Light manipulation via nanostructured materials plays a significant role in modern nanophotonics. Specially, combining the functional materials with engineered structures provides an exceptional route for exploring new principles and expansive applications for dynamic light manipulation. For example, tunable metasurfaces are widely used in zoom lens^[1,2], beam generation^[3,4], optical switches^[5,6], and dynamic holographic displays^[7–9] via incorporating a functional material into the nanostructured design. The optical properties can be affected by different external excitations, such as electrical^[10], optical^[11], thermal^[12], mechanical^[13], and magnetic^[14] stimulation. Notably, the active metasurface via magnetic control has the advantages of sub-nanosecond ultrafast response and is non-invasive, which exhibits an important potential in dynamic light manipulation.

The magneto-optical (MO) metasurface can provide multiple degrees of freedom for light control via magneto-optical effects, such as the Faraday effect^[15–17] and Kerr effect^[18,19]. This feature makes it widely applied in various fields such as modulator^[20,21], isolator^[22–24], chiral sensing^[25,26], biochemical sensing^[27,28], magnetic field sensing^[29–31], and MO switch^[32,33]. However, in terms of the MO modulation, it is challenging to make the nanostructure achieve a strong MO response due to the weak effect of the MO material. Therefore, most studies emphasize using magneto-plasmonic or dielectric resonance to improve the modulation efficiency of the amplitude and polarization rotation of the MO metasurface^[34–38]. Nevertheless, a few studies have focused on the phase modulation of MO metasurfaces by flexibly designing the nanostructure. Although it has been proved that an MO metasurface can realize superchiral light field manipulation and dynamic wavefront control by elaborately arranging the nanoantennas, they are mainly applicable in the terahertz regime, and less attention has been paid to the applications of the MO metasurface in the optical regime and holographic display^[39,40]. Therefore, flexibly designing the meta-atoms to achieve the information encoding function in the optical regime should be studied extensively. In the previous work, we reported the method for realizing the magnetically controllable holographic encryption based on an MO metasurface. Nevertheless, it can only realize a dynamic holographic display in two linearly polarized channels via magnetic control and does not delve into the resonance behavior of the structure^[41].

Here, we investigate the complex amplitude modulation and resonance properties of a tunable MO metasurface, which comprises elaborately designed metallic nanoantennas arranging on the MO intermediate layer and the metallic reflecting layer. Particularly, we demonstrate that the identical MO metasurface can realize switchable tri-channel polarization multiplexing holography by using magnetic control and suitable nanoantenna arrangements. When an external magnetic field is applied or not, the three different holographic images are reconstructed in the $E_{xx}$ linear polarization channel and the $E_{ll}$ and $E_{rl}$ circular polarization channels. The switchable reconstructed images, such as the pattern “flower” (in the $E_{xx}$ channel), the Chinese character “中” (in the $E_{ll}$ channel), and the pattern “butterfly” (in the $E_{rl}$ channel), can be observed in the Fourier plane using the finite-difference time-domain (FDTD) and the modified Gerchberg–Saxton (GS) holographic algorithm. This work will pave the way for the application of dynamic multichannel metasurface holographic display via magnetic control, which is significant in optical information encryption.

As is shown in Fig. 1, the proposed MO metasurface consists of a tri-layer structure deposited on a glass substrate. Specifically, the delicately designed metallic (Au) nanoantennas are arranged on the MO intermediate layer, which is placed on the metallic (TiN) reflecting layer. This configuration is chosen because the resonator cavity formed by the double-layer metals can improve the MO response and polarization conversion efficiency. In this structure, we chose bismuth-substituted yttrium iron garnet (Bi:YIG) as the MO layer due to its high MO coefficient in the optical regime. Since the applied magnetic field is along the $z$-axis, which makes the magnetization of the Bi:YIG film perpendicular to the sample and parallel to the incident plane ($x–z$ plane), the off-diagonal elements ${\epsilon }_{xy}$ and ${\epsilon }_{yx}$ of its dielectric tensor become non-zero components, and the dielectric tensor of the MO material can be described as follows: $$\left(\begin{array}{ccc}{\epsilon }_{xx}& {\epsilon }_{xy}& 0\\ {-\epsilon }_{xy}& {\epsilon }_{yy}& 0\\ 0& 0& {\epsilon }_{zz}\end{array}\right),$$(1)where ${\epsilon }_{xy}=-ig$, and $g$ describes the magnetization-induced gyration of the Bi:YIG film. Here, we assume that the Bi:YIG film is optically isotropic, and its second-order MO effect is negligible. Since the dielectric tensor of the Bi:YIG film is slightly dispersive over the designing wavelength range, the average value of the tensor with ${\epsilon }_{xx}{\text{=ε}}_{yy}{\text{=ε}}_{zz}=5.5+i0.0025$ and $g=(1-i0.15)\times {10}^{-2}$ is adopted^[42,43]. When there is no external magnetic field, the off-diagonal elements turn into zero, which means the Bi:YIG film will not produce the MO effect. Additionally, the frequency-dependent permittivity of the gold is characterized by the well-known Drude model, which is given by Ref. [44] and can be expressed as $$\epsilon ={\epsilon }_{\infty }-\frac{{\omega }_p^2}{{\omega }^2+i\gamma \omega },$$(2)where ${\epsilon }_{\infty }=7.9$, ${\omega }_p=8.77\mathrm{eV}$, and $\gamma =1.13\times {10}^{14}{\mathrm{s}}^{-1}$ is set to fit the empirical data over the designing wavelength range. The dielectric function of the TiN is provided by Palik in the material database of the FDTD, and the permittivity of glass is set to 2.13.

To characterize the reflection of the MO metasurface, we build the model using FDTD. Initially, we set the height of the Au nanoantennas to 50 nm and the thicknesses of the TiN reflecting layer to 200 nm, respectively. The intermediate layer is a continuous Bi:YIG film with a thickness of 400 nm, and the lattice is identical in the $x$- and $y$-directions, i.e., P_x = P_y = P. Here, we set the period of the lattice to 600 nm, and we set the periodic boundary conditions in the $x$- and $y$-directions while the perfectly matched layer boundary condition is set in the $z$-direction. Moreover, the mesh sizes in the $x$-, $y$-, and $z$-directions are set as 20 nm, 20 nm, and 5 nm, respectively. Normally, the incident linearly $x$-polarized plane wave or circularly polarized light is used to excite the structure, and the latter is formed by the superposition of two linearly polarized lights with a polarization angle and phase difference of 90°. The phase is set as 90° or $-90°$ to distinguish the left or right circularly polarized (LCP or RCP) light. When the TM-polarized ($x$-polarized) light is illuminated, the reflectance spectrum of the structure is calculated, as shown in Fig. 2. It can be seen that the maximum reflectance is approximately 0.8, and there are two resonant dips in the reflectance spectra. The decrease in the diffraction efficiency is mainly originated from the loss of the metal materials. The generated plasmon resonance mode at the interface of the metal/dielectric layer and the waveguide mode inside the MO layer make for strong electromagnetic field enhancement and further exhibit asymmetric Fano resonance in the reflectance spectra.

Additionally, to delve into the physics of the observed resonance modes, we take a deeper look into the resonant behavior of the hybrid MO metasurface. The spatial distributions of the electric and magnetic fields at the resonant wavelength 922 nm are demonstrated in Fig. 3. The field distributions clearly reveal that a TM waveguide-plasmon hybrid mode is excited. On the one hand, the TM-polarized light drives a collective oscillation of electrons in the metallic nanoantenna and excites a particle plasmon resonance, which enhances the near field. On the other hand, the periodically arranged nanoantennas make the light scatter into the MO waveguide layer and excite a TM-guided mode. Additionally, the double-layer metals form the resonator cavity, which can enhance the reflected light.

To acquire the complex amplitude modulation of the MO metasurface, we conduct a structural parameter sweep to the periodic nanoantenna unit. The length and width of the nanoantenna are varied from 100 to 500 nm with an interval of 10 nm. Figure 4 shows the complex amplitude modulation of the structure in the linearly and circularly polarized channels when the external magnetic field is applied. Specifically, Figs. 4(a)–4(d) show the amplitude and phase modulation of the co- and cross-polarized reflected light with the $x$-polarized incident light, while Figs. 4(e)–4(g) show the amplitude and phase modulation of the LCP and the RCP reflected light with the LCP incident light. It should be noted that in the absence of an external magnetic field, there exists no $y$-polarized reflected light when the $x$-polarized light is incident, which indicates that the reflected light in the magnetized MO layer has undergone a polarization rotation. However, the diffraction efficiency of the $y$-polarized reflected light with the applied magnetic field only reaches up to 0.02, which means it is not suitable for reconstructing the holograms. Moreover, there exists a considerable difference of the complex amplitude modulation in the linearly and circularly polarized channels. The diffraction efficiency in the $E_{xx}$ channel covers from 0.19 to 0.88. Also, the diffraction efficiencies in the $E_{ll}$ and $E_{rl}$ channels cover from 0.37 to 0.75 and 0.53 to 0.91, respectively. It can be seen that the amplitude modulations vary widely while the phase modulations vary slightly. Therefore, to realize switchable multichannel holographic display via magnetic control, it is necessary to select the desired structures to encode the binary amplitude-only holograms. Remarkably, the black circles in the sub-diagram of Fig. 4 represent the amplitudes and phases of the selected nanoantenna structures in different polarization channels.

As is known, the hologram of each polarization channel is encoded by a 2-bit amplitude, and each bit amplitude corresponds to a nanoantenna structure. Therefore, to encode independent binary-amplitude holograms in the three switchable polarization channels, eight ($2^3$) nanoantenna structures need to be selected. The phase modulations of the selected nanostructures in each polarization channel are required to be as uniform as possible, and the amplitude modulations are required to be as large a proportion of high amplitude to low amplitude as possible. Specifically, the amplitude combinations of the selected structures in both switchable polarization channels (in the $E_{xx}$ and $E_{ll}$ channels or in the $E_{xx}$ and $E_{rl}$ channels) need to satisfy (0, 0), (0, 1), (1, 0), and (1, 1), in which 0 and 1 represent only the low and high amplitude types, not the actual modulation efficiency. Meanwhile, this principle should also apply to the $E_{ll}$ and $E_{rl}$ channels. The selected geometric parameters are shown in Table 1, and the complex amplitudes of the selected structures in the three polarization channels are shown in Fig. 5. It is obvious that the phase fluctuation of most of the structures is slight in a specific polarized channel, which contributes to the noise reduction of the generated holograms. Moreover, the amplitude combinations of the selected structures in the $E_{xx}$ and $E_{ll}$ channels, the $E_{xx}$ and $E_{rl}$ channels, or the $E_{ll}$ and $E_{rl}$ channels all satisfy (0, 0), (0, 1), (1, 0), and (1, 1). Notably, the amplitudes of the selected structures are not absolute 0 or 1, only that there is a relatively large difference between high and low amplitudes. Although the amplitude modulation in individual polarization channels does not satisfy absolutely uniform high and low amplitudes, since it is a binary-amplitude hologram, the uneven amplitude values can be regarded as multiplied by a constant, which will only affect the overall efficiency of the reconstructed hologram but will not affect the imaging quality. Also, although the individual phase values are biased, this does not affect the reconstruction of the holographic image due to its tolerance to the phase noise.

Furthermore, we use the modified GS algorithm and FDTD to reconstruct the switchable holographic images in the Fourier plane of the MO metasurface. The encoding scheme of the multiple binary-amplitude holograms within one identical MO metasurface and the design principle of the nanoantenna arrangement are illustrated in Fig. 6. Suppose that the MO metasurface is made up of many pixel units, and the selected structures are respectively arranged in each unit. The amplitude modulation of one identical structure in different polarization channels might be 0 or 1. The amplitude combinations of the selected structures should satisfy the three-bits amplitude modulation (0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 1) (1, 0, 1), (1, 0, 0), (1, 1, 0), and (1, 1, 1) in the $E_{xx}$, $E_{ll}$, and $E_{rl}$ channels, respectively. Consequently, the independent holographic images can be reconstructed between each polarization channel.

First, we generate the multiple binary-amplitude holograms using the modified GS algorithm. Considering the required capacity for the calculation, we make images of $100\times 100$ pixels. Based on the complex amplitude of the selected structure, the multiple iterative loops of inverse fast Fourier transform (FFT) are performed between the hologram and reconstructed image. Afterwards, the optimal complex amplitude holograms can be generated based on the binary-amplitude hologram algorithm. The three reconstructed hologram images in the different polarization channels are calculated by the GS algorithm, as shown in Figs. 7(a)–7(c). Then, we encode the three holograms into one identical MO metasurface according to the coding method illustrated in Fig. 6, and the designed MO metasurface array is further modeled using the FDTD method. Since the unit period of the structure is 600 nm, the size of the modeled MO metasurface is $60\mathrm{\mu m}\times 60\mathrm{\mu m}$, and the far-field reconstructed images in the Fourier plane are simulated as shown in Figs. 7(d)–7(f).

Similarly, we can successfully observe the reconstructed images of the structure in different polarization channels. The pattern “flower” is reconstructed in the $E_{xx}$ polarization channels at the state of the applied magnetic field, while the Chinese character “中” and the pattern “butterfly” are reconstructed in the $E_{ll}$ and $E_{rl}$ polarization channels without the applied magnetic field. The results are comparable with the ones based on the GS algorithm, and there is almost no crosstalk between each polarization channel. Since the reconstructed images are based on the binary-amplitude holographic algorithm, there exists conjugate images. Also, we can note that the reconstructed image quality using the full-wave simulation is deteriorated a bit compared to the ones using the GS algorithm. On the one hand, the image pixel count and the meshing accuracy are limited given the capacity required for the calculation. On the other hand, the near-field coupling between the adjacent nanoantenna will affect the image quality. Nevertheless, due to the strong robustness and relative larger tolerance of the amplitude noises of the binary amplitude-only hologram, we can still get the reconstructed image prototype to verify the switchable multichannel holographic display function of the MO metasurface.

Here, we propose the method for fabricating the device and building the experimental setup. In terms of device fabrication, the metallic TiN film of 200 nm on the silica substrate can be first deposited by pulsed laser deposition (PLD) equipped with a KrF excimer laser. Then, the MO film can be deposited by PLD or by the magnetron sputtering process, of which PLD is the better method since it may take several hours to deposit the Bi:YIG film with a thickness of 400 nm by magnetron sputtering. After deposition, the Bi:YIG film should undergo the high-temperature annealing process to make it crystallized. The TiN film can support the high-temperature atmosphere. Subsequently, gold nanoantennas can be fabricated by sputtering, electron beam lithography, and lift-off process, respectively. As for the experimental setup, a light source illuminates the sample after passing through the polarizers, lens, and beam splitter. Therein, a pair of linear polarizers or a combination of linear polarizers and quarter-wave plates is placed ahead and behind the sample to obtain the desired incident or reflective linearly/circularly polarized beam. Meanwhile, the MO metasurface sample is placed in the focal plane of an objective lens and a set of perforated permanent magnets. The permanent magnet produces a fixed magnetic field, which is perpendicular to the sample surface, to magnetize the MO film. The minimum magnetic field intensity used to produce the MO effect is 150 mT, which is the saturation magnetic field intensity of the Bi:YIG, and the objective lens collects the reflective light from the sample and reconstructs the holographic images in the Fourier plane. The reconstructed holographic images are captured by a CCD camera.

In summary, we have demonstrated the polarization multiplexing holography of MO metasurface via magnetic control based on the binary amplitude-only hologram. The involved MO metasurface is a tri-layer structure deposited on a glass substrate. Specifically, the rectangular Au nanoantennas are properly arranged on the MO intermediate layer, which is placed on the TiN reflecting layer. We acquire the complex amplitude modulation of the MO metasurface, which changes with the geometric size of the nanoantennas, by using the FDTD method. We deliberately design the nanoantenna arrangement to achieve three independent binary amplitude-only holograms that carry different information in the $E_{xx}$, $E_{ll}$, and $E_{rl}$ polarization channels. Three-bits binary amplitude hologram encoding is performed by properly arranging the selected eight nanoantenna structures, which can satisfy all the possible amplitude combinations to incorporate the three holograms into one identical MO metasurface. The holographic images are reconstructed using both the modified binary amplitude GS algorithm and full-wave simulations. The reconstructed holographic images of the MO metasurface switchable in the $E_{xx}$, $E_{ll}$, and $E_{rl}$ polarization channels via magnetic control are comparable with the ones based on the GS algorithm, which manifests the dynamic multichannel holographic display function of the MO metasurface. Our proposed MO metasurface holographic multiplexing offers a new paradigm for designing multifunctional metadevices utilizing the MO phenomenon, especially in the optical regime.