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Abstract
As a flexible and compact nanophotonic device, the metasurface exhibits excellent potential in holographic display and optical information encryption. However, most metasurfaces are passive devices due to the limitations of fixed material properties and structural components. Magneto-optical metasurface is a hybrid device that integrates tunable functional material with elaborately designed nanostructures. It can realize dynamic modulation of the properties of light since the permittivity tensor for the magneto-optical material can be changed by applying an external magnetic field. Here, we propose a tunable metasurface composing metallic nanohole arrays with a bismuth-substituted yttrium iron garnet interleave layer and a metallic film underlayer placed on a glass substrate. The magneto-optical metasurface can achieve dynamic switchable holographic display in different polarization channels via magnetic field control based on the optical rotation of magnetic material and the complex amplitude modulation of the elaborately designed nanoholes. This feature provides a novel approach for the construction of an active tunable metasurface, which can improve the information storage capacity and security of the device. This concept is expected to be applied to various dynamic modulation fields, such as magnetically tunable lens, beam shaping, and optical information encryption.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurface is a two-dimensional planar device composed of subwavelength plasmonic or dielectric nanoantennas that can realize artificial modulation of the amplitude, phase, and polarization of electromagnetic field [1–6]. The modulation is achieved by elaborately designing the geometry and spatial arrangement of the nanoantennas. Compared with the three-dimensional metamaterial, metasurface possesses the advantages of ultrasmall footprint, subwavelength pixels, facile integration, high design flexibility, and relatively easy to be fabricated. Such features make the metasurface emerge as a powerful tool in the fields of holographic display [7,8], beam shaping [9–11], metalens [12,13], optical information encryption [14], integrated optical communication [15] and so on.
Metasurface holography has attracted numerous interests due to its ability to relieve some defects that exist in traditional holography. The subwavelength period of metasurfaces is in favor of reconstructing holographic images with high resolution, large field of view and broad bandwidth [16,17]. To improve the image storage capacity and security of the device, many holographic multiplexing technologies have been proposed such as multi-wavelength multiplexing [18,19], polarization multiplexing [20,21], and angle multiplexing [22–24]. However, these modulations are passive and can’t meet the application requirements of real-time control, such as dynamic modulation of the signal in optical communication and switchable imaging display. Therefore, the evolution of metasurface from passive to active is highly desired.
The current physical methods for constructing active metasurfaces mainly include mechanical [25,26], thermal [27–29], electrical [30–32], optical [33–35], and magnetic control [36–37]. The magnetic control method possesses the advantages of ultrafast response, non-contact and continuous adjustment. These notable features can make it become a promising candidate for dynamic modulation of the optical field. Once an external magnetic field is applied, the magnetooptical (MO) material-based device will dynamically modulate the amplitude, phase, and polarization of light. It is owing to that the non-diagonal components of the permittivity tensor of the MO material are changed, which exhibits the MO effect. In previous works, MO material-based spatial light modulators used for display technology have been originally evolving, which is promising for nonvolatile, ultrafast, and high-resolution spatial modulation of light [38–40]. However, the challenges with device functionality includes the intrinsic weakness of MO effect, large size and power requirement. Therefore, MO metasurface is a promising candidate due to its advantages of ultrasmall footprint, facile integration, and high design flexibility. Nevertheless, for micro-nano scale MO metasurface, it also suffers the weakness of MO effect, which results in lower modulation efficiency. In recent years, many works are proposed to improve the modulation efficiency of the amplitude and polarization rotation for the MO metasurface composed of periodic arrays by using the magnetoplasmonics and dielectric resonance effects [41–45]. However, there are few works on realizing phase modulation by flexibly designing the arrangement of meta-atoms. Moreover, although some attractive schemes for active wavefront control of MO metasurfaces have been demonstrated [46–48], magnetically tunable metasurfaces for holographic display in the visible and near infrared range have not been thoroughly investigated.
In this work, a novel method for realizing the magnetically controllable holographic display is theoretically demonstrated based on MO metasurface. The MO metasurface is composed of metallic nanohole arrays with a bismuth-substituted yttrium iron garnet interleave layer and a metallic film underlayer placed on a glass substrate. Dynamic switchable holographic display in different polarization channels is realized via magnetic field control within one identical MO metasurface. This functionality is achieved utilizing the polarization conversion of the MO layer when stimulated by an external magnetic field. Meanwhile, the amplitude and phase of light can be tailored by elaborately designing the nanohole arrays. The reconstructed images such as the letter “B” and the pattern “heart” can be switched at the Fourier plane in the optical regime which is verified by the finite difference time domain (FDTD) method. The proposed concept may fill the vacancy in the phase modulation based on MO metasurface and lead to a new frontier for applications related to the dynamic holographic display.
2. Methods and results
The schematic illustration of magnetically controllable holographic encryption based on MO metasurface is shown in Fig. 1. The metasurface is a metal-MO dielectric-metal structure comprising gold (Au) nanohole arrays with a bismuth-substituted yttrium iron garnet (Bi:YIG) interleave layer and an Au film underlayer placed on a glass substrate. Constructing the double-layer metal structure as a Fabry-Perot resonator can improve the reflection efficiency and compensate for the high optical loss of metal. Many studies indicate that such structure can greatly improve the modulation efficiency of light and be well applied in various fields [49–51]. And the Bi:YIG layer is chosen due to its high MO coefficient in the visible and near-infrared range. It can make the incident linearly polarized light produce orthogonal components since the non-diagonal elements of its permittivity tensor become non-zero value once applying an external magnetic field [52]. In this paper, we only demonstrate the case of p-polarized incident light for that the reflection characteristics of s-polarized incident light are axisymmetric with the ones of p-polarized incident light. As shown in Fig. 1, the applied magnetic field is along the z-axis, that is the magnetization direction is perpendicular to the sample surface and parallel to the incident plane, which belongs to polar MO Kerr effect. In this case, the polarization and intensity of the reflected light can be simultaneously modulated. Additionally, the complex amplitude of the light can be modulated by changing the geometry of the Au nanoholes. Combining the two functions allows the MO metasurface to achieve dynamically switchable holographic display in the identical and orthogonal polarization channel (a letter “B” and a pattern “heart” can be switched) corresponding to the case of without and with an external magnetic field, respectively. The modified Gerchberg-Saxton (GS) algorithm is adopted to generate the desired independent holograms [53]. Moreover, the obtained holograms can be encoded to the MO metasurface by elaborately designing the size of Au nanohole in each unit.
2.1 Metasurface
We design and optimize the single structure illustrated in Fig. 2(a) based on the FDTD method. We set the period as 500 nm and the thicknesses of top and bottom Au layers as 50 nm and 200 nm, respectively. The refractive index of Au is taken from Palik in the material database of FDTD [54], and the permittivity tensor of Bi:YIG refers to the literature [55,56]. Since the applied magnetic field is along the z direction and considering the case of saturated magnetization, it can be expressed as $[{\varepsilon _{xx}},{\varepsilon _{xy}},0;{\varepsilon _{yx}},{\varepsilon _{yy}},0;0,0,{\varepsilon _{zz}}]$. The off-diagonal elements ${\varepsilon _{xy}}$ and ${\varepsilon _{yx}}$ are non-zero components. Also, due to the slight dispersion of the permittivity tensor of Bi:YIG over the spectrum from 600 nm to 1100 nm, the average value of the tensor with ${\varepsilon _{xx}} = {\varepsilon _{yy}} = {\varepsilon _{zz}} = 5.5 - i0.0025$ and ${\varepsilon _{xy}} ={-} {\varepsilon _{yx}} ={-} ig ={-} 0.0015 - i0.01$ is adopted in the numerical simulation, where g is the optical gyration coefficient. In the absence of an external magnetic field, g turns to zero. The thickness of Bi:YIG film of 410 nm and the target-working wavelength 750 nm are determined by the simulation results when the length and width of the nanoholes are fixed as 300 nm, as shown in Fig. 2(b). They are chosen according to the relatively higher reflectance of the cross-polarization when an external magnetic field is applied and the p-polarized light illuminates owing that the reflectance of the cross-polarization is crucial to the image quality of orthogonal channel. Based on the above structural and material parameters, we sweep the length and width of nanoholes in the range of 80 nm to 400 nm with an interval of 10 nm. Moreover, the mesh sizes in the x, y, z directions of the top layer Au are 20, 20, and 5 nm, respectively. And we set periodic boundary conditions in the x and y directions while perfect matched layer (PML) boundary condition in the z direction. The complex amplitudes modulated by the MO metasurface without and with the applied magnetic field while changing the length and width of the nanoholes are shown in Figs. 2(c)–2(f). It indicates a great difference in the amplitude and phase modulation of the co-polarized and cross-polarized reflected light, which is crucial to realize double holograms. The amplitudes of identical polarization channel are generally higher, while the ones of orthogonal polarization channel are significantly lower. This is due to the limited polarization conversion of MO films. Moreover, the phase distributions of both channels cover a wide modulation range.
To generate two independent binary-phase holograms corresponding to the letter “B” and the pattern “heart”, four nanohole structures should be chosen from the scanning results, and the specific geometric dimensions are shown in Table 1. Also, the complex amplitudes in the co-polarized and cross-polarized channel corresponding to the case of without and with applied magnetic field are shown in Fig. 3(a) and Fig. 3(b), respectively. The amplitude fluctuation in the cross-polarized channel is slight, which is conducive to reducing the intensity/phase noise of the generated holograms. Moreover, the phase shift combinations of the four selected structures in both polarization channels are (0, 0), (0, π), (π, 0), (π, π), covering the full combinations of two situations, that is without and with applied magnetic field. Although one of the amplitudes in the co-polarized channel is fluctuant and the phase shift of the selected structures is not strictly equal to π, this does not affect the quality of the reconstructed image due to the robustness of the hologram.
Fig. 2. Structure parameters and sweep results. (a) Schematic of a single structure; (b) Reflectance of the cross-polarized light with changing the thickness of Bi:YIG film and the incident wavelength when fixed other parameters; (c) Amplitude and (e) phase profiles of the co-polarized reflection light for the MO metasurface without applied magnetic field; (d) Amplitude and (f) phase profiles of the cross-polarized reflection light for the MO metasurface with applied magnetic field.
Fig. 3. Complex amplitudes of the four selected structures in the (a) co-polarized and (b) cross-polarized channel corresponding to the case of without and with applied magnetic field, respectively. The horizontal-axis represents the number of the four selected structures. The left vertical axis demonstrates the amplitude distribution, with the stars and rhombs representing the co-polarized and cross-polarized reflectance, respectively. The right vertical axis depicts the phase for both cases, with red and orange bars representing the phase of the co-polarized and cross-polarized channels, respectively
Table 1. Geometric parameters of the four selected structures
Furthermore, we generate two independent binary phase holograms using the modified GS algorithm and encode the holograms into the identical MO metasurface by elaborately arranging the selected structures in each unit. Initially, we choose two original images “B” and “heart” corresponding to without and with magnetic field case. And their amplitude distributions are multiplied by the random phase factor to obtain the Fourier transform. Considering the computing resources requirements of full-wave numerical simulations, we choose the pixel arrays of 100×100. First of all, the multiple iterative loops of inverse Fourier transform and Fourier transform are performed between the hologram plane and reconstructed image plane, and the binary phases are set accordingly. Afterwards, we retrieve the optimal complex amplitude holograms distribution and generate the double binary phase holograms. Then we encode the double holograms into the identical MO metasurface, the coding method is illustrated in Fig. 4. The scheme can cover all combinations of the double independent binary phase holograms.
Fig. 4. Schematic illustration of encoding double independent holograms into the identical MO metasurface. The block represents each pixel unit. The yellow/green/magenta/orange boxes correspond to the selected four groups of structures. The 0 and π in the boxes represent the phase shift of each structure in different polarization channels. The hologram reconstructed images of the upper and lower layer correspond to the letter “B” and the pattern “heart” in the co-polarized and cross-polarized channels on the right respectively. Black arrows indicate input/output polarization..
To compare with the reconstructed images using the GS algorithm, the full-wave numerical simulation verification of the far-field reconstructed image based on the encoded MO metasurfaces is carried out using the FDTD method. Since the period of a single structure is set as 500 nm, the overall size of the simulated metasurface is 50 μm × 50 μm. And we set the boundary conditions in the x, y, z directions as PML. The material parameters and mesh sizes setting are completely the same as the single structure. Finally, the double hologram images of an identical MO metasurface in the co-polarized and cross-polarized channels corresponding to both states (without and with applied magnetic field) are reconstructed, and the procedure is shown in Fig. 5(a). The numerical reconstructions calculated by GS algorithm in Matlab are shown in Figs. 5(b) and 5(c). The far-field reconstructions using full-wave calculations based on FDTD are shown in Figs. 5(d) and 5(e). The letter “B” and the pattern “heart” are reconstructed in the co-polarized and cross-polarized channels corresponding to without and with H states. It should note that the image quality of the full-wave simulation is deteriorated a bit compared to the ones from numerical reconstructions, this is due to the deviations of meshing accuracy in FDTD and limitation of computing resources. Moreover, the unneglectable near field coupling between each pixel also leads to the decrease of image quality. Nevertheless, the full-wave simulation results are helpful to verify the tunable effects.
Fig. 5. Double hologram images reconstructed from an identical MO metasurface in the co-polarized and cross-polarized channel corresponding to case of without and with applied magnetic field, respectively. (a) Procedure of hologram reconstruction; (b)-(c) Numerical reconstructions calculated by Fourier transformation in Matlab; (d)-(e) Simulated reconstructions using full-wave calculations based on FDTD. Black arrows indicate input/output polarization.
3. Conclusions
In conclusion, the binary phase-only dynamic holographic display based on the magnetically controllable metasurface is originally implemented by a theoretical method. The proposed MO metasurface is composed of Au nanohole arrays with a Bi:YIG interleave layer and an Au film underlayer placed on a glass substrate. Since the constructed double-layer metal structure acts as a Fabry-Perot resonator, the local electric field in the MO film layer is continuously accumulated, thereby improving the modulation efficiency of the MO metasurface [57]. It is evaluated that the polarization conversion efficiency can be improved by at least an order of magnitude compared with pure MO film of the same thickness. The complex amplitude modulation of the MO metasurface in the co-polarized and cross-polarized channels corresponding to case of without and with applied magnetic field is obtained using the FDTD method by optimizing the sizes of Au nanoholes and utilizing the magneto-induced polarization conversion from MO film. Four structures with basically uniform amplitude and phase shift combination of (0, 0), (0, π), (π, 0), (π, π) are selected, then an identical MO metasurface system that can display two independent holograms is designed based on the modified binary phase GS algorithm. The holograms reconstructed by numerical and full-wave simulation are both demonstrated. And the simulated results verify the tunable effects of the proposed MO metasurface. So far, the dynamic holographic display of metasurface in different polarization channels via magnetic field manipulation has not been reported. It shows great potentials in dynamic display and optical information encryption.
Funding
National Key Research and Development Program of China (2021YFA1401200); Beijing Outstanding Young Scientist Program (BJJWZYJH01201910007022); National Natural Science Foundation of China (U21A20140, 92050117); Fok Ying Tung Education Foundation (161009); Beijing Municipal Science and Technology Commission; Administrative Commission of Zhongguancun Science Park (Z211100004821009).
Disclosures
The authors declare no conflict of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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