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Abstract
This study uses a dielectric metasurface to demonstrates a multicolor holographic movie. Overlapping of multiple-wavelength images at 445 nm, 532 nm, and 633 nm was achieved by maintaining the ratio between the wavelengths and the pixel periods constant. Polarization-independent pillar waveguides made of single-crystal silicon are used as meta-atoms. A movie of the rotating earth was designed by the iterative Fourier transform algorithm and fabricated using electron beam lithography to a silicon-on-sapphire substrate. The multicolor movie consists of 20 frames was successfully reproduced at the maximum speed of 30 frames per second.
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1. Introduction
Holography is a technology that reproduces the wavefront of the object light by using a hologram that records the amplitude and the phase distribution of light. Holography attracts much interest because it can display three-dimensional images. It can be classified as optical, digital, and computer-generated holography (CGH) from the viewpoints of recording and reproducing media. In optical holography, the interference fringes between the object light and the reference light are recorded on film media [1,2]. The object light wavefront is reproduced by irradiating the hologram with the reference light. In digital holography, the interference fringes are recorded using an image sensor. The wavefront is reproduced using a spatial light modulator (SLM) [3–9] or an acousto-optic modulator (AOM) [10,11] instead of a hologram. In CGH, a light wavefield from a virtual object is computationally calculated using the diffraction theory. It can be recorded to the hologram through a lithographic technique or reproduced using the SLM. Using SLMs provides the advantage of dynamic control applicability (i.e., holographic movies). In SLM-based holograms, many efforts have been dedicated to the expansion of the viewing angle [12,13]; however, achieving a subwavelength pixel size has remained a challenging issue.
In the recent years, metasurfaces, which are a planar arrangement of subwavelength-scale phase retarders, have been applied to CGH holograms to achieve a wide viewing angle [14–23]. Metasurfaces can tailor to the properties of light not only amplitude, phase, and polarization, but also wavefront; hence, they have been applied to various optical elements, including waveplates [24–28], vector beam converters [29–31], and lenses [32–36]. Metasurface holograms can have a period smaller than the working wavelength; thus, their viewing angle can widen. A unit cell or a pixel of metasurface holograms, also known as meta-atoms, can be made both of metals [14–16] and dielectrics [17–21]. Dielectric metasurfaces are promising from the viewpoint of efficiency because the transmittance of the former is low due to the Ohmic loss of the metallic material [37].
The development of multicolor and animated holography is an interesting challenge. For optical holography, animation based on a cinematographic approach [38] and multicolor animation based on multi-angle total internal reflection illumination [39,40] have been reported. For digital holography, multicolor animation based on spatial multiplexing or temporal stack using SLMs or a digital mirror microdevice (DMD) has been presented [41–44]. Meanwhile, wavelength selection based on the aid of the Pancharatnam–Berry (geometric) phase has been reported for metasurface holograms [45,46], although their efficiency is reduced by half at most because of its polarization dependence. A metasurface multicolor hologram based on spatial multiplexing has also been created by shifting the projection plane of the hologram for each wavelength [47]. As a metasurface holographic movie, a structured illumination by using DMDs [48] and a cinematographic approach [49] also achieved sufficient frame rate. However, in spite of the above-mentioned progress, a multicolor holographic movie has not yet been reported.
In this study, we developed a multicolor holographic movie consisting of three distinct wavelengths of 445 nm, 532 nm, and 633 nm based on a cinematographic approach. Accordingly, a polarization-independent metasurface hologram based on single-crystal silicon octagonal pillar meta-atoms was adopted for both low absorption and high-throughput fabrication. A holographic color movie consisting of 20 frames was successfully reproduced at the maximum speed of 30 frames per second.
2. Principle
Holography is a technology that utilizes diffraction and interference of light. To reproduce a stored picture, the propagation to the image plane $u_1(x_1, y_1, z)$ from the diffraction at the hologram plane $u(x, y, 0)$ along with the $z$ axis can be calculated as follows using the angular spectrum [50]:
which is the Fourier transform of the incident field. $\mathbf {k}=(k_x, k_y, k_z), |\mathbf {k}|=2\pi /\lambda$ is the wave vector to the diffraction direction and $\lambda$ is the vacuum wavelength. We considered herein the phase hologram expressed with a metasurface comprising $M\times N$ pixels (meta-atoms) arranged in the square lattice with a period of $p$ illuminated with a uniform normal plane wave. The Cartesian coordinate $(x, y)$ can be expressed with a pair of integers $(m, n)$, where $x=mp$ and $y=np$; thus, the Fourier transform is also discretized as follows:This equation provides the maximum of wavenumber components $k_{x\textrm {max}}=k_{y\textrm {max}}=\pi /p$. The diffraction angle $\theta$ from the $z$-axis can be given as follows:
When we consider the $x-z (k_y=0)$ or $y-z (k_x=0)$ planes, the maximum diffraction angle $\theta _{x,y\textrm {max}}$ can be presented as $\theta _{x,y\textrm {max}}=\arcsin (\frac {\lambda }{2p})$, where $\varphi = 2\theta _{x,y\textrm {max}}$ is referred to as the viewing angle. Thanks to the small pixel period $p$, the viewing angle of the metasurface hologram can widen and even exceed the full hemisphere when $p<\lambda /2$ is satisfied. Furthermore, a multicolor hologram can be achieved by maintaining a constant $\lambda /p$. In this study, we designed and fabricated hologram sequences at each of the three wavelengths of 445 nm (blue), 532 nm (green), and 633 nm (red) and superimposed the reproduced images of each color by keeping the value of $\lambda /p$ constant for each.
3. Design and fabrication of the multicolor metasurface hologram
The metasurface hologram to be fabricated is a structure consisting of nanoscale regular octagonal pillars arranged in a square lattice (Fig. 1). The substrate and the pillar were made of sapphire and single-crystal silicon (SC-Si), respectively. Each pillar generates a different phase delay in the transmitted light depending on its dimensions [51]. One pillar was used to represent one pixel of the image. In this study, we kept the height $h$ of the pillars constant and used the width-across-flat $w$ of the pillars to express the phase delay variation. The octagonal cross-sectional shapes were adopted for the high-throughput fabrication using the character projection (CP) method of the electron beam lithography. This method utilizes dedicated stencils to form shaped electron beams for high-speed drawing and improvement of the edge quality, whereas the selectable sizes are limited [52]. The phase delay was calculated by analyzing the electromagnetic field using a commercial finite element method software, COMSOL Multiphysics 5.1 (COMSOL Inc., USA). The period between the pixels $p$ was chosen for each design wavelength to maintain the viewing angle constant using Eq. (4). The metasurface holograms were fabricated by arranging the silicon nanopillars of different widths and reproducing the phase distribution that can project an arbitrary image.
Fig. 1. (a) Schematic illustration of multicolor metasurface holographic movie based on a cinematographic approach. (b) The layout of the metasurface. Hologram sequences consisting of 20 frames were arranged for wavelengths of 445 nm, 532 nm, and 633 nm. (c) Schematic diagram of the dielectric metasurface made of a single-crystal silicon nanopillar array. Octagonal pillars were arranged in a simple lattice.
3.1 Calculation of transmittance and phase delay
The transmittance and the phase delay of the meta-atoms were calculated using COMSOL. The steady-state solution of Maxwell’s equations for the harmonic oscillation at a specific wavelength was calculated with the electromagnetic wave, frequency domain (ewfd) physics with the following governing equation:
where $\boldsymbol {E}$ is the electric field; $\varepsilon _r$ is the relative permittivity of the medium; and $k_0$ is the wavenumber in vacuum. The height $h$, period of pixels $p$, and pillar width $w$ were used as the calculation parameters.The material model by Vuye (SC, 20$^\circ$C) [53] for single-crystal silicon (SC-Si) was used. The incident light wavelengths were chosen as 445 nm (blue), 532 nm (green), and 633 (red) nm. The height $h$ was set to 400 nm. Complex refractive indices ($n+i\kappa$) and transmittances calculated with Lambert–Beer law ($\exp (-4\pi \kappa t/\lambda )$) of the SC-Si film with the thickness $t$ of 400 nm were summarized in Table 1. Although the transmittance decreases as the wavelength decreases, the color would be balanced by adjusting the power of illuminating light.
Table 1. Refractive indices and transmittances of 400 nm-thick SC-Si film.
The periods between the pixels $p$ were set to 280, 335, and 398 nm to maintain the maximum diffraction angle $\theta$ at 52.6$^\circ$ using Eq. (4). The widths, $w$, were varied at the 50–300 nm range. The calculations were performed at a 10 nm step because of the available CP limitations. Figure 2 shows the calculated transmittance and phase delay as a function of the pillar width $w$ under the above-mentioned conditions. At each wavelength, the widths of the pillars were selected to make the phase range as large as possible. The 140–210 nm widths for the incident light wavelengths of 445 nm and 140–200 nm for 532 nm and 120–180 nm for 633 nm were used in the design. The average transmittance for each wavelength was 22.1%, 67.2%, and 83.9% for the 445 nm, 532 nm, and 633 nm wavelengths, respectively. The dips in transmittance at 160 nm on $\lambda =445$ nm and 140 nm on $\lambda =532$ nm were attributed to the transition between leaky mode and waveguide mode. On the other hand, dips at 200 nm on $\lambda =532$ nm and 180 nm on $\lambda =633$ nm can be attributed to the interference of the higher-order mode.
Fig. 2. Transmittance and phase delay of the single-crystal silicon meta-atom calculated by the finite element method for the wavelengths of 445 nm (a), 532 nm (b), and 633 nm.
3.2 Calculation of the phase distribution
The phase distribution at the hologram plane can be obtained using the iterative Fourier transform (IFT) method (Fig. 3). The optimum phase distributions at the hologram plane were calculated by repeating the following steps until a sufficient phase distribution was obtained:
- 1. Combine the intensity of the target image with the phase distribution (initially assumed to be a random distribution).
- 2. Inverse Fourier transform.
- 3. The resulting phase is the phase distribution to be reproduced by the hologram.
- 4. Set the incident light intensity and combine it with the phase distribution obtained at Step 3.
- 5. Fourier transform of the obtained values. This step corresponds to propagation and reproduction.
- 6. The resulting intensity becomes the projected image. The phases are combined again in Step 1.
Figure 4 shows the selected frames of the target movie in this study, that is, the moon orbiting the earth, which is to be projected by the metasurface hologram. The original movie was downloaded from the free video site “Videvo.net”, and transformed under CC-BY 3.0 license [54]. The transformed movie can be seen in Visualization 1. The total number of frames was 20. The oceans, lands, and the combination of the moon and clouds are represented in blue, green, and red, respectively. We corresponded the colors to the 445 nm, 532 nm, and 633 nm wavelengths. The black padding to the right half of each frame was used to avoid the 0th-order diffraction and alias images.
Fig. 4. Selected frames of the target movie. The oceans, lands, and the combination of the moon and clouds are represented in blue, green, and red, respectively.
We adjusted the target image resolution for each wavelength to maintain the hologram frame size constant. If we set the target image with the same resolution, the hologram size will be different because of the different period $p$. This adjustment enabled both smooth frame-to-frame transition and constant-speed drive for the frame feed. For this adjustment, the target image resolutions for 445 nm, 532 nm, and 633 nm were set to 1920$\times$1080, 1604$\times$902, and 1350$\times$758, respectively, for 20 frames using Eq. (4). Therefore, the frame size is maintained to be 854$\times$480 µm2.
We implemented the IFT algorithm using Python code. The calculated phase distributions were discretized based on the phase profile calculated in Fig. 2, and mapped to the GDSII layout file using the Python library Gdstk. The peak signal-to-noise ratios (PSNR) between the target images and the calculated images using discretized phase distributions were 17.33, 16.93, and 17.32 dB for red, green, and blue channels, respectively. The lowest PSNR in the green channel is considered to be due to the narrower phase coverage, as shown in Fig. 2. Table 2 summarizes the design dimensions of the determined metasurface holograms.
Table 2. Design dimensions of the metasurface holograms.
3.3 Fabrication
The metasurface holograms were fabricated based on the design dimensions shown in Table 2. Figure 5 presents a schematic of the fabrication process flow. (a) A commercially available silicon-on-sapphire (SOS) wafer was used, where a single-crystal 400 nm-thick silicon (100) film was epitaxially grown on the R-plane of a double-side polished sapphire substrate with 460 µm thickness. The wafer was diced into 2$\times$2 cm$^2$ square chips along with the orientation flat (45$^\circ$ from the c-axis projected on the R-plane). (b) The layout pattern was drawn by direct-writing EB lithography (F7000S-VD02, Advantest, Japan). A hexamethyldisilazane surfactant, a positive EB resist FEP171-D (FUJIFILM Electronic Materials Co., Ltd., Japan), and an antistatic agent ESPACER 300AX01 (Showa Denko Co., Japan) were spun-coated on the cleaned SOS chip. The exposure dose of the electron beam was set at 7.0 µC/cm2. Octagonal pillar patterns were drawn by using the CP method to improve the writing performance. After the resist development, (c) the pattern was transferred to a 50 nm-thick aluminum film through vacuum evaporation. (d) The substrate was immersed in acetone and sonicated for 30 min to remove unnecessary aluminum (lift-off). (e) The silicon layer was removed using an inductively coupled plasma reactive ion etching apparatus CE-300I (Ulvac Co., Japan) with aluminum masks. (f) Finally, the unnecessary aluminum mask pattern was removed by a wet etchant.
Figure 6 depicts the photograph of the fabricated substrate. Three horizontal lines represent the hologram sequences consisting of 20 frames for each design wavelength of 445 nm, 532 nm, and 633 nm. The arrays of squares at the bottom depict the test patterns for the fabrication size assessment.
Fig. 6. Photograph of the fabricated hologram. The three horizontal lines depict the hologram sequences consisting of 20 frames for each design wavelength of 445 nm, 532 nm, and 633 nm. The arrays of squares at the bottom are the test patterns for the fabrication size assessment.
4. Results and discussions
4.1 Observation of the fabricated metasurface hologram
The fabricated metasurface holograms were observed using a scanning electron microscope (SEM). Figure 7 shows the close-up images for the corner of each hologram sequence. The pillars of different widths were arranged in a square lattice with different periods. Through the fabrication processes, the cross-sectional shape was reduced from octagonal to nearly circular. Since either the octagons and circles does not have polarization dependence, this is considered to cause a slight effect on optical properties. The hologram sequences for 445 nm and 532 nm were well fabricated, whereas that for 633 nm exhibited some missing pillars. A comparison of the CAD layout file confirmed that most of the 120 nm-wide pillars were missing.
Fig. 7. Scanning electron microscope images of the metasurface hologram sequences for the 445 nm (a), 532 nm (b), and 633 (c) nm wavelengths. Each images shows a close-up to the corner of each hologram sequence. The color bars indicate 1µm.
Figure 8 shows the SEM images of the test pattern with the 398 nm period (for the 633 nm wavelength) with widths of 120 (a), 130 (b), and 140 (c)nm. As shown in 8(a), most of the 120 nm-wide pillars were missing, whereas the wider pillars were fabricated well. This result is attributed to the minimum pillar width for the 633 nm hologram being the smallest among the three wavelengths (Table 2). However, as depicted in Fig. 2, the error of the phase distribution for the 633 nm hologram was not considered to be significant because the phase delay of the 120 nm-pillar was small. This problem, on the other hand, could be used to improve both transmittance and phase coverage by intentionally removing meta-atoms (i.e. meta-vacancy) as the vacancy have zero phase delay and no absorption loss. It would be effective, especially in the case of $\lambda =532$ nm, where the small meta-atoms have large phase delays as shown in Fig. 2. To verify this, we calculated the propagation image using phase distributions, assuming that the smallest meta-atoms were replaced by meta-vacancies, and calculated the PSNR with the target image for each color channel. The PSNRs were 21.46, 18.66, and 17.41 dB for red, green, and blue channels, respectively. The improved PSNRs in red and green channels can be attributed to the wider phase coverage, whereas almost unchanged PSNR in the blue channel is because the phase delay of the smallest meta-atom for 445 nm is close to zero.
Fig. 8. SEM images of the test pattern with the period of 398 nm (for the 633 nm wavelength) and widths of 120 (a), 130 (b), and 140 (c)nm. The color bars indicate 1 µm.
4.2 Reconstruction of a multicolor holographic movie
Figure 9 shows the optical setup for the multicolor hologram reconstruction. The fabricated metasurface was mounted on an automatic stage, and the hologram sequences were illuminated with parallel incident laser beams with three wavelengths of 445 nm, 532 nm, and 633 nm by using dichroic mirrors. The half-wave plates, linear polarizers, and irises were used to adjust the light intensity and the beam diameters. Diameters of the incident beams were maintained to be 0.9 mm, 0.6 mm, and 0.6 mm (Full width at half maximum) for wavelengths of 445, 532, and 633 nm, respectively, by using irises to avoid the crosstalk between the three wavelengths. The diffracted images of three wavelengths were projected on the 150 $\times$ 150 mm$^2$ screen situated 135 mm away from the metasurface in the center-to-center distance. Although the hologram sequences are separated by 3.6 mm in the vertical direction, the hologram plane and the projection plane are sufficiently far apart that there is almost no shift in the hologram images. The holographic movie was achieved by actuating the stage along with the horizontal direction of Fig. 6 with fixed optical axes of the incident lasers. In this projection method, the frame rate of the movie was determined by the frame size and stage speed. As we actuated the stage at the maximum speed of 25.6 mm/s, the frame rate of 30 frames per second (fps) is expected. The projected movie on the screen was captured using a camera. Figure 10 displays photographs of the selected frames that corresponding to the target images shown in Fig. 4. Visualization 2 and Visualization 3 show holographic movies at the frame rates of 2 and 30 fps, respectively, captured using a camera (iPhone X). The target movie was successfully projected in spite of some pillars missing for the 633 nm sequence. In other words, the metasurface hologram has tolerance on its design. Although different wavelengths were projected at the same time, the image magnifications can be kept constant, indicating that the images were successfully overlapped as designed. The obtained maximum diffraction angle $\theta _{x\textrm {max}}$ was 52.8$^\circ$ from the distance and size of the image. This value agreed well with the design value of 52.6$^\circ$. Therefore, a multicolor holographic movie was successfully demonstrated by maintaining the ratio between the wavelengths and the pixel periods constant. Diffraction efficiencies were 5.9%, 1.9%, and 7.5% for 445, 532, and 633 nm wavelengths. The lowest efficiency at 532 nm can be attributed to the narrowest phase coverage. It should also be noted that the effect of birefringence of the sapphire substrate was negligible as it is thin enough. This was confirmed by the observation when a polarizer was inserted.
Fig. 10. Pictures of the selected frames corresponding to Fig. 4 of the multicolor holographic movie consisting of 20 frames.
A possible strategy to improve image quality is increasing the discretization levels and the introduction of amplitude modulation for better reproducibility of the complex amplitude distribution. However, this would result in complex meta-atom geometry, and as long as the aforementioned equipment is used, drawing time will increase significantly due to the limitations of the selectable CPs. Another way is the use of more transparent materials, for example gallium nitride, titanium oxide, and silicon nitride. This will require fabrication with higher aspect ratios.
5. Conclusion
This study presented a multicolor metasurface holographic movie consisting of 20 frames. Single-crystal silicon pillars were used as meta-atoms for low absorption at the three distinct wavelengths of 445 nm, 532 nm, and 633 nm. To achieve overlapping, the ratio between the wavelengths and the pixel pitches was kept constant. The resolution of each hologram sequence frame was varied to maintain the frame size constant among the three wavelengths.
Funding
Japan Society for the Promotion of Science (21H01781); Ministry of Education, Culture, Sports, Science and Technology (JPMXP09F11859); Japan Science and Technology Agency (JPMJTM20MK).
Acknowledgments
Part of this work was conducted at Takeda Sentanchi Supercleanroom, The University of Tokyo. The authors thank Prof. Y. Mita, Dr. E. Lebrasseur, and Mr. M. Fujiwara (The Univ. of Tokyo) for their help and assistance with the sample fabrication and Prof. Lucas H. Gabrielli (The Univ. of Campinas) for the development of the Python library gdstk. Part of the numerical calculations was carried out on the TSUBAME3.0 supercomputer at Tokyo Institute of Technology.
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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