2.1.1.

Angular multiplexing method

In this section, we discuss multicolor holograms realized by an angular multiplexing method. Li et al. demonstrated this approach with geometric metasurfaces consisting of nanoslits in gold films⁷⁰ [Fig. 1(a)]. The design process can be summarized as follows. The multicolor target image is first decomposed into R, G, and B components,⁷⁰ which are to be reconstructed by the R, G, and B laser beams, respectively. The red component is displaced from the original position $(x_0,y_0)$ to the new position $(x_1,y_1)$. In other words, when the hologram is illuminated by the normally incident laser beam, the reconstructed red image will be located at $(x_1,y_1)$. However, by adjusting the incident angle, the reconstructed image can be made to be at $(x_0,y_0)$. The crosstalk images generated by the red laser beam will thus occur at other locations and will be excluded from the observation zone near $(x_0,y_0)$. Similar processes are carried out for green and blue beams. This results in the observation zone near $(x_0,y_0)$ containing the correct R, G, and B components, with the crosstalk images occurring at other locations (i.e., not in the observation zone). A phase-only hologram corresponding to this target image is then calculated by the Gerchberg–Saxton (GS) algorithm.⁷³ Each sampled phase pixel is then substituted by a nanoslit with a certain orientation angle. When the metasurface is illuminated by R, G, and B laser beams at the designed incident angles, a multicolor holographic image is reconstructed. To further verify the feasibility of this approach, Li et al. experimentally reconstructed an image with seven colors. The method can also be used for 3D holography,⁷⁰ where a 3D target image is decomposed into a series of points. The superposition of the complex amplitudes of the light emitted from these points comprises a multicolor hologram that generates the 3D image in the Fresnel range. Zhang et al. combined angular multiplexing with polarization-dependent geometric phase to produce two independent multicolor holographic images, one for transmitted light while the other for reflected light.⁷⁴ Wan et al. demonstrated multicolor holograms with aluminum geometric metasurfaces [Fig. 1(b)] with two amplitude levels and eight phase levels of modulation.⁷¹ Amplitude modulation is implemented by pixels that include or omit the nanoslit. Phase is modulated in eight levels (0, $\pi /4$, $\pi /2$, $3\pi /4$, $\pi$, $5\pi /4$, $3\pi /2$, $7\pi /4$) via (eight different) orientation angles for the nanoslits.

Fig. 1

Multicolor holograms that employ angular multiplexing. (a) Multicolor images generated by off-axis illumination of the metasurface hologram. The metasurface consists of nanoslits in a gold film. (b) Multicolor hologram that consists of nanoslits in an aluminum film. (c) Schematic of phase modulation by athermal photoreduction using a single fs pulse. A pulse passes through a parallel digitalization objective and generates a focal spot array with different intensities, which in turn leads to refractive-index modulation of the rGO composite. (d) Multicolor image generated by illuminating the metasurface with R, G, and B beams at different angles. The figures are reproduced with permission from (a) Ref. 70, (b) Ref. 71, (c), (d) Ref. 72.

Nanoslit-based multicolor holograms are polarization sensitive. Li et al. showed that, by contrast, a polarization insensitive multicolor hologram can be realized with reduced graphene-oxide (rGO), obtained via the athermal photoreduction of graphene-oxide using a femtosecond laser.⁷² The refractive index of the rGO is related to the intensity of the incident light spot [Fig. 1(c)] and is spectrally flat in the visible region. It is, therefore, ideal for multicolor image generation through angular multiplexing. More colors (i.e., beyond R, G, and B), such as yellow and white, can be achieved by adjusting the powers of the R, G, and B laser beams [Fig. 1(d)].

2.1.2.

Polarization multiplexing method

As discussed above, angular multiplexing is one way to implement independent R, G, and B channels. Another way of achieving this is via the polarization states of the input/output light. This approach requires the metasurface to comprise a spatially varying arrangement of polarization-modulation elements. Hu et al. demonstrated a metasurface consisting of ${\mathrm{TiO}}_2$ rectangular nanopillars with different shapes and orientations on an ${\mathrm{SiO}}_2$ substrate.⁶⁴ Each nanopillar can be regarded as a linearly birefringent wave plate with a certain orientation angle. The length, width, and orientation angle of the nanopillars vary with position on the metasurface. The design process of the hologram is as follows [Fig. 2(a)]. A multicolor target image is decomposed into R, G, and B components. The sizes of these target image components are scaled to account for the inherent wavelength-dependence of the hologram. In other words, the red component will be made smaller than the green component, while the blue component will be made larger, so that the R, G, and B parts of the reconstructed image are of the same size. The hologram is designed with the GS algorithm, with the Fourier transform as the propagation function. Therefore, if the field of view (FOV) is large, there will be distortion since the design principle makes the paraxial approximation. In other words, a large FOV will make the paraxial approximation imprecise. This distortion can be prevented by appropriate design. After that, the phase profiles of the three components are retrieved and encoded into the three independent polarization channels of the metasurface. One may thus regard the metasurface as storing three types of information in an independent fashion, accessible by different combinations of input/output polarization states [Fig. 2(a)]. Here, when the input/output are $x\text{-}/x$- polarized, only the red component of the holographic image is reconstructed. Similarly, the green and blue components correspond to the $x\text{-}/y$- and $y\text{-}/y$- combinations, respectively. These images in the three channels are selected and combined through the optical setup to form a color holographic vectorial image.

Fig. 2

Multicolor holograms by the polarization multiplexing method. (a) Design process for the vectorial color holographic metasurface. (b) Schematic of 6-bit metasurface. Holographic images that result from the state (color and polarization) of the incident light as denoted by codes 010000, 001000, 000100, 000110, 000101, 000011, 111000, and 001110 are shown in the right panel of the image. Figures reproduced with permission from (a) Ref. 64 and (b) Ref. 75.

Instead of controlling the input/output polarization combination, Jin et al. showed a polarization multiplexing method in which only the polarization of the incident light needs to be changed.⁷⁵ The combination of the three color channels (R/G/B) and the two different helicities results in six channels (red LCP, red RCP, green LCP, green RCP, blue LCP, and blue RCP). The presence or absence of a channel in the incident light denotes the bit being “1” or “0,” respectively. The incident light can thus be thought of as representing the combinations “010000,” “001000,” etc. [Fig. 2(b)]. The metasurface is designed as follows. A hologram consisting of an array of silicon nanobricks is first devised for the red LCP, green LCP, and blue LCP channels, with the goal of producing three independent images at the chosen observation plane (within the Fresnel diffraction region). A second hologram, this time for red RCP, green RCP, and blue RCP channels, is then generated, with the goal to produce another set of independent images at the same observation plane. The two holograms are then combined to form a single metasurface. As a result, it is possible to reconstruct 63 ($=2^6-1$) spin- and wavelength-dependent holographic images by controlling the 6 bits corresponding to the RGB-polarization states of the incident light. It is interesting to notice that, although there are six available channels of incident light, a colorful holographic image can be reconstructed when two or more channels of different colors are used (such as, red LCP and green LCP).^76,77

2.2.1.

Narrow-band CP converters

Although the multiplexing method enables multicolor image generation, a more straightforward and general method involves structures that serve as both nanofilters for color and as phase controlling elements. Wang et al., for example, used three types of silicon nanoblock structures $({\mathrm{S}}_{\mathrm{R}},{\mathrm{S}}_{\mathrm{G}},{\mathrm{S}}_{\mathrm{B}})$,⁷⁸ with each serving as a narrowband half-waveplate [Figs. 3(a) and 3(b)]. Consider the ${\mathrm{S}}_{\mathrm{R}}$ structures illuminated by broadband CP light of a certain helicity (e.g., LCP). In the spectrum of the transmitted light with opposite helicity (e.g., RCP), a peak appears at around 633 nm. Similarly, the peaks of the cross-polarization spectra for ${\mathrm{S}}_{\mathrm{G}}$ and ${\mathrm{S}}_{\mathrm{B}}$ are around 532 and 473 nm, respectively. Due to the fact that these peaks in the cross-polarization spectra are narrow, when a metasurface comprising these nanoblocks is illuminated by a CP laser beam at one of the design wavelengths (e.g., R), scattering of the cross-polarized light from the nanoblocks of the corresponding type (${\mathrm{S}}_{\mathrm{R}}$ for this example) is far stronger than from the other types (${\mathrm{S}}_{\mathrm{G}}$ and ${\mathrm{S}}_{\mathrm{B}}$ in this example). The authors note that the efficiency for the ${\mathrm{S}}_{\mathrm{B}}$ blocks is lower than that of ${\mathrm{S}}_{\mathrm{R}}$ and ${\mathrm{S}}_{\mathrm{G}}$. The authors thus have the supercell contain two blue blocks, while just one red block and one green block to balance the total scattering at each wavelength. Each supercell simultaneously provides the desired phases at the three wavelengths. A schematic diagram of multicolor image generation by the metasurface is shown in Fig. 3(c). Laser beams illuminate the metasurface from the substrate side, and the image is observed on the transmission side. Zhao et al. demonstrated that the silicon nanoblocks can also be designed to work in the reflection mode to provide narrow resonance peaks.⁷⁹ As shown in Fig. 3(d), in this configuration, the reflected color holographic image is collected using a beam splitter. Via similar principles, the concepts used for multicolor hologram can be extended to allow color-tunable holograms.⁶³ In the work of Wang et al. [Fig. 3(e)], a holographic image whose color can be tuned by polarization state is demonstrated. The image consists of a chameleon on a tree branch. The hologram consists of silicon nanoblocks with resonances at red and green wavelengths. The nanoblocks designed for the green generate the tree branch in the holographic image, regardless of incident polarization state. This is realized by designing the hologram to produce the same phase shifts (and thus the same holographic image of the tree branch) for RCP and LCP incident light. The nanoblocks designed for the green also generate a holographic image of a chameleon when illuminated by an LCP green laser beam ($\lambda =532\mathrm{nm}$). The nanoblocks designed for the red generate a chameleon image only when illuminated by an RCP red laser beam ($\lambda =632.8\mathrm{nm}$). When the incident light (i.e., red and green lasers) is varied from RCP to linear to LCP, the color of the chameleon thus changes gradually from red to yellow to green, while the tree branch remains green.

Fig. 3

Narrow band CP converters-based multicolor holograms. (a) Solid curves: simulated diffraction efficiency of three nanoblock types, denoted by ${\mathrm{S}}_{\mathrm{R}}$, ${\mathrm{S}}_{\mathrm{G}}$, and ${\mathrm{S}}_{\mathrm{B}}$. The circle, square, and rectangle represent the simulated efficiency when the ${\mathrm{S}}_{\mathrm{R}}$, ${\mathrm{S}}_{\mathrm{G}}$, and ${\mathrm{S}}_{\mathrm{B}}$ are merged into the same pixel as shown in (b). (c) Schematic of multicolor image reconstruction. (d) Multicolor hologram in reflection mode. The metasurface consists of three types of silicon nanoblocks that work as narrow band CP converters. (e) Schematic of the polarization-controlled multicolor hologram. The figures are reproduced with permission from (a)–(c) Ref. 78, (d) Ref. 79, and (e) Ref. 63.

The multicolor holograms we have described thus far produce holographic images when illuminated by R, G, and B laser beams. However, the hologram itself can be designed so that it functions as a color printed image when viewed with bright-field illumination. As shown in Fig. 4(a), Zhang et al. showed that shallow plasmonic gratings made from silver can be used for this purpose.⁸⁰ The grating structure can excite propagating surface plasmons and localized surface plasmons simultaneously, with the former dominating.⁸³ When the incident CP light is away from the resonance, the vast majority of the reflected light from the grating will have helicity opposite to that of the incident light. In this case, the grating functions as a normal mirror. However, when illuminated on resonance, the reflected components parallel and perpendicular to the grating lines have a $\pi$ phase difference. Therefore, most of the reflected light from the grating will have the same helicity as the incident CP light and carries the geometric phase. The resonance is narrow and is determined by the period, width, and depth of the gratings, thereby providing a means for color selection. The gratings can furthermore be patterned to produce a color printed image. In other words, the metasurface exhibits vivid color under illumination by CP white light and with optics used to detect only the reflected light with the same helicity [Fig. 4(b)]. The gratings are oriented such that the metasurface also functions as a hologram. When illuminated with R, G, and B laser beams, a colorful holographic image is produced [Fig. 4(c)]. Wei et al. devised a metasurface consisting of amorphous silicon nanoblocks and nanoblock dimers [Fig. 4(d)]. These show transmission peaks in the green and red regions of the cross-polarization spectrum.⁸¹ The nanoblocks and nanoblock dimers are arranged to form a metasurface hologram that also functions as a color printed image [map of the world, Fig. 4(e)] when illuminated with white light. The holographic image is that of a plant [red flower and green leaves, Fig. 4(f)] and produced under illumination by red and green laser beams. Similarly, Yoon et al. showed a crypto-display⁸⁴ that consists of two sets of dimers, which have different reflectance spectra in the visible range, but the same cross-polarization conversion efficiency at a certain design wavelength (635 nm). A multicolor image of a red “$\pi$” symbol on a green background is observed under white light illumination, and a monochromatic holographic image containing the value of “$\pi$” is reconstructed for illumination by a laser with a wavelength of 635 nm.

Fig. 4

Color printing and holography by the narrow band CP converters. (a) Schematic of a shallow plasmonic grating. (b) Printed image observed with the white light microscope. This chip would be used with a “decryption device” that ensures that the incident light and the detected light are both CP with the same helicity. (c) Holographic image generated when the chip is illuminated by R, G, and B laser beams. (d) Schematics of a nanoblock (right) and a nanoblock dimer (left), which make up the metasurface. (e) Optical microscope image of the hologram when viewed under white light illumination. (f) Two-color (R & G) holographic image. (g) Unit cell of the metasurface hologram, containing two crystalline silicon nanoblocks. (h) Color printed image (left) and reconstructed holographic image (right). The figures are reproduced with permission from: (a)–(c) Ref. 80; (d)–(f) Ref. 81; (g), (h) Ref. 82.

The favorable attributes of amorphous silicon as a material with which to realize nanoblock-based metasurfaces [Fig. 4(d)] include its high refractive index and the fact that it can be readily deposited by standard microfabrication processes. On the other hand, crystalline silicon presents the opportunity for a higher conversion efficiency at visible wavelengths, as the imaginary component of its complex refractive index is smaller. Figure 4(g) shows the unit cell of the metasurface of Bao et al. that comprises two crystalline silicon nanoblocks.⁸² The dimensions of the nanoblocks determine the position of the peaks seen in the cross-polarized transmission spectra. For example, for blocks with a pixel size $p=400\mathrm{nm}$, width $w=40\mathrm{nm}$, and height $h=600\mathrm{nm}$, spectral peaks in the cross-polarization transmission spectra occur at B, G, and R wavelengths for block lengths $l$ of 80, 110, and 160 nm, respectively. The rotation angles of the two nanoblocks are ${\phi }_1$ and ${\phi }_2$, respectively [Fig. 4(g)]. When illuminated by LCP light, the RCP transmitted light from the two blocks can be summed up as $E_t\propto e^{2i{\phi }_1}+e^{2i{\phi }_2}=2\cos \delta e^{i(2{\phi }_1+\delta )}$, where $\delta ={\phi }_2-{\phi }_1$. Therefore, the intensity and phase of the transmitted RCP light can be controlled by the rotation angles of the two nanoblocks. As a printed color image, the metasurface covers not only the primary R, G, and B colors but also achieves arbitrary hue-saturation brightness [Fig. 4(h)]. As the metasurface achieves independent control over intensity and phase, it can also generate a full-color holographic image.

2.2.2.

Dispersion phase-based metasurface

In Sec. 2.2.1, color filtering is achieved via geometric metasurfaces that achieve well-separated peaks in their cross-polarization transmission or reflection spectra, i.e., when converting the incident CP light to CP light of opposite helicity for transmission-type devices and to CP light of the same helicity for reflection-type devices. We next discuss another metasurface type that can also function as both a color printed image and a multicolor hologram, namely the dispersion phase metasurface. In Fig. 5(a), we show the work of Huang et al., who develop a metasurface consisting of an Al-$\text{nanorod}/{\mathrm{SiO}}_2/\mathrm{Al}$-mirror configuration.⁸⁵ This structure has resonances that span the visible wavelength range as the rod length is varied from 50 to 150 nm. Figure 5(b) shows simulations of the reflectance and of the phase of reflected light versus nanorod length for illumination at three wavelengths that represent B, G, and R, i.e., 405, 532, and 658 nm. This configuration allows two-level phase modulation to be achieved by proper selection of nanorod length. This can be understood as follows. For blue light (i.e., at 405 nm), two nanorods with $L=55\mathrm{nm}$ and $L=70\mathrm{nm}$ provide equal reflectance and a phase difference of $\pi$, which is ideal for a two-level phase-only hologram. It can be seen that the phase difference between such nanorods is minor for green (532 nm) and red (658 nm), meaning that there will be little crosstalk from the blue channel to the green and red channels. Similarly, the nanorods with $L=84\mathrm{nm}$ and $L=104\mathrm{nm}$ are suitable for the green channel, while $L=113\mathrm{nm}$ and $L=128\mathrm{nm}$ are suitable for the red channel. These nanorods are interleaved to form supercells that contain two red subcells, one green subcell, and one blue subcell. These supercells constitute a multiwavelength hologram, with the reconstructed image shown in Fig. 5(c). It should be noted that a red letter “G” appears near red “R,” which the authors attribute to being the result of resonance overlap of the green subpixels (into the red channel).

Fig. 5

Dispersion phase-based multicolor holograms. (a) Simulated reflectance spectra, with the nanorod length varied. (b) Simulated reflectance and phase at $\lambda =405$, 532, and 658 nm. Blue circles, green triangles, and red squares indicate the nanorod lengths used for the blue, green, and red channels, respectively. (c) Experimentally obtained color holographic image. (d) Unit cell of the multicolor hologram. (e) Calculated phases at wavelengths of 460, 540, and 700 nm. The color used for the data points represents the nanopillar width, as indicated by the colorbar. The star symbol (labeled “A”) represents an example of a target phase point, while the red dot (labeled “B”) represents the nanopillar that is closest to this target. (f) Simulated color holographic image produced by the metasurface. The figures are reproduced with permission from: (a)–(c) Ref. 85, (d)–(f) Ref. 86.

In the example mentioned above, color holographic images are generated using structures with different dimensions that provide the phase delays needed for the R/G/B channels. These structures are interleaved to produce the hologram device. On the other hand, it is possible for a single nanostructure geometry to provide the desired phase delay for the R/G/B channels. Shi et al. demonstrated this via a metasurface based on ${\mathrm{TiO}}_2$ nanopillars on silver, with a thin ${\mathrm{SiO}}_2$ spacer [Fig. 5(d)].⁸⁶ The device operates in reflection mode, which means that the propagation distance per pillar is effectively doubled in comparison with what would occur if it were instead operating in transmission mode. This means that the device thickness can be minimized, which is desirable from a manufacturing standpoint. As the width of the nanopillar is varied, the phases of the reflected light at the three different wavelengths also change [Fig. 5(e)]. It can be seen that the points (resulting from varying the nanopillar width) span a large region of the phase space. To understand the process that would be used for metasurface design, consider the case that the target phases are those represented by the star symbol denoted “A” in Fig. 5(e). It be seen that the point that is denoted “B” is quite close to “A.” In other words, because the data set that results from varying the nanopillar width covers a large region of the phase space, any phase target can be achieved with only a small error. The authors used 460, 540, and 700 nm as examples [Fig. 4(e)], and they fabricated a lens with the same focal distance at the three wavelengths. With the same principle, a multicolor hologram working at 480, 530, and 630 nm is also proposed [Fig. 5(f)].

2.2.3.

Detour phase-based metasurface

We next describe another metasurface that acts as both a color printed image and as a hologram, this time based on Mie resonances. It has been experimentally demonstrated that ${\mathrm{TiO}}_2$ nanoparticles can support resonances at visible wavelengths.^87–89 The resonance position (wavelength) is determined by the geometric parameters and the packing density of the nanoparticles. ${\mathrm{TiO}}_2$ nanoparticles can thus be designed to scatter strongly at wavelengths corresponding to R, G, and B. One can thus realize a color printed image by including ${\mathrm{TiO}}_2$ nanoparticles of the appropriate geometric parameters and packing density so that each part of the metasurface achieves the desired color. The metasurface can furthermore simultaneously function as a hologram via the detour phase concept,^90–92 i.e., with the ${\mathrm{TiO}}_2$ nanoparticle arrays [Figs. 6(a) and 6(b)] being displaced in each pixel to achieve the desired phase.⁶⁶ Optical microscope images of a fabricated metasurface are shown in Figs. 6(c) and 6(d) and demonstrate the color printed image functionality. The multicolor holographic image produced by illumination of the metasurface with R, G, and B laser beams is shown in Fig. 6(e). To further demonstrate the flexibility of this technique, Wen et al. showed that two different target holography images [Figs. 6(e) and 6(f)] can be encoded into color printed images with very similar appearances. This approach is different from previously demonstrated color printed images or holograms and presents opportunities for optical document security and data storage applications.

Fig. 6

Detour phase-based metasurface consisting of color holograms encoded into color printed images. (a) Schematic of a ${\mathrm{TiO}}_2$ nanocone array that comprises the metasurface. Each cone has height $h$, period $p$, top radius $r$, and taper angle $\beta$. (b) Illustration of the detour phase concept. Each supercell has width $\mathrm{\Delta }x$ and length $\mathrm{\Delta }y$. $\delta x$ is the distance of the cone array from the supercell center. The detour phase of each pixel is controlled by $\delta x$. (c), (d) Optical image of the metasurface captured by the polarization microscope. The outer diameter of the pattern in (c) is 1.5 mm. The scalebar in (d) represents $50\mu \mathrm{m}$. (e) Reconstructed holographic image with sample A, whose optical image is shown in (c). (f) Reconstructed holographic image with sample B, whose optical image is similar to (c). Color bars in (e) and (f) both represent 5 cm. The figures are reproduced with permission from (a)–(f) Ref. 66.