Three-dimensional (3D) holographic display technology, as a cutting-edge display technology, provides depth vision to present a genuine 3D effect compared with 2D holography, aiming at achieving a more immersive user experience. With the in-depth research of 3D display technology, it has been gradually applied to optical data storage [1–3], virtual reality (VR), and augmented reality (AR) displays [4–6] as well as medical imaging [7,8]. However, the complex structure, high cost, large volume limitations, and optical performance problems of traditional 3D holographic components pose significant challenges in integrated display technology for AR/VR [9,10]. In recent years, metasurfaces based on the generalized laws of reflection and refraction have significantly advanced the integration of miniaturized optical devices due to their remarkable capability in achieving nanoscale wavefront modulation through phase or amplitude modulation [11]. The metasurface with a highly engineered subwavelength structure enables precise regulation of the amplitude, phase, polarization, and wavelength of electromagnetic waves through the flexible design of its structural parameters. Benefiting from rapid progress in micronano manufacturing technology and computer technology, metasurfaces with diverse optical functionalities have been developed and successfully implemented in various miniaturized optical fields, including holographic displays [12–16], optical encryption [17–21], nanoprinting [22–24], edge detection [25,26], and diffraction neural networks [27,28]. As one of the important applications, metasurface 3D holography can reconstruct far-field images with superior spatial resolution and greatly reduce manufacturing costs compared with traditional 3D holography [29–31].

The subwavelength structure of the metasurface and its precise light-field modulation capabilities enable the creation of holographic displays with high visual effects and easy integration. The geometric phase metasurface is capable of manipulating arbitrary wavefronts across the entire 0−2π phase range and serves as the primary device for holographic displays. For instance, Zheng et al. employed a 16-level phase metasurface to implement a monochromatic hologram with an efficiency of 80% [32]. Wen et al. proposed a helical multichannel metasurface hologram with high efficiency and excellent image fidelity [33]. However, most of the metasurface holograms proposed by the aforementioned researchers are monochromatic and lack depth information. To create realistic visual scenes, holograms must retain the depth, color, and other properties of the original object. By introducing various physical properties of light, such as polarization and wavelength, holograms for 3D color imaging can be generated [34,35]. However, the crosstalk among wavelength channels caused by the coupling between meta-atoms in the previously proposed 3D holographic metasurface leads to a degradation in the quality of reconstructed 3D images. Further, the complex geometry also inevitably increases the complexity of the design and manufacturing process, making integration more challenging [22,36–40]. For instance, the coupling between interleaved structures [Fig. 1(a)] leads to crosstalk among wavelength channels within the same plane [22,36,37]. In addition, for a hologram, under the same polarization and different incident wavelengths λ1 and λ2, there will be crosstalk images at the far-field reconstruction distances z1 and z2 [Fig. 1(b)], respectively (the mathematical relationship can be expressed as λ1z1=λ2z2) [29,41]. Based on this, Arbabi et al. converted the polarization hologram of the original target image into a false color image using the Stokes parameter, thus enabling the independent display of holograms under different polarization states [45]. This design method can only be used for single-wavelength holographic display and has limitations in the application of low crosstalk full-color holographic display. Hu et al. utilized three orthogonal linearly polarized light combinations to achieve high-quality color holographic displays [12]. Because the phase and amplitude regulation of linearly polarized light are related to the size of the nanorod structure, this scheme requires searching hundreds of nanorods with different sizes for the structural design, which increases the complexity of design and is not universal. Thus far, although the metahologram provides a sufficient viewing range, there is still lack of a 3D color holographic display strategy to avoid in-plane and interplane crosstalk caused by different wavelength channels. Fortunately, the single-cell metasurface based on geometric phase possesses a simple structure and a continuous phase gradient, effectively reducing the complexity of the design strategy for metasurface holograms. Therefore, we are exploring the strategy of utilizing a single-cell metasurface to reduce interchannel crosstalk in 3D color holographic displays.

In this paper, we propose a novel single-cell metasurface to achieve polarization and wavelength-encoded crosstalk free 3D full-color holography. By combining amplitude holography and phase holography to encode multiple holograms, three different amplitude and phase profiles are assigned to three independent photonic base channels that are coregulated by polarization and wavelength. The polarization and wavelength of the three different photonic base channels are independent of each other; thus, the crosstalk between channels is negligible in principle, leading to the absence of the additional undesired in-plane and interplane holograms. Compared with the previous reported complex interleaved or multilayer structures, this single-cell metasurface can integrate multiple holographic information into a single atom without sacrificing design simplicity, providing greater flexibility in regulating the light field. This method simplifies the hologram design and metasurface fabrication process and achieves crosstalk free 3D full-color vector element holography, which has great application potential in AR/VR, color display, information storage, and so on.

Figure 1(c) illustrates the concept of a 3D full-color metahologram based on a single-cell metasurface. Most of the current metasurfaces can be used for broadband transmission; however, holographic images of different wavelengths will deliver the same in-plane and interplane crosstalk information in various far-field reconstruction regions. The proposed scheme enables the integration of three completely independent holographic images onto a single-cell metasurface, thereby eliminating in-plane and interplane crosstalk caused by different wavelengths. By encoding the 3D color holographic image into an independent photon base consisting of three wavelengths and three polarization channels, the crosstalk image of the undesired channel is eliminated, resulting in the reconstruction of a nearly crosstalk-free 3D color holographic image. By controlling three independent bases of incident photons (LCP-LCP-633 nm, RLL; LCP-RCP-532 nm, GLR; RCP-LCP-488 nm, BRL) encoded by polarization and wavelength, the designed single-cell metasurface is capable of reconstructing crosstalk-free 3D full-color images in the far field, where R represents the 633 nm wavelength channel, and the subscript LL represents the LCP light component emitted after the incidence of LCP light on the metasurface, and so on. The single-cell metasurface reconstructs high-quality 3D color holographic images by selecting wavelengths and polarization states, thus reducing the complexity and cost of device manufacturing.

To achieve this target hologram, we have developed a novel metasurface structure that utilizes wavelength and polarization coding in three independent color holograms. Here, the metasurface that encodes the color hologram is composed of a series of TiO2 nanorods on a quartz substrate. To manipulate the hologram of three independent photon groups (RLL,GLR,BRL) on a single-sized TiO2 nanorod, we made use of amplitude and phase holography to encode the hologram. By designing the metasurface composed of the aforementioned anisotropic nanostructures [Fig. 2(a)], we can independently control the amplitude and phase of transmitted light in different polarization and wavelength channels. In this paper, particle swarm optimization (PSO) is adopted to optimize the structural parameters of TiO2 nanorods [Fig. 2(b)]. The design goal is to maximize the conversion efficiency (CE) of circular polarization at the three target wavelengths (488, 532, and 633 nm) in order to ensure high-quality 3D color holographic images. To match with the current metasurface manufacturing process, a fixed cell period of 450 nm is utilized, and the optimal rectangular TiO2 nanorods are selected based on their CE values, with a height (H) of 690 nm, a length (L) of 330 nm, and a width (W) of 110 nm. Figure 2(c) shows the spectral response of cross-circular polarization transmittance of nanorods simulated by using the finite-difference time-domain (FDTD) method. At the three target wavelengths, the cross-polarization transmittance is 82.7% at 488 nm, 89.9% at 532 nm, and 64.5% at 633 nm, respectively. Figure 2(d) depicts the distribution of electric field components on the y-z plane when X-polarized light is incident on an atom with an orientation angle θ of 45°. The numerical calculations were performed using the FDTD method to further verify the capability of nanorod rotation in modulating the geometric phase (PB phase), as shown in Fig. 2(e). When the nanorods are rotated from 0° to 180°, the PB phase spans the entire range of 0−2π. Thus, by arranging a series of nanorods with varying rotation angles to form a phase gradient at the interface, the metasurface is able to induce abnormal beam deflection. Figure 2(f) illustrates the variations in simulated cross-polarization transmittance of nanorods with lengths and widths ranging from 100 to 350 nm, under three different incident wavelengths. It can be observed that optimizing the size of the nanorod structure maximizes CE at the three desired wavelengths. Based on the determined size of the atomic elements, the amplitude modulation and phase modulation arising from the rotation of the orientation angle φ of the nanorods are further verified through numerical simulation. Therefore, we finally made use of amplitude modulation and phase modulation, respectively, for hologram optimization at the three target wavelengths to achieve a crosstalk-free 3D color holographic display.

To achieve a crosstalk-free 3D holographic display with wavelength-independent modulation, we optimize the design by using an amplitude hologram at 488 nm and phase holograms at 532 and 633 nm. First, we consider the amplitude hologram and then proceed to design a cell structure that meets the required amplitude distribution at the target wavelength. Binary holograms, as a special case of continuous-amplitude holograms, consist only of amplitudes with either “0” or “1”. In the design process of the amplitude hologram, we utilize the copolarization transmission efficiency (LCP-LCP) at a wavelength of 488 nm for amplitude modulation. During the cell period, when the nanorods are removed, the light intensity of the copolarized component reaches its maximum, while that of the cross-polarized component is suppressed. Thus, the amplitude (or intensity) of the incident light can be manipulated by appropriately configuring the nanorods in a way that either removes or reserves them within the period. Specifically, the output intensity I of the metasurface after the above operation can be expressed as ILL_R={0,withNRGB1,withoutNRGB,ILL_G={0,withNRGB1,withoutNRGB,ILL_B={0,withNRGB1,withoutNRGB,(1)where ILL_R, ILL_G, and ILL_B represent the light intensities of the copolarized components at 633, 532, and 488 nm, respectively. The interesting mapping relationship between light intensity and meta-atoms offers new possibilities for manipulating the amplitude of incident light. Based on this property, we utilize various combinations of nanorod structures to achieve the desired two amplitude distributions. Further, the copolarization transmission efficiency and phase of the nanorods remain constant with the orientation angle, offering additional flexibility for the metasurface to independently manipulate amplitude and phase in the holographic display of incident circularly polarized light.

The PB phase caused by the cross-polarization component of the incident light is introduced for phase modulation in order to encode the phase hologram image. The PB phase across the meta-atoms can be expressed as φLR_R=2θNRGB,φLR_G=2θNRGB,φLR_B=2θNRGB,(2)where φLR_R, φLR_G, and φLR_B represent the phase delay of the cross-polarized component at the wavelengths of 633, 532, and 488 nm, and θNRGB are the rotation angles of meta-atoms. By combining the above two operations, an amplitude hologram and a phase hologram can be integrated into the same metasurface. It is noteworthy that, in comparison with the traditional interleaved metasurface, this single-cell metasurface effectively improves information capacity and reduces manufacturing difficulty.

We demonstrate the efficient integration of amplitude and phase holograms into this single-cell metasurface. We achieve this integration by Eqs. (1) and (2) to control the intensity and phase of the three main RGB colors on the metasurface. Figure 3(a) illustrates the flow diagram for designing the single-cell metasurface. First, the RGB components of the target 3D color image are obtained. The target amplitude holographic image is selected as the 3D holographic image of the red component, and the corresponding amplitude distribution is obtained using the modified Gerchberg–Saxton (GS) algorithm. The amplitude information is then encoded into the spatial distribution of the atom array using Eq. (1) (amplitude-type holographic metasurface). By rationally arranging the array of nanorods, the single-cell metasurface can achieve high spatial resolution and good diffraction efficiency through binary amplitude modulation [42]. In the second step, the phase distribution of the 3D hologram with green and blue components is designed using the modified GS algorithm based on determining the amplitude distribution. In particular, the meta-atoms exhibit complementary geometric phase distributions for two incident CP lights that are orthogonal to each other. Based on this property, two different hologram images can be displayed by switching the incident spin direction through selecting the appropriate orientation angle of the meta-atom. The phase distribution φLR is therefore used to reconstruct the 3D holographic image at a wavelength of 633 nm, while the phase φRL is employed for reconstructing the 3D holographic image at a wavelength of 532 nm. For two orthogonal CP beams incident on the meta-atom at different wavelengths, the total geometric profile of the cross-polarization component ϕLR+RL can be expressed as φLR+RL=arg[exp(iφLR_G)+exp(iφRL_B)],(3)where φLR_G(φRL_B) is the geometric phase of 532 nm LCP (488 nm RCP) light incident on a meta-atom. The phase distribution φLR_G and the phase distribution φRL_B are combined into a single-phase distribution using Eq. (3). In the third step, Eq. (2) is utilized to rotate various meta-atoms to achieve the desired geometric phase distribution [44]. By following the three steps mentioned above, it is possible to achieve a crosstalk-free 3D color holographic display on a single-cell metasurface.

Figure 3(b) depicts a detailed flow chart of the modified GS algorithm. The intensity of the three RGB components of the color holographic image Ak(k=R) is first extracted; then, the random phase φk(k=R) is introduced. The light field is then propagated backward into the hologram plane using an inverse Fresnel transform (IFRT). The intensity distribution Bk is normalized, and the phase φk′ is optimized to a binary value of 0 or π/2. The forward Fresnel transform (FFRT) is then performed to obtain the intensity distribution in the observation plane. The phase keeps unchanged, and the intensity distribution Ak′ is replaced with the desired holographic image intensity Ak. Finally, the final optimized amplitude distribution Ck can be generated through finite iterations of calculation. The intensity of the three RGB components of Ck is then extracted, and a new random phase φk(k=G,B) is introduced into another GS algorithm for iterative operation. The light field is propagated forward to the observation plane through FFRT. Replace the obtained intensity distribution with the expected holographic image intensity Dk. IFRT is then used to propagate the light field backward into the hologram plane. The light field is then propagated backward to the hologram plane using IFRT, and the intensity distribution Dk′ is replaced with Ck. After several iterations, the final phase distribution φtotal_k is returned.

We compared the detailed process of reconstructing 3D color holographic images in the far field using traditional metasurfaces (such as interleaved metasurface and cascaded metasurface) and this single-cell metasurface, as shown in Fig. 4. For the traditional metasurface, the distance and wavelength of the far-field reconstructed holographic image satisfy λ1z1=λ2z2. Therefore, for incident beams of different wavelengths passing through the metasurface at different distances in the far field, the same image can be reconstructed, as depicted in Fig. 4(a). It can be observed that the traditional metasurface exhibits significant interplane crosstalk during the process of reconstructing 3D color images, which poses some obstacles to achieving advanced AR/VR 3D stereoscopic display components. In contrast, the single-cell metasurface we designed allows three independent photon bases to control the reconstruction of 3D holograms, effectively avoiding crosstalk among the propagation planes [Fig. 4(b)]. It is important to note that, since we use a metasurface with a single-cell structure, there is no in-plane crosstalk. Further, the designed metasurface significantly simplifies the manufacturing process, offering a potential solution for achieving efficient 3D display devices.

To validate our proposed strategy for avoiding crosstalk in 3D color holographic displays, we developed a single-cell metasurface composed of an array of nanorods with the same size. As depicted in Fig. 5(a), color images of various patterns are reconstructed at different distances in the far field by simultaneously adjusting the self-selected directions of incoming and outgoing beams. The hologram is designed with 1000×1000pixels, resulting in a total contour area of 450μm×450μm. The presence or absence of atoms and the orientation angles in each period are designed to provide amplitude and phase modulation, respectively. This is illustrated in Fig. 5(b-I) of the single-cell metasurface configuration. Figure 5(b-II) illustrates the amplitude and phase distributions of the hologram in relation to wavelength and spin. It can be observed that two phase profiles with opposite spin directions are also maintained in an opposite manner to achieve the integration and regulation of different polarization states of individual nanorods. By changing the circular polarization state of the incident beam, the designed metahologram reconstructs the patterns of “ship,” “airplane,” and “car” at different distances d in the far field. Since the input/output polarization combination of each channel is independent, there is almost no in-plane and interplane crosstalk for each channel. The images in these three polarization and wavelength channels are selected and combined through optical settings to form the 3D color holographic image, as shown on the left side of Fig. 5(c). The color image of the reconstructed RGB component in the simulation is shown on the right side of Fig. 5(c). It can be observed that the simulation results exhibit good agreement with the target image, further confirming the effectiveness of single-cell metasurfaces in suppressing crosstalk between channels during 3D color hologram reconstruction.

Depth resolution, as an important evaluation index for 3D holographic displays, is crucial for achieving high-performance 3D display. Due to the shortening of the distance between imaging planes, the image crosstalk between different planes gradually increases, as shown in Fig. 6(a). The depth resolution of this single-cell metasurface was analyzed to assess its excellent performance. To intuitively analyze the crosstalk between different planes, we distributed holographic images of different colors in three regions and calculated the crosstalk values for each region. Here, we use the root-mean-square error (RMSE) to calculate crosstalk for the specified region, as shown in Fig. 6(b). The RMSE varying with the distance between the depth planes is illustrated in Fig. 6(c), taking two planes as an example. It can be seen that, as the distance increases, the RMSE decreases gradually and finally becomes stable. We also calculated the average RMSE at different wavelength channels for all planes, and its expression is as follows: Average_RMSE=1KN∑kK∑nN1PQ∑p,q[In,k′(p,q)−In,k(p,q)]2,(4)where K represents the number of target wavelength channels, and N represents the number of target planes. The left side of Fig. 6(d) displays the average RMSE for all combined components. Here, when the distance between the depth planes is 12 μm, there is obvious color crosstalk between different planes. However, when the distance between the depth planes is increased to 15 μm, the crosstalk between the depth planes can be ignored. The depth resolution of the single-cell metasurface is therefore excellent. Moreover, the depth resolution can be further improved by adjusting the number of metasurface pixels or utilizing intelligent algorithms for hologram optimization.

The advantages of the metasurface, such as miniaturization and multiple degrees of freedom, are expected to accelerate the application of full-color display, encryption, and information storage. In recent years, the realization of 3D color holographic display through optical metasurfaces has emerged as a prominent research area. To demonstrate the unique advantages of our single-cell metasurface, a detailed comparison summarizing several holographic display technologies is presented in Table 1. Arbabi et al. converted the red, green, and blue data in color images into Stokes parameters and stored the color image data in monochrome holograms, providing an effective method to increase data storage capacity [45]. However, compared with monochromatic holograms, full color holographic display technology based on wavelength regulation increases the number of wavelength channels and is more appealing in the field of visual display [12,36,41]. For instance, Hu et al. utilized three orthogonal linearly polarized light combinations to achieve high-quality color holographic displays [12]. However, this design strategy necessitates the use of multiple nanorods of varying sizes to form a metasurface, thereby increasing the complexity of the design. Compared with the above traditional metasurface 2D display technology [12,36,41,45], 3D display technology provides depth information and effectively increases the amount of information. In addition, the interaction between nanorods in the holographic display technology based on interleaved metasurface leads to crosstalk among different wavelength channels [36]. To effectively avoid this situation, a single-cell metasurface exhibits significant advantages and reduces the difficulty of processing and manufacturing. However, the previously proposed metasurface 3D color display exhibits crosstalk between the depth planes due to different wavelength channels under the same polarization condition [31,40]. The single-cell metasurface 3D color display technology, which combines amplitude modulation and phase modulation, effectively avoids in-plane and interplane crosstalk compared with the previous work, greatly reducing the difficulty and cost of device processing.Table 1.

Comparison of Full-Color Display Metasurfaces

In summary, we demonstrate a design strategy for metasurface 3D color holographic displays that make use of single-sized nanorods to avoid in-plane and interplane crosstalk caused by holograms encoded with different polarization channels and wavelength channels. This strategy utilizes the modified GS algorithm to optimize the hologram by combining amplitude coding and phase coding, enabling multiple different holograms to be encoded into a single-cell metasurface. Specifically, by employing three polarization bases (LCP-LCP, LCP-RCP, and RCP-LCP) and three visible wavelengths (633, 532, and 488 nm), the incident photons can independently encode different color images on different depth planes and effectively suppress in-plane and interplane crosstalk of different wavelengths. It is worth mentioning that the designed metasurface can achieve a 3D color holographic display without increasing processing difficulty or manufacturing cost, potentially providing a solution for lower-cost holographic technology based on metasurfaces. Additionally, our approach can be easily combined with other inverse design algorithms to increase the number of 3D color image channels encoded in a single-cell metasurface. The single-cell metasurface has a wide range of applications in the fields of optical encryption, optical imaging, and color display.