1. Introduction

3D stereoscopic film provides an illusion of depth perception to the film audience similar to human eyes sensing the 3D world. The principle of 3D film lies in that two different planar images (record the images as seen from two perspectives) with orthogonal polarization states are projected on the screen and the film audience wearing polarized glasses observing two perspectives through his (her) left and right eyes, and hence providing depth. Conventional 3D imaging systems are bulky and expensive (two projectors are required in a stereo-vision system) [1]. However, the booming 3D display market (mobile, wearable, and portable consumer electronics and medical devices, etc.) requires a thin, lightweight, and flexible device to generate depth perception based 3D images. Optical metasurfaces offer a promising approach for realization of such optical component.

In the past several years, research on metasurfaces has led to many unconventional optical properties and interesting physics [2–26]. Among various types of metasurfaces, polarization-independent metasurfaces that consist of nanobrick arrays with spatial varying dimensions, have shown unique phase control to the orthogonal polarization states independently in the incident light [27–30]. As the nanobrick arrays are capable of generating binary phase profiles in the subwavelength scale, polarization-independent metasurfaces have facilitated new perspectives in designing phase-only optical elements in the two orthogonal polarizations separately. In this paper, we demonstrate the realization of high-performance and depth perception based 3D hologram with the polarization-independence nanobrick arrays. These carefully designed thin nanobrick arrays, characterized by periodic nanostructures with identical cell size but different nanobrick dimensions, can diffract the incident beam into two different images on the same plane in the far field according to their polarization states. As the two different diffraction images constitute the stereo image pair of the target object, one can observe 3D effect of the holographic images with the help of polarized glasses.

2. Unit cell design

The schematic diagram of our proposed polarization-independent silicon nanobrick arrays is shown in Fig. 1, whereby periodic nanobricks with length$L_x$, width$L_y$, height $H$and cell size $C$sitting on a fused silica substrate. To manipulate the phase of an incident beam in the two orthogonal polarizations, one need to generate different phase delays in the$x$and$y$directions while maintaining the amplitude of incident beam unchanged. Since each nanobrick can be considered as a truncated waveguide [27], nanobricks with different dimensions can generate different effective refractive indices and thus providing different phase distribution in the x and y directions (as illustrated in Fig. 1). Therefore, by carefully tailoring the phase distribution of the nanobrick arrays, they can act as an effective phase modulator in the x and y directions. More importantly, the functionality of phase modulation is independent in the two orthogonal directions and one can design the phase distribution of holograms separately. This forms the basic phase modulation principle of the polarization-independent metasurfaces based 3D holograms.

 

Fig. 1 Illustration of the polarization-independent silicon nanobrick arrays sitting on a fused silica substrate. All the nanobricks have the same height of 310 nm and cell size of 250 nm, but different length and width.

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As mentioned above, the phase delay of each cell is strongly related to the width and length of nanobrick. Therefore, it is important to find the suitable width/length of each nanobrick to obtain the desirable phase delays which lie in between 0 and 2π radians. We have designed and simulated the structures of nanobrick cells by CST microwave studio software. The incident electromagnetic field is assumed to be a linearly polarized plane wave whose wavelength is 658 nm, propagating along the $z\text{-axis}$with electric and magnetic field vectors lying in the x-y plane. The transmitted light is collected by field ports to retrieve the phase delay and transmission efficiency. Since periodic boundary conditions are utilized in the model and each cell has a lateral dimension smaller than the wavelength, only zeroth-order diffraction beam can propagate. To optimize the performance of our nanobricks arrays, we swept the nanobricks width from 40 to 200 nm and the length from 40 nm to 200 nm in steps of 5 nm. At the same time, nanobricks are fixed with cell size of 250 nm and height of 310 nm. Figure 2 shows the color-coded values of numerical simulation results of the phase delays and transmittances in the x and y directions. As shown in Figs. 2(a) and 2(c), the Si-SiO₂ dielectric metasurfaces can generate phase delays varying from 0 to 2π in two orthogonal polarizations. At the same time, most of the transmittances are larger than 55% shown in Figs. 2(b) and 2(d). To obtain a 4-step hologram, we carefully chose 16 different nanobricks which can provide phase delays combinations of 0, π/2, π and 3π/2 in two orthogonal polarizations. The detailed structural parameters of nanobricks are shown in Table 1.

 

Fig. 2 (a, c) The phase variation of the transmitted light for nanobricks sitting on a fused silica substrate and (b, d) the transmittance as a function of nanobrick size L_x and L_y in the x and y directions, respectively.

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Table 1. Optimized Nanobricks Dimensions

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3. Demonstration of a 2x2 fan-out optical element

Using polarization-independent metasurfaces comprising an array of silicon nanobricks sitting on a silica substrate, an ultracompact fan-out optical element [31] can be obtained to generate uniform 2 × 2 spot arrays in different spatial arrangements, shown in Fig. 3. The 2 × 2 fan-out optical element was designed with a unit cell size of 250 nm × 250 nm, grating period of 5 μm × 5 μm and operation wavelength of 658 nm. We optimized the 4-step phase distribution of nanobrick arrays to generate the two target images shown in Figs. 3(a) and 3(c) by the Gerchberg-Saxton algorithm [32]. In the phase design, we took the conversion efficiency, signal-noise ratio (SNR) and uniformity as merit functions for optimization. The designed phase distribution in one period are shown in Figs. 3(b) and 3(d). After that, we simulated the designed fan-out optical element by Lumerical FDTD Solutions and the simulated holographic images can be seen in Figs. 3(e) and 3(f). It is shown that the location of the spots does not distort and the power distribution is almost uniform, which agrees well with the theoretical prediction.

 

Fig. 3 (a, c) The target 2 × 2 spot arrays and (b, d) their corresponding phase distribution of the designed fan-out element in one period when the incident beam is linearly polarized along the x and y directions, respectively. (e, f) The normalized light intensity in far field generated by the fan-out element when the incident beam is linearly polarized along the x and y directions, respectively.

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To evaluate the performance of the 2 × 2 fan-out optical element, we define conversion efficiency as the ratio between the optical power projected into the target diffractive orders and the input power, zeroth-order leakage (ZOL) as input power divided by the zeroth-order power, and uniformity as $\frac{I_{max}-I_{min}}{I_{max}+I_{min}}$, where$I_{max}$and$I_{min}$ are the maximum and minimum powers of the desired orders, respectively. Signal-noise ratio is defined as the ratio of the average intensity of signal to the average intensity of the background noise [33,34]. For the light intensity formed with linearly polarized sub-beams in the x direction shown in Fig. 3(e), numerical simulation shows that the conversion efficiency reaches 51%, while the uniformity, ZOL and SNR are 6.9%, 0.62% and 257, respectively. For the light intensity formed with linearly polarized sub-beams in the y direction shown in Fig. 3(f), the conversion efficiency, the uniformity, ZOL and SNR are 54%, 3.2%, 0.62% and 247, respectively. The numerical simulations show that our designed metasurfaces have performed well to control the phase delays of two orthogonal polarized beams independently.

4. Demonstration of a complex hologram

To further verify our proposed concept of three-dimensional (3D) hologram based on polarization-independent metasurfaces, we demonstrate the design of a complex 3D hologram with which the Wuhan University Badge was taken as the target images, shown in Fig. 4(a). The target planar images in design are different for left and right eyes, including four parts with four different parallaxes. Therefore, the 3D holographic images consist of four layers in different depths based on the principle of stereo vision. After optimizing the phase distribution of the 3D hologram in the x and y directions separately, we can facilitate the 3D hologram with the polarization-independent metasurfaces mentioned above. Therefore, the stereo image pair of the Wuhan University Badge can be generated in the far field. With polarized glasses, 3D holographic images with four-layer information can be sensed by observer’s eyes.

 

Fig. 4 (a) Illustration of the nanobrick arrays under a randomly polarized incident beam. Sub-beams polarized along the x and y directions form the holographic images in the far-field. With polarized glasses, a 3D Wuhan University Badge with four-layer portions would be sensed by observer’s eyes. Layer1, layer2, layer3, and layer4 represent the relative positions of the four parts (“WUHAN UNIVERSITY”, “Building”, “1893”, and “the Wuhan University in Chinese”) with different parallaxes in stereo imaging. (b) The designed nanobrick arrays (partial view) with 4-step phase delays in both x and y directions. (c, e) The target letter “U” from two perspectives and (d, f) simulated holographic images in the far field when the incident beam is linearly polarized along the x and y directions, respectively. In (d) and (f), the zeroth-order sub-beams were removed to increase the contrast of the holographic images.

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Due to the limitation of computation resource and time, we only take a 3D letter “U” from the Wuhan University Badge as a design example, shown in Figs. 4(c) and 4(e). The two different target letter “U” with different perspectives can be formed by two orthogonally polarized sub-beams along the x and y directions, respectively. The hologram was designed to create a wide image angle of 80° × 80°. 2 × 2 periodic arrays of the hologram pattern were used to avoid the laser speckles [15]. To create a holographic image with a pixel array measuring m × n within the angular range $a_x$ × $a_y$in the far field, the period of the hologram in the x and y directions can be calculated according to $d_x=m\lambda /[2\tan ({\alpha }_x/2)]$ and $d_y=n\lambda /[2\tan ({\alpha }_y/2)]$, respectively. As an example, the hologram with periods of 25 μm × 25 μm and operation wavelength of 658 nm was designed according to the classical Gerchberg-Saxton algorithm. The phase distribution obtained for the hologram is generated by the nanobrick arrays with different dimensions, shown in Fig. 4(b). The two simulated target letter “U”, which are formed by the two orthogonal sub-beams along the x and y directions, are separately shown as Figs. 4(d) and 4(f) with high fidelity (1 m away from the nanobrick arrays).

The conversion efficiencies of the reconstructed images reach 43% and 40% for linearly polarized sub-beams in the x and y directions, respectively. SNRs are 50 and 34, ZOLs are 0.8% and 0.6% in the x and y directions, respectively. The unwanted zeroth-order beam is caused mainly by the non-uniform amplitude response of nanobricks. In Gerchberg-Saxton algorithm, the hologram was taken as a phase-only element, that is, the amplitude is a constant. However, the amplitude response of the nanobricks (shown in Tab. 1) is non-uniform and these errors lead to the inaccuracies for every diffraction orders, especially for zeroth-order. Besides, the inaccurate phase delays, and mode coupling between neighboring cells also contribute to the unwanted light in the zeroth-order. This strong zeroth-order light can be avoided by using an off-axis design [15].

5. Conclusions

In summary, we propose a new-concept and depth perception based 3D hologram enabled with polarization-independent metasurfaces that is capable of controlling the phase delay of the two orthogonal polarized light independently. Generally, the proposed 3D hologram can overcome the limitations of the conventional 3D imaging system (bulky and expensive) since it occupies many unparalleled advantages such as one-step lithography, untracompactness and compatibility with semiconductor technology, which dramatically reduces the cost of fabrication and enables mass production. Therefore, our concept could be viable for various practical applications such as three-dimensional television, video, and display.