1. Introduction

Metasurface, a kind of two-dimensional (2D) artificial metamaterial, is composed of planar nanostructure arrays with subwavelength dimensions [1–8]. Different from conventional phase-only optical devices, which mainly manipulate light in the way of accumulating phase in the propagation path, metasurfaces can control optical properties (amplitude, phase and polarization, etc.) by adjusting their geometric parameters (e.g. shapes, dimensions and orientation angles) of their subwavelength structures cell-by-cell. Owing to the elaborate manipulation capability, plenty of novel optical elements and devices have been proposed in the past decades, such as metalens [9–17], meta-holograms [18–23], nanoprints [24–33], vortex-beam generators [34–36], etc. Among them, meta-holograms have drawn a lot of attention because of its ultra-compactness, high resolution and large viewing angle. In the past several years, numerous achievements like holography with high efficiency [37,38], 2D holography [39,40], three-dimensional (3D) holography [41–43], multicolor holography [44–46] and various kinds of multiplexing holography [47,48] flourished. Nevertheless, current holographic imaging is usually realized in half of the imaging space (transmission or reflection space), which may limit metasurface’s further applications. With another half of space not utilized, there still remains room to improve the information density of meta-hologram. In 2018, Li et al. proposed a metasurface hologram which can work in both reflection and transmission spaces to produce full-space clouds of random points [49]. But the point arrays displayed in two spaces share the same distribution, which makes no contribution to the improvement of information capacity. In another reported article, colorful meta-hologram with independent control of different images in both transmission and reflection spaces was studied [50]. However, due to the limitation of design degrees, the orientation angle of every nanobrick on the meta-hologram should be decided considering all the desired images, which will hinder the further improvement of holographic imaging quality.

Here, based on both PB phase and magnetic resonance, we present a full-space metasurface in both reflection and transmission spaces, which can fulfill the independent display of two irrelevant holographic images respectively. As an example, a PB phase-based metasurface-hologram was designed and fabricated. Both numerical simulation and experimental results show that two different holographic images can be independently reconstructed in reflection and transmission spaces simultaneously. The superiority of full-space holographic image reconstruction may find its way in information storage, high-end imaging technique and future projection.

2. Unit-cell design

The proposed resonant metasurface is based on silicon-on-sapphire (SOS) material, which is composed of a sapphire based planar substrate and a silicon nanobrick array sitting on it. Here, we designed two types of nanobricks (named as nanobrick I and nanobrick II, respectively) with a mere difference in geometry parameters to get independent holographic displays in both reflection and transmission spaces. Nanobrick I works in reflection mode while nanobrick II works in transmission mode in our design. Schematic diagram of the two types of nanobricks are shown in Fig. 1(a). When a circularly polarized (CP) light illuminates a nanobrick, the Jones vector of output beam can be expressed as

 

Fig. 1. (a) Schematic diagram of unit-cell I and II. Unit-cell I works in reflection mode and another one works in transmission mode. Each of the unit-cells is composed of a sapphire substrate and a c-Si nanobrick. The parameters L, W and H represent the lengths, widths and heights of the nanobricks. The subscript ‘1’ and ‘2’ correspond to nanobrick I and nanobrick II respectively. (b) Reflection coefficients along the long and short axes and the phase delay between the two orthogonal axes of nanobrick I. (c) Transmission coefficients along the long and short axes and the phase delay between the two orthogonal axes of nanobrick II. (d) Simulated cross-polarized reflectivity and transmissivity of nanobrick I and nanobrick II. The black and pink curves reveal the cross-polarized reflectivity of unit-cell I (R_1cro) and cross-polarized transmissivity of unit-cell II (T_2cro), which contribute to the designed target images. The unwanted cross-polarized transmissivity of unit-cell I (T_1cro) and the cross-polarized reflectivity of unit-cell II (R_2cro) are depicted by the red and blue lines, respectively.

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In these equations, A and D are reflection coefficients along the long and short axes for nanobrick I and transmission coefficients for nanobrick II. Symbol δ is the phase delay between the two orthogonal axes. Orientation angle α is the angle between the long axis of a nanobrick and x axis. Variables p and q determine efficiency of co-polarized light and cross-polarized light respectively.

When A = D=1 and δ=π, the nanobrick works as an ideal half-wave plate and transforms the incident CP light into a beam with totally opposite handedness. In addition, a geometric phase 2α is introduced to this part, which is determined by the orientation angle. In our design, the orientation angle distribution is elaborately manipulated to fulfill holographic display. As both the coefficients along two orthogonal axes and the phase delay between them are varied with the change of the dimensions of the unit-cell, a trade-off between high coefficients and accurate phase delay of π should be made to get high cross-polarization reflectivity or transmissivity.

CST STUDIO SUITE software is utilized in optimizing the geometric parameters of the two kinds of unit-cells. For unit-cell I, we need to maximize its reflectivity of cross-polarized light and reduce transmissivity of cross-polarized light in order to ensure that it only exert influence in reflection space. As shown above, reflectivity of cross-polarized light is associated with not only the response along the long and short axes but also the phase delay between them. On the balance of the two factors, we finally get the dimensions of unit-cell I (L₁=220 nm, W₁=100 nm, H=230 nm and CS=340 nm). The reflection coefficients (the amplitude ratio between the reflected light and the incident light) along long and short axes of unit-cell I and the phase delay between the two orthogonal axes are shown in Fig. 1(b). Similarly, for unit-cell II, the optimal dimensions (L₂=270 nm, W₂=80 nm, H=230 nm and CS=340 nm) were got by weighing up the two factors. The transmission coefficients (the amplitude ratio between the transmitted light and the incident light) along long and short axes of unit-cell II and the phase delay between the two orthogonal axes are shown in Fig. 1(c). The reflectivity and transmissivity of cross-polarized light of both unit-cells are depicted in Fig. 1(d). To guarantee that images in reflection and transmission spaces don’t disturb each other, we choose a working wavelength ranging from 580nm to 620nm in which the unwanted reflectivity or transmissivity of cross-polarized light are with low values.

To further investigate the high reflectivity mechanism of nanobrick I, we placed field monitors at two wavelengths of 624.8 nm and 609.1 nm (the peak wavelengths of reflection coefficients along the short and long axes of nanobrick I, respectively) with linearly polarized incidence to simulate the electric and magnetic field distribution at the cross-section of the nanobrick (as shown in Fig. 2). Vortex electric fields (shown in Fig. 2(a), (c)) and enhanced magnetic fields (Fig. 2(b), (d)) are observed inside nanobrick I, which indicate the occurrence of magnetic dipole resonance along both long and short axes of the nanobrick [18].

 

Fig. 2. (a), (b) The electric and magnetic fields of nanobrick I with y-polarized incidence at 624.8 nm. (c), (d) The electric and magnetic fields of nanobrick I with x-polarized incidence at 609.1 nm.

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3. Design of the full-space metasurface hologram

To realize the simultaneous display of two independent distinct images, we firstly designed two separate metasurfaces based on nanobrick I and II respectively (named as metasurface I and II), based on the classic G-S algorism [51]. In our design, two target images (English letters of “Wuhan University” for one image and “Information” for another) have wide extending-angles of 45° × 34° and 35° × 32°, respectively. To avoid the zero-order light overlapping with the target images, an off-axis angle of 10° is conducted in both hologram designs. Here, metasurface I is designed to work in a reflection mode. Therefore, the nanobricks I array was arranged upon LCP illumination in the reflection space, while produce nothing in the transmission space. When metasurface II is irradiated with LCP light, a totally different image can be observed in the transmission space and exert no influence on the reflection side. Finally, we extract half pixels from each metasurface and merge them into one. For the special characteristic of the Fourier holography, incompleteness of the two metasurfaces have no obvious influence on holographic image quality except for brightness. Therefore, the two target images can still be reproduced respectively in the reflection and transmission spaces on a normal incidence, as shown in Fig. 3(a).

 

Fig. 3. (a) Schematic diagram of the space multiplexing holography. (b) Nanobricks layout of the 2D periodic scheme. (c), (d) Simulated images displayed by metasurface in the 2D periodic scheme. (e) Nanobricks layout of the randomly chosen scheme. (f), (g) Simulated images displayed by metasurface in the randomly chosen scheme.

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During the process of integrating the two metasurfaces as one, two methods are tried to get desired images without distortion. In the first method (shown in Fig. 3(b)), nanobricks I and II are distributed periodically on both vertical and horizontal directions at a period of 5 unit-cells. In the simulated images (Fig. 3(c),(d)), there is not only the target images, but also periodic duplicates at lower gray levels on both horizontal and vertical directions. As a result, the images are blurred and the imaging qualities are deteriorated. According to the sampling theorem, the series of duplicates are inevitably introduced in by periodic sampling on metasurface. To eliminate images on higher orders, the periodicity should be removed. Thus, we divide the 500 × 500 unit-cells on metasuface I and II into 100 × 100 groups, each of which is composed of 5 × 5 unit-cells. Then half of the 100 × 100 groups on metasurface I are selected randomly and removed. We finally insert groups from metasurface II on the corresponding positions into metasurface I to get the designed metasurface (shown in Fig. 3(e)). The periodicity is broken obviously on this final hybrid metasurface and the simulated imaging results from metasurface based on this scheme are presented in Fig. 3(f), (g). When the metasurface is exposed to an LCP light beam, the reflected and transmitted RCP light with geometric phase can simultaneously reconstruct a “Wuhan University” and an “Information” images in two spaces respectively, which is rid of the images on higher orders.

4. Experiments and discussions

To verify our design, we fabricate the sample based on SOS material by the standard electron beam lithography (EBL). The detailed information is presented in Methods. This fabricated sample has dimensions of 170 µm × 170 µm, which is composed of unit-cells of 340 nm × 340 nm sizes. Through our elaborate design, the sample can reconstruct two different holographic images in the reflection and transmission spaces, respectively. In detail, a “Wuhan University” pattern will be displayed in the reflection space and an “Information” pattern will be observed in the transmission space. The experimental setup is illustrated in Fig. 4(a). A laser beam with linear polarization state and wavelength of 600 nm firstly passes through a quarter-wave plate (QWP) and is transformed into CP polarization state. By rotating the QWP, state of the incident light can be switched from left-circularly polarized (LCP) to right-circularly polarized (RCP). After the laser beam being modulated by the sample, images can be reconstructed on a white screen placed 0.16 meter away from the sample either in reflection or transmission space. A commercial digital camera (Nikon D5100) is used to capture the holographic images. The obtained experimental holographic images are shown in Fig. 4(b)–(g). In the reflection space, the “Wuhan University” image can be clearly observed on the upper part of the screen (as shown in Fig. 4(b)). Due to the opposite phases introduced by incidence of the opposite handedness, the image under RCP illumination is at the conjugate place compared to that under LCP illumination (shown in Fig. 4(c)). After reflection by the sample, the LP light, which can be decomposed into LCP part and RCP part, can project a couple of centrosymmetric “Wuhan University” images on the screen as exhibits in Fig. 4(d). Similarly, the transmitted cross-polarized light carrying the modulated phase will reconstruct “Information” image on the screen. The images under the illumination of three distinct polarization state are shown in Fig. 4(e)–(g). In the transmission space, the crosstalk from the “Wuhan University” image is negligible (as shown in Fig. 4(e)–(g)). However, after the beam penetrating into the sample and arriving at the surface between sapphire and the air, part (nearly 4%) of the transmitted cross-polarized light will be reflected back into the reflection space and project a crosstalk “Information” image on the screen, as shown in Fig. 4(b)–(d). This crosstalk can be alleviated by more precise nanofabrication of metasurface sample and coating antireflection film at the sample surface.

 

Fig. 4. (a) Experimental setup of the metasurface for holographic display. The quarter-wave plate (QWP) is used to generate circularly polarized incident light. (b)–(d) Experimental images in reflection space under illumination with left-circular polarization (LCP), right-circular polarization (RCP) and linear polarization (LP) respectively. (e)–(g) Experimental images in transmission space under illumination with left-circular polarization (LCP), right-circular polarization (RCP) and linear polarization (LP) respectively. The working wavelength is 600 nm.

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To investigate the broadband response of our fabricated sample, we perform a further experiment. We alter the wavelength of the laser source from 580 nm to 620 nm by a step of 20 nm. By rotating the QWP, the linearly-polarized laser beam is changed into a left-polarized one. The photographed holographic images are presented in Fig. 5. As the wavelength changes from 580 nm to 620 nm, we can see a slight growth in the size of the images, which accords with the diffraction theory. However, variation of the light wavelength has no impact on geometry phase. Thus, the sample can always produce target images with high fidelity in both the reflection and transmission spaces (shown in Fig. 5(a)–(c) and Fig. 5(d)–(f) respectively).

 

Fig. 5. (a)–(c) Reflected holographic images under LCP illumination with wavelength ranging from 580 nm to 620 nm by a step of 20 nm. (d)–(f) Holographic images reconstructed in the transmission space when the sample is irradiated by LCP light with wavelength varying from 580 nm to 620 nm.

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The hologram in our design is composed of nanobricks with continuous orientation angles, which is capable of elaborately manipulating the geometric phase of the output light. Therefore, although only two simple images were reconstructed in our experiment, the reconstruction of complex images can also be accomplished. Based on all the experimental results given above, we can find that the fundamental application of our designed metasurface is full-space holographic image displays, since abundant information can be reconstructed from a chip with merely 170 µm × 170 µm dimensions. By enlarging the diffraction angles in two spaces, the full-space holography can be fulfilled. Many other phase-modulated optical elements such as metalens with different focal lengths in reflection and transmission spaces can also be implemented by our approach. With the virtues such as ultracompactness and full-space geometric phase modulation, our proposed metasurface can find its markets in optical sensing, image displays, optical storages and many other potential applications.

5. Conclusion

In a sum, we proposed a full-space holography using a single-layer metasurface based on geometric phase modulation. By assigning two types of dielectric nanobricks with the same height in a metasurface, the incident CP light will be either reflected or transmitted simultaneously, with independent geometric-phase modulation. The key point of designing the trans-reflective meta-component is that, if magnetic resonance is involved or not, i.e., one type of nanobrick would reflect most of incident light enabled with magnetic resonance while another one would transmit it without resonance involved. To eliminate the duplicate images on higher diffraction orders, we adopt the randomly chosen scheme to form a metasurface as a combination of two types of nanobricks. The experimental results have verified our design and two independent holographic images appear in the reflection and transmission spaces simultaneously. By virtue of ultracompactness, independent full-space holography and broadband working window, our proposed trans-reflective meta-component possesses vast potential in full-field-of-view optical sensing, high-density information storage, full-space holography and high-end image displays.

6. Methods

Using a standard EBL process, our metasurface sample was fabricated with SOS material. For cleaning, the SOS material was firstly immersed into the acetone, ethyl alcohol and deionized water (DI water) by sequence. Then the material was dried on a hot plate. Secondly, the SOS material was spinning coated with a conductive polymer mask. Then nanobrick structures were patterned on the mask using EBL (Raith 150, 30kV). Afterwards, the superfluous polymer part was removed with DI water. An etch mask, which is a 30 nm chromium film, was deposited on the sample by the thermal evaporator. For immersion, the fabricated sample was dipped into 75 °C hot acetone. Then the sample was cleaned with ultrasonic waves. In the last step, reactive ion etching (RIE) was utilized to remove the silicon- and chromium-free parts. As a result, we got a sapphire substrate with silicon nanobrick arrays on it. The SEM image of a part of the fabricated sample was shown in Fig. 6. The refractive index of silicon and sapphire used in our design are shown in Fig. 7.

 

Fig. 6. The SEM image of a part of the fabricated sample. Scale bar of 1 µm is denoted.

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Appendix

Refractive index of silicon and sapphire is shown (Fig. 7).

 

Fig. 7. Refractive index (the real part n and the imaginary part k) of silicon and sapphire.

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Funding

National Natural Science Foundation of China (91950110, 11774273, 11904267); National Postdoctoral Program for Innovative Talents (BX20180221); China Postdoctoral Science Foundation (2019M652688); Natural Science Foundation of Jiangsu Province (BK20190211); Open Fund of the Key Laboratory for Metallurgical Equipment and Control Technology of Ministry of Education in Wuhan University of Science and Technology (MECOF2020A01).

Disclosures

The authors declare no conflicts of interest.

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