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Abstract
We demonstrate multi-channel metasurface holograms, where the pixels of holographic images are represented by the focal points of metalens, leading to the nanoscale resolution. The required phase profiles are implemented by elaborately arranging the hybrid all-dielectric meta-atoms with specific orientation angles. For verification, two-channel single-color images are reconstructed on the focal plane of the metalens by polarization control. Alternatively, three-channel color holograms are exhibited by manipulating the incident wavelengths. More uniquely, the metalens can be further engineered to generate polarization-wavelength multiplexing color holograms in six channels. Our work provides an effective approach to reconstructing holographic images and enables potential applications including color display, information engineering, and optical encryption.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurfaces offer an efficient way to control lights by skillfully tailoring the subwavelength structures. Due to the capability of arbitrarily manipulating the amplitude, phase, and polarization of light, metasurfaces have attracted widespread attention in recent years and become a potential substitute for conventional bulky optical components [1–4]. The applied areas of metasurfaces include anomalous refraction/reflection [1,2,5], waveplates [6,7], optical vortex generator [8–10], metalens [11–13], meta-holography [14–16], nonlinear optics [17,18], etc. Particularly, meta-holography, with the capability of recording and reconstructing wavefronts, has potential applications in optical communications, information storage and encryption [19]. Compared with conventional computer-generated holograms, metasurfaces provide more degrees of freedom to design holograms because of the powerful manipulation of light in different dimensions [11]. The geometric metasurfaces composed of anisotropic nanostructures were demonstrated for achieving high-efficiency phase-only holograms [20,21]. In addition, a holographic metasurface was proposed that enables complex-amplitude modulation of visible light through the superposition of the geometric phase [22].
Since enormous achievements have been made to the metasurface holograms with customized single functionality, researchers pay their attention to the multifunctional and multiplexing metasurfaces that possess advantages of miniaturization, integration, multiplicity, and high storage capacity. The multiplexing metasurfaces include polarization multiplexing metasurface holograms [23–27], wavelength multiplexing metasurface holograms [28,29], angle multiplexing metasurface holograms [30,31], orbital angular momentum multiplexed metasurface holograms [32–35], and so on. For instance, two separate reconstructed images are demonstrated for left-handed circularly polarized (LCP) light and right-handed circularly polarized (RCP) light [24], and silicon metasurfaces are capable of realizing color holograms for three primary color simultaneously [28]. Besides, the number of channels can be expanded by making use of two or more of the above multiplexing methods. Via the combination of wavelength-angle multiplexing method, multiple different images can be switched [36]. Simultaneous near-field display and far-field holography can be accomplished by constructing a series of flat liquid crystal elements [37]. Multitasked meta-holograms based on iterative optimization algorithms were also presented with different holographic images encoded along multiple optical dimensions [38–40], which further broadens their applications. Nevertheless, the twin-image and zero-order diffraction appear unavoidably in the reconstructed holographic images [41,42].
Recently, the capability for manipulating light with multiple degrees of freedom promotes the versatile functionalities of metalenses, including multi-focal metalenses [43], polarization-selective metalenses with interleaved meta-atoms [44], achromatic metalenses [45] and reconfigurable metalenses [46]. Notably, the focal plane of metalens can be regarded as a reconstructed image with only a single bright spot. It has been reported that the metalens can be used for polarization detection [47], customized vectorial focal curve and color-selective three-dimensional polarization structures generation [48,49], and terahertz holographic images reconstruction [50]. This provides inspiration for our work where the hologram can be regarded as a linear superposition of bright spots, which can solve the problems of twin-image and zero-order diffraction in conventional hologram designs.
In this work, we design metalenses for generating multi-channel polarization-wavelength multiplexing metasurface holograms, which is different from conventional lenses that cannot reconstruct holographic images. By utilizing the focal points of metalens as the pixels of a holographic image, the nanoscale-resolution image can be reconstructed on the focal plane. Such designs can be implemented with hybrid all-dielectric meta-atoms arranged according to the phase profiles of metalens. As proof, two-channel single-color images are reconstructed using different incident polarizations. Besides, three-channel holographic images are exhibited under the normal incidences of the red (R), green (G), and blue (B) wavelengths with specific polarization. More uniquely, six-channel multicolor holograms are generated by manipulating the combination of polarization and wavelength of incident lights. Such ultra-compact metasurface holograms have potential in the applications of color display, information storage, and optical encryption.
2. Theoretical analysis and structural design
The design of metalens plays a fundamental role in generating holographic images on the focal plane. According to Fermat′s principle, the phase profile for a typical metalens can be written as: [50]
When a light beam with specific polarization and wavelength propagates through the metalens, an image is reconstructed on the focal plane. Figure 1(a) shows the artistic impression of the transmissive all-dielectric Huygens-geometric metasurface for the multi-channel polarization-wavelength multiplexing color holograms. The phase profile is accomplished by rotating the hybrid all-dielectric meta-atoms by an angle ${\theta _{i,j}}({x,y} )={\pm} {{{\varphi _{i,j}}({x,y} )} / 2}$, where “+” and “‒” correspond to the incident LCP and RCP lights, respectively. As shown in Fig. 1(b), the meta-atom is composed of a silica (SiO2) nanofin sandwiched between two silicon (Si) nanofins. Specially, the meta-atom, supporting two magnetic dipoles (MDs), behaves as a half-wave plate, which can convert the incident LCP(RCP) light into the RCP(LCP) light with an additional phase that is twice the rotation angle θ. To achieve this, the phase difference between the x- and y-directions should be π. When the period of the meta-atom and heights of the Si and SiO2 nanofins are set as 270 nm, 125 nm, and 50 nm, respectively, the phase difference in the two orthogonal directions is π at the length of 215 nm and width of 75 nm, satisfying the condition of a half-wave plate. Thus, the optimized structural parameters are $L = 215\textrm{ nm}$, $W = 75\textrm{ nm}$, ${H_1} = 125\textrm{ nm}$, ${H_2} = 50\textrm{ nm}$, and $P = 270\textrm{ nm}$, respectively. Figures 1(c) and 1(d) present the electric and magnetic field distributions under x-linearly polarized (XLP) and y-linearly polarized (YLP) lights illumination, respectively, in which the blue arrows represent the circular displacement currents and the red arrows represent the MDs. The MDs correspond to the circular displacement currents, which validates the predominance of magnetic dipole resonances in our well-designed meta-atom [52]. Besides, the phase accumulation in the meta-atom can be given by ${\varphi _p} = \frac{{2\pi }}{\lambda }({2{n_{eff\_\textrm{Si}}}{H_1} + {n_{eff\_\textrm{Si}{\textrm{O}_\textrm{2}}}}{H_2}} )$, where ${n_{eff\_\textrm{Si}}}$ and ${n_{eff\_\textrm{Si}{\textrm{O}_\textrm{2}}}}$ represent the effective refractive indexes of Si and SiO2, respectively. Thus, on the condition that the total height is fixed and the proportion of silica increases, blue shifts of the cross-polarized transmittance spectrum will appear. The effective refractive indexes can be quantitatively provided by reproducing the propagation constant in a hybrid meta-atom [12]. The theoretical result of the relationship between the wavelength and height H2 is plotted in Fig. 1(e) with a white line. The simulation results using the finite-difference-time-domain (FDTD) method are also shown in Fig. 1(e), consistent with the theoretical result. It can be seen that H2 = 50, 130, and 180 nm correspond to three working wavelengths R (${\lambda _1} = 633\textrm{ nm}$), G (${\lambda _2} = 532\textrm{ nm}$), and B (${\lambda _3} = 480\textrm{ nm}$), and the cross-talk of transmittance between them can be negligible. Notably, the proposed metasurface can be fabricated on quartz wafer substrate by standard electron beam lithography and etching process [53]. However, there is still a challenge in the process of Si and SiO2 etched using inductively coupled plasma (ICP) since the etching rates for these two materials are different, which may lead to structural deformation, especially at the interface between the two materials.
Fig. 1. (a) Artistic impression of the transmissive all-dielectric Huygens-geometric metasurface for the multi-channel polarization-wavelength multiplexing color holograms. The six channels are in the blocking 0 or transmission 1 state. (b) The schematic illustration of the Si-SiO2-Si meta-atom with rotation angle θ. L and W are the length and width of the meta-atom, respectively. The heights of the Si and SiO2 nanofins are H1 and H2, respectively. Cross sections of the normalized electric and magnetic field distributions under (c) XLP light and (d) YLP light illumination, respectively, where he blue arrows indicate the circular displacement currents and the red arrows represent the MDs. (e) The cross-polarized transmittance with the wavelength ranging from 400 to 700 nm and H2 changing from 40 to 200 nm under the LCP light incidence. The theoretical result is shown with a white line.
3. Results and discussion
To achieve a high-resolution holographic image, we investigate the intensity distribution of the focal point because the focal point is utilized as the pixel of the image. Generally speaking, the focal point is related to the focal length and clear aperture of the metalens. The clear aperture of metalens is $D = PN$, where N represents the phase pixel number along the diameter of the metalens [50]. The optical intensity distributions for one focal point with various N and f are plotted in Fig. 2(a). When the focal length remains the same, the clear aperture increases as the phase pixel number of the metalens increases, while the size of the focal point decreases. It is noteworthy that more concentric ring fringes locate on the focal plane at a smaller focal point size, which means that the diffraction becomes more severe. Conversely, with a fixed phase pixel number, the size of the focal point grows with the focal length increases. The relationship between the focal length and phase pixel number (clear aperture) is consistent with the classical formula of the lens focal spot diameter ${d_0} = {{2{\lambda _0}f} / D}$ [50]. Here, we define the focal point diameter d′ as twice the width at which the intensity drops to 1/e2 (13.5%). The quantitative relationship between the focal point diameter d′ and the phase pixel numbers N at different focal lengths f can be seen in Fig. 2(b). With the increase of N, there is a significant decreasing trend of d′. Since the holographic image is reconstructed by the metalens, the equivalent pixel size depends on the focal point diameter. However, the highest resolution comes at the cost of serious diffraction, which degrades the quality of a holographic image. It is vital to make a trade-off between the resolution and the quality of the reconstructed image. Thus, two crucial parameters, i.e., the focal length $f = 30{\mathrm{\mu} \mathrm{m}}$ and the phase pixel number $N = 240$, are employed to generate the focal point at the nanoscale without excessive diffraction. Notably, the incident wavelength is 633 nm. In addition, the intensity distributions of the focal point with the incident wavelengths of 532 nm and 480 nm are presented in Figs. 2(c) and 2(d), respectively. Figure 2(e) shows the corresponding horizontal cross-sections of the intensity at y = 0 µm for the wavelengths of R, G, and B. It can be seen that the focal point diameter d′ is 630 nm at the R wavelength. Meanwhile, the diameter of the focal point with the incident G and B wavelengths is almost the same as that with the incident R wavelength (630 nm). These results prove the achievement of nanoscale resolution for the incident R, G, and B wavelengths and ensure the distance d of 630 nm is suitable for all working wavelengths.
Fig. 2. (a) Normalized intensity distributions of a single focal point at the focal plane with various combinations of phase pixel numbers N and focal lengths f. (b) The quantitative relationship between the focal point diameter and the phase pixel numbers at different focal lengths. Normalized intensity distributions of a single focal point at the focal plane with the selected parameters of f = 30 µm and N = 240 for the incident wavelength of (c) G and (d) B. (e) The corresponding horizontal cross-section of the intensity at y = 0 µm with the incident R, G, and B wavelengths. (f) Normalized intensity distributions of two focal points generated on the x-axis with the distance between the center of two adjacent foci chosen to be 630 nm. (g) Corresponding horizontal cross-section of the intensity at y = 0 µm.
Besides, the continuous distribution of pixels with non-overlap and uniform intensity is a prerequisite for the better quality of a holographic image. It means that the distance d between the center of two adjacent foci plays a key role in the formation of holographic images with better quality. We examine the results of two focal points generated on the x-axis with ${x_1} = 315\textrm{ nm}$ and $d = d^{\prime} = 630\textrm{ nm}$. As shown in Figs. 2(d) and 2(e), the continuity between the two focal points can be treated as square pixels which are needed. Generally, the continuity of focal points depends on the distance d, which can emerge from the concept of diffraction limit. When the distance d is smaller than 630 nm, the two focal points cannot be distinguished due to the severe overlap. When the distance d is equal to 630 nm, the continuous distribution between two pixels with non-overlap and uniform intensity is satisfied. As the distance d continues to increase, the two focal points are clearly distinguished. However, there is obvious cutoff between two focal points, indicating that the intensity is not uniform. Thus, to achieve a better holographic image quality, the distance d between the center of two adjacent foci is chosen to be 630 nm. Notably, the pixel size and pixel number of metasurfaces in the following design are kept as 630 nm and 240, respectively.
For verification, we demonstrate a metalens for generating two-channel polarization- multiplexing holograms at the operating wavelength of 633 nm. As shown in Fig. 3(a), the phase profiles of the hologram for the incident LCP and RCP lights are implemented by interleaved meta-atoms with the orientation angles θL(x,y) and θR(x,y), respectively. The two channels are in the blocking 0 or transmission 1 states. To achieve the two-channel single-color holographic images, we encoded the phase profiles onto the metalens according to Eq. (2). A combination of word and number patterns forms the target holographic image, which is separated into different images corresponding to two channels (i.e., RCP and LCP input lights with sequences 01 and 10, respectively). The retrieved phase profile for hologram patterns with sequences 11 is presented in Fig. 3(b). Figures 3(c) and 3(d) show the reconstructed images with clear words “HIT” and numbers “2022” on a specific position of the focal plane, respectively. When a linearly polarized (LP, i.e., LCP + RCP with sequences 11) light illuminates the metasurface, the designed words “HIT” and numbers “2022” are displayed in the reconstructed holographic image in Fig. 3(e). It can be seen from Fig. 3 that by utilizing focal points as the pixels of holographic image, the metalens can reconstruct the target image on its focal plane and work well.
Fig. 3. (a) The designed metasurface with merged phase profile ${\varphi _{i,j}}({x,y} )$ manipulates two channels to reconstruct polarization-multiplexing holographic images at the focal plane. The two channels are in the blocking 0 or transmission 1 state. (b) Retrieved phase profile for the hologram patterns with sequences 11. The reconstructed images with sequences (c) 01, (d) 10, and (e) 11 at the operating wavelength of 633 nm.
Moreover, by manipulating the incident wavelengths, we can achieve three-channel color holograms. Three meta-atoms with different heights of H2 are exploited, corresponding to three working wavelengths of 633, 532, and 480 nm, respectively. As shown in Fig. 4(a), meta-atoms with the red, green, and blue colors correspond to different response wavelengths. The phase profile under the normal incidence of the monochromatic RGB lights corresponding to the three wavelengths can be rewritten as follows:
Fig. 4. (a) The designed metasurface with merged phase profile ${\varphi _{c,i,j}}({x,y} )$ manipulates three channels to reconstruct wavelength-multiplexing holographic images at the focal plane. The three channels are in the blocking 0 or transmission 1 state. (b) Retrieved phase profile for the hologram patterns with sequences 111. The reconstructed images with sequences (c) 100, (d) 010, and (e) 001 under the incidence of LCP lights.
Figure 4(b) presents the retrieved phase profile of the three-channel holograms with sequences 111. The reconstructed images for three channels (i.e., R, G, and B with sequences 001, 010, and 100, respectively) are shown in Figs. 4(c)–4(e). Three color images are divided into their RGB components for target images. With the help of extra spatial freedom, the cross-talk among multiwavelength can be suppressed. Here, we demonstrate the holographic images with half of the pixels to clearly show the distributions of foci at each location. There is a fixed interval between two adjacent foci rather than the continuous profile in Fig. 3, proving that the holographic images are formed by focal-point pixels. The designed metasurface reconstructs the letters “H”, “I”, and “T” at the same holographic plane since the focal length keeps the same for different incident wavelengths. Besides, other hologram results under sequences 011, 101, 110, and 111 are the corresponding combination of the three bases, which are not shown here.
To further demonstrate the flexibility of the design strategy, we propose a six-channel holographic metasurface with a “libra” pattern as shown in Fig. 5(g) by inputting trichromatic LCP and RCP lights. The corresponding phase profile for the hologram patterns is presented in Fig. 5(a). Various geometric shapes including rectangular, triangular, and half ring are displayed in the focal plane. The combined phase profile can be expressed as:
Fig. 5. (a) Retrieved phase profile for the hologram patterns with sequences 111111. The reconstructed images on the focal plane to present the six-channels polarization-wavelength multiplexing holograms with sequences (b) 110000, (c) 001100, (d) 000011, (e) 010101, (f) 101010, and (g) 111111.
4. Conclusion
In conclusion, we design metalenses composed of hybrid all-dielectric meta-atoms with specific orientation angles, where the focal point on the focal plane can be regarded as a holographic image with a single bright spot. By leveraging a quasi-continuous profile of focal points, multi-channel metasurface holograms can be achieved. This method achieves both holographic images with nanoscale resolution and multi-channel color holograms. By exploiting the property of the geometric phase, two-channel polarization-multiplexing holograms are demonstrated with the help of extra spatial freedom. Due to the merits of design flexibility, three-channel color holograms can be reconstructed on the focal plane by manipulating the incident wavelengths. Besides, the metasurfaces can be further engineered to generate six-channel holographic images by polarization-wavelength multiplexing. Benefiting from the design strategy, the unwanted twin-image and zero-order diffraction disappear in the reconstructed images, which is promising for applications in color display, information engineering, and optical encryption.
Funding
National Natural Science Foundation of China (62075048); Natural Science Foundation of Shandong Province (ZR2020MF129).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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