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Abstract
In this work, we propose dynamic holography based on metasurfaces combining spatial channel multiplexing and polarization multiplexing. In this design, spatial channels can provide up to 3N holographic frames, which not only increase the possibility of dynamic control but also increase the privacy of the holographic display. This design is also sensitive to polarization, so it further expands the spatial channel capacity. For the left and right circular polarization incident light, there are different dynamic pixel schemes. Therefore, this approach holds promise in the holographic display, optical storage, optics communication, optical encryption, and information processing.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Holographic display which can generate arbitrary wavefronts is regarded as the ultimate 3D visualization technology [1]. Since computer-generated holography (CGH) was proposed by Brown and Lohman in 1966 [2], virtual object reconstruction and dynamic display have been able to be implemented. With the assistance of digital devices, such as the spatial light modulators (SLM), and the digital micro-mirror devices (DMD), the phase distribution varied with time can be generated in real-time to achieve the dynamic holographic display [3]. However, CGH based on SLM or DMD is usually accompanied by some challenges such as twin imaging, small field of view (FOV), and unwanted multiple orders of diffraction [4]. The challenges for SLM-based and DMD-based holographic displays are caused by their micron-level pixels. For example, the FOV of the holographic image for the SLM with a pixel period of 8 μm is limited in a small range of ≈5° for visible light [5]. Although the FOV can be expanded through some optimization algorithms, there will be a lot of high-order diffraction and noise, when the FOV exceeds the value of (sin-1(λ/2P)), resulting in poor image quality and low efficiency. Fortunately, as a novel encoding medium, the metasurface with subwavelength structures can solve these challenges and can realize 180° FOV without high-level diffractions in principle.
As a planar branch of metamaterial, metasurfaces retain unique electromagnetic properties of traditional metamaterials [6]. They have great potential in various fields such as lightweight planar imaging [7], electromagnetic absorption, virtual shaping [8], and large field of view holography [9]. Holography based on metasurface(meta-holography) is currently considered as one of the most significant discussions in 3D visualization technology [10], owing to its many advantages including high resolution, a large FOV, and the elimination of high orders of diffraction. However, once metasurfaces are fabricated, most of them will remain static and non-tunable. Hence, the realization of the dynamic hologram based on metasurface is a great challenge nowadays.
There are two distinct ways to achieve dynamic hologram by metasurfaces. One is using tunable metasurface and another is using static multiplexing metasurfaces. Firstly, the design of tunable or dynamic metasurfaces is implemented via changing the external conditions to modulate the physicochemical properties of the metasurface itself, such as mechanical strain [11], chemical transformation [12], phase-change-materials [13], rewriting graphene oxide metasurfaces [14], applying voltage [15], changing surrounding medium [16] and so on. Secondly, for static multiplexing metasurfaces, which have different effects on different incident light properties, the realization of dynamic holography relies on the diversity of incident light properties. Many multiplexing methods have been studied in recent researches, including wavelength [17], polarization [18,19], incident angle [20,21], orbital angular momentum (OAM) [22], spatial channel multiplexing [23], and so on. Most of these methods can only provide a few frames, which means that the dynamic display is almost limited to the appearance and disappearance of holographic images. Although some methods mentioned above can provide more frames, the large frame number and the high frame rate are incompatible. It is noted that a large frame number (228) and a high frame rate (maximum frame rate of 9523 fps) can be provided by the design of spatial channel meta-hologram (SCMH) with 28 spatial channels proposed by Gao [23]. The proposed spatial multiplexing metasurfaces can effectively combine the advantages of high-speed switching of DMD and large FOV of metasurfaces, achieving high-speed dynamic holography. As for the SCMH, each channel corresponds to the part of preset graphs (also called subgraphs), and different combinations of spatial channels determine different displays respectively. The dynamic display is achieved by switching the channel combination, and its frame refreshes with the combination change. There are two effects on each channel, so the SCMH with N spatial channels brings the total frame number to 2N based on the traditional spatial channel multiplexing method, and there is room for further improvement.
In this paper, we design a polarization-dependent spatial channel meta-hologram (PSCMH) based on metasurfaces that use composite phase encoding to improve channel capacity and energy utilization. The propagation phase and the geometric phase are adopted to realize the polarization-independent spatial channel meta-hologram. The corresponding phase is encoded by the all-dielectric metasurface structure which consists of a series of high aspect ratio titanium dioxide (TiO2) nanopillars located on quartz (SiO2) substrate with different orientations and sizes. The spatial channel has different effects on the different polarization of incident lights, hence there are 3 different display states for each spatial channel, and the frame number of PSCMH with N spatial channel is up to 3N. Compared to the reported spatial channel meta-holograms, the spatial channel capacity of this design is improved significantly by the composite phase encoding method mentioned above. Meanwhile, we adopt a unique dynamic pixel design scheme for different circular polarization incidents, which greatly expands the scope of the dynamic display and enhances the security of information. The dynamic hologram structure we designed also has a certain potential in the field of optical information encryption [24], optical storage [25], optics communication [26], and information processing [27].
2. Theoretical analysis
2.1 Physical mechanism of the PSCMH
In the PSCMH design shown in Fig. 1(a), the preset image ‘OE’ is displayed by selecting a specific structural light field. Different combinations of subgraphs can be realized via modulating different polarization incident lights and switching the spatial channels that are irradiated at different times. The corresponding holographic display will change with time, and the designed metasurface holographic device is sensitive to the polarization of incident lights. Each spatial channel has different effects on the polarization of incident lights, as depicted in Fig. 1(b), thus, for the same spatial channel combination, different circularly polarized incident lights will have diverse image displays. Figure 1(c) presents the change curve of the frames number with spatial channel number N for different designs, and compared to the SCMH, the frame number of PSCMH is improved significantly when it has the same number of spatial channels as SCMH.
Fig. 1. The schematic diagram of polarization-dependent dynamic spatial channel meta-hologram. (a) The scheme of the polarization-dependent spatial channel meta-hologram design. (b) The different effects of a single spatial channel on the incident light. (c) The change curve of the frame number along with spatial channel number N for different designs.
The overall display of the holographic image is formed by the combination of several subgraphs, and the corresponding subgraphs have two completely different designs for two circularly polarized incidents. Every basic dynamic pixel is controlled by a superchannel composed of i channels, and the entire image plane contains m×n dynamic pixel arrays. The final holographic display is decided by m×n×i channels which are illuminated by a structured light field. As for the metasurface, the modulation of the amplitude is almost uniform, so its amplitude is set as 1 after normalization. The modulated complex amplitude by designed metasurface is depicted as follows [23]:
It introduces the physical mechanism of the PSCMH, where + and – denote LCP and RCP, respectively. U refers to the complex amplitude after metasurfaces’ modulation at time t. φ± is the phase map of the static metasurface, and it’s given by the formula as follows:
In the process of designing the subgraphs corresponding to the spatial channels, it should be taken into consideration that not only designing two sets of subgraphs for different polarized incident lights but also the reusability of the display elements. Given the control precision and the number of spatial channels, each dynamic pixel is controlled by 8 spatial channels, which means i=8.
2.2 Design of dynamic pixel
All reconstructed images will overlap together if all spatial channels are irritated at the same time, as depicted in Fig. 2(a). The displayed images of the single dynamic pixel designed for LCP and RCP look completely different, but from the perspective of the pixel array, the two groups’ results of dynamic image planes look very similar as a whole, just with a certain displacement. For different circularly polarized incident lights, two completely independent sets of holographic display units can be designed, and it is necessary to construct a dynamic pixel unit in combination with the design principle of the spatial multiplexing metasurface holography. The dynamic pixel unit is the basis for realizing the dynamic holographic display. To make the final holographic display diversified and practical, two requirements for the pixel unit are proposed here. First, the pixel unit needs to produce certain changes. Second, these changes need to be reused and combined with other dynamic pixel units. Based on the two requirements, and considering that the pixel design should be the most expansive square, we got inspiration from the copybook. Each square of the copybook is divided into several parts to standardize the writing of Chinese characters. These divided lines happen to connect several key points (including the four corner points, the midpoint of the four sides, and the center point) of the grid and are related to other grids. Therefore, based on these considerations, we design two groups of different dynamic pixels for the left and right circular polarization, as shown in Fig. 2(b).
Fig. 2. The schematic diagram of a polarization-dependent dynamic pixel. (a) Schematic illustration of combining display of dynamic pixels. The entire image is composed of several dynamic pixels. (b) Spatial channel multiplexing dynamic pixel design. The reconstructed images of different spatial channels are subgraphs of a pixel.
It presents the two sets of spatial channel subgraph designs. A superchannel composed of 8 spatial channels controls a dynamic pixel of the preset frame, and a high frame number depends on the various combinations of dynamic pixels. For a single pixel, a part of it is controlled by a spatial channel, and the tunability is achieved by switching spatial channels. The appropriate lines connecting these points are selected to be used as a subgraph of dynamic pixels. Due to the expansion of dynamic pixels, these controllable line types can be the basis for constructing complex displays. Whether the dynamic pixel corresponds to LCP or RCP, each dynamic pixel is simultaneously controlled by eight spatial channels and very similar to other dynamic pixels, except that the corresponding position on the overall image plane is different. Hence, by selecting the appropriate spatial channel, the final image plane composed of several dynamic pixels can freely display various characters, including Arabic numerals 0-9, uppercase and lowercase English characters A-Z (a-z), and even some Chinese characters. Taking into account the polarization, there are 38 different combinations for each dynamic pixel to be presented via switching the corresponding spatial channel. The dynamic combinations of different pixels can make the overall image plane change exponentially and the total number of holographic frames of N spatial channels can reach 3N.
2.2 Composite phase encoding by the metasurface
Because a circularly polarized incident light is usually written as [1,$i\sigma$]T, the resulting output light field can be expressed as [29]:
Meanwhile, the propagation phase is hardly affected by the polarization of the incident light, which means it can be combined flexibly with the PB phase, and the two phase gradients are independent and do not interfere with each other [30]. In this case, two different phase distributions are designed for two circular polarization incident lights to achieve a preset holographic display. The rotation angle θ and the propagation phase φ can be written as follows:
φ and θ are in the range of 0-2π by taking the 2π modulus of the results. As the phase quantization levels increase, the diffraction efficiency for the first diffracted order of the device will increase. For 2, 4, 8, and 16 phase quantization levels, the diffraction efficiency will be 40.5%, 81.1%, 95.0%, and 98.7%, respectively [31]. We designed eight unit cells under 632.8 nm to discretize the polarization-independent phase into eight-level at intervals of π/4. These nanopillars with specific rotation angles and sizes are arranged according to a preset phase to achieve the corresponding holographic display.3. Simulations and discussions
3.1 Unit cell
We propose an all-dielectric metasurface to encode the holographic phase. The metasurface is composed of a series of unit cells with a lattice constant P. It should be noticed that high-aspect dielectric TiO2 nanopillars with different rotation angles θ and geometries (length L and width W) but the same height H, are located in the center of SiO2 substrate. Figure 3(a) shows the three-dimensional structure of the unit structure, and in conjunction with Fig. 3(b), it shows the height H, width W, length L, and the rotation angle θ of the structure. Both the height of nanopillars is set to 700 nm and the period P is 440 nm. Width W and length L of unit cells from 1 to 4 are depicted as follows: L = 360 nm, 355 nm, 321 nm, 301 nm; W=155 nm, 135 nm, 120 nm, 100 nm. The unit cells from 5-8 are obtained by swapping the length and width of unit cells from 1-4. Simulations are obtained by using the finite element method (FEM) in CST microwave studio. The materials of the nanopillars and substrate are TiO2 and SiO2, and the refractive indexes are 2.43 and 1.46, respectively.
Fig. 3. Design of the unit structure and the deflector based on the unit. (a) The scheme of the metasurface unit cell. (b) The top view of the unit cell. The nanopillar is characterized by several parameters, such as height H, width W, length L, rotation angle θ, and the period P. (c) The simulated transmission characteristics of eight unit cells at the wavelength of 632.8 nm. It shows the cross-polarized and co-polarized transmissivities of the eight unit cells, as well as the propagation phase. (d) The schematic of the polarization-dependent deflector. (e) Far-field intensity distributions of the designed deflector under the illumination of LCP and RCP incident light. (f, g) The distribution of the real part (Ex) on the xoz plane for LCP and RCP light excitation.
The total phase gradient is composed of the polarization-independent propagation phase and polarization-dependent geometric phase, which are produced by the rotation angle and the size of the nanopillars, respectively. We have carefully designed 8 unit cells with the working wavelength of 632.8 nm, and the polarization-independent phase increment between adjacent nanopillars is π/4. The simulation results including simulated polarization-independent phases, and the cross-polarized and co-polarized transmissivities of eight unit cells are shown in Fig. 3(c). The performance of the cross-polarization results is pretty great, and the average conversion efficiency for λ=632.8 nm is ∼89.4%.
The sub-wavelength metasurface based on the composite phase produces different responses to different polarization incident light. First of all, to validate this method, we design a deflector device independent for the LCP and RCP incident light based on the generalized Snell principle. The anomalous refraction angle is written as follows [32]:
where Px is the period of metasurfaces in x-direction and λ is the wavelength of the incident light. The deflection angles are set as -20° and 10° for the LCP and RCP incident light. The diagram of the deflector is illustrated in Fig. 3(d). Its intensity distribution of the far-field is shown in Fig. 3(e), and The LCP incidence is almost completely transmitted with a refraction angle of ∼ 20.3°, which of the RCP incidence is ∼ 9.8°. Figure 3(f) and (g) show the electric field distributions of the x-components and y-components when the metasurface device is excited by LCP and RCP incident light, respectively. The simulated phase distribution of LCP and RCP incident light is in good agreement with the theoretical results. The deflector based on the unit works well as designed, which proves the composite phase encoding method and design of the unit structure. The catenary structure can be adopted to solve the problem of the limited phase sampling of the discrete metasurfaces. Our previous research found that the catenary structure can provide continuous phase manipulation [29,33]. Through the composite manipulation of the propagation phase and geometric phase in the dielectric catenary structure, the average diffraction efficiency in a wide spectrum and angular band is higher than 90% and diffraction-limited imaging with 178° FOV has been realized by a sing catenary-based metasurface [34]. Besides, the quasi-continuous structure is also used to construct holograms, which can effectively improve the diffraction efficiency under a large field of view [35].”3.2 Full-wave simulations
To verify the effectiveness of the design of PSCMH, simulated experiments were performed on a small image plane consisted of 2×2 dynamic pixel arrays, and the number of the dynamic pixel can be expended according to requirements. The phase distributions of the 2×2 image planes for LCP and RCP incident light are calculated according to formula (2) in the previous chapter. As a result, the preset phase information is encoded into the arrangement of the metasurface unit structure. Increasing the number of structures can improve the quality of the holographic image, but requires more calculation time. In the simulation process, each spatial channel is finally coded by 201× 201 unit structure arrays to calculate the full-mode simulation efficiency and imaging resolution. Simulations are conducted via the finite integral method (FIM) in CST microwave studio. We select a single spatial channel for simulation verification, and its holographic simulation result can also be obtained. To simplify the calculation, the holographic display results in Fraunhofer far-field are calculated by MATLAB.
As shown in Fig. 4, full-wave simulation verification results perfectly agree with the preset dynamic pixel design. This means that using LCP or RCP incident light alone can realize the similar dynamic display content, but when they are used at the same time, the resolution of the dynamic display can be improved. Although the dynamic pixel units corresponding to LCP and RCP look completely different, when they are periodically expanded, they are somewhat similar on the whole but with a certain displacement. Therefore, under certain conditions, the LCP and RCP incident light can display the same pattern by illuminating different spatial channels. We reconstruct the Arabic numeral ‘8’, under LCP and RCP incident alone, respectively, and the corresponding structured light field and selected spatial channels are completely different. Also, by exchanging the combination of the incident light polarization and the spatial channel, it will obtain some meaningless display results, as shown in Fig. 4(b) and (d). The polarization of incident light provides an additional degree of freedom for the optical information. It means that incident light polarization and the spatial channel can double-encrypt the display results, which improves the security of the holographic display. Figure 4(i) and (k) show the holographic images of the Arabic numeral ‘8’ displayed under different light illuminations shown in Fig. 4(a) and (c). At this time, though only a half of dynamic pixels are used under the RCP illumination, it can still be seen that a reasonable arrangement of holographic patterns makes more effective use of spatial channels. The 2*2 image plane can also realize the lowercase display of any 26 English letters. Therefore, when the dynamic pixel is further expanded, it can display more complex dynamic displays.
Fig. 4. Theoretical and simulation results of dynamic polarization-dependent meta-hologram. (a-d) spatial channel under the specially structured laser beam (purple and green correspond to LCP and RCP, respectively). (e-h) Theoretical far-field diffraction results of preset phase distribution. (i-l) Simulation far-field diffraction results of encoding metasurface. Among them, (a) presents the selection status of the spatial channels with the LCP incident when the far-field diffraction result finally displayed as the Arabic numeral 8, and (e, i) present the theoretical and simulation result, respectively. In contrast, (c, g, k) represent the corresponding result under RCP irradiation. (b) and (d) are based on (a) and (c), respectively, changing the incident light without changing the selection of spatial channel. Scale bars, 0.1 kx/k0
4. Conclusion
In summary, we propose a new all-dielectric metasurface dynamic holographic design scheme based on the composite phase control. Through an array of TiO2 nanopillars located on SiO2 substrate with spatially varied sizes and orientations, the geometric phase and propagation phase are integrated, so the metasurface based on this method is sensitive to the polarization of the incident light, which further expands the spatial channel capacity. Meanwhile, a group of special dynamic pixel design schemes is proposed, and they are different and complementary for LCP and RCP. By switching the spatial channel combination in real-time, the combination of dynamic pixels can be realized, which can achieve a continuous and diverse dynamic holographic display. The image plane composed of several dynamic pixels can freely display various results including but not limited to English characters, Arabic numerals, and Chinese characters. The number of dynamic pixels can be freely expanded as required to satisfy more complex display scenarios. The various combinations of spatial channels and the polarization of the incident light not only increase the possibility of dynamic but also the privacy of the holographic display, making this design also apply to the field of optical information encryption [24], optical storage [25], optics communication [26], and information processing [27].
Funding
National Natural Science Foundation of China (61822511, 61875253); China Postdoctoral Science Foundation (2020M680153).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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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