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Abstract
In recent years, metasurfaces have attracted considerable interest for their unprecedented capabilities to manipulate intensity, phase, and polarization of an electromagnetic wave. Although metasurface-based wavefront modulation has achieved numerous successful results, implementation of multifunctional devices in a single metasurface still meet significant challenges. Here, a novel multilayer structure is designed using properties of vanadium dioxide (VO2). Propagation phase and geometric phase are introduced in this structure to achieve multichannel holographic imaging in terahertz band. When the temperature is above 68°C, VO2 becomes a metal and it plays a role in wavefront modulation for terahertz wave. The left-handed channel realizes a hologram letter L and the right-handed channel realizes a hologram letter R. When the temperature is below 68°C, VO2 changes to an insulator, and electromagnetic wave is controlled by gold structures embedded inside a VO2 film. In this case, hologram number 2 is realized in the left-handed channel and hologram number 6 appears in the right-handed channel. Our structure has advantages of low crosstalk, multiple channels, and large bandwidth. This novel design paves a new road for multichannel imaging and information encryption.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Terahertz band is a part of electromagnetic spectrum that lies between microwave and infrared radiation. There is no complete agreement on exact range of terahertz, but the band is generally fixed at 0.1 THz∼10.0 THz. Historically, terahertz band is often overlooked because this radiation is difficult to produce and detect effectively at ambient temperature. Moreover, terahertz band has been largely overshadowed by tremendous developments in microwave and infrared technologies. All these elements together limited the use of terahertz band in the past years [1–3]. Fortunately, terahertz waves have gradually attracted attention due to their unique characteristics and shown great potential in areas of wireless communication [4,5], public and food security [6,7], and detection [8,9]. Terahertz waves have higher channel capacity, which allows them to play an important role in sixth generation wireless communications [10,11]. However, with increasing complexities of application scenarios, terahertz devices are eagerly desired to have small size, multichannel, and broadband characteristics.
Most natural materials are not suitable for direct modulation of terahertz waves due to large absorption loss, so metamaterials are presented to solve this question [12]. Conventionally, metamaterials, which have large volume and are complicated to fabricate, are characterized by effective medium theory and widely applied in control of electromagnetic wave [13]. In comparison with metamaterials, metasurfaces have attracted great popularity because of their simple structure, low loss, and low price [14,15]. Because of excellent capabilities exhibited by metasurfaces in control of electromagnetic properties, significant achievements have been realized in many domains especially in holograms [16]. In 2015, Zheng et al. integrated a grounded metal plane and a geometric metasurface to achieve holograms with extremely large diffraction efficiency and broad bandwidth [17]. In 2017, Mueller et al. constructed a metasurface utilizing linear birefringent wave plate units to impose two arbitrary phase profiles, and achieved chiral holograms with completely independent far fields [18]. In 2021, Georgi et al. presented a cascaded metasurface for splitting and sharing encrypted holographic information [19]. Two metasurfaces displaying different holograms are spatially cascaded to generate completely new holographic images. Recently, multichannel holographic imaging has gradually become a focal point, yet most of approaches are constructed in form of meta-molecules. In 2016, Wang et al. proposed a meta-molecule composed of three types of nano-blocks, and their design allowed simultaneous wavefront modulation of trichromatic light [20]. In 2018, Zang et al. came up with a kind of metasurface that encodes color and intensity into a polarization profile of wavelength dependence [21]. In 2022, Wan et al. presented a method to multiplex holographic phase and conjugate hologram phase corresponding to two orthogonal circularly polarized (CP) beams [22]. They achieved a full-color vector hologram with independent spatial polarization control. However, all above works are mainly designed by interleaved subarrays. Such structures are complex and only perform specific functions with narrow band widths. Moreover, meta-atoms in interleaved subarrays produce relatively large crosstalk. Therefore, there is an urgent necessity to propose a new method to solve the above issues.
Phase change materials (PCMs) are a class of active materials that are introduced into design of metasurfaces to give them tunable properties. Among these various PCMs, VO2 is one of the most desirable materials [23]. VO2 is a strongly correlated material, and it attracts research attention because of the ability of switching between metallic and insulated states. VO2 is an insulator at room temperature and turns into metal above 68 °C. Moreover, the above changes are reversible [24]. In addition, phase change of VO2 can be achieved by other means, such as current application [25,26] and optical pumping [27,28]. During state switching, the conductivity of VO2 changes significantly in terahertz band [29]. Taking advantage of this property, researchers conducted numerous studies in domain of dynamic modulation for electromagnetic wave. In 2016, Liu et al. achieved multifunctional control of electrical triggering by integrating a VO2 sheet into an optical metamaterial absorber [30]. In 2019, Liu et al. experimentally verified that temperature-dependent dynamic holograms are achievable by using VO2 [31]. In 2022, Yang et al. realized multifunctional terahertz transparent electrodes with VO2 slit arrays [32]. Therefore, VO2 is very prospective and holds promise for more complex wavefront modulation from the perspective of future development.
In this work, a novel metasurface based on phase-change properties of VO2 is designed, and propagation phase and geometric phase are introduced in this structure to achieve multichannel holographic imaging for terahertz wave. To further explain concept of our work, schematic diagrams of functional performance of metasurface are shown in Fig. 1 under CP incidences. When temperature is heated above 68 °C, VO2 becomes a metal. Electromagnetic wave cannot pass through VO2 film, and VO2 patches play the role in controlling wavefront modulation. Left-handed spin channel realizes a hologram letter L with a square border and right-handed spin channel achieves a hologram letter R with a square border. As temperature cools below 68 °C, VO2 reverts to an insulator. In this case, electromagnetic wave is controlled by gold patches embedded inside a VO2 film. To investigate interference effect of insulated VO2 patches and VO2 film on gold patches, simulations are performed. Results show that interference effect of insulated VO2 patches and VO2 film on gold meta-atoms is very low, which greatly simplifies design process. A hologram number 2 with a circular border is realized under left-handed circularly polarized (LCP) incidence. Meanwhile, a hologram number 6 with a circular border is observed under right-handed circularly polarized (RCP) incidence. This metasurface has advantages of low crosstalk, large bandwidth, and possibilities of displaying different images in the same frequency band. Our design opens up a new window for multichannel imaging and information encryption in terahertz band.
Fig. 1. Schematic diagram of a spin-multiplexing reflective metasurface. Two CP waves with different chiralities are incident on the metasurface to produce a holographic letter R and a letter L when temperature is above 68 °C. A holographic number 2 and a number 6 are generated in other two channels under CP incidences with different chiralities when temperature is below 68 °C.
2. Principle and design
Propagation phase Φ depends on structural dimensions of meta-atoms and is unrelated to spin state [33,34]. Geometric phase is phase delay with spin dependence and it is represented by $\varphi _{cp}^g ={\pm} 2\theta $, where θ is rotation angle of meta-atom and $\mathrm{\ \pm }$ depends on chiralities of CP waves [35,36]. The above description is briefly expressed in the following form
where φp represents propagation phase and φg represents geometric phase. Modulation techniques of geometric phase and propagation phase are incorporated into designed meat-atoms to achieve multiple information for encoding spin decoupling. As a result, each atom produces completely independent phases depending on different CP waves [37]. When LCP and RCP waves are respectively incident on meta-atoms, full phase is equal to the superposition of propagation phase and geometric phase. Therefore, the following relationship is obtained Consequently, θ and Φ are expressed byTo achieve wavefront modulation of LCP and RCP waves, φLCP and φRCP have to meet full 360° phase coverage. It is well recognized that changing only one structural parameter to achieve 360° coverage of propagation phase and maintaining high amplitude at the same time is a really challenging task in terahertz band. However, changing geometric phase is a simple way by altering θ. Hence, design difficulty of propagation phase is reduced by rotating θ. The way is as follows.
Three-dimensional structure of the designed meta-atom is given in Fig. 2(a). It is composed of six elements including a VO2 patch, a SiO2 spacer, a VO2 film, a gold patch embedded inside a VO2 film, a SiO2 spacer, and a gold substrate from top to bottom. Figures 2(b) and 2(c) depict top views of a VO2 patch and a gold patch, respectively. Thicknesses of VO2 patch, VO2 film, and gold substrate are 1.0 µm. The thickness of gold patch embedded inside VO2 film is 0.9 µm, which is beneficial to obtaining the optimized amplitude and phase of meta-atoms. Parameters w1 and w2 are widths of VO2 patch. Parameters w3, w4, w5, and w6 are widths of gold patch. Period of a meta-atom is p. Lengths of VO2 patch and gold patch are l1 and l2. Propagation phase is controlled by varying l1 and l2, and geometric phase is controlled by altering θ1 and θ2. By combining propagation and geometric phases in this metasurface, photonic spin-orbit interaction is broken in a conjugated symmetric manner, hence achieving spin multiplexing [38]. For a clearer representation, structure dimensions of meta-atoms are listed in Table 1. In terahertz band, relative permittivity of SiO2 is 3.85 [39,40], and gold is regarded as lossy metal whose conductivity is 4.561 × 107 S/m [41]. Dielectric permittivity of VO2 is represented by Drude model $\varepsilon(\omega)= {\varepsilon _{inf}} - \frac{{\omega _p^2(\sigma )}}{{{\omega ^2} + i\gamma \omega}}$, where ${\mathrm{\varepsilon }_{\textrm{inf}}}$ is 12 and γ is 5.75 × 1013 s−1 [42–44]. ωp(σ) is plasma frequency associated with conductivity, and it is roughly defined as $\omega _p^2(\sigma )= \frac{\sigma }{{{\sigma _0}}}\omega _p^2({{\sigma_0}} )$ with σ0 = 3 × 105 S/m and ωp(σ0) = 1.4 × 1015 rad/s. When temperature is heated above 68 °C, conductivity σ is 3 × 105 S/m and plasma frequency ωp(σ) is 1.4 × 1015 rad/s at this time. After a state transition, σ becomes 200 S/m and the corresponding ωp(σ) is 3.6148 × 1013 rad/s. Finite element method (Comsol Multiphysics 5.3) is applied to simulate amplitude and phase of the designed meta-atoms with CP incidences for different states of VO2. In addition, periodic boundaries are employed in x and y directions, while perfect matching layers (PMLs) are set in z direction.
Fig. 2. (a) Three-dimensional schematic diagram of the designed meta-atom. (b) Top view of a VO2 patch. (c) Top view of a gold patch. Thicknesses of VO2 patch, VO2 film, and gold ground are 1.0 µm. The thickness of gold patch is 0.9 µm. Other optimized geometric parameters are shown in Table 1.
Table 1. Structure parameters of meta-atoms
The dispersionless characteristic of geometric phase largely reduces the requirement for propagation phase, which facilitates the broadband performance of the designed device [45]. Thus, φLCP and φRCP are discretized as 0°, 90°, 180°, and 270° according to Eqs. (5) and (7), and propagation phase is deduced as 0°, 45°, 90°, and 135°. Figures 3(a) and 3(b) depict broadband performance of reflection amplitude and propagation phase for σVO2 = 3 × 105 S/m via variation l1 under CP incidences. It is clearly seen that reflection amplitude of the designed atoms is around 0.8 and phase coverage is over 135° at 1.1-1.6 THz. White circles in Figs. 3(a) and 3(b) represent four selected meta-atoms with 45° phase difference at 1.5 THz, and four selected meta-atoms are displayed in the upper part of Fig. 3(c). The goal of the designed atoms is to enable a single meta-atom to produce two independent encoded states for two independent CP waves. As shown in the lower part of Fig. 3(c), combining four states of LCP wave and four states of RCP wave yields a library containing sixteen meta-atoms. Due to uncertainty in absolute phase of meta-atom, coded element is defined as reflected phase of digital state “0/0” for ease of representation. For example, when digital state of LCP and RCP waves is “1/3”, it corresponds to the third meta-atom in the upper part with rotation θ1=-45° and parameter l1 = 32 µm at 1.5 THz. When these meta-atoms are combined with a pre-designed phase distribution, a spiral-controlled bifunctional device is achieved.
Fig. 3. Amplitude (a) and phase (b) distributions of simulated reflection spectra for the conductive VO2 with different l1. White circles represent four selected meta-atoms. (c) Structural dimensions of the selected meta-atoms and a meta-atom library for metasurface design under LCP and RCP incidences.
As VO2 changes to insulator, phase response is modulated by gold patches. To investigate interference effect of insulated VO2 patches and VO2 film on gold patches, length l1 and rotation angle θ1 of VO2 patches are changed in Fig. 4. Figures 4(a) and 4(b) respectively show interference effect of VO2 patches and VO2 film on phase and amplitude of gold patches under LCP and RCP incidences, where size of ball represents amplitude. Ignoring effect caused by perspective problem, VO2 patches with σVO2 = 200 S/m has little impact on amplitude. It is concluded from projection results that the smaller encoding value of meta-atom is, the greater interference on phase will be. This is mainly due to the fact that the smaller encoding of meta-atom is, the larger the corresponding structural size will be, which makes interactions among adjacent meta-atoms stronger. Moreover, maximum phase interferences of VO2 patches on gold patches are only 10.77° and 11.29° as LCP and RCP waves are incident. Therefore, when designing parameters of gold patches, there is no need to additionally consider complex shapes and rotation angles of VO2 patches, which greatly simplifies design difficulty.
Fig. 4. By varying length l1 and rotation angle θ1 of VO2 patches with σVO2 = 200 S/m, interference effect of VO2 patches and VO2 film on phase and amplitude of gold patches under LCP (a) and RCP (b) incidences. Sizes of balls represent reflection amplitudes of gold patches. Numbers “1”, “2”, “3”, “4” represent different gold patches.
Figures 5(a) and 5(b) illustrate broadband performance of amplitude and phase varying l2 when l1 is 47 µm and θ1 is 0°. White circles in Figs. 5(a) and 5(b) are four selected meta-atoms, and the corresponding structure dimensions are shown in the upper part of Fig. 5(c). Compared with results of VO2 with σVO2 = 3 × 105 S/m, although modulations of amplitude and phase by gold patches are degraded, results for four selected meta-atoms are acceptable from 1.1 THz to 1.6 THz. The lower diagram of Fig. 5(c) shows the selected meta-atom library.
Fig. 5. Amplitude (a) and phase (b) distributions of simulated reflection spectra for the insulated VO2 with different l2. White circles represent four selected meta-atoms. (c) Structural dimensions of the selected meta-atoms and a meta-atom library for metasurface design under LCP and RCP incidences.
3. Results and discussions
With the continuous development of computer technology and optical theory, computer algorithms gradually replace wavefront recording process in traditional optical holography. Using this technique, it is possible to avoid building complex optical paths. Metasurface-based holography provides enormous spatial resolution, huge information capacity, and large field of view [46]. To compute phase of hologram, Gerchberg-Saxton algorithm (GSA) is applied [47,48]. GSA is a phase retrieval method, and it iterates through Fourier transform between hologram plane and object plane to obtain the desired phase distribution for designing metasurface. Crucially, this algorithm is used to design required phase matrices (φ1, φ2, φ3, and φ4) to generate completely different holographic pictures in four channels. These holograms are displayed with different VO2 states for different CP waves.
For the proof of concept, a multichannel terahertz metasurface is designed and validated by simulations based on the accomplished design of meta-atoms. Metasurface is made up of 48 × 48 meta-atoms, and PMLs are used as boundary conditions in x, y, and z directions. Figure 6(a) depicts position distribution of metallic VO2 patch according to Eq. (5), and Fig. 6(b) plots rotation angle θ1 of the corresponding position according to Eq. (6). At this time, VO2 patches carry out the task of wavefront modulation while gold patches do not work. Root-mean-square error (RMSE) is generally used to evaluate deviation between simulated intensity and theoretical value to depict manipulative ability of energy distribution. The closer simulated hologram is to the target image, the closer RMSE value is to 0 [49]. Figures 6(c) and 6(d) show holographic images under LCP and RCP incidences at 1.5 THz, where left side is the targeted image and right side is the simulated result. The corresponding normalized RMSEs between simulated images and target images are 0.14 and 0.11 under LCP and RCP incidences, respectively. It indicates that simulated results are close to target images at 1.5 THz. Holographic efficiency of the metasurface is formulated as
Fig. 6. Position arrangement (a) and rotation angle θ1 (b) of VO2 patches with σVO2 = 3 × 105 S/m. Codes “1”, “2”, “3”, “4” represent different VO2 patches. Target images and simulated holograms are displayed under LCP incidence (c) and RCP incidence (d).
Figures 7(a) and 7(b) represent position distribution of gold patch and rotation angle of the corresponding position, and they are calculated according to Eqs. (5) and (6). Figures 7(c) and 7(d) depict target images and simulated results for LCP and RCP waves, respectively. According to Eq. (9), imaging efficiencies for LCP and RCP waves are 48.0% and 46.4%. These holograms show high efficiency of the designed metasurface. Obviously, there is no residual image observed from imaging results after switching VO2 state. This means that the imaging is not disturbed much as σ of VO2 is 200 S/m. The above results demonstrate the fitness and superiority of the proposed meta-atoms. Normalized RMSEs between simulated and target images are 0.13 and 0.12 for LCP and RCP waves, respectively. Therefore, compared with RMSEs in Figs. 6(c) and 6(d), the existences of VO2 patches and film almost do not affect qualities of holographic images as VO2 is insulator.
Fig. 7. Position arrangement (a) and rotation angle θ2 (b) of gold patches are shown with σVO2 = 200 S/m. Codes “1”, “2”, “3”, “4” represent different gold patches. Target images and simulated holograms are displayed under LCP incidence (c) and RCP incidence (d).
To study broadband performance of four-channel holograms, far-field images in the range of 1.1-1.6 THz are observed in Figs. 8(a)-8(d) by changing chiralities of incident CP waves and states of VO2. It is clearly seen that image size decreases with increasing frequency due to a constant geometric phase and period of meta-atoms at each frequency. The best results of holograms are obtained at 1.5 THz. Imaging quality of the metasurface is slightly degraded when the working frequency is far away from the targeted frequency, yet it still has a clear visualization. As σ is 200 S/m in Fig. 5(b), amplitude and phase of gold patches fluctuate significantly at 1.6 THz. This leads to a great increase in background noise in Figs. 8(c) and 8(d) at 1.6 THz. The proposed metasurface is more convenient for practical applications due to its broadband characteristics [51].
Fig. 8. Four-channel broadband holograms from 1.1 THz to 1.6 THz. Two different channels are generated with σVO2 = 3 × 105 S/m under LCP (a) and RCP (b) incidences. The other two channels are obtained with σVO2 = 200 S/m under LCP (c) and RCP (d) incidences.
4. Conclusion
In summary, a multilayer structure based on VO2 phase transition is designed, and this configuration employs propagation phase and geometric phase to achieve a four-channel holographic display. VO2 is a metal when temperature is above 68 °C. At this time, VO2 patches play the absolute role in the control of electromagnetic wavefront. A letter L with a square border is realized in the left-handed spin channel and a letter R with a square border is achieved in the right-handed spin channel. VO2 turns into an insulator when temperature is below 68 °C. Electromagnetic wave is controlled by gold patches while interference effect from VO2 patches and VO2 film is too weak. Therefore, a holographic number 2 with a circular border is realized in the left-handed channel and a holographic number 6 with a circular border is realized in the right-handed channel. Compared with the previous works [37,38,51], our metasurface has the advantage of dynamic four-channel displays. Our scheme breaks new ground for multichannel display, information security, and communication encryption.
Funding
National Natural Science Foundation of China (11974294).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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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