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Abstract
Polarization multiplexing of metasurfaces conventionally requires the synthesis of both geometric and dynamic phases of meta-atoms. We propose a dynamic-phase-only polarization-multiplexing metasurface that consists of three types of polarization-decoupled meta-atoms and covers the 0–2π phase range. As illustrative examples, we designed and investigated a polarized beam splitter that can independently deflect x- and y-polarized incident lights at arbitrary angles. Furthermore, we designed and studied polarization-multiplexing metasurface-holography embracing double channels of orthogonal polarizations. Both metadevices demonstrate the effectiveness of our approach. This study paves the way for the design of polarization-multiplexing electromagnetic structures for application in metamaterials and metasurfaces.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurfaces, as artificial planar electromagnetic (EM) structures, have been attracting increasing interest from researchers because of their novel applicability to wavefront engineering, compact size, and good versatility to form unique optical effects [1,2]. Owing to the flexible modulation of the phase, amplitude, and polarization of EM waves, a variety of applications such as beam shaping [3–6], metalens [7–9], information processing [10,11], asymmetric transmission [12–15], polarization conversion [16,17], and spin-controlled photonics [18,19], have been proposed and demonstrated recently. The wavefront engineering of a metasurface, according to Huygens’ principle, can be regarded as the superposition of the EM wave modulation by each unit cell, also called as “meta-atom”, of the metasurface. Therefore, it is significant to design meta-atoms and explore their properties.
The fundamental methods of wavefront engineering by a meta-atom are mainly based on the geometrical phase modulation and dynamic phase modulation of the incident EM wave. Both the above types of meta-atoms, except those that are designed to be polarization-independent, work only at some specific polarized incident light. Consequently, it is difficult to implement polarization-multiplexed wavefront engineering using a conventional metasurface, limiting the availability of information channels for applications.
The geometric (or Pancharatnam-Berry) phase, introducing equal and opposite phase profiles on the two orthogonal circular polarizations, emerges from the polarization change. When circularly polarized light propagates through anisotropic meta-atoms (e.g., rectangular nanostructures), the transmitted cross-polarized light obtains a phase change Φ depending on the rotation angle θ of each meta-atom. Conventionally, the simple relationship is Φ = ±2θ, but it can be complicated if meta-atoms with high-fold rotational symmetries are applied [20]. Based on geometric-phase engineering, a multiplexing-metasurface hologram, which has symmetric reconstructed images of different helicities of the incident circularly polarized light, was proposed and demonstrated experimentally [21]. However, the intrinsic symmetry of the geometric phase limits polarization-multiplexing applications because it cannot engineer the phases of two orthogonally polarized lights independently.
By contrast, the dynamic phase, also called the propagation phase, usually depends on the geometry and refractive index of the meta-atom. It is also relevant to the polarization of the incident light if an asymmetric meta-atom is applied. This provides the possibility of polarization multiplexing via the dynamic phase. Conventional meta-atoms with simple and single structures can realize polarization-dependent phase modulation by the dynamic phase in some applications such as metasurface holography [22] and polarized beam splitting [23–25]. However, it is usually difficult to assemble a set of simple meta-atoms with single geometry yielding complete polarization-decoupled modulation with arbitrary phase retardation and transmission [26]. For example, in some previous works on metasurface-based polarized beam splitters (PBSs), the x- and y-polarized light beams were deflected at symmetric angles, originating from polarization-coupled dynamic phase profiles [23–25]. Recently, some researchers have used a spatial multiplexing scheme to realize polarization-multiplexing metasurfaces [27]. That is, they combined two types of meta-atoms (each one corresponds to x- or y-polarization) to form a meta-molecule (unit cell) so that two orthogonally polarized components get phase modulation independently. Besides, some researchers, based on grating theory, designed and demonstrated a polarization-multiplexing metasurface grating that can convert the incident light with known polarization to arbitrary polarization states on defined diffraction orders [26]. In addition, by introducing additional freedom of phase engineering, such as combining the geometric and dynamic phases, orthogonal-polarization multiplexing can also be realized [28,29]. However, the scheme of polarization-decoupled modulation with arbitrary phase retardation and transmission using the dynamic phase of a single meta-atom rather than a meta-molecule that is comprised of several meta-atoms remains to be studied.
In this study, we designed and demonstrated an all-dielectric polarization-multiplexing metasurface in the optical region. The proposed metasurface consists of three types of asymmetric rectangle-shape-based meta-atoms, which acquire independent and arbitrary phase modulation with high transmission, covering the whole range from 0 to 2π, for x- and y-polarized lights. Based on the designed polarization-decoupled meta-atoms, we can engineer arbitrary phase gradients of the orthogonal linear polarizations simultaneously but independently at each position of the metasurface, realizing polarization multiplexing. As illustrative examples, we designed a PBS based on a polarization-multiplexing metasurface. We conducted three-dimensional (3D) finite-difference time-domain (FDTD) simulations to study the PBS metadevice and proved that it can split the x- and y-polarized components of the incident light beam into arbitrary transmission directions with different angles. Further, we designed and numerically demonstrated polarization-multiplexing holography using the proposed metasurface scheme. It can realize different reconstructed images by corresponding polarization channels, implying potential applications in the fields of optical information processing, beam shaping, polarization sensing, etc. This study provides a novel method for the design of polarization-multiplexed wavefront-engineering EM structures for applications in metamaterials and metasurfaces.
2. Design of the polarization-multiplexing metasurface
Figure 1 shows a schematic of the proposed polarization-multiplexing metasurface with asymmetric polarization-decoupled meta-atoms. The substrate layer at the bottom was SiO2, which was transparent to incident light. On the substrate, each unit cell, with a period of 300 nm, consists of a 600-nm-thick TiO2 nanopost serving as the meta-atom. To achieve independent phase retardation for orthogonal linear polarizations from 0 to 2π, three types of meta-atoms with six geometries were designed and used in this work, as shown in Fig. 1(c).
Fig. 1. (a) Schematic of the polarization-multiplexed wavefront-engineering metasurface structure. (b) One meta-atom constitutes a unit cell. (c) Top view of three types of meta-atoms with six geometries. Geometries I and IV are rectangular meta-atoms, Geometries II and V are rectangular nanoposts with circular holes in the center, and Geometries III and VI are rectangular nanoposts with semi-elliptical sidewalls.
When the incident light passes through the meta-atom from the substrate, the electric field at the exit surface can be written as:
We conducted 3D finite-difference time-domain simulations using the Lumerical FDTD solution-based commercial software package to study and design polarization-decoupled meta-atoms. The refractive indices of TiO2 and SiO2 were set to 2.6 and 1.45 at the incident wavelength of 800 nm, respectively [31]. In the simulation, the period boundaries were used in the horizontal directions for the unit cell calculation, while the perfectly matched layers (PML) were set in longitudinal boundaries to absorb the reflective waves. A uniform mesh size of 5 nm was set in the computation area, balancing good convergence and rapid calculation time.
We swept approximately 20,000 structures of meta-atoms and elaborately selected topologies with eigen coefficients; that is, only diagonal txx and tyy exist in the transmission matrix, while txy and tyx need to be nearly zero, ensuring the ability of independent phase engineering. Then, we abandoned the structures with transmission coefficients lower than 0.8 to guarantee the efficiency of the final polarization-multiplexing metasurface. Finally, we obtained the phase retardations of selected meta-atoms that cover 0–2π for x- and y-polarizations independently, as plotted in Fig. 2(a). Notably, the meta-atoms based on single geometry, for example, the rectangular ones (Geometries I and IV), can only cover limited points in the dataset in Fig. 2(a), as the degrees of freedom in the geometrical structure are insufficient to engineer the entire phase range. In previous study, researchers suggested to obtain phase retardations covering 0–2π by enlarging the height of meta-atoms [32]. However, normally a high aspect ratio of meta-atoms will significantly increase the fabrication difficulty. In this study, we designed three types of meta-atoms with moderate height, providing a novel method to design polarization-multiplexing metasurface. Geometries II and V are rectangular nanoposts with circular holes in the center, while Geometries III and VI are rectangular nanoposts with semi-elliptical sidewalls. All three types of meta-atoms can form eigenmodes for x- and y-polarizations, as shown in Fig. 2(b), indicating their polarization-decoupled phase-engineering properties.
Fig. 2. Electromagnetic properties of the polarization-decoupled meta-atoms. (a) Independent phase retardations of the x- and y-polarization. (b) Electric field intensity distributions of the eigenmodes for x- and y-polarizations. The XLP and YLP correspond to the x-linearly polarized light and y-linearly polarized light, respectively. The dashed black lines show the profiles of the meta-atoms.
Based on the established dataset in Fig. 2, an all-dielectric metasurface can be designed for polarization-multiplexed wavefront engineering. This proposed metasurface can be fabricated by standard nanofabrication processes [33]. The TiO2 layer can be deposited on a fused silica substrate by atomic layer deposition, while the patterns of meta-atoms can be fabricated using electron beam lithography, followed by reactive ion etching. Considering that the three types of meta-atoms may have too small feature size to be accessible with the fabrication technique, we elaborately selected the structures in Fig. 2 dataset with as low aspect ratio as possible. Since it is well recognized that the FDTD can faithfully simulate the propagation of electromagnetic field, the numerical experiments based on the FDTD modelling is performed to obtain measured results for the designed metasurface. Here, we focused on the proof-of-principle study of polarization-multiplexing metasurface in this paper, and conducted 3D-FDTD simulations to verify the effectiveness of our proposed scheme. As illustrative examples, we proposed and demonstrated numerically two metadevices, the arbitrary-angle PBS and polarization-multiplexing holography, which will be discussed in detail in the following sections.
3. Results and discussions
3.1 Multiplexing-metasurface-based PBS
PBS, a conventional element, which is widely used in optical systems, has recently been miniaturized by a metasurface-based device. Most previous metasurface-based PBSs separate x-linearly polarized (XLP) and y-linearly polarized (YLP) lights into anti-symmetric angles [23–25], lacking independent control of the beam deflection. In this study, we designed and investigated a novel PBS based on our proposed polarization-multiplexing metasurface. It leverages independent wavefront engineering for XLP and YLP, thereby enabling arbitrary and asymmetric deflection angles for XLP and YLP, as demonstrated by 3D-FDTD simulations.
For simplicity but without loss of generality, we defined the phase-zero point at the rightmost nanopost for XLP light and the phase-zero point at the leftmost nanopost for YLP light; that is, the XLP light is deflected to the left side of the normal line, and vice versa for the YLP light. The phase setting of the metasurface satisfies the following equations:
where λ is the wavelength of the incident light, m is the number of nanoposts, p is the lattice constant of the metasurface, and θx and θy are the desired deflection angles of XLP and YLP, respectively. The index n is the corresponding position from left to right (1≤n ≤ m) in one group of meta-atoms. This group of meta-atoms is periodically arrayed to form a metasurface-based PBS.After specifying the deflection angles, an appropriate m should be selected to obtain a set of φnx-φny, and the corresponding meta-atoms in Fig. 2(a) can be extracted to form the PBS. Notably, the choice of m is not arbitrary, as the periodic condition should be satisfied as much as possible; that is, the φm+1 of the corresponding meta-atom should be as close to φ1 as possible, avoiding phase discontinuity between the two groups of meta-atoms. By setting periodic boundaries in x- and y-directions, and PML boundaries in z-direction, the metasurface PBS based on periodically arrayed groups of meta-atoms can be numerically investigated by FDTD simulations. For illustrative examples, we designed four PBSs that deflect -30° and 30°, -45° and 45°, -30° and 60°, and -30° and 15° for XLP and YLP light, respectively. The phase shifts, as well as the amplitudes, of the transmission coefficients of the meta-atoms in the four PBSs, are shown in Figs. 3(a)–(d). Figure 3(e) shows the position distribution of the phase points in the dataset in Fig. 2(a), represented by points with different symbols.
Fig. 3. Phase retardations (φxx and φyy) and amplitudes (|txx| and |tyy|) of the transmission coefficients (txx and tyy) of the meta-atoms for desired deflection angles of (a) -30° and 30°, (b) -45° and 45°, (c) -30° and 60°, and (d) -30° and 15°. (e) The corresponding phase map of four groups of meta-atoms in (a)-(d). For each plot in (a)-(d), each location n refers to one meta-atom that brings phase retardations for XLP and YLP independently, and the insert on the top describes the designed periodic group of meta-atoms. Solid lines of phase retardations correspond to the theoretical results in Eqs. (2) and (3), while the symbols of phase retardations correspond to the simulated results of meta-atoms.
The transmission fields of our designed PBS under plane-wave illumination with circular polarization are shown in Fig. 4. The left column in each figure corresponds to XLP light, whereas the right column corresponds to YLP light. For each case, the position of the meta-atoms is framed by the white dashed line, and the deflection angles are marked by a white straight line. This shows that the beam deflections of our PBS are all consistent with the designed angle, confirming the independent and arbitrary splitting angles for orthogonal-polarization components. The transmittance of each metasurface PBS in Figs. 4(a)-(d) is 82.3%, 88.9%, 89.9%, and 90.3% for XLP light, and 87.6%, 77.1%, 71.7%, and 83.8% for YLP light, respectively, realizing high-efficient beam splitting. From the demonstration of PBS, our proposed all-dielectric metasurface with polarization-multiplexed wavefront engineering applicability is verified.
Fig. 4. Electric field and phase distributions of the PBSs with designed deflection angles of (a) -30° and 30°, (b) -45° and 45°, (c) -30° and 60°, and (d) -30° and 15°. For each case, the left column corresponds to the XLP while the right one corresponds to the YLP; the first row depicts the real part of the electric field, while the second row depicts the phase distribution.
Furthermore, we investigated the far-field distribution of the transmission of PBS. For instance, we numerically calculated the far field of the PBS with deflection angles of -30° and 30°, which are plotted in Fig. 5. The blue and red curves illustrate the angles at which the major energy exists in the far field for XLP and YLP, respectively, indicating that the deflection angles remain almost unchanged during propagation. Our designed PBS shows stability and flexibility and can find practical applications in fields such as beam shaping and steering.
Fig. 5. Far-field intensity profile of the PBS. The insert is the electric field intensity distribution in far field.
3.2 Polarization-multiplexing metasurface-holography
With the development of artificial electromagnetic materials, metasurface-based holography has emerged in the last decade. In contrast to most conventional holograms, metasurface holograms have the advantages of unprecedented spatial resolution, low noise, and suppressed higher-order diffraction, thereby enabling wide applications in the fields of information processing, computational imaging, 3D display, optical metrology, and holographic storage [34,35]. As embracing additional information channels within a single metasurface, multiplexing holograms, among various hologram devices, deserves greater research interest. We propose and investigate a novel hologram device based on our proposed polarization-multiplexing metasurface that encodes different image information of XLP and YLP into designed meta-atoms.
The flowchart of the design of the polarization-multiplexing metasurface hologram is based on the Gerchberg–Saxton (GS) algorithm, as shown in Fig. 6. First, the phase distributions of the computer-generated holograms (CGHs) for XLP and YLP were designed using the GS algorithm. Here, we used Fourier transform holography as an example. The input image of XLP denotes the initial amplitude constraint, whereas a random initial phase is applied. After a general GS algorithm iteration, the phase distribution of the XLP hologram is obtained. This process is repeated for the YLP. Second, we encode the phase distributions of XLP and YLP into a single meta-atom pixel by pixel. Finally, a metasurface-based multiplexing hologram was designed.
Fig. 6. Flowchart of the design of polarization-multiplexing metasurface hologram. The FFT, IFFT, and corrcoef in the flow chart are the aberrations of fast Fourier transform, inverse fast Fourier transform, and correlation coefficients, respectively.
Figure 7 illustrates the detailed process of meta-atom encoding and metasurface design. We used eight-level phase quantization in the phase coding of the meta-atoms. Meanwhile, owing to the limitation of computational resources, we calculated a 51 × 51-periods metasurface as a proof-of-principle demonstration of multiplexing holography, which worked well and verifies our strategy. As each period covered 300 nm in both x- and y-directions, the size of metasurface was 15.3 × 15.3 μm2. First, we rewrote the phase distribution of the XLP (or YLP) hologram, calculated by the GS algorithm in Fig. 6, into a phase matrix with 51 × 51 elements with eight-level phase quantization. Then, we combined the two phase matrices of orthogonal polarizations into the multiplexing phase matrix in which each element fulfilled both phase demands of XLP and YLP and contributed to 64 combinations in total. Finally, we elaborately selected 64 polarization-decoupled meta-atoms in Fig. 2 to complete the multiplexing phase matrix. The length and width of all the six geometries covered in the range from 70–300 nm, while the diameter of the circular hole in the Geometries II and V was chosen from 10–150 nm, and the length of the minor axis in the Geometries III and VI was selected from 10–180 nm. Consequently, a polarization-multiplexing metasurface hologram was designed.
We used 3D-FDTD simulations to calculate the designed metasurface and plotted the reconstructed image in Fig. 8. For XLP and YLP, we use 51 × 51-pixels dolphin and rabbit as the original images, as shown in Figs. 8 (a) and (b). The phase-only holograms are shown in Figs. 8 (c) and (d), and the corresponding theoretically reconstructed images are plotted in Figs. 8 (e) and (f). As a comparison, the images reconstructed from the designed metasurface hologram under illumination with circular polarization are shown in Figs. 8 (g) and (h), showing good agreement with the original ones, thereby confirming our proposal for a polarization-multiplexed wavefront-engineering metasurface. This also indicates the ability of energy-multiplexing for different polarization states, opening up potential applications in the fields of multiplexing holography and optical information processing.
Fig. 8. Polarization-multiplexing metasurface hologram. (a) and (b) correspond to the original images for XLP and YLP respectively. (c) and (d) are the phase-only CGH calculated by GS algorithm. (e) and (f) are the theoretically reconstructed images of (c) and (d), respectively. (g) and (h) are the images reconstructed from the metasurface hologram that is designed in Figs. 6 and 7.
4. Conclusion
In this study, we proposed a novel polarization-multiplexed wavefront-engineering metasurface. It consists of three types of polarization-decoupled meta-atoms and can cover the entire phase range from 0–2π for x- and y- polarizations independently. Based on our proposed polarization-multiplexing metasurface, we designed and demonstrated two metadevices by 3D-FDTD simulations as proof-of-principle examples. First, we designed and studied a metasurface-PBS and then numerically confirmed that it can independently split the x- and y-polarized incident light beams into different deflection directions at arbitrary angles. Second, we devised and demonstrated multiplexing-metasurface holography with double channels of orthogonal polarizations, realizing different reconstructed images depending on the polarization channel. Our strategy of polarization-multiplexing metasurfaces, whose validity is verified by the aforementioned metadevices, is promising for a wide range of applications, such as optical information processing, polarization sensing, metalens, and beam shaping. We believe that our method provides a novel way to design polarization-multiplexing EM structures and can advance the design methodology and applications of metamaterials and metasurfaces.
Funding
National Natural Science Foundation of China (91750202); National Key Research and Development Program of China (2018YFA0306200, 2017YFA0303700).
Acknowledgments
We thank Mr. Wenhui Xiong, Mr. Xian Long, and Mr. Wenxiang Yan for fruitful discussions during this work.
Disclosures
The authors declare no conflicts of interest.
Data availability
The 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.
References
1. H. T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep. Prog. Phys. 79(7), 076401 (2016). [CrossRef]
2. G. Yoon, T. Tanaka, T. Zentgraf, and J. Rho, “Recent progress on metasurfaces: applications and fabrication,” J. Phys. D: Appl. Phys. 54(38), 383002 (2021). [CrossRef]
3. J. Zhou, H. Qian, H. Luo, S. Wen, and Z. Liu, “A spin controlled wavefront shaping metasurface with low dispersion in visible frequencies,” Nanoscale 11(36), 17111–17119 (2019). [CrossRef]
4. S. Tang, B. Ren, YX. Feng, J. Song, and YY. Jiang, “Asymmetric acoustic beam shaping based on monolayer binary metasurfaces,” Appl. Phys. Express 14(8), 085504 (2021). [CrossRef]
5. M. Kim and GV. Eleftheriades, “Guided-Wave-Excited Binary Huygens’ Metasurfaces for Dynamic Radiated-Beam Shaping with Independent Gain and Scan-Angle Control,” Phys. Rev. Applied 15(5), 054037 (2021). [CrossRef]
6. S. J. Li, Y. B. Li, L. Zhang, Z. J. Luo, B. W. Han, R. Q. Li, X. Y. Cao, Q. Cheng, and T. J. Cui, “Programmable Controls to Scattering Properties of a Radiation Array,” Laser Photonics Rev. 15(2), 2000449 (2021). [CrossRef]
7. B. Groever, WT. Chen, and F. Capasso, “Meta-Lens Doublet in the Visible Region,” Nano Lett. 17(8), 4902–4907 (2017). [CrossRef]
8. GY. Lee, JY. Hong, S. Hwang, S. Moon, H. Kang, S. Jeon, H. Kim, JH. Jeong, and B. Lee, “Metasurface eyepiece for augmented reality,” Nat Commun 9(1), 4562 (2018). [CrossRef]
9. YL. Wang, QB. Fan, and T. Xu, “Design of high efficiency achromatic metalens with large operation bandwidth using bilayer architecture,” Opto-Electron Adv 4(1), 200008 (2021). [CrossRef]
10. J. Li, S. Kamin, G. Zheng, F. Neubrech, S. Zhang, and N. Liu, “Addressable metasurfaces for dynamic holography and optical information encryption,” Sci. Adv. 4(6), eaar6768 (2018). [CrossRef]
11. M. Ma, Z. Li, W. Liu, C. Tang, Z. Li, H. Cheng, J. Li, S. Chen, and J. Tian, “Optical Information Multiplexing with Nonlinear Coding Metasurfaces,” Laser Photonics Rev. 13(7), 1900045 (2019). [CrossRef]
12. Q. H. Song, P. C. Wu, W. M. Zhu, W. Zhang, Z. X. Shen, P. H. J. Chong, Q. X. Liang, D. P. Tsai, T. Bourouina, Y. Leprince-Wang, and A. Q. Liu, “Split Archimedean spiral metasurface for controllable GHz asymmetric transmission,” Appl. Phys. Lett. 114(15), 151105 (2019). [CrossRef]
13. Z. C. Li, S. Q. Chen, C.C. Tang, W. W. Liu, H. Cheng, Z. Liu, J. X. Li, P. Yu, B. Y. Xie, and Z. C. Liu, “Broadband diodelike asymmetric transmission of linearly polarized light in ultrathin hybrid metamaterial,” Appl. Phys. Lett. 105(20), 201103 (2014). [CrossRef]
14. J. T. Li, J. Li, C. L. Zheng, Z. Yue, S. L. Wang, M. Y. Li, H. L. Zhao, Y. T. Zhang, and J. Q. Yao, “Active controllable spin-selective terahertz asymmetric transmission based on all-silicon metasurfaces,” Appl. Phys. Lett. 118(22), 221110 (2021). [CrossRef]
15. B. W. Han, S. J. Li, Z. Y. Li, G. S. Huang, J. H. Tian, and X. Y. Cao, “Asymmetric transmission for dual-circularly and linearly polarized waves based on a chiral metasurface,” Opt. Express 29(13), 19643–19654 (2021). [CrossRef]
16. Z. Y. Li, S. J. Li, B. W. Han, G. S. Huang, Z. X. Guo, and X. Y. Cao, “Quad-Band Transmissive Metasurface with Linear to Dual-Circular Polarization Conversion Simultaneously,” Adv. Theory Simul. 4(8), 2100117 (2021). [CrossRef]
17. S. J. Li, Y. B. Li, H. Li, Z. X. Wang, C. Zhang, Z. X. Guo, R. Q. Li, X. Y. Cao, Q. Cheng, and T. J. Cui, “A Thin Self-Feeding Janus Metasurface for Manipulating Incident Waves and Emitting Radiation Waves Simultaneously,” Ann. Phys. 532(5), 2000020 (2020). [CrossRef]
18. C. Meng, SW. Tang, F. Ding, and SI. Bozhevolnyi, “Optical Gap-Surface Plasmon Metasurfaces for Spin-Controlled Surface Plasmon Excitation and Anomalous Beam Steering,” ACS Photonics 7(7), 1849–1856 (2020). [CrossRef]
19. X. F. Zang, B. S. Yao, Z. Li, Y. Zhu, J. Y. Xie, L. Chen, AV. Balakin, AP. Shkurinov, Y. M. Zhu, and S. L. Zhuang, “Geometric phase for multidimensional manipulation of photonics spin Hall effect and helicity-dependent imaging,” Nanophotonics 9(6), 1501–1508 (2020). [CrossRef]
20. X. Xie, M. Pu, J. Jin, M. Xu, Y. Guo, X. Li, P. Gao, X. Ma, and X. Luo, “Generalized Pancharatnam-Berry Phase in Rotationally Symmetric Meta-Atoms,” Phys. Rev. Lett. 126(18), 183902 (2021). [CrossRef]
21. D. Wen, F. Yue, G. Li, G. Zheng, K. Chan, S. Chen, M. Chen, K. F. Li, P. W. H. Wong, K. W. Cheah, E. Y. B. Pun, S. Zhang, and X. Chen, “Helicity multiplexed broadband metasurface holograms,” Nat. Commun. 6(1), 8241 (2015). [CrossRef]
22. R. Z. Zhao, B. Sain, Q. S. Wei, C. C. Tang, X. W. Li, T. Weiss, L. L. Huang, Y. T. Wang, and T. Zentgraf, “Multichannel vectorial holographic display and encryption,” Light Sci. Appl. 7(1), 95 (2018). [CrossRef]
23. Z. Y. Guo, L. Zhu, K. Guo, F. Shen, and Z. P. Yin, “High-Order Dielectric Metasurfaces for High-Efficiency Polarization Beam Splitters and Optical Vortex Generators,” Nanoscale Res. Lett. 12(1), 512 (2017). [CrossRef]
24. Z. Y. Guo, L. Zhu, F. Shen, H. P. Zhou, and R. K. Gao, “Dielectric metasurface based high-efficiency polarization splitters,” RSC Adv. 7(16), 9872–9879 (2017). [CrossRef]
25. J. Li, C. Liu, T. S. Wu, Y. M. Liu, Y. Wang, Z. Y. Yu, H. Ye, and L. Yu, “Efficient Polarization Beam Splitter Based on All-Dielectric Metasurface in Visible Region,” Nanoscale Res. Lett. 14(1), 34 (2019). [CrossRef]
26. N. A. Rubin, A. Zaidi, M. Juhl, R. P. Li, J. P. B. Mueller, R. C. Devlin, K. Leósson, and F. Capasso, “Polarization state generation and measurement with a single metasurface,” Opt. Express 26(17), 21455–21478 (2018). [CrossRef]
27. Z. F. Li, P. W. Qiao, G. Y. Dong, Y. S. Shi, K. Bi, X. L. Yang, and X. F. Meng, “Polarization-multiplexed broadband hologram on all-dielectric metasurface,” EPL 124(1), 14003 (2018). [CrossRef]
28. A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015). [CrossRef]
29. J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118(11), 113901 (2017). [CrossRef]
30. C. Pfeiffer and A. Grbic, “Bianisotropic Metasurfaces for Optimal Polarization Control: Analysis and Synthesis,” Phys. Rev. Appl. 2(4), 044011 (2014). [CrossRef]
31. “Refractive Index Database,” https://www.filmetrics.com/refractive-index-database.
32. Z. B. Fan, Z. K. Shao, M. Y. Xie, X. N. Pang, W. S. Ruan, F. L. Zhao, Y. J. Chen, S. Y. Yu, and J. W. Dong, “Silicon Nitride Metalenses for Close-to-One Numerical Aperture and Wide-Angle Visible Imaging,” Phys. Rev. Appl. 10(1), 014005 (2018). [CrossRef]
33. M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016). [CrossRef]
34. L. Huang, S. Zhang, and T. Zentgraf, “Metasurface holography: from fundamentals to applications,” Nano Photonics 7(6), 1169–1190 (2018). [CrossRef]
35. Q. Jiang, G. Jin, and L. Cao, “When metasurface meets hologram: principle and advances,” Adv. Opt. Photonics 11(3), 518–576 (2019). [CrossRef]
