and the power is dynamically tuned between ±56.5° diffraction angles as the rotation angle changes. Therefore, the rotation of the QWP can be regarded as an efficient strategy to actively distribute the power between the diffraction beams.

We carry out the experiments in the AR-THz-TDPS system. The diffraction angles measured in the experiment are calculated by substituting the selected frequencies of 0.7, 0.8, and 0.45 THz into the diffraction angle equation for different diffraction orders. The actual measurement frequencies were 0.69, 0.78, and 0.45 THz due to the mechanical error introduced by the instrument. As discussed in Secs. III A and III B, spin-asymmetric transmission can be achieved theoretically by cascading metasurface at 0.69 and 0.78 THz, while spin-symmetric transmission can be achieved at 0.45 THz. The results at these three frequencies are shown in Figs. 5(a)–5(c). At 0.69 THz, when *α* is rotated from 45° to 135°, beam power is gradually distributed from 54.5° (+3rd) diffraction angle to 32.5° (+1st) diffraction angle. At the same time, two diffraction beams have opposite spin states. Similar results are found at 0.78 THz. While at 0.45 THz, the beam power is distributed between 56.5° (±1st) diffraction angles on different sides, and two diffraction beams also have opposite spin states. In addition, there is a residual signal for the LCP transmission at 54.5° and 45.5° diffraction angles. The reason is that under the oblique incidence condition, the PB phase matching condition in high-order diffraction is no longer perfectly satisfied, but this residual peak below 15% only causes a small negative impact on the overall performance of the device.

The angular resolution of the diffractive beam is determined by the number of metasurface supercells and working frequency, which have been given in Sec. II A. The larger the aperture of the metasurfaces, the narrower the beam angle width will be. According to the dependence between frequency and diffraction angle, the full width at half maximum (FWHM) of the transmission peak in the experiment can also reflect the diffraction angle width. The experimental results in Fig. 5 reveal that the FWHM is in the range of 28–48 GHz.

We define the power modulation ratio (PMR): *R*_{α} = (*T*_{max} − *T*_{α})/*T*_{max} to characterize the performance of active power distribution between the diffraction beams, where *T*_{α} is the intensity transmittance at different QWP rotation angles, and *T*_{max} is the maximum intensity transmittance at the corresponding diffraction angles. The results are shown in Figs. 6(a) and 6(b). At 0.78 THz, the PMR of the two diffraction orders reaches 99.3% and 95.1%, respectively, indicating that the energy is allocated to the other diffraction beam with the rotation of QWP. At 0.45 THz, the PMR of the two diffraction orders also reaches 88.2% and 92.8%, respectively. The experimental results show that no matter the spin-asymmetric transmission or the spin-symmetric transmission, the beam power can be actively distributed between the two diffraction beams depending on the rotation of QWP. In the actual device, the PMR is affected by the spin conversion efficiency of the decoupled metasurface and the PB metasurface. Moreover, when the frequency of the deflected beam deviates from the center frequency of QWP, the modulation efficiency will also be reduced. Consequently, the modulation depth is determined by the matching degree of the bandwidth and center frequency of these three components.

Finally, this controllable beam steering and power distribution method is expected to show great potential applications. For example, in a point-to-point THz communication network, when the network link is blocked, active beam steering can effectively establish a new link without mechanical movement to realize the function of fast anti-shielding interference. Active beam manipulation with large deflection angles and a wide scanning range can also effectively realize multi-azimuth target monitoring in radar monitoring. It should be pointed out that mechanically rotating the QWP is only intended to demonstrate the physical process of device modulation in the simplest way by changing the incident polarization states. Other active modulation mechanisms for the metasurfaces excited by the electric, optical, and magnetic fields are more practical options,^{44–48} but this issue is not the main focus of this work.

## IV. CONCLUSION

In summary, we demonstrated an all-dielectric cascaded metasurface consisting of a decoupled metasurface and a PB metasurface for THz beam manipulation. Spin-asymmetric and spin-symmetric diffraction transmission is realized in different frequency bands for two conjugate photonic spin states, and active power distribution between the diffraction beams of the same frequency is achieved by the rotation of QWP. Some conclusions can be drawn: (1) In a frequency band of 0.6–0.87 THz, the cascaded metasurface can induce the +1st and +3rd order diffraction for the two spin-locked states *RR* and *LL,* respectively, realizing the spin-asymmetric transmission. (2) In a frequency band of 0.42–0.67 and 0.85–1.05 THz, the cascaded metasurface degenerates to the PB metasurface, which can induce the +1st and −1st order diffraction for the two spin–flip states *RL* and *LR*, respectively, thus achieving a spin-symmetric transmission. (3) Relying on the polarization conversion characteristic of the QWP, the active power distribution between the diffraction beams is realized. The experimental results show that the power modulation ratio of the two diffraction orders at 0.78 THz reaches 99.3% and 95.1%, respectively. Therefore, this work provides a scheme of active THz manipulation and realizes controllable wavelength division multiplexing, spin separation, conversion, and power distribution. The proposed metasurface has a significant impact on designing ultra-compact multifunctional devices and has certain application potential in terahertz wireless communication, radar, and imaging.

## SUPPLEMENTARY MATERIAL

See the supplementary material for further details on metasurface structure and fabrication, metasurface design, transmission matrix derivation, simulation modeling, and a discussion of the distance between two metasurfaces.

## ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (Grant Nos. 62371258, 62335012, 61971242, 61831012, 62205160) and the National Key Research and Development Program of China (Grant No. 2017YFA0701000).

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

### Author Contributions

**Jiayue Liu**: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Methodology (lead); Resources (equal); Validation (lead); Visualization (lead); Writing – original draft (lead). **Fei Fan**: Conceptualization (equal); Formal analysis (supporting); Funding acquisition (equal); Methodology (supporting); Resources (equal); Visualization (supporting); Writing – review & editing (equal). **Zhiyu Tan**: Resources (equal); Writing – review & editing (equal). **Huijun Zhao**: Methodology (supporting); Visualization (supporting); Writing – review & editing (equal). **Jierong Cheng**: Methodology (supporting); Resources (equal). **Shengjiang Chang**: Funding acquisition (equal); Resources (equal).

## DATA AVAILABILITY

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