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Abstract
Visual arts and entertainment related industries are continuously looking at promising innovative technologies to improve users’ experience with state-of-the-art visualization platforms. This requires further developments on pixel resolution and device miniaturization which can be achieved, for instance, with high contrast materials, such as crystalline silicon (c-Si). Here, a new broadband stereoscopic hologram metasurface is introduced, where independent phase control is achieved for two orthogonal polarizations in the visible spectrum. The holograms are fabricated with a birefringent metasurface consisting of elliptical c-Si nanoposts on Sapphire substrate. Two holograms are combined on the same metasurface (one for each polarization) where each is encoded with four phase levels. The theoretical bandwidth is 110 nm with a signal to noise ratio (SNR) >15 dB. The stereoscopic view is obtained with a pair of cross-polarized filters in front of the observers’ eyes. The measured transmission and diffraction efficiencies are about 70% and 15%, respectively, at 532 nm (the design wavelength). The metasurfaces are also investigated at 444.9 nm and 635 nm to experimentally assess their bandwidth performance. The stereoscopic effect is surprisingly good at 444.9 nm (and less so at 635 nm) with transmission and diffraction efficiencies around 70% and 18%, respectively.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In the past few years, visual arts and entertainment related industries, as well as many research groups around the world, have invested a great deal of effort and resources directed at improving users’ experience by means of state-of-the-art visualization techniques, such as telemedicine, holographic projections, three-dimensional (3D) cinema screens, and 3D mobile displays, to mention a few. These technologies have benefited from rapid advances in nanofabrication techniques that have had a direct impact on the pixel resolution and on the miniaturization of optical systems. One remarkable example of optical miniaturization is the concept of planar photonic components, or flat optics, enabled through metasurfaces, i.e. a dense arrangement of subwavelength resonators designed to modify the optical response of the interface [1]. Metasurfaces, the two-dimensional (2D) equivalent of (volumetric) metamaterials, are periodic or semi-periodic materials that allow light properties (phase, amplitude and/or polarization) to be tailored by geometrical adjustments on the size and/or orientation of the subwavelength unit-cell geometry. The metasurface concept was first introduced in the context of plasmonic nanostructures for diffractive optics applications such as lenses, beam splitters and holograms, to name a few [2–11]. These structures have proved to be quite efficient particularly in holographic applications operating in reflection mode [8,9,12]. However, the nonradiative (Ohmic) losses associated with the plasmon generation severely hinders the efficiencies of these structures when operating in transmission-mode [5,10,11,13]. Only recently, this issue has been circumvented with the advent of all-dielectric metasurfaces where the metal is replaced preferably by a high index material such as amorphous silicon (a-Si) [14–22], polycrystalline silicon (p-Si) [23–27], crystalline silicon (c-Si) [28–30], TiO2 [31–35] and GaN [36]. In fact, dielectric metasurfaces have become the prevalent choice for a wide variety of diffractive optics applications, including lenses [17–19,32,35,36], holograms [16,20–22,24,25,27,30,31,37], anomalous refraction generation [23,29], and vortex beam generation [23,38]. In general, these structures are designed based on either the accumulated phase after wave propagation through a high- (or low)-contrast grating [11], or the interference between the lowest magnetic and electric Mie resonances [11,39]. Moreover, these structures can be used to phase shift transmitted or reflected light depending on the polarization state of the incident field. This feature was successfully demonstrated for polarization optics applications such as half- and quarter-wave plates [15,26], polarization dependent beam splitter [16], chiral holograms [16,34], polarization dependent metalenses [16,33], and vector beam generation [16,26]. The list of new metasurface applications is sure expected to grow much further as this technology becomes more accessible, and the visual arts and entertainment industries have much to benefit from it (notably 3D visualization devices).
Interestingly enough, a decades-old 3D visualization technique known as stereoscopic viewing has only recently been theoretically explored with metasurfaces [40]. Briefly, a stereoscopic image (stereogram) is composed of a pair of orthogonally polarized images taken from the same scene but recorded in slightly shifted positions to replicate the natural parallax of the human eye. For the stereoscopic effect to occur, each of these two images should be directed to one of our eyes separately with the help of cross-polarized glasses. Most of the proposed metasurfaces to this date operate either with single [4,41,42] or multiple discrete wavelengths [10,30,36,43] in the visible and infrared ranges. Nevertheless, many applications such as metalenses, holography and polarization optics could benefit from or even require broadband operation. This issue has already been addressed both in reflection [15,44] and transmission mode [12,26,31,44–46] metasurfaces. Notably, it was recently shown that c-Si metasurface can provide high efficiency in transmission even for UV light [44].
In the present work, we show that c-Si metasurfaces using elliptical posts can provide independent phase control for two orthogonal polarizations. We then take advantage of such a functionality to propose and fabricate the first broadband holographic stereogram made with a birefringent crystalline silicon (c-Si) metasurface at visible wavelengths. The metasurface design is based on c-Si nanoposts with elliptical cross-section and different effective indices, and excited by linearly polarized light aligned to each of its semi-axes [16]. The holograms (one for each polarization) are combined on the same metasurface and encoded with four phase levels each, calculated via modified Gerchberg-Saxton (G-S) phase-retrieval algorithm to maximize the signal-to-noise-ratio (SNR). Furthermore, a coordinate transformation correction is performed on the target images to avoid wide angle aberration of the reconstructions [47]. Two additional metasurface holograms, whose reconstructions yield two completely distinct images, are also fabricated aimed at addressing possible cross-talk between the two polarizations. We show that the relative phase shift of the nanostructures has a high tolerance over a broad bandwidth and a high diffraction efficiency even at the blue region of the spectrum. Diffraction efficiencies >20% within a 110 nm bandwidth are numerically obtained with a SNR>15 dB. We also show that the operating band of the structure can be blueshifted by simply reducing the nanoposts diameter with minimum impact on the relative phase. Even in this case the calculated diffraction efficiency remains >20% within an 80 nm bandwidth with a SNR>10 dB.
The experimental stereographic reconstruction is obtained on a fine-sanded aluminum surface. This choice not only preserves the polarization of the scattered light but also minimizes the mirror effect of the aluminum surface, which increases the 3D perception. The measurements are carried out at three different wavelengths, namely 444.9 nm, 532 nm (the design wavelength) and 635 nm, to assess the metasurface bandwidth performance. The measured transmission and diffraction efficiency maxima at 532 nm are 70% and 15% for both polarizations, respectively. The reconstructed images at 444.9 nm are as good as at 532 nm in terms of noise, polarization cross-talk, and depth perception. The measured transmission and diffraction efficiencies in this case are 69.5% and 18.5%, respectively. This good performance at lower wavelengths can be attributed to the reduced semi-axis size of the fabricated nanoposts that cause the metasurface operating point to blueshift. The reconstructed images at 635 nm, in contrast, are noisier with stronger polarization cross-talk when compared to those at 532 nm, making it difficult to observe the stereoscopic effect. Consequently, the diffraction efficiencies are small (<10%), despite the high transmission (>80%) due to the c-Si low absorption at this wavelength.
2. Metasurface design
The unit cell geometry of the proposed birefringent metasurface structure is shown in Fig. 1(a). It consists of c-Si elliptical nanoposts 230 nm high (same as the c-Si layer thickness) on top of a sapphire substrate, with the design wavelength of 532 nm. This structure can be regarded as a truncated waveguide with elliptical cross section exhibiting polarized modes with different effective wavelengths along each semi-axis of the ellipsis [16]. In other words, the transmitted light experiences different phase changes when polarized along each semi-axis. Therefore, independent phase control can be achieved for each polarization by tuning the ellipses’ diameter. The design is carried out by calculating the transmission phase and efficiency of an infinite array of identical nanoposts under normal plane-wave incidence from air. We use a square unit cell 190 nm in size and sweep both semi-axes (Dx and Dy) to determine the optimum phase levels and transmission efficiencies of the array using the rigorous coupled-wave analysis (RCWA) [48]. This unit cell period not only guarantees a high transmission efficiency for each independent phase level (four in our case), but also helps to reduce the degrees-of-freedom in the design of the elliptical nanoposts to only two, namely, the two ellipsis’ semi-axes. The refractive indices of c-Si and sapphire adopted in the simulations are, respectively, nc-si = 4.3 + j0.072 [49] and nS = 1.77 [50].
Fig. 1 (a) Schematic of the unit cell for high birefringent contrast grating (not to scale). Transmission efficiency (b) (dimensionless) and relative phase maps (c) in units of rad/2π of the c-Si nanopost array as function of the structure’s semi-axes for light polarized along x. (d) and (e) represent analogous results for light polarized along y. The transmitted phase difference (Φx - Φy) in units of rad/2π is shown in (f). The operating wavelength is 532 nm in all cases. The colored symbols represent the map boundaries for achieving four phase levels. Their correspondences are listed in Table 1. The stars mark the chosen structures inside each region.
The transmission efficiencies and phase maps (in units of rad/2π) as function of Dx and Dy are shown, respectively, in Figs. 1(b) and 1(c) for polarization along x, and in Figs. 1(d) and 1(e) for polarization along y. Full phase control [0-2π] is obtained for each polarization with high transmission efficiency. Moreover, these maps present as major features both birefringence and high transmission efficiency. The next step is to check whether independent full phase control [0-2π] for both polarizations can be achieved with these maps. In other words, if n phase levels are needed for each polarization, then a total of n2 different elements are required to satisfy all possible phase combinations (Φx,i, Φy,j), i, j [1,n]. Therefore, the phase difference map (Φx- Φy) needs to cover the range [-π, π], as shown in Fig. 1(f).
The final step is to check which structures satisfy these phase level requirements. Assuming a 10% tolerance on the phase value, independent phase control is achieved only with n ≤ 4 phase levels. In the case of n = 4, there are associated sixteen different structures, one for each of the 4 × 4 possible combinations. The symbols in Figs. 1(b)-1(f) (listed in Table 1) delimit the boundaries where a given structure geometry satisfies the required phase level. The chosen structures are marked with white stars in Figs. 1(b)-1(f). The pertinent parameters of the 16 structures that satisfy the stablished design criteria, namely, semi-axes’ length, transmission phase and efficiency values, are listed in Table 2 for each polarization.
Table 1. Symbol definition relative to Figs. 2(b) –2(f). Each color (symbol) corresponds to a relative phase level obtained for electric field polarized along x or y direction.
Table 2. Target and obtained phase and transmission values of each pixel with four phase level control at 532 nm. The chosen structures are marked with white stars in Figs. 1(b)-1(f).
Next, we assess the metasurface bandwidth in terms of both relative phase and transmission efficiency. As shown in our previous work [30], c-Si metasurfaces do have broadband behavior in the visible spectrum. However, here we address this issue by averaging the metasurfaces’ spectra that provide the same phase level Φx at 532 nm according to Table 2 (a similar result can be obtained for Φy). The resulting averaged spectra are shown in Fig. 2(a) for the following phase levels: 0 (red), 0.25 (blue), 0.5 (black) and 0.75 (green) rad(2π)−1. The dots in Fig. 2(a) indicate the optimum phase levels at 532 nm. The error bars indicate the phase and transmission standard deviations of the average values. Note that the phase curves relative separation does not change significantly over a broad spectral region around 532 nm. Note further that the corresponding averaged transmission spectra, shown in Fig. 2(b), are not only high but also broadband, therefore confirming the broadband nature of c-Si metasurfaces.
Fig. 2 Averaged phase (a) [(c)] and transmission (b) [(d)] of the unperturbed [perturbed, semi-axes reduced by 20 nm] structures designed to give relative phase levels of 0 (red), 0.25 (blue), 0.5 (black) and 0.75 (green) rad(2π)−1. The average is taken over the spectra of metasurfaces that provide the same phase level Φx (a similar plot can be obtained for Φy) at 532 nm according to Table 2. The error bars indicate the phase and transmission standard deviations of the average values.
This analysis is now further extended assuming a 20 nm reduction of the nanoposts’ semi-axes, which is compatible with our nanofabrication resolution. The resulting averaged phase and transmission spectra are shown in Figs. 2(c) and 2(d), respectively. Note that the metasurface optimum operating point (dots in Figs. 2(c)) blueshifts by approximately 52 nm (to ~480 nm). Moreover, this occurs without significantly changing the relative phase separation over a broad band (see Fig. 2(c)) and with high transmission (>60%, as shown in Fig. 2(d)). Finally, Figs. 2(a)-2(d) indicate that variations in transmission (wide error bars) at a given wavelength are less detrimental to the metasurface SNR and diffraction efficiency than variations in phase.
3. Optical characterization
The stereoscopic metasurface characterization is carried out in two different ways, one for reconstructing the encoded 3D image and other for measuring the transmitted and diffracted powers [30]. The image reconstruction setup, Fig. 3(a), consists of a solid-state laser, two polarizers (P1 fixed at 45° and P2 to adjust the polarization of the incident light), two lenses (L1 and L2 with focal length f1 = 7.5 cm and f2 = 2.5 cm, respectively), and an iris to block unwanted scattered light by the optical interfaces. As in [30], the lenses are arranged in a Keplerian configuration to reduce the beam waist size to a collimated spot diameter of ~400 µm All metasurfaces have a total area of 389.12 µm × 389.12 µm. The reconstruction plane is located 20 cm away from the hologram in all cases. The image reconstructions are captured with a Nikon Coolpix p100 camera positioned in front of the reconstruction plane. The power measurement setup, in turn, is essentially as in (a) but with only a single lens L3 (f3 = 25 cm), as illustrated in Fig. 8(b). The power measurement requires the light to be focused on a region smaller than the hologram size, which is achieved by positioning the sample close to the lens focal point resulting in a beam waist of ~200 µm [9]. The total transmitted power is then measured with a power meter (Thorlabs S120C) at position T1 in Fig. 3(b) to guarantee it falls mostly onto the detector’s active area). The zeroth-order transmitted power is measured simply by moving the detection head to its location represented by T2 in Fig. 3(b).
Fig. 3 (a) and (b) show the measurement setup used for the holograms’ image reconstruction and power measurements, respectively. Note in (a) that the lenses L1 and L2 are arranged as a Keplerian telescope. (c) and (d) are the metasurface’s SEM micrographs, whose scale bars represent 200 nm and 500 nm, respectively.
As in our previous design [30], the metasurface is fabricated on a commercially available 230 nm thick c-Si (100) epitaxially grown on a sapphire substrate (from UniversityWafer, Inc.). The structure is patterned on a HSQ electron beam resist using electron beam generator Vistec EBPG 5000 + at 100 KeV. After developing the resist, the pattern is transferred from the resist to the silicon layer using inductively coupled plasma etching (PlasmaPro System 100ICP180). The remaining HSQ is removed with Hydrofluoric acid. The scanning electron micrographs (SEM) of one of the metasurfaces are shown in Figs. 3(c) and 3(d).
4. Discussion
We assess the birefringent metasurfaces’ performance by way of two different hologram designs (Designs 1 and 2). Each design encodes two target images as illustrated in Fig. 4. In Design 1, we use two different superposed target images (images A and B) with the purpose of assessing the cross-talk between each polarization and comparing their efficiencies. In Design 2 we use two similar images (C and D) which are slightly separated in space with respect to each other. This is done to mimic the human eye parallax and thus guarantee stereoscopic reproduction. This effect is created with the open source 3D computer-graphic software Blender [51] (to see the depth effect in the Design 2 anaglyph hold a blue filter in front of the right eye and a red filter in front of the left eye). However, in the proposed image reconstruction setup these images (both at the same wavelength) must be orthogonally polarized to each other and separated at the observer’s eyes with the help of a pair of cross-polarized filters. This arrangement successfully reproduces the depth perception characteristic of 3D projections.
Fig. 4 Concept of the two birefringent c-Si metasurfaces. Design 1 consists of two different target images (A encoded for x- and B for y-polarization) with the purpose of accessing the efficiency and polarization cross talk of both images. Design 2 consists of two similar parallax-separated images (C encoded for x- and D for y-polarization) for 3D stereoscopic reconstruction.
The computer generated holograms (CGHs) of each target image A-D, all with 1024 × 1024 pixels and pixel dimension of 190 nm × 190 nm are calculated via the modified Gerchberg-Saxton Algorithm [47,52–54]. The total size of each CGH is 194.56 µm × 194.56 µm. The small pixel dimension compared to the operating wavelength (532 nm) causes the reconstructed images to suffer from wide angle aberration. Thus, a correction is required for each target image to avoid this effect prior to hologram calculation [47]. Finally, the target images are vertically displaced to avoid cross-talk with the unwanted zeroth-order beam. The resulting CGHs of A and B (similarly for C and D) are then encoded in a c-Si birefringent metasurface for x and y polarized light, respectively, according to Table 2. Each encoded CGH is then assembled as 2 × 2 arrays D1 and D2 as the final metasurfaces with total size of 389.12 μm × 389.12 μm.
We now carry out a broadband reconstruction analysis based on the Rayleigh-Sommerfeld integral [47], which can be successfully used for all metasurfaces. We apply this analysis to metasurface D1 to obtain its SNR, diffraction and transmission efficiencies spectra. As usual, the transmission efficiency is defined as the ratio between the hologram’s transmitted power to the transmitted power through the substrate, while the diffraction efficiency is defined as the ratio between the power at the image window to the power transmitted through the substrate. The calculated efficiencies and SNR are shown in Figs. 5(a) and 5(b), respectively. Note in both plots that the metasurface’s operating point is blueshifted to 480 nm when the semi-axes are reduced by 20 nm. Furthermore, the diffraction efficiencies (dotted and continuous lines in Figs. 5(a) from CGHs A and B, respectively) are >20% within a 110 nm [80 nm] region for the unperturbed [perturbed, semi-axes reduced by 20 nm] metasurfaces, as indicated by the blue [black] curves. In this region, the transmission efficiency remains >70% [>50%] and the SNR, shown in Figs. 5(b), >15dB[>10dB], resulting in high quality reconstructions. These results confirm once again the broadband nature of c-Si metasurfaces as suggested by the phase and transmission spectra in Figs. 2(a) and 2(b), respectively. More importantly, it demonstrates that by simply rescaling the nanoposts it is possible to tune the operating bandwidth of the proposed design.
Fig. 5 (a) and (b) show the Transmission (dashed lines) and diffraction efficiencies spectra (continuous and dotted lines for CGH A and B, respectively) with (a) referring to the unperturbed design and (b) to the design reduced by 20 nm. The transmission efficiency spectra of A and B are overlapped. SNR of the unperturbed (c) and reduced (d) designs. The continuous and dotted lines refer to the result of CGHs A and B, respectively.
We start the experimental characterization at the design wavelength of 532 nm. The measured transmission and diffraction efficiencies are listed in Table 3 for both metasurfaces and polarizations. The difference in transmission efficiency between x and y polarized waves is due to fabrication imperfections. The transmission efficiencies of all metasurfaces are very high because of c-Si low absorption at the operating wavelength when compared to amorphous or polycrystalline silicon [30]. However, the diffraction efficiency is modest for all samples because the fabricated metasurfaces suffer from semi-axis size deviations of their elliptical nanoposts. As a result, the phase shift imparted by each nanopost on the transmitted light deviates from the desired values listed in Table 2, as shown in Fig. 1. In this sense, more light is cast as noise in addition to being lost to the zeroth-order beam. Both these effects contribute to reduce the diffraction efficiency and to increase the polarization cross-talk.
Table 3. Measured (calculated for the design reduced by 20 nm) efficiencies at the holograms’ reconstruction plane operating at 532 nm.
The experimental reconstructions of metasurface D1 are shown in Figs. 6(a) and 6(d) for x- and y-polarized light, respectively. Both present good reconstruction quality despite the noise caused by variations on the nanoposts’ size. Part of this noise comes from the hologram encoded on the other polarization. Note that the reconstructions are polarized along one direction, x or y, meaning that these spurious reconstructions are essentially due to polarization cross-talk. To provide a phenomenological explanation for the mechanism behind this effect, we carry out numerical reconstructions of the holograms based on the approach described in [30]. Initially, we assume that each CGH pixel has a homogeneous field distribution whose phase and amplitude accounts for the nanopost response according to Table 2. Since CGHs are close to ideal, the reconstructions for x and y polarizations shown in Figs. 6(b) and 6(e), respectively, are very good and without the polarization cross-talk image.
Fig. 6 Experimental reconstructions of metasurfaces D1 for (a) x- and (d) y- polarized light. (b) and (e) [(c) and (f)] show the numerical reconstructions of the unperturbed [perturbed] metasurface. The reconstructions are taken 20 cm away from the metasurface. These images are not stereoscopic and are used to assess polarization cross-talk. The operating wavelength is 532 nm.
Next, we perturb the nanoposts’ semi-axes by 20 nm (within the error from the metasurface’s SEM measurements), leading to new phase and amplitude values for each pixel read from the maps in Fig. 1. The reconstructions for x and y polarizations are shown in Figs. 6(c) and 6(f), respectively. As expected, this perturbation diverts more power to both the zeroth-order beam and the Hermitian copy of the reconstruction for x and y polarizations, respectively, which increases the noise and reduces the diffraction efficiency as a result. Note also that the shadow of the orthogonal polarization reconstruction is visible around the desired image in this perturbed numerical reconstruction. Therefore, these numerical results, mimicking the fabrication error and its impact on both the reconstruction noise and diffraction efficiency, fully corroborate the experimental observations.
The experimental stereoscopic reconstructions of hologram (D2) are shown in Figs. 7(a) and 7(b) for x- and y-polarized light, respectively. The stereoscopic reconstruction requires the hologram to be illuminated with x + y polarized light. The image is then reconstructed on a fine-sanded aluminum plate surface, used as reconstruction plane, to preserve the polarization of the scattered light. The stereoscopic view, however, requires the observer to wear a pair of cross-polarized filters in front of his/her eyes as used in our experiment (or a pair of cross-polarized glasses). Note that the cross-polarized spurious reconstructions are also present, but they are subtler to observe due to the similarity between images.
Fig. 7 Experimental reconstructions of each image from the holographic stereogram for (a) x- and (b) y-polarized light. The reconstructions are taken 20 cm away from the metasurface. The operating wavelength is 532 nm.
Finally, we investigate the metasurfaces at 444.9 nm and 635 nm to assess their bandwidth performance. Table 4 lists the resulting diffraction and transmission efficiencies for both metasurfaces and polarizations. Surprisingly, the efficiencies at 444.9 nm are as high as those at 532 nm, even though c-Si is more absorptive at this wavelength. This result can be attributed to the nanoposts’ semi-axes size variations during fabrication, that caused the metasurface operating point to blueshift, as shown in Figs. 5(a) and 5(b). The image reconstructions at 444.9 nm are shown in Figs. 8(a), 8(b), 8(e) and 8(f), where Figs. 8(a) and 8(e) are not stereoscopic and used only to assess polarization cross-talk while Figs. 8(b) and 8(f) are obtained from the holographic stereogram. These images exhibit not only low noise, but also virtually inexistent cross-talk, indicating that phase control is more efficient at this wavelength resulting in improved depth perception. In contrast, the stereoscopic effect is not observed at 635 nm despite the metasurface high transmission efficiencies (>80%) due to c-Si low ab-sorption at this wavelength. Moreover, the low diffraction efficiencies (<10%) are due to the poorer phase control at this wavelength, leading to higher noise and stronger polarization cross-talk compared to lower wavelengths, as seen in Figs. 8(c), 8(d), 8(g) and 8(h). Similarly, Figs. 8(c) and 8(g) are not stereoscopic and used only to assess polarization cross-talk while Figs. 8(d) and 8(h) are obtained from the holographic stereogram. It is important to point out that the reconstructions at 444.9 nm and 632 nm are distorted because the wide-angle correction is wavelength dependent and is carried only for 532 nm.
Table 4. Measured (calculated for the design reduced by 20 nm) efficiencies at the holograms’ reconstruction plane at 444.9 nm and 635 nm.
Fig. 8 Experimental reconstructions for x- (first row) and y- (second row) polarized light at 444.9 nm (first two columns) and 635 nm (last two columns). The reconstructions are taken 20 cm away from the metasurface. (a), (e), (c) and (g) are not stereoscopic and are used to assess polarization cross-talk. (b), (f), (d) and (h) are obtained from the holographic stereogram.
5. Conclusion
We have presented the first broadband stereoscopic hologram fabricated with a birefringent c-Si/Saphire metasurface designed to operate at 532 nm. The birefringent metasurface was designed with c-Si nanoposts with elliptical cross-section and different effective indices, excited with linearly polarized light aligned to each of its semi-axis. The stereoscopic holograms (one for each polarization) were combined on the same metasurface and encoded with four phase levels each, calculated via the modified Gerchberg-Saxton (G-S) phase-retrieval algorithm to maximize the signal-to-noise-ratio (SNR). A coordinate transformation correction was carried out on the target images to avoid wide-angle aberration. The reconstruction plane used for the stereogram consisted of a fine-sanded aluminum surface to preserve the polarization of the scattered light and to minimize the mirror effect of the aluminum surface. We also fabricated two additional metasurface holograms using two completely uncorrelated images to address polarization cross-talk issues. The broadband nature of the metasurfaces was assessed by means of phase and transmission spectra calculation. We noticed that the wavelength band can be easily tuned simply by reducing the nanoposts’ diameter without significantly affecting their phase response. We also performed numerical reconstructions to assess the metasurface wavelength response in the visible range. The results showed diffraction efficiencies >20% within a 110 nm bandwidth with SNR>15 dB. Moreover, when the nanoposts’s semi-axes were reduced by 20 nm (to account for fabrication errors), the diffraction efficiency remained >20% within a 80 nm bandwidth with SNR>10 dB. The measured transmission efficiencies were very high (about 70%) because of the c-Si low absorption at the operating wavelength when compared to amorphous or polycrystalline silicon. The diffraction efficiency, in contrast, was modest because the semi-axes size of the fabricated nanoposts were smaller than originally designed. This caused more light to be diverted to noise and to the zeroth-order, in addition to increasing the polarization cross-talk. We have also investigated the metasurfaces’ performance at 444.9 nm and 635 nm to assess their bandwidth. The stereoscopic effect was surprisingly good at 444.9 nm with transmission and diffraction efficiencies as high as 70% and 18%, respectively, with good depth perception. The same was not true at 635 nm due to low diffraction efficiencies (<10%, due to poor phase control), despite high transmission efficiencies (>80%, due to c-Si low absorption at this wavelength). This occurred because the nanoposts’ semi-axes size variation blueshifted the operating wavelength. Nonetheless, the proposed structure was able to successfully capture depth effect on the reconstructed images, with potential applications in diverse areas such as visual arts, entertainment, and security. The latter in particular will certainly benefit from the increased degree-of-freedom conveyed by stereoscopic information.
Funding
São Paulo Research Foundation (FAPESP) (2015/21455-1, 2013/07276-1, 2016/05809-0, FAPESP/OSU 2015-AWARD 2015/50268-5); National Natural Science Foundation of China (NSFC) (11674402, 11761131001, 91750207), National Council for Scientific and Technological Development (CNPq) (303562/2017-0), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.
Acknowledgements
The authors would like to acknowledge the computational support of the Núcleo de Apoio a Óptica e Fotônica (NAPOF-USP).
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