With the growing demand for high-speed 5G/6G wireless communication in various fields such as biological detection,1 holographic imaging,2 and security detection,3 terahertz (THz, $1\mathrm{THz}={10}^{12}\mathrm{Hz}$) technology has emerged as a research hotspot in recent years.4^–6 Among that, the THz wavefront technology especially is crucial in THz communication systems, such as dynamically adjusting multi-channel deflection and providing multiple operating frequency points to enhance information transmission capacity.

As a synthetic subwavelength periodic structure, metasurfaces have a high degree of freedom in manipulating electromagnetic wavefront (including amplitude,7^,8 phase,9 and polarization10), ranging from optical to microwave frequency band. By changing the geometric sizes of meta-atoms, the phase of the output light, including the transmission phase and geometric phase, can be effectively coded. Through precisely designed phase and amplitude profiles, various exotic functions based on metasurfaces have been demonstrated, such as abnormal reflectors,11 meta-lenses,12 holograms,13 special beam generators,14 and beam scanning.15^,16 Therefore, the metasurface is an excellent method for wavelength division multiplexing (WDM) and polarization division multiplexing (PDM) in the THz region. However, its practical application in THz communication systems is limited by fixed properties and passive responses once manufactured.

To extend the controllability and multi-functionality of metasurfaces, the integration with active materials [such as liquid crystals,17^,18 phase-change materials,19^,20 and magnetic-optical (MO) materials,21^–24] is widely used to realize dynamic wavefront manipulation and reconfiguration. Among that, benefit from the various MO responses under external magnetic field (EMF) in the THz region (e.g., Faraday rotation effect,25 MO Kerr effect,26 and MO circular dichroism27), the MO materials (e.g., InSb,28 graphene,29 and ferrite30) have been paid much attention. Different from ultraviolet (UV)-visible-near-infrared bands, limited by the weak interaction between THz waves and materials, there are many disadvantages of low efficiency, high insertion loss, and harsh working environment in the THz region,31^–33 which severely limits the application in THz wavefront technology. Fortunately, in recent years, yttrium iron garnet (YIG) has been widely studied which has an obvious Faraday rotation effect with relatively small absorption, low loss, and no need for strong EMF excitation. In 2024, Zhang et al.34 prepared substrate-free La:YIG films with the Verdet constant of 74 deg/(mm T) at room temperature. From the perspective of MO modulation, it is a promising candidate for the WDM and PDM in the THz communication system.

In this study, a magnetic phase-coding meta-atom (MPM) is designed, which achieves the heterogeneous integration of the La:YIG MO crystal working at room temperature and the Si-dielectric meta-atom. By coupling the magneto-induced phase with the propagation phase, each MPM can arbitrarily manipulate the output phase of the incident linear polarization (LP) light at different frequencies and EMFs simultaneously. Using the MPM as a pixel, a MO metasurface is fabricated which integrates various output phase distributions into one surface under different EMFs at 0.25 and 0.5 THz, so achieving the function of dynamic multi-channel beam deflection by EMFs with dual-working frequencies. Furthermore, coupled with the nonreciprocal phase delay in the MO layer, the MO metasurface also realizes the one-way beam steering.

The designed structure of MPM is composed of two rectangular meta-atoms and an MO layer, as shown in Figs. 1(a) and 1(b). The thickness of the MO layer is $h_1=2\mathrm{mm}$. The transmission characteristics of La:YIG crystal are shown in Fig. S6 of the Supplementary Material. Besides, the metasurface was prepared on high-resistance ($>10\mathrm{K}\mathrm{cm}$) Si chips with a height of $H=1\mathrm{mm}$, and the etching depth is $h_2=500\mu \mathrm{m}$. The transverse period is $P=425\mu \mathrm{m}$. The sample fabrication method and the detailed geometry of each rectangular cell are given in Sec. 5 and Sec. 1 of the Supplementary Material, respectively. The schematic diagram of the paraxial approximation is given in Fig. S7 of the Supplementary Material.

Based on the Faraday rotation effect of the MO layer and rectangular Si-dielectric units, the transmission characteristics can be analyzed using the Jones matrix of one meta-atom, which can be written as35$$J=\left(\begin{array}{cc}{E}_{xx}& E_{xy}\\ E_{xy}& E_{yy}\end{array}\right)=\left(\begin{array}{cc}\cos \phi & -\sin \phi \\ \sin \phi & \cos \phi \end{array}\right)\left(\begin{array}{cc}{E}_{x0}& 0\\ 0& E_{y0}\end{array}\right)\left(\begin{array}{cc}\cos \phi & \sin \phi \\ -\sin \phi & \cos \phi \end{array}\right),$$(1)where $\phi =B\mathrm{V}{h}_1$ is the Faraday rotation angle of the MO layer, $B$ is the intensity of EMF, and $V$ is the Verdet constant. $E_{x0}$ and $E_{y0}$ are the transmit complex fields produced by the rectangular meta-atom. Then, each element of $J$ can be written as $$\begin{gathered} E_{xx}=E_{x0}{\cos }^2\phi +E_{y0}{\sin }^2\phi \\ {E}_{xy}=E_{yx}=\frac{1}{2}(E_{x0}-E_{y0})\sin 2\phi \\ {E}_{yy}=E_{x0}{\sin }^2\phi +E_{y0}{\cos }^2\phi . \end{gathered}$$(2)

Besides, $E_{xx}$, $E_{yy}$, and $E_{xy}$ are the complex fields of the co-polarization and cross-polarization components. According to a paraxial approximation, for a unit cell composed of $N$ rectangular met-atoms, the Jones matrix can be expressed as $$\left(\begin{array}{cc}{E}_{xx}^{\mathrm{tot}}& E_{xy}^{\mathrm{tot}}\\ E_{xy}^{\mathrm{tot}}& E_{yy}^{\mathrm{tot}}\end{array}\right)=\frac{1}{N}\sum _{i=1}^N\left(\begin{array}{cc}{E}_{xx}^i& E_{xy}^i\\ E_{xy}^i& E_{yy}^i\end{array}\right)(i=1,2,\dots ,N),$$(3)where $N=2$ for the designed MPM. The paraxial approximation has been introduced in detail in Sec. 5 of the Supplementary Material. When there are $M$ different channels under the corresponding EMF, the transmission response can be written as $$O=\left(\begin{array}{c}\begin{array}{l}{O}_1\\ O_2\\ .\\ .\end{array}\\ O_M\end{array}\right)=\left(\begin{array}{ccc}{\cos }^2{\phi }_1& \sin 2{\phi }_1& {\sin }^2{\phi }_1\\ \begin{array}{l}{\cos }^2{\phi }_2\\ \dots \end{array}& \begin{array}{l}\sin 2{\phi }_2\\ \dots \end{array}& \begin{array}{l}{\sin }^2{\phi }_2\\ \dots \end{array}\\ {\cos }^2{\phi }_M& \sin 2{\phi }_M& {\sin }^2{\phi }_M\end{array}\right)\tilde{E}=A\tilde{E},$$(4)$$\tilde{E}=\left(\begin{array}{c}{E}_{xx}\\ E_{xy}\\ E_{yy}\end{array}\right)=(A^{T}A{)}^{-1}{A}^{T}O.$$(5)

Based on Eqs. (4) and (5), the target $[E_{xx},E_{xy},E_{yy}{]}^T$ can be inferred by the designed THz field distribution. In this work, the optical response of each unit cell at 0.25 and 0.5 THz has been simulated under the working EMFs of $+0.24$, 0, and $-0.24\mathrm{T}$ (i.e., $M=3$). The incident polarization is set as $+45\text{-}\mathrm{deg}$ LP to the $x$-axis, and the output polarization is set as 0 deg for channel 1, 45 deg for channel 2, and 90 deg for channel 3, both at the designed dual frequencies.

Then, the database is built $[{\tilde{E}}_{xx1},{\tilde{E}}_{xy1},{\tilde{E}}_{yy1}{]}^T$ for $f_1=0.25\mathrm{THz}$ and $[{\tilde{E}}_{xx2},{\tilde{E}}_{xy2},{\tilde{E}}_{yy2}{]}^T$ for $f_2=0.5\mathrm{THz}$ by scanning different lengths ($l_1$ and $l_2$ are set from 50 to $450\mu \mathrm{m}$), widths ($w_1$ and $w_2$ are set from 50 to $450\mu \mathrm{m}$), and rotation corners (${\alpha }_1$ and ${\alpha }_2$ are set from $-90$ to 90 deg) under the working EMFs of $+0.24$, 0, and $-0.24\mathrm{T}$ as shown in Fig. 1(b). Moreover, under the three different EMFs for three channels, corresponding phase distributions are designed to produce multi-deflection modes for $f_1$ and $f_2$. The interval of the output phase is 60 deg with the range from 0 to 300 deg. Then, as shown in the design flowchart of the MO metasurface in Fig. 1(d), the required $[{\tilde{E}}_{xx1},{\tilde{E}}_{xy1},{\tilde{E}}_{yy1}{]}^T$ and $[{\tilde{E}}_{xx2},{\tilde{E}}_{xy2},{\tilde{E}}_{yy2}{]}^T$ can be deduced by Eqs. (1)–(5). According to the phase distributions for different channels, the deflection angle can be calculated by the phase matching equation: $K_x=c/(\mathrm{\Delta }\times f)$, where $c$ is the speed of light in vacuum and $\mathrm{\Delta }$ is the period of one complete phase cycle.36

When $f_1=0.25\mathrm{THz}$, $\mathrm{\Delta }=6P$, $12P$, and $-6P$ are for channels 1, 2, and 3, respectively. Besides, when $f_2=0.5\mathrm{THz}$, $\mathrm{\Delta }=3P$, $6P$, and $-3P$ are for channels 1, 2, and 3, respectively. Next, by the gradient descent algorithm and least squares approximation algorithm, the ideal value of the Jones matrix effective unit of each meta-atom is solved. The analysis for the error function of the gradient descent algorithm has been given in Sec. 6 of the Supplementary Material. The error of each meta-atom is shown in Fig. S8 of the Supplementary Material. Then, the multi-functional MO metasurface is determined with $6\times 12$ meta-atoms, and the actual photographic and scanning electron microscope image of the metasurface is shown in the inset graph of Fig. 1(d). Because the output THz beam is deflected to the $x\text{-}y$ plane, the deflection angle is defined as $\mathrm{\Phi }=({\theta }_1,{\theta }_2)$. The schematic diagram of the magnetically controlled beam deflections with dual-frequency multiplexing is shown in Fig. 1(e). The three spatial deflection angles are ${\mathrm{\Phi }}_1=(+28\mathrm{deg},0\mathrm{deg})$ for channel 1, ${\mathrm{\Phi }}_2=(0\mathrm{deg},12\mathrm{deg})$ for channel 2, and ${\mathrm{\Phi }}_3=(-28\mathrm{deg},0\mathrm{deg})$ for channel 3 both at $f_1=0.25\mathrm{THz}$ and $f_2=0.5\mathrm{THz}$.

To verify the functions of the MO dual-frequency metasurface, the transmission spectra at different deflection angles and various EMFs in the $0.2\text{–}0.7\mathrm{THz}$ band are simulated by the finite-difference time-domain method. The polarization of the incident THz wave is set as $+45\text{-}\mathrm{deg}$ LP wave. See Sec. 2 and Fig. S1 of the Supplementary Material for the detailed simulation method and far-field distribution. As shown in Fig. 2, the simulation results are as follows: (1) when $B=+0.24\mathrm{T}$, the strongest deflection signal is detected at the deflection angle of ${\mathrm{\Phi }}_1$ at 0.25 and 0.5 THz simultaneously; (2) when the EMF is changed to 0 T, for the dual-operating frequencies, the deflection angle with maximum transmission efficiency is changed to ${\mathrm{\Phi }}_2$. The experimental results of the frequency-domain spectrum transmission under different deflection angles and EMFs are shown in Fig. S3 of the Supplementary Material. Therefore, the simulation results confirm that the MO device achieves an active multi-channel beam steering controlled by the EMF with a dual-frequency multiplexing function.

After that, the transmittance spectrum of the MO metasurface is measured by an AR-THz-TDPS as shown in Fig. 1(c), which is in detail in Sec. 5. According to the time-domain signal of $\pm 45\text{-}\mathrm{deg}$ polarization direction obtained by the AR-THz-TDPS, the amplitude transmittance ($A\pm 45\mathrm{deg}$) and output phase ($\delta \pm 45\mathrm{deg}$) can be simulated by Fourier transform. The $L$ state and $R$ state of the emitted light can be obtained as $${\mathrm{A}}_L(\omega )=\frac{1}{2}[A_{+45°}(\omega )e^{i{\sigma }_{+45°}(\omega )}-i{A}_{-45°}(\omega )e^{i{\sigma }_{-45°}(\omega )}]{\mathrm{A}}_R(\omega )=\frac{1}{2}[A_{+45°}(\omega )e^{i{\sigma }_{+45°}(\omega )}+i{A}_{-45°}(\omega )e^{i{\sigma }_{-45°}(\omega )}].$$(6)

Based on the complex amplitudes, the transmission of $x$, $y$, $+45\text{-}\mathrm{deg}$ component, and total output single can be calculated by $$\begin{gathered} T_x=|\frac{A_L(\omega )+A_R(\omega )}{2}{|}^2 \\ {T}_y=|\frac{A_L(\omega )-A_R(\omega )}{2i}{|}^2 \\ {T}_{+45°}=\frac{1}{2}|\frac{A_L(\omega )+A_R(\omega )}{2}+\frac{A_L(\omega )-A_R(\omega )}{2i}{|}^2 \\ {T}_{\text{tot}}=|A_L(\omega )+A_R(\omega ){|}^2. \end{gathered}$$(7)

Thus, the intensity transmission of different channels at the deflection angles of ${\mathrm{\Phi }}_1$, ${\mathrm{\Phi }}_2$, and ${\mathrm{\Phi }}_3$ can be obtained.

In addition, the experimental deflection spectra are shown in Fig. 3(a): (1) when $B=+0.24\mathrm{T}$, the deflection angle covers from $(+24\mathrm{deg},0)$ to $(+36\mathrm{deg},0)$, and the deflection efficiency reaches the maximum when ${\mathrm{\Phi }}_1=(+28\mathrm{deg},0)$ at 0.25 and 0.5 THz; (2) when the EMF is changed to 0 T, the deflection angle covers the range from (0, 10 deg) to (0, 18 deg) with the max deflection efficiency at ${\mathrm{\Phi }}_2=(\mathrm{0,12}\mathrm{deg})$ at the dual-operating frequencies; and (3) when $B=-0.24\mathrm{T}$, the deflection situation is symmetrical along the $y$-axis with that of $B=+0.24\mathrm{T}$. The beam can be deflected to an angle of $(-24\mathrm{deg},0)$ to $(-36\mathrm{deg},0)$ with the max deflection efficiency when ${\mathrm{\Phi }}_3=(+28\mathrm{deg},0)$. Moreover, for all the above situations, when the detection angle decreases, the dual-operating frequencies move to a higher frequency band until the deflection efficiency changes to 0. The experimental results are well consistent with the simulations. Therefore, the dynamical multi-channel beam steering with dual-frequency multiplexing has been verified by the experiment.

Next, the accurate transmission efficiency in three channels of ${\mathrm{\Phi }}_1$, ${\mathrm{\Phi }}_2$, and ${\mathrm{\Phi }}_3$ under different EMFs is analyzed to characterize the modulation depth of the MO metasurface. As we can see from Figs. 3(b) and 3(c), the most energy is deflected to ${\mathrm{\Phi }}_1$, ${\mathrm{\Phi }}_2$, and ${\mathrm{\Phi }}_3$, respectively under different working EMFs. The deflection intensity efficiency is $>60\%$, which is strictly consistent with the simulation results. Then, the modulation depth of the three dynamical channels at dual-working frequencies is calculated quantitatively as shown in Fig. 3(d) by the equation: $M=T_{\max }/T_{\min }$, where $T_{\max }$ and $T_{\min }$ represent the maximum and minimum deflection efficiency, respectively. The modulation depth can reach more than 75% with a maximum of 97.6%. So, the MO metasurface realizes high-efficiency switching among different channels.

Besides, to feature the characteristics of the crosstalk between each channel, the energy distribution in the focal surface of the focusing lens with a 25-mm focal length is measured by the far-field scanning system (the detailed introduction can be obtained in Sec. 5) under the three working EMFs, as shown in Figs. 4(a) and 4(b). Next, the analysis primarily revolves around the dynamical focal position, the crosstalk intensity, and the efficiency of target polarization:

1. (1)First, as shown in Fig. 4(c), the measured focused spots intuitively demonstrate the dynamical multi-channel function with dual-frequency multiplexing of the MO metasurface, which is highly consistent with the simulation results.
2. (2)Then, to quantitatively describe the crosstalk among channels, the ratio of ${\mathrm{\Gamma }}_{\text{channel}}$ is defined as ${\mathrm{\Gamma }}_{\text{channel}}=I_{\text{spot}}/I_{\text{total}}$, where $I_{\text{spot}}$ represents the intensity of the target focused spot, which is indicated by the white dashed circular marker in Fig. 4(c). $I_{\text{total}}$ denotes the total intensity of the output field (which can be obtained in Fig. S4 in Sec. 3 of the Supplementary Material). As shown in Fig. 4(d), the maximum values of ${\mathrm{\Gamma }}_{\text{channel}}$ at ${\mathrm{\Phi }}_1$, ${\mathrm{\Phi }}_2$, and ${\mathrm{\Phi }}_3$ correspond to $+0.24$, 0, and $-0.24\mathrm{T}$, respectively, which is strictly consistent with our design. The value of ${\mathrm{\Gamma }}_{\text{channel}}$ is all $>85\%$ with the crosstalk energy between each channel $<4\%$.
3. (3)In addition, to describe the efficiency of the designed output polarization, the ratio $R_{\mathrm{LP}}$ is defined as $R_{\mathrm{LP}}=I_{\mathrm{LP}}/I_{\text{total}}$, where $I_{\mathrm{LP}}$ is the intensity of the target LP state. The detailed results are given in Fig. S5 of the Supplementary Material. In a word, $R_{\mathrm{LP}}$ can reach $>92\%$, which verifies that the polarization of the output light is highly consistent with the initial design.

Based on the above experimental results, it can be confirmed that the designed MO device can effectively suppress the crosstalk between each channel, ensuring the stability of information transmission.

Finally, whether the reflected echo of the deflected THz wave can pass through the transmission system composed of MO metasurface and a $+45\text{-}\mathrm{deg}$ LP THz polarizer at the deflection angle of ${\mathrm{\Phi }}_1$ and ${\mathrm{\Phi }}_3$ is focused on the research, as shown in Fig. 5(a). Because the propagation property of the Si-dielectric metasurface is reciprocal, the polarization state of backward THz beams incident into the YIG layer again remains unchanged polarization with the Faraday angle of $\phi$, so the incident $+45\text{-}\mathrm{deg}$ LP beam rotates the angle of $2\phi$ after passing through the whole MO metasurface due to the nonreciprocal phase shift of the MO layer. For the incident $+45\text{-}\mathrm{deg}$ LP wave, the Jones matrix of the reflective THz wave can be written as $$\begin{gathered} \left[\begin{array}{c}{E}_x^{\mathrm{ref}}\\ E_y^{\mathrm{ref}}\end{array}\right]=\frac{\sqrt{2}}{2}\left[\begin{array}{cc}\cos (-\phi )& \sin (-\phi )\\ -\sin (-\phi )& \cos (-\phi )\end{array}\right]J^{-1}J\left[\begin{array}{cc}\cos \phi & -\sin \phi \\ \sin \phi & \cos \phi \end{array}\right]\left[\begin{array}{c}1\\ 1\end{array}\right] \\ =\frac{\sqrt{2}}{2}\left[\begin{array}{c}\cos 2\phi -\sin 2\phi \\ \cos 2\phi +\sin 2\phi \end{array}\right]. \end{gathered}$$(8)

Among that, the component of the reflective THz wave in $+45\text{-}\mathrm{deg}$ polarization direction can be represented: $E_{+45°}^{\mathrm{ref}}=\cos (45°)E_x^{\mathrm{ref}}+\sin (45°)E_y^{\mathrm{ref}}=\cos 2\phi$. Therefore, after passing through the initial $+45\text{-}\mathrm{deg}$ LP polarizer, the intensity of the reflective signal can be expressed as $I_{\mathrm{ref}}=I_{\text{in}}{\cos }^2(2\mathrm{V}B{h}_1)$, where $I_{\text{in}}$ represents the intensity of incident waves. Then, the isolation rate can be calculated by $$R_{\mathrm{iso}}=-10\log (I_{\mathrm{ref}}/I_{\text{in}})=-20\log (\cos 2VB{h}_1).$$(9)

When the FR angle $\phi =VB{h}_1$ is $\pm 45\mathrm{deg}$, $R_{\mathrm{iso}}$ reaches the maximum. This shows that the MO metasurface not only achieves the dynamical multi-channel function with dual-frequency multiplexing but also has the same one-way transmission function as the common Faraday optical isolator when $B=+0.24$ and $-0.24\mathrm{T}$.

Due to the nonreciprocal MO property of La:YIG crystal, the forward and backward transmission can equalize to the forward and backward EMFs. Figure 5(b) shows the experimental results of the transmission at $0.15\text{–}0.65\mathrm{THz}$ under the deflection angles of ${\mathrm{\Phi }}_1$ and ${\mathrm{\Phi }}_3$. It is obvious that when EMFs change from $-0.24$ to $+0.24\mathrm{T}$ at the deflection angle of ${\mathrm{\Phi }}_1$, the transmission at dual-working frequencies gradually increases. On the contrary, when the deflection angle is ${\mathrm{\Phi }}_3$, the transmission gradually decreases. Therefore, the MO device exhibits significant nonreciprocal transmission characteristics under the forward and reverse EMFs.

Then, the detailed deflection efficiencies with different EMFs at the deflection angles of ${\mathrm{\Phi }}_1$ and ${\mathrm{\Phi }}_3$ are measured as shown in Figs. 5(c) and 5(d). With the forward EMF gradually increasing to $+0.24\mathrm{T}$, the proportion of energy deflected to ${\mathrm{\Phi }}_1$ increases gradually. On the contrary, when the EMF is reversed to $-0.24\mathrm{T}$, the most energy is deflected to the deflection angle of ${\mathrm{\Phi }}_3$. Therefore, the MO system can achieve the nonreciprocal deflection function. Then, the isolation rate of the MO system at dual-operating frequencies under different EMFs can be calculated as $$R_{\mathrm{iso}}=-10\log (T_{+B}/T_{-B}),$$(10)where $T_{+B}$ and $T_{-B}$ indicate the transmission at forward and backward EMFs, respectively. As shown in Fig. 5(e), with the EMF changing from 0 to 0.24 T, the isolation rate gradually increases with the maximum value reaching up to 29.8 dB. This nonreciprocal deflection characteristic can effectively reduce the reflected THz signal to depress echo noise and improve accuracy in THz communication systems.

To sum up, an MO metasurface based on MPM is proposed, composed of La:YIG crystal and Si-dielectric metasurface, which realizes dynamical multi-channel modulation with dual-frequency multiplexing function, and the highlights are as follows:

(1) The proposed MPM couples the magnetic induction phase with the propagation phase and achieves the design of different arbitrary phases for dual frequencies under different EMFs at room temperature; (2) based on the MPM structure, the MO metasurface realizes dynamical multi-channel modulation with three different deflection angles for the dual-frequency multiplexing at 0.25 and 0.5 THz, and the experimental modulation depth can reach up to 97.5% with the ratio of crosstalk energy $<4\%$; and (3) more importantly, due to the nonreciprocal phase delay in the MO layer, the MO metasurface also realizes the one-way transmission function at dual-working frequencies with the maximum isolation of 29.8 dB.

This nonreciprocal THz beam steering mechanism with dual-frequency multiplexing has significant application prospects in future 6G high-speed communication systems with multi-channel and multi-frequency multiplexing functions.

In Sec. 3.1, the AR-THz-TDPS with the working frequency band of $0.1\text{–}1.5\mathrm{THz}$ is used to characterize the MO metasurface, as shown in Fig. 1(c). The output reference signal passing through the air and the corresponding frequency-domain spectrum are shown in Fig. S2 in the Supplementary Material. The metadevice is located in the center of a pair of mechanically adjustable magnets, which are placed on both the front and back sides of the sample to generate the adjustable EMFs from $-0.24$ to $+0.24\mathrm{T}$, which consists of a high-precision excitation system incorporating a pair of electromagnets. Among those, the THz signal is generated by the photoconductive antenna (PCA) with 780-nm femtosecond laser pumping. The detection signal is coupled by the optical fiber to the detector, which can be rotated to detect the THz wave from different angles. Different from the traditional THz time-domain spectroscopy (THz-TDS) system, a couple of additional polarizers are placed in front of and behind the sample, which can be rotated to measure the orthogonal LP components that are incident or pass through the MO metasurface. Then, the complete polarization information of the emergent light can be obtained, such as the transmission, phase shift, and polarization rotation angle. Furthermore, the modulation speed of the MO metasurface is exceptionally rapid, governed by the ultra-short magnon–phonon relaxation time (${\tau }_{\mathrm{mp}}=44\mathrm{ps}$) in the La:YIG crystal, as reported in previous studies.37^,38 Nevertheless, under experimental conditions, the operational modulation speed of the MO device is predominantly limited by the switching time of the EMF. The alternating electromagnet employed in our experiments demonstrates a minimum modulation time of 100 ms.

In addition, a THz two-dimensional (2D) far-field scanning system is used to measure the focus spots of multi-channels, as shown in Fig. 4(a). The optical component of the 2D far-field scanning system is almost the same as that of the AR-THz-TDPS. The biggest difference is that the THz probe is located in an electromechanical 2D-scanning equipment, and a THz lens with a focal length of 25 mm is placed behind the sample. The output THz signal is focused on the focal plane after passing through the THz lens. Therefore, the experimental system can detect the output signals on the focal plane point by point. Then, the complete output electric distribution of the 2D far-field from the sample can be obtained.

For the Si-dielectric metasurface, the $500\text{-}\mu \mathrm{m}$-height Si microstructures were fabricated by UV lithography and plasma etching with a $1000\text{-}\mu \mathrm{m}$-thick Si wafer with high resistivity ($>\mathrm{10,000}$) crystalline. The YIG crystal, of which the thickness is $d=2400\mu \mathrm{m}$, was grown from a supersaturated melt based on the $\mathrm{PbO}\text{-}{\mathrm{B}}_2{\mathrm{O}}_3$ flux by the standard liquid phase epitaxy method on a 7.62 cm (111)-orientated gadolinium gallium garnet substrate. After the growth is completed, the substrate is ground off. Then, the proposed metasurfaces were tightly bonded to the MO YIG crystal using UV adhesive.

Dan Zhao received his BS degree from the School of Precision Instrument and Opto-Electronics Engineering, Tianjin University, Tianjin, China, in 2019. He is currently pursuing his PhD in optical engineering from the Institute of Modern Optics, Nankai University, Tianjin, China. His research interest focuses on terahertz microstructure functional devices.

Fei Fan received a BS degree from Tianjin University, Tianjin, China, in 2009 and a PhD in optical engineering from the Institute of Modern Optics, Nankai University, Tianjin, China, in 2014. He is presently a full professor at the Institute of Modern Optics, Nankai University. His research interests include terahertz microstructure functional devices and terahertz spectroscopy.

Jining Li received his BS degree in opto-electronic science and technology and his PhD in optics from Nankai University in 2007 and 2013, respectively. In 2015, he joined the Faculty of the School of Precision Instrument and Opto-electronics Engineering, Tianjin University. His research includes laser technologies & applications, THz technology, and functional devices based on metamaterials.

Shengjiang Chang received his MS degree in laser physics and PhD in optical engineering from Nankai University, Tianjin, China, in 1993 and 1996, respectively. Since 2000, he has been with the Institute of Modern Optics, Nankai University, where he is presently a full professor. His current research involves microstructural terahertz devices, terahertz time-domain spectroscopy technology, and the applications of artificial neural networks in pattern recognition.

Biographies of the other authors are not available.