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Abstract
We propose and experimentally demonstrate a polarization-selective waveguide hologram at optical wavelengths, based on an all-dielectric metamaterial multilayer system. We show that two spatially separated or overlapped holographic images can be produced with two orthogonally polarized beams, incorporated into a binary computer generated hologram (CGH). These two images can be combined into a single 3D stereoscopic image observable using linearly or circularly polarized glasses. The two polarized beams can also be utilized to construct radially and azimuthally polarized “vortex” beams. The fundamental and first higher-order TM and TE modes of an optical waveguide are used to guide the two polarization states with distinct propagation constants. The two guided waves act as spatially distinct reference waves such that the integrated, on-chip hologram can distinguish the two and provide two independent images corresponding to the two polarizations. Polarization selective waveguide holograms can be used in a diverse set of applications, from chip-scale displays and augmented reality (AR) to optical trapping.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The ongoing development of nanofabrication technology has made polarization-sensitive holograms increasingly attractive in applications such as information security, high-density data storage, optical communication, material science, imaging and display technologies. Examples include polarization-controlled dual image holography using gold cross nanoantennas [1] or silver nanorods [2], and polarization-encoded color images based on silicon nanoblocks [3]. In these instances, the holograms are encoded by several sets of polarization-sensitive profiles instead of just phase or amplitude information. However, because it is hard to find materials that have low absorption at optical wavelengths, most of the reported work on polarization-sensitive holography is based on metasurfaces (two-dimensional metamaterials) in which the optical field interacts with the material only within an ultrathin layer so as to reduce the propagation loss. These holographic metasurfaces thus work mainly in either reflection or transmission mode and are not generally suitable for integration into on-chip photonic devices. In addition, these metasurfaces consist of assemblies of sub-wavelength nanoscatterers that usually require demanding hologram designs and complicated fabrication processes [4]. Furthermore, if metallic and plasmonic metamaterials are used—in which surface plasmon resonances are excited on the metal inclusions—the absorption of the light in the metal structure at visible wavelengths can be substantial, limiting the efficiency of on-chip devices. By contrast, the use of some specific type of dielectrics—which are capable of producing high-efficiency, low-loss devices—for polarization-controlled or polarization-selective waveguide holograms has remained largely unexplored.
Among the applications of polarization selective optics, three-dimensional (3D) holography is one of the more intriguing, in which polarization plays a central role in the projection of three-dimensional images. In general, there are several ways to present stereoscopic 3D holographic images. One method is to reconstruct images at different depth planes to create an “exact” 3D object, using a ping-pong algorithm during the hologram generation process [5]. Initial investigations into this approach formed images from a collection of point sources (a “star map”)—for example, forming a spiral helix pattern—in which holographic images need to be captured on various planes along the longitudinal axis [6,7]. Because this approach involves sophisticated image collection and data post-processing, it is hard to develop practical applications. Alternatively, from a more economical point of view and considering the way the human observer perceives optical depth, the multiview stereoscopic approach is appealing [8]. In a recent study on 3D full-color holographic images based on graphene oxides, the left and right parts of a 3D object could be independently reconstructed at the vertical and horizontal polarization angles of a polarization analyzer [9]. The two images could also be viewed simultaneously at the 45$^{\circ }$ position of the analyzer. In another example, a deformable mirror and strongly scattering holographic diffusers were used to realize a dynamic 3D holographic display [10]. Yet, despite the progress in the realization of various 3D holograms, no 3D waveguide holography work has been reported.
Another application related to polarization-sensitive optics is vortex holography, in which a vortex beam is formed using a combination of two polarized holograms [11–13]. Within this emerging research area, studies on cylindrical vector beams have become one of the more focused topics [14–16]. In contrast to the spatially homogeneous polarization states of a plane wave (or planar beam)—such as linear, circular or elliptical—cylindrical vector beams, including radial and azimuthal, have distinct and spatially variant polarization patterns. Radial or azimuthal vortex beams have been investigated in applications such as laser-driven particle accelerators, detectors, high-power vacuum electron devices, space science, electron focusing, and optical trapping [17–24]. These vectorial vortex beams may thus have important applications in such fields as lithography, optical data storage, quantum information processing, and nonlinear optics. Traditionally, radial or azimuthal polarization states can be obtained actively in a laser resonator using conical elements [25–27], or passively using a resonator based on an interferometer or mode-forming holographic elements [28,29]. On the other hand, a waveguide metamaterial holographic structure can provide a more compact device from which radial or azimuthal vortex beams are generated.
In this work we propose and experimentally demonstrate polarization-selective metamaterial waveguide holograms utilizing a multilayer, all-dielectric waveguide system, building on our previous multicolor waveguide holography study [30]. Figure 1 schematically illustrates the 3D image case of the proposed configuration, which can provide chip-scale, polarization-sensitive, waveguide holograms producing spatially separated or overlapped images, stereoscopic 3D images, or radial and azimuthal vortex beams. In the context of 3D holography, illuminating these holograms with two orthogonal polarizations of light results in the formation of two distinct images that can be selected by rotating a polarization analyzer, or combined into a single image and viewed as a stereoscopic 3D image through a pair of polarized glasses.
Fig. 1. Illustration of polarization-selective waveguide holography (artistic rendering). Two different polarization beams (TE and TM) illuminate the grating coupler at different angles, propagate in the waveguide, and then are decoupled out of the surface through a computer-generated hologram(CGH), forming three-dimensional (3D) images.
The construction of the waveguide hologram system is similar to that reported in our previous study [30], which consists of a guiding layer of an electron-beam photoresist, a buffer layer of silicon dioxide, and a support substrate of silicon. In this previous work, a grating coupler and a hologram decoupler are fabricated on a relatively thin surface-guiding layer. In the present work, a different design approach is used that encodes the dual polarizations into a computer-generated hologram for which a TE (transverse electric) and a TM (transverse magnetic) mode serve as the guided reference waves, requiring a much thicker waveguide region that supports higher order modes.
It should be noted that the waveguide hologram more closely resembles a volume hologram than a surface hologram in two key aspects. First, as the reference wave propagates it is perturbed by the hologram, unlike the situation for a surface hologram in reflection or transmission mode, in which the incident wave illuminates all portions of the device at once and is minimally distorted by the hologram. Second, the waveguide hologram can distinguish among reference waveguide modes having different propagation constants, which have spatially distinct field patterns. This ability to select and operate on waves of different propagation constants translates into a multiplexing capability—a feature associated with volume holograms, in which many distinct holograms can be encoded, each unique to a certain reference wave incident on the structure at a specific angle and wavelength. While the multiplexing feature of a volume hologram is advantageous, the perturbation of the reference wave makes the design of a volume hologram challenging except in the weakly coupled limit, where the reference wave is assumed unperturbed. Thus, to facilitate the experiment presented here, it is assumed that the waveguide hologram does not perturb the reference waves. Because the efficiency of the designed hologram is relatively low ($<\;1\%$), this assumption proves to be reasonable. Higher efficiency waveguide holograms can be designed following a more elaborate iterative method based on inverse scattering formulation [31].
2. Theory and results
2.1 Mode analysis in waveguide
The underlying operation of the waveguide hologram is illustrated in Fig. 1. Two beams of light are incident on an input grating coupler, which couples the two beams to two waveguide modes that propagate in-plane down the guiding layer of the structure. The incident beams have the same wavelength, but have orthogonal polarization states (TE and TM). The waveguide modes subsequently excite the hologram, which serves both to couple the light out of the structure and to form two images, maintaining the distinct orthogonal polarization states of the original beams. The waveguide layer, as well as the input grating coupler and the computer generated hologram (CGH) decoupler, are formed in a layer of commonly used electron beam resist (ZEP), deposited on a substrate of $\textrm {SiO}_2$.
In our previous work on a multicolor waveguide hologram [30], the waveguide structure was fabricated using an ultrathin (300 nm) layer of ZEP, which was measured to have extremely low absorption at optical wavelengths and therefore suitable as a waveguide medium. In that study, three incident beams at different wavelengths (red, green, blue) were coupled into the waveguide layer to three waveguide modes. Those waveguide modes corresponding to the three different reference waves had sufficiently distinct propagation constants such that they could be easily distinguished by the hologram. Since the polarization state was not of concern, the polarization of the guided modes was not considered and only the fundamental modes were used.
In the present configuration, where the two incident beams have the same wavelength, one of the incident beams must be coupled to a TE waveguide mode and the other to a TM waveguide mode. This is almost impossible in the ultrathin waveguide structure used previously because the fundamental TE and TM modes have nearly the same propagation constants and cannot be distinguished by the hologram. An approach to circumvent this difficulty is to make use of the fundamental and one of first higher-order TE or TM modes, which have suitably distinct propagation constants. In the ultrathin ZEP layer case, the higher-order modes are not well confined in the guiding layer and thus become too lossy or weak to be useful. Thus we increase the thickness of the ZEP layer for the polarization sensitive hologram, introducing higher-order confined modes and enabling a second TE or TM mode to be guided by the ZEP layer, in addition to the fundamental modes.
An example of the design considerations can be found in Fig. 2, which shows the field profiles and propagation constants for the fundamental and first higher-order TE and TM modes. We take a green laser ($\lambda$ = 532 nm) as the light source and analyze that the 800 nm is a proper thickness for the guiding ZEP layer. The corresponding field profiles of the TE and TM modes are shown in Fig. 2(a), which reveal that the fields are predominantly confined in the guiding ZEP layer and exponentially decay into the substrate $\textrm {SiO}_2$ layer. Figure 2(b) shows the propagation constants for the fundamental and first higher-order TE and TM modes in this waveguide. If a combination is chosen of the fundamental and the first higher-order modes (e.g. TE1 and TM0, or TE0 and TM1), the difference in the propagation constants of the modes is large enough that the two waves can be distinguished by the hologram. As the two modes propagate out of phase over a distance of less than 5 $\mu$m, for waves propagating along a hologram spanning 300 $\mu$m, the total distance corresponds to about 60 dephasing lengths, ensuring that about 60 unique features or pixels may be encoded along the hologram in the direction of propagation.
Fig. 2. Mode profiles and propagation constants of the fundamental and first higher-order TE and TM modes in a waveguide holography system with a green light source and a thickness of 800 nm ZEP.
2.2 Grating and hologram structure design
We choose the TE1 and TM0 modes for the design of the grating coupler and the computer-generated hologram decoupler. As the propagation constants for the TE1 and TM0 modes are different in the guiding layer, the corresponding incident angles of the TE and TM beams entering the grating coupler are correspondingly different. For a system with a green light source and an 800 nm ZEP layer, the incident angle for the TE1 mode is around −24.6$^{\circ }$ and for TM0 mode is around −21$^{\circ }$ for a grating with a period of 280 nm. In the design of the CGHs that are to be viewed as spatially separated images, we continue using the same outgoing angular range in x direction as in the multicolor holography case to store more image information in the hologram plane, which is 10$^{\circ }$ for both polarizations. In the case where the images are to overlap (for stereoscopic images or vortex beams), since the images diffracted from the other polarization would show up and be close to the desired images, the outgoing angle in the x direction is adjusted to lie within a smaller range (e.g. −45 $^{\circ }$ to −40 $^{\circ }$) to obtain a bigger divergence angle so as to avoid image mixture. A schematic diagram for a polarization-selective waveguide holography system is presented in Fig. 3 with all the sign and symbol definitions inherited from the previous study [30].
Fig. 3. Polarization-selective waveguide holography with a green light source. (a). Angle information at grating coupler. (b). Situation in the case that the incident beams illuminate the hologram directly. (c). Outgoing angle information shown near the hologram. (d). Polarization-selective waveguide holography system illustration. The local coordinate systems ($LCS_1$ and $LCS_2$) and icons of TE and TM indicate the polarization directions in the characterization process.
2.3 Sample fabrication
As described in the multicolor holography study, the samples with hologram sizes of 300 $\mu m$ $\times$ 300 $\mu m$( or 450 $\mu m$ $\times$ 450$\mu m$) are fabricated using a relatively simple nanofabrication process. First, a thick layer (e.g. 2 $\mu m$) of silicon dioxide ($\textrm {SiO}_2$) is deposited on a clean, 4-inch silicon wafer through PECVD (plasma enhanced chemical vapor deposition, Advanced Vacuum Vision 310) at $250^\circ$C. Then, a relatively thin layer (800 nm) of electron beam resist of ZEP (ZEP-520A, ZEON Corporation, Japan) is formed on the surface of a small piece of the $\textrm {SiO}_2$ sample by spin-coating and heating. The designed patterns of gratings and the polarization-selective binary computer-generated hologram are then transferred to the ZEP metasurface by EBL (Electron Beam Lithography, Elionix ELS-7500 EX). Note that here ZEP is not used as the EBL mask but as the main system structure after partial development. The structural details of the fabricated gratings and binary holograms are checked by SEM (Scanning Electron Microscope, FEI XL30 SEM-FEG) and AFM (Atomic Force Microscope, Digital Instruments Dimension 3100). One SEM image showing the structure details in plane with the smallest feature size of 100 nm and one AFM image measuring the depth of the etched hologram with the etched depth of 60 nm are shown in Fig. 4(a) and 4(b).
Fig. 4. Optical characterization setup for polarization-selective waveguide holography in case of spatially separated and overlapped images. (a). One SEM image is used to show the structure details of a fabricated hologram with 100 nm as the finest feature size. (b). One AFM image illustrates the depth of the etched hologram structure. (c). The optical setup is used to characterize the fabricated samples. Note that the incident angles for TE and TM modes are different. Various reconstructed images could be shown under different polarization directions of the analyzer (P1), as labelled with red arrows.
2.4 Optical characterization
The optical measurement setup depicted in Fig. 4(c) is used to characterize the fabricated polarization-selective waveguide hologram samples in the case of spatially separated and overlapped images. A polarization beamsplitter separates the original light source into TE and TM polarized beams. Two groups of lenses with focal lengths of 25 mm (L1 and L3) and 50 mm (L2 and L4) are used to adjust the beam sizes. Unlike other studies of metasurface polarization-sensitive images in which a polarization analyzer can be placed either before or after the sample since the incident angles for the fundamental TE and TM modes are the same [1–3], in this study the analyzer (P1) is placed after the sample to avoid any possible light distortion for that the incident angles for the TE and TM modes are different. Here, the hologram sample is mounted on a rotation stage and the incident angle can be easily adjusted for the TE beam. A reflective mirror is used to adjust the incident angle for the TM mode. When the polarized beams illuminate the grating coupler at the designed angles, the coupled waves propagate in the waveguide and are subsequently decoupled out of the waveguide through the hologram, producing the desired images in the expected outgoing angular range. As the linear polarization analyzer is rotated into the TE (vertical, y-polarized) direction, the corresponding designed TE1 image appears, and similarly for the TM direction (horizontal, x-polarized) the designed TM0 image is observed. This optical setup works for the cases of both spatially separated images and overlapped holographic images. The generated image can then be projected onto a screen to be observed by eye directly, or captured by a digital camera through a collector lens (L5) with the focal length of 200 mm.
2.5 Spatially separated images waveguide holography
By leveraging the two orthogonal polarizations of light, two holograms can be simultaneously encoded into the CGH. Using the designed structure and characterization system, two different holographic images are obtained by rotating the analyzer to different polarization directions. As an example, we investigate resolving two spatially separated images from a fabricated hologram. Figure 5 shows that the theoretical designs and corresponding experimentally measurement results have a very good agreement(see real-time experimental video of Visualization 1).
Fig. 5. Polarization-selective spatially separated holography. The top row figures are theoretical designs while the second row figures are the experimental results. The yellow arrows show the polarization direction of the analyzer in experiment.
2.6 Overlapped images waveguide holography
In Fig. 6 we compare the computed and experimental images for the case where the images overlap, finding excellent agreement between the design and realized images. The two reconstructed images are superimposed when the analyzer is positioned at 135$^{\circ }$ or 45$^{\circ }$ -polarized. An experimental video can be found Visualization 2 that shows the transition between the images as the analyzer is rotated.
Fig. 6. Polarization-selective overlapped images waveguide holography. The top row figures (a) $\sim$(c) are theoretical predictions while the second row figures (d) $\sim$(f)) are the experimental results with (d) y-polarized, (e) 135$^{\circ }$-polarized and (f)x-polarized.
2.7 3D stereoscopic waveguide holography
Human vision perceives objects as three-dimensional using a binocular disparity, so that the views of an object are slightly different between the left and right eyes, with an average interpupillary distance (IPD) for a normal person being about 60 mm. This distance corresponds to an angular difference between the images for an object viewed at a particular distance, usually approximately 10$^{\circ }$ for an object 340 mm from the viewer, for example. Therefore, to form an image that appears to be 3D at this distance from a viewer, two separate images of an object rotated by this angle in the horizontal plane need to be encoded into two polarization states. However, as mentioned earlier to avoid image mixture the outgoing angle range is set to be 5$^{\circ }$ and hence the two images can not be simultaneously viewed by both eyes. To scatter the two images to a wide angle such that both eyes can view the holograms, a diffuser is needed to make the transmitted optical field have highly scattered speckle patterns in a volume [10]. In this study, a lenticular lens that consists of two molded plastic lens blanks placed in a crossover way is used as such a diffuser, which can diverge the beams but preserve the polarization states. Another crucial item used for viewing is a pair of linearly polarized glasses, with one eye having a TE polarized filter and the other a TM filter for the working wavelength, as presented in Fig. 7(a). In this case, the glasses serve as the polarization analyzer. As the relative linear polarization to the glasses depends on the orientation of the viewer, the viewer must be oriented perfectly relative to the linear polarizations of the outgoing beams to completely separate the views. To make the detection more robust to misalignment, circularly polarized states can be used. Thus, the setup was modified to include a quarter wave plate to convert the TE and TM modes to left- and right-circular polarization states, with a pair of glasses having right- and left-circular polarization filters (circular polarizers mounted in reverse) used to observe the final composite image. This setup is depicted in Fig. 7(b), in which case the viewer can tilt his or her head but the left/right image separation is maintained.
Fig. 7. Part of the 3D effect waveguide holography characterization setup. (a). Using a lenticular lens and a pair of linear polarized glasses. (b). Using a lenticular lens and a quarter-wave-plate (QWP) as well as a pair of circularly polarized glasses. (c) $\sim$(e). The generated holographic experimental results with a lenticular lens but without glasses in the cases with only TE, both TE and TM, and TM incident beams.
A comparison of a designed and experimentally observed 3D “cube” hologram is shown in Fig. 8, with the two different perspective images captured by a digital camera. For these images, the (linear) polarization analyzer was set to different directions so as to acquire the TE1 image, the TM0 image, and the combination of the two. A video shows the different images could be observed (see Visualization 3), in which a pair of linearly polarized glasses are used. Another video showing a 3D “cat” hologram as visualized through a pair of circularly polarized glasses is shown Visualization 4.
Fig. 8. Polarization-selective 3D effect images comparison. The top row images are theoretically reconstructed images, while the bottom row images are experimentally captured images by a digital camera. TE and TM are two perspective views of the same 3D object “cube”.
2.8 Vortex waveguide holography
2.8.1 Theory
Since the coherence length for an unstabilized diode-pumped solid-state green laser (532 $nm$) is quite small (on the order of $mm$ scale), it would be very difficult to obtain the interference patterns of the TE and TM beams after the analyzer. Hence, to form a vortex beam, we use a Helium-Neon (HeNe) red laser (633 $nm$) with a larger coherence length (on the order of $cm$ scale) to make the characterization process be feasible. With the source wavelength increased, the thickness of the ZEP layer needs to be scaled up (e.g. 950 $nm$).
It is known that the radial and azimuthal beams can be obtained by interfering structured linearly polarized TE and TM beams [15]. Figure 9(a) and 9(b) show how the radial vortex patterns are generated in this study. The field distributions of orthogonally linearly polarized beams vary as either $cos\theta$ or $sin\theta$, with $\theta$ being the azimuthal angle of the vortex beam. These two image patterns are used to digitally generate and are superimposed in the vortex CGH; the reconstructed image based on the CGH is shown in Fig. 9(c), in which false color is used to indicate the TM or TE polarization state. Without an analyzer, the generated beam pattern appears as a red disk if both TE and TM beams are present. To show the spatially-varying polarization of the radial vortex beam, a quiver diagram (Matlab) is used to represent the generated beam pattern, as shown in Fig. 9(d). The magnified central area (Fig. 9(e)) clearly illustrates that for the radial vortex pattern the polarization, represented by the arrows, points into or out of the center. With a polarization analyzer (indicated with a red arrow), the polarization state from the two beams can be extracted and an interference pattern obtained. In this case, the vortex hologram beam, when passed through the analyzer, produces an intensity variation that follows the orientation of the analyzer as the analyzer is rotated.
Fig. 9. Radial vortex patterns generation. (a). Field intensity distribution of TM mode pattern for radial vortex. (b). Field intensity distribution of TE mode pattern for radial vortex. (c). Reconstructed image based on CGH. (d) Desired radial vortex beam generated with a quiver function. (e). Zoomed-in central part of the radial vortex beam.
Similarly, the TE and TM beams shown in Fig. 10(a) and 10(b) may be designed to form an azimuthal vortex beam for which the polarization points in the azimuthal direction. Figure 10(c) shows the reconstructed image, with the false color showing the fields of the two polarizations swapped as compared to the radially polarized beam. Figure 10(d) is a quiver diagram showing the azimuthal orientation of the polarization, as indicated by the arrow directions, with Fig. 10(e) showing only the center of the beam. As a linear polarization analyzer is rotated, the intensity maximum follows the orientation of the analyzer, but is orthogonal to the analyzer orientation rather oriented along it as it would be for a radially polarized beam.
Fig. 10. Azimuthal vortex patterns generation. (a). TE mode intensity distribution for azimuthal vortex. (b). TM mode intensity distribution for azimuthal vortex. (c). Reconstructed image based on CGH. (d). Desired azimuthal vortex beam generated with a quiver function. (e). Zoomed-in central part of the azimuthal vortex beam.
The divergence of beams that have a uniform phase are determined by the size of the beam at the hologram plane. For a beam with a divergence of 5$^{\circ }$, this would result in a small beam size at the hologram plane, much smaller than the available patterning area, which in turn would result in little of the incident power being diffracted to form the beam. To increase the divergence angle while maintaining a sufficiently large beam size at the hologram plane to diffract a significant amount of the incident wave, a quadratic phase was added to the vortex beam to increase the divergence of the beam. The apparent gaps in the beam in Fig. 9(d) and Fig. 10(d) are caused by the added phase due to the fact that only the real-valued part is shown while plotting the field.
2.8.2 Fabrication
The fabrication process for the vortex beam hologram is quite similar to that of the dual image holograms presented above, including the steps of spin-coating ZEP and EBL patterning. Figure 11(a) shows a CGH vortex hologram fabrication file in which it is clear that the beam occupies much of the available area of the hologram (450$\mu m \times 450 \mu m$), which is the elliptical center region of the hologram. Figure 11(b) shows the fabricated hologram is consistent with the design. The smallest feature size in the SEM (Scanning Electron Microscope) image of Fig. 11(c) is measured to be 100 $nm$, just as designed.
Fig. 11. Radial vortex hologram fabrication. (a) Theoretically generated hologram. (b). A fabricated hologram sample under a dark-field microscope; (c). An SEM image of a small part of fabricated hologram sample.
2.8.3 Characterization
The optical characterization system for vortex holography is shown in Fig. 12. First, we modify the setup to accommodate the randomly polarized HeNe source (Spectral, RMM225L). A linear polarizer with the polarization direction at 45$^{\circ }$ is needed to filter mutually coherent TM and TE components to be split by the first polarizing beamsplitter. As the output beam diameter of the HeNe source is relatively large (around 3 $mm$), a telescope which consists of two converging lenses needs to be used to reduce the beam size to that of the sample (i.e. 450 $\mu m$). Since the two incident angles of TE and TM are very close (difference is around 3$^{\circ }$), two separate telescopes for TE and TM would not fit together without occluding one or the other beams. Instead, here a single telescope consisting of lenses (L1 and L2) is shared by both polarizations. Furthermore, a Mach-Zehnder interferometer is utilized to obtain the interference of the two beams. The first polarizing beamsplitter (BS1) is used to separate the light source into TE and TM, while the second one (BS2) recombines the two beams and keeps the output beams parallel. The mirror M1 is used to shift the TE beam to a certain position on the second lens (L2) to obtain a different incident angle from that of TM beam, while the other mirror M2 is set for the optical path compensation to have the TE and TM mode beams interference. Through fine adjustment of the mirrors to have TE and TM beams in the same plane and in phase, the vortex hologram patterns can be observed with an analyzer (LP2).
The theoretical prediction and experimental results for the radial vortex holography including the in-phase rotation videos can be found in Visualization 5, Visualization 6, Visualization 7. Figure 13 shows the theory and experimental verification results for azimuthal vortex holography (see Visualization 8, Visualization 9). In the experimental results, it can be clearly observed that the holographic image rotates as the polarization direction of the analyzer but with 90$^{\circ }$ difference. The lines shown in the experimental patterns are caused by the added quadratic phase. These results could be further improved by finer fabrication and more accurate optical characterization.
Fig. 13. Experiment verification for azimuthal vortex holography. Top row (a) $\sim$(d) is the theoretical images under different polarization directions of the analyzer, while the figures in middle rows (e) $\sim$(h) are experimentally captured by a digital camera ( the rotation out-of-phase). The lower row images (i) $\sim$(l) show that the generated holographic images are projected directly on a screen and could be observed by human eyes without any visual tools.
3. Discussion and conclusion
In this study we have demonstrated for the first time, to the best of our knowledge, polarization-selective waveguide holography, including spatially separated images, overlapped images, 3D stereo images as well as radial and azimuthal vortex beams—all based on a dielectric multilayer metamaterial system. The unique capability afforded through the combination of polarization-selective holographic components with a guided wave platform offers new paths for developing full-color, dynamic and reconfigurable holographic displays, as well as virtual reality (VR), augmented reality (AR) and mixed reality (MR) displays. The fact that the designed computer-generated holograms are binary holograms leads to a relatively low resolution in the reconstructed images. The binary hologram fabrication, however, is much simpler than that of plasmonic metasurface holograms, making the technology a good match to mass production methods. In addition, the field of view (FOV) of the holography images can be improved through design, as has been shown in a study on metagratings [32]. If the dielectric constant can be modulated in a point-by-point fashion, such as might be the case using liquid crystal, a dynamic waveguide, chip-scale, holographic display could be realized based on the techniques described here.
Funding
Air Force Office of Scientific Research (FA9550-18-1-0187).
Acknowledgments
The authors thank Duke University Shared Materials Instrumentation Facility (SMIF) for fabrication support.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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