1. Introduction

Metasurfaces, ultra-thin patterned structures, have attracted a lot of attention in recent years [1–4] for their extraordinary capabilities, such as negative refraction [5–7] and hyperbolic dispersion [8]. Generally, the constitutive nanostructures of metasurfaces are mainly made by either metal or dielectric, depending on the resonant characteristics. Metasurfaces composed of metallic nanostructures can inherit many merits of surface plasmon resonances, such as deep sub-wavelength unit cell, strong light confinement and flexible tunability. However, the significant Ohmic losses of metals in visible regime often lead to low efficiency, limiting their realistic application. Alternatively, metasurfaces based on all-dielectric unit cells utilize Mie-type resonances, for example dielectric Huygens metasurfaces [3], which are also attracting increasing attentions recently owing to their advantages such as small loss, high transmission and full-range phase modulation. But compared to the metal nanostructures, the dimension of dielectric unit cells is relatively large and its band is rather narrow.

In principle, metasurfaces can manipulate the wavefront of the transmitted/reflected light in essentially arbitrary way. And this performance has been demonstrated in both isotropic and anisotropic systems [9, 10]. Compared to bulk metamaterials and conventional optical devices for wavefront shaping, such as typical diffractive optical elements and spatial light modulators, metasurfaces not only have much lower loss, but also are relatively easy for design and fabrication, allowing conformal integrations with planar system [11, 12]. Overall, metasurfaces can overcome the challenges encountered in bulk metamaterials and conventional optical devices, while their interactions with the incident waves can be still sufficiently strong to obtain remarkable functionalities. As such, metasurfaces have shown promising potential in a wide range of applications, including flat lens [13], coherent perfect absorber [14], beam steering [15], topological insulators [16], wide angle filters [17], holograms [18, 19], polarization rotation [20] and so on [21, 22].

Hologram, as one of the most striking applications of wavefront shaping, has been known for decades [23]. It is a technique to record and reconstruct both amplitude and phase information of 2D/3D images. Traditional hologram works by recording the interference patterns of the light scattered by the object and a coherently shed beam. The patterns contain the complex amplitude information that can be used to reconstruct the target image in a complete sense. However, such holographic scheme requires real objects, highly temporal and spatial coherent light sources. Later on, computer generated holograms (CGHs) were proposed, which use numerical calculation of virtual objects to ease the recording process [24]. Recently, the CGHs have been achieved in optical metasurfaces consisting of subwavelength nanoantenna arrays to overcome several limitations of the traditional holograms. Moreover, the metasurface CGHs are also able to modulate the phase of an optical beam with high accuracy in broadband frequency range. In [25], Ni et al. demonstrate a hologram based on an ultra-thin metasurface in which the amplitude and phase can be simultaneously modulated. This holographic scheme has raised a lot of attentions in nanophotonic and plasmonic community [26–29].

However, most proposed metasurfaces have been designed to achieve holograms only with single color [28]. Although one could use holographic multiplexing with several subpixels to record different color patterns, it would increase the complexity of the unit cell design and usually requires larger pixel size [30]. These drawbacks greatly hinder the real applications of the full-color metasurface holography. Besides, many metasurface holograms are designed to only record amplitude or phase information, leading to the degradation of the quality of reconstructed images. Particularly, the reconstructed image of a phase-only hologram is inevitably accompanied by spackle noises, although its amplitude is more uniform in the hologram plane [31].

In this work, we propose an effective approach to reconstruct 2D and 3D full-color optical images with both amplitude and phase modulations recoded in a single metasurface CGH. Furthermore, this method can be extended to achieve various full-color images in the same metasurface hologram with multiple recording channels. As a matter of fact, polarization, position, and angle can be regarded as the independent channels to uniquely and correspondingly recover each primary image at the specifically designed state. In addition, the designed metasurface hologram is based on the geometric phase, e.g., Pancharatnam−Berry (PB) phase, and thus bears large fabrication tolerances. We show that the proposed metasurface hologram can work for wavelength ranging from 400 nm to 750 nm. We note, however, that all the reconstruction parameters of the individual metasurface CGH should be carefully chosen to avoid cross-talking between the channels.

2. Unit cell electromagnetic wave control

To create the metasurface CGH, a 40-nm-thick aluminum film drilled with nanoslits that have various orientation angles is placed on a SiO₂ substrate. The unit cell of the metasurface hologram with period$p_x=p_y=230$nm is shown in the inset of Fig. 1(a). The major axis and minor axis of the unit cell of the nanoslit are denoted by $l_0$ and$w_0$, and the nanoslits can rotate in the x-y plane with an angle $\theta$with respect to x axis. Here in this work, we use a fully-vectorial electromagnetic solver based on the finite element method (FEM, COMSOL Multiphysics) to simulate the amplitude and phase modulation of the transmitted light (see Appendix A); the incident electromagnetic field is assumed to be a circularly polarized plane wave, propagating along + z axis, and only the cross-polarized light is considered.

 

Fig. 1 Nanoslit unit cell structure and its optical performance. (a) Phase and transmission for the unit cell with the rotate of the$\theta$. The blue line and red line correspond to the phase-angle relation and transmission-angle relation, respectively. The frequency is set with 632 THz. The inset is an illustration of the unit cell. The nanoslit could rotate in the x-y plane with an orientation of $\theta$to produce a particular phase delay. The periods$p_x,p_y$ are both 280 nm. The major axis and minor axis of the unit cell of nanoslits are$l_0,w_0$. (b) Transmission as a function of nanoslit size $l_0$ and$w_0$. (c) Phase shift of the transmitted RCP light and (d) the transmission of RCP light with different orientation when the incident frequencies from 375 THz to 750 THz. (e) Schematic of the orientation angle corresponding eight PB phase delay, labeled above the respective panel.

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For the geometric-phase metasurface, the transmitted light consists of two circularpolarization states: one has the same handedness as the incident circularly polarized light without phase delay and the other one has the opposite handedness but with an additional phase delay. The additional phase delay, i.e. PB phase $\Phi$, has approximately linear relation with the orientation angle of each nanoslit ($\Phi \text{=}\pm 2\theta$), where the sign “+” and “-” represent the phase delay for the incident left-handed and right-handed circularly polarized light (LCP and RCP), respectively [32]. Note that the phase delay resulting from the PB phase, is based on the geometric effect, so that it is robust against fabrication tolerances, variations of material properties, and the neighboring unit cells [33]. As such, the phase shift can be modulated from 0 to $2\pi$by changing the orientation angle of each nanoslit [see the blue line in Fig. 1(a)]. Figure 1(a) further shows that the transmission efficiency (the red line) almost keeps the same as $\theta$ varies from 0 to 180 degree, which can be used to create nearly pure phase hologram. Figure 1(b) shows the normalized transmission spectra of the nanoslit metasurface as a function of $l_0$ and$w_0$ at working frequency $f=630$THz ($\lambda =470$nm). The spectrum is symmetric with respect to the line $l_0=w_0$, as expected. Here, we set the unit cell size 190 nm × 120 nm, to get a relatively high transmission coefficient. To evaluate the broadband characteristics of the selected unit cell, we show respectively in Figs. 1(c) and 1(d) the phases and transmission efficiency for working frequency $f=$370 THz to 750 THz ($\lambda =810-400$nm), Fig. 1(c) shows that the additional phase delay is solely determined by the orientation angle of each nanoslit, covering almost the entire interested frequency band. Notice that a weak coupling between neighboring nanoslits introduces a small phase deviation when the frequency is close to $f=750$THz. Although the transmission efficiencies of the cross-polarized light change with the shift of the wavelength, it is almost the same at a single wavelength with different orientation angle$\theta$ [schematically shown in Fig. 1(e)].

3. Metasurface holograms

Figure 2(a) illustrates the operating principle of the metasurface CGH, which can modulate the wavefront of the incident beam, and then generate the target object on the image plane.

 

Fig. 2 The designed hologram and reconstructuon procedure. (a) Schematic illustration of the designed hologram in the Fresnel range. Only opposite handedness CP light are collected. (b) Calculated amplitude and (c) phase pattern of the target image as shown in Fig. 3(a).

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Here, we take ‘HIT’ badge as the target object and choose the LCP as the incident light at wavelength $\lambda =475.9$nm. The LCP incident light normally hits the metasurface from the dielectric substrate, and the transmitted RCP light is recorded. In the far-field region, Huygens-Fresnel principle is applied to calculate the complex amplitude distribution of the field on the hologram. Figures 2(b) and 2(c) respectively show the amplitude and the phase distribution of the designed CGH of the badge [see Fig. 3(a)]. The resolution of the CGH is 71.3 μm × 71.3 μm, containing 310 × 310 pixels and the distance between the hologram plane and the image plane is $d=500$μm. For simplicity, a two-level amplitude distribution and eight-level phase distribution of the field on the hologram are considered, similar as in [31]. In detail, we use two states (on and off) with a chosen threshold of $0.1\times A_{\max }$(where$A_{\max }$is the maximum of all of the amplitudes), which is realized by setting a pixel with or without the nanoslit, to modulate the amplitude. Amplitudes smaller than the threshold are modulated to be zero, whereas other amplitudes are modulated to be unity. The phase modulation is modulated by using eight discrete phase levels between 0 and 2π (0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4), represented by the identical nanoslits with eight orientation angles within the unit cells, when the amplitudes equal to one.

 

Fig. 3 (a) Original 2D object compared with (b) theory, (c) simulation reconstructed holographic image for two-level amplitude and eight-level phase modulated hologram and (d) simulation image for an eight-level phase modulated hologram without the amplitude modulation. The original, theory, and simulation agree with each other very well.

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The simulated results of the reconstructed image using the above two-level amplitude and eight-level phase modulation method are presented in Figs. 3(b) and 3(c), respectively. Figure 3(b) shows the simulated holographic image directly using point sources with corresponding amplitude and phase to represent each pixel on the metasurface CGH. Figure 3(c) shows the image reconstruction of the designed metasurface CGH using 3D full wave solver in COMSOL Multiphysics. The details of the computation setup are described in Appendix B. On the other hand, to demonstrate the importance of both the amplitude and phase information, we have designed a reference sample image [as shown in Fig. 3(d)] with the same eight-level phase modulation but a constant amplitude. Noticeably, the reconstructed images [Fig. 3(c)] with both two-level amplitude and eight-level phase modulations suffer less speckle noise than that [Fig. 3(d)] with phase-only modulation. The results highlight the importance of using both the amplitude and phase modulation.

The unique advantages of the proposed metasurface CGH with both amplitude and phase modulation enable the creation of high definition and high noise tolerance images with complicated imaging patterns. By multiplexed encoding method, not only three primary colors, e.g. red (R), green (G) and blue (B), but also multiple images can be encoded within one individual metasurface CGH [31, 34]. Combining them together, we can get both single/multiple 2D and 3D full-color images with low noise and high quality. For the proof-of-concept demonstration, we firstly carry out the design for two different full-color 2D images that are designated to reconstruct the targets at different image planes ($z=500$μm and$z=900$μm). Here, the distance, specially, is regarded as an independent channel and plays an essential role in recovering primary image together with the amplitude and phase. Note that this image plane multiplexing scheme works well at the Fresnel diffraction range; While in the Fraunhofer diffraction range it might fail due to large depth of focus of each image which leads to strong cross-talk.

For instance, in Figs. 4(a) and 4(b) we choose a tree image and “Lf ” letters as the target object images. In the next step, the CGH profiles for the two different full-color images are separately calculated. For individual full-color image, the pattern generated by different color component (including R-CGH, G-CGH and B-CGH) can overlap with each other, thus the pattern of a colorful image can be generated. By linearly combing these profiles of different full-color image with different phase shifts (see Appendix B), we can finally get the synthetic holograms, as shown in Figs. 4(c) and 4(d). The size of the synthesized CGH is 600 × 600 pixels and the nanoslit remains the same as in Fig. 1. The reconstructed images by the CGH illuminated by a LCP light (consisting of 420 nm, 532 nm, and 633 nm laser beams) are shown in Figs. 4(e) and 4(f), correspondingly. On the image plane at $z=500$μm away from the CGH, we can see the reconstructed image of the tree, and the reconstruction image of the letters “Lf ” appears clearly at the plane of $z=900$μm. The displayed images in the two planes agree well with the design purpose. Both of these two examples show that the holographic images have great fidelity to the original objects, in terms of color, shape, and size. These results demonstrate that by utilizing the position selectivity (encoding channel), we are able to simultaneously encode multiple 2D full-color images on the same metasurface CGH.

 

Fig. 4 Simulation demonstration of multiple 2D full-color reconstructed images by the metasurface. The 2D full-color object (a) tree image and (b) letters “Lf ”. Calculated synthetic (c) amplitude pattern and (d) phase pattern on the hologram of the tree image and letters “Lf ”. Reconstructed images of the tree image (e) and letters “Lf ” (f) that for different distances $z=500$μm and$z=900$μm relative to the hologram metasurface, respectively.

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We next investigate the reconstruction of 3D color holographic images. For this case, we use a simplified double helix structure to represent a part of a DNA molecule, as sketched in Fig. 5. Each helix of the model contains six segments with different colors of RGB and MCY (magenta, cyan and yellow). And in every segment, there are 10 particles with 0.2 μm separation along z-direction. Different from the 2D holographic characterization setup, the full representation of the 3D object needs a scan through the optical axis direction (z-axis here) across the image space. We then encode 60 z-slices [i.e.,$p=60$as in Eq. (2) in Appendix B] of such 3D colorful structure to synthesis the hologram. As a matter of fact, an ideal 3Dimage requires only one particle is clearly visualized at a particular image plane. Despite the fact that we haven’t optimize our design here to obtain such high resolution, the 3D information of the colorful DNA model has already been embodied in the generated holographic image. To illustrate this point, we show six slices along z-direction with 2 μm spacing in sequence in Fig. 5(b). The distance z to the hologram is labeled in each panel as $z=301$ μm, 303 μm, 305 μm, 307 μm, 309 μm, and 311μm. As can been seen that at each image plane, only a specific segment of one color is in focus and can be clearly observed, whereas the other out of focus segments appear blurry. As a result, the target 3D object has been successfully reconstructed with both color and position, representing a full-color 3D holographic imaging process.

 

Fig. 5 Reconstruction of 3D model of DNA with six colors. (a) Side view, top view and front view of the DNA model. (b) Simulated on axis evolution of the holographic images of the DNA model on six 2D planes along z direction. For more z-slices in sequence, see Visualization 1.

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4. Conclusions

In summary, we have shown that geometric metasurface can be constructed by spatial orientation of identical nanoslits and is very suitable for holographic applications. It is demonstrated that by combining with a synthetic spectrum approach in a broadband wavelength range, the reconstruction of full-color single/multiple 2D or 3D holographic images can be realized, without adding extra complexity on the design and fabrication. It is worth mentioning that there are some aspects that could further improve the image quality and the efficiency, such as involving more amplitude modulation levels, using low-loss dielectric materials [35–37] and/or optimizing the geometric parameters of the unit cell [38, 39]. We believe the presented approach could potentially be used in optical imaging, data storage and color filters with high contrast. Also it can be linked to other techniques, such as the nanoimprint [40] for mass production.