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Abstract
Halogen perovskites have high refractive indexes and adjustable bandgaps, making them promising materials for all-dielectric and tunable metasurfaces. Herein, we design tunable polarization-converted halogen-perovskite metasurfaces and explained their characteristics in theory by using the Jones matrix. We propose a halogen-perovskite color holographic metasurface with low crosstalk owing to the excellent monochromatic permeability of three halogen perovskites (MAPbCl3: 450 nm; MAPbBr3: 550 nm; MAPbI3: 740 nm). In addition, we build three independent imaging channels to prevent color crosstalk between them to achieve fantastic imaging applications. This study serves as a good reference for research on optical information storage, polarization optics, holographic image encryption.
© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurfaces are artificially designed two-dimensional (2D) planes composed of sub-wavelength scale nanoantennas. A metasurface can control the light field, which can precisely control the amplitude, phase, and polarization of the wavefront [1–3]. Recently, research on metasurfaces has further developed along with the development of nanofabrication technology. To reduce material loss, more metasurfaces with low-loss materials, such as TiO2 [4,5] and GaN [6], have been studied. Many applications, such as metalenses [7–10], holographic [11–14], structural color [15], and vortex beam generators [16,17] have been experimentally verified. However, since the structural parameters of metasurfaces are difficult to change once designed, traditional metasurfaces can achieve only fixed functions. Therefore, tunable metasurfaces have attracted great research interest [18–20]. In this case, researchers have introduced phase-change materials (GST and VO2) and flexible materials to prepare metasurfaces [21,22]. However, phase changes in phase-change materials cause a huge contrast in the refractive index, which limits the application of tunable metasurfaces. On the other hand, metasurfaces composed of flexible materials are not portable enough due to the need for complex additional equipment. Halogen perovskites have adjustable bandgaps and portable sizes, which solve the above-stated problems. Halogen perovskite has tunable properties, making it an excellent material for tunable metasurfaces, but its potential lead toxicity issues limit the feasibility of its application. In recent years, the research on solving the toxicity problem of halogen perovskite has been proposed [23], which makes halogen perovskite aroused the attention of scholars again.
Halogen perovskites are promising optoelectronic materials owing to their excellent properties, such as fast carrier migration speed, tunable bandgaps, efficient photoluminescence, low cost, and high refractive index [24–27]. Halogen perovskites have excellent performance in photovoltaic power generation, nonlinear optics, lasers, and other fields [28–32]. The efficiency of perovskite-based solar cells has been increased to 24.2% [25]. Halogen perovskites have a refractive index equal to or higher than that of traditional transparent materials, and owing to their tunable bandgaps, which have great potential for tunable metasurfaces [33]. Until now, perovskite-based metasurfaces have been successfully fabricated for photoluminescence and structural color [34–40]. Dynamic tunable-perovskite metasurface holography in the reflection mode has also been experimentally verified [41]. Notably, only a few studies on the tunable-halogen-perovskite metasurfaces in the transmission mode have been reported. Compared with the reflection mode, halogen-perovskite metasurfaces in the transmission mode have more interesting applications.
Herein, we investigate the transmission spectrum of three halogen-perovskite nanoantenna cells in the visible light band (400-800 nm) and use them to design polarization-converted metasurfaces. We explain the principle of polarization conversion using the Jones matrix. Halogen perovskites have tunable bandgaps. The bandwidth of halogen perovskites can be adjusted through halogen exchange, which, in turn, affects the refractive index of the materials. We use halogen perovskites to design two tunable metasurfaces. One of them can switch an image display by adjusting the bandwidth of halogen perovskite, and the other integrates three designed patterns into metasurfaces. By changing the bandgap of the halogen perovskites and the incident wavelength, different patterns can be displayed. In addition, we consider the monochromatic permeability of three halogen perovskites (MAPbCl3, MAPbBr3, and MAPbI3 correspond to the wavelengths of 450 nm, 550 nm, 740 nm, respectively). Three halogen perovskites are uniformly arranged on one metasurface, and the RGB phase information of the color image is designed in the corresponding imaging channel to realize color holographic imaging. Tunable metasurfaces in the transmission mode have more flexible applications.
2. Structure and method
Recently, halogen perovskites have been synthesized through chemical methods, and halogen perovskite metasurfaces have been successfully processed [41]. Owing to the adjustable bandgaps, halogen perovskites have attracted remarkable research attention for adjustable metasurfaces. Herein, we use halogen-perovskite nanoantennas to design metasurfaces on SiO2 substrate, which can exhibit a full phase change in transmission mode. Variational analysis and topological optimization are performed using the finite-element solver, COMSOL Multiphysics. We set periodic boundary conditions in the x- and y-directions to simulate the situation of infinite periodic arrays. A perfect matching layer is set in the z-direction to perfectly absorb scattered stray light and prevent its influence on the simulation results. The grid size was optimized to one-fifth of the incident wavelength to improve the accuracy of the simulation results. The nanoantenna is a cuboid, the height of the perovskite nanoantenna H = 740 nm, the long-axis length L = 290 nm, the short-axis length w = 100 nm, and the period of each unit P = 365 nm (Figs. 1(a) and 1(b)). The rotation angle of the nanoantenna is θ (the coordinate system is shown in Fig. 1(f)). As the θ increased, the nanoantenna could produce a phase change in the range of 0–2π.
Fig. 1. (a) Top view of a unit with the structural parameters indicated. (b) Schematic of the unit. (c)–(e) Units of different halogen perovskites. (f) Design of the polarization-converted metasurface.
The rectangular cross-section of the nanoantenna resulted in different effective refractive indexes along the long and short axes. Therefore, each nanoantenna is a linear birefringent wave plate, which can produce different phases with orthogonal linear polarization. We represent each unit using the Jones matrix. The near-field coupling between adjacent nanoantennas is negligible; therefore, such a single Jones matrix can be decomposed into the multiplication of two rotation matrices and a diagonal matrix, as shown below [42–44]:
The relationship between the input light field (Ei) and output light field (Eo) can be expressed as Eo = J·Ei. We define the incident field strength as 1 when the incident light is x-polarized. Thus, Exi = 1, and Eyi = 0 (Exi and Eyi are the x- and y-components of the incident electric field, respectively). We can further obtain Eq. (3).
From Eq. (3), when x-polarized light is incident on the anisotropic metasurface, the emitted light field not only contains the original x-polarization component but also excites the y-polarization component. Arbitrary polarization conversion can be achieved by designing the dimensions and orientation of units to control the amplitude ratio of the two components. If the anisotropic unit is rotated 90° around the z-axis, the emitted light field can be expressed as
3. Results and discussion
Halogen perovskites have tunable bandgaps, which can be reversibly adjusted by replacing the anions of the halogen perovskites via chemical vapor deposition (CVD). The refractive index of the perovskites is varied by adjusting the material bandgap, and the working band of the metasurface is adjusted (Figs. 2(b)–2(d)). This is important in the study of tunable metasurfaces.
Fig. 2. (a) Polarization-conversion efficiency of 200–1000 nm of halogen-perovskites (MAPbCl3, MAPbBr3, MAPbI3). (b)–(d) Real (left axis) and imaginary (right axis) parts of the refractive index of MAPbCl3, MAPbBr3, and MAPbI3.
We study the polarization-conversion efficiencies of MAPbCl3, MAPbBr3, and MAPbI3. Figures 2(b) and 2(c) show the real part n and imaginary part k of the refractive indexes of the three halogen perovskites in the visible light band [45–47]. As shown in the simulation results (Fig. 2(a)), we determined the working band of the three halogen-perovskite nanoantennas to be 450 nm (MAPbCl3), 550 nm (MAPbBr3), and 740 nm (MAPbI3). Figure 2(a) shows that these three materials have good monochromatic permeability. Combined with their adjustable bandgap characteristics, halogen perovskites provide many interesting possibilities for tunable metasurfaces.
To explore the monochromatic transmittance of halogen perovskites and their phase-control abilities, the polarization-conversion efficiencies of the three halogen perovskites under incident wavelengths of 450, 550, and 740 nm are simulated. In addition, we study the functional relationship between the rotation angle of the nanoantenna and the phase shift (LCP input RCP output). As shown in Fig. 3(c), at an incident wavelength of 450 nm, the MAPbI3 nanoantenna cannot produce a 2π phase shift with an increase in θ. This result is related to the low polarization-conversion efficiency of the MAPbI3 unit at 450 nm. However, the units in other cases could produce full phase changes with an increase in θ (Fig. 3(a), 3(b), and 3(d)–3(i)). With an incident wavelength of 450 nm, only the MAPbCl3 unit exhibits high polarization-conversion efficiency, reaching ∼55%, and the other two halogen-perovskite units are almost opaque (Fig. 3(a)–(c)). The polarization-conversion efficiency of the MAPbBr3 under 550 nm is as high as 90%, while the other two halogen-perovskite units have relatively low efficiency at 550 nm (Fig. 3(d)–3(f)). At 740 nm, only the MAPbI3 unit shows a higher efficiency (Fig. 3(g)–3(i)). The above results are consistent with Fig. 2(a), which shows that the three halogen perovskites have great monochromatic permeability.
Fig. 3. Wave phase retardation and polarization-conversion efficiency as a function of the unit cell orientation (MAPbCl3, MAPbBr3, MAPbI3) under (a)–(c) 450 nm, (d)–(f) 550 nm, and (g)–(i) 740-nm incident light, respectively.
The halogen perovskites have a refractive index similar to some traditional metasurface materials. Therefore, halogen-perovskite metasurfaces can realize the functions of traditional metasurfaces. Herein, we use these three halogen perovskites to design focusing metasurfaces. The polarization-converted metasurfaces are 14.6 um × 14.6 um, and their phase distribution can be determined using Eq. (5). According to the phase information shown in Fig. (3), the units are arranged according to the phase distribution of metalens (Eq. (5)). The designed metasurfaces are shown in Fig. 4(a).
where λ is the wavelength, f the focal length, and $R = \sqrt {{x^2} + {y^2}}$ the distance from each pixel on the plane of the metasurfaces to the center. The focusing intensity of MAPbCl3 metalens at 450, 550, and 740 nm wavelengths is shown in Fig. 4(b)–4(d), and that of MAPbBr3 and MAPbI3 metalens are shown in Fig. 4(e)–4(g) and Fig. 4(h) –4(j), respectively. Figure 4(b)-4(j) show the normalized intensity (|E|2) at the focal point. For convenience, we normalized the focus intensities of the same material at different wavelengths. The simulation results show that the three halogen perovskites only produce superior focal points at their transmitted wavelengths. The focusing intensity is weak when other wavelength is incident, or even cannot produce focal points. The results agree well with the polarization-conversion efficiencies of the three halogen-perovskite units shown in Fig. 3, which verifies the monochromatic transmittance of the three halogen perovskites.Fig. 4. (a) Schematic of polarization-converted halogen-perovskite metasurfaces. Light of different wavelengths (450, 550, and 740 nm) are incident on the MAPbX3 (X = Cl, Br, and I) metasurfaces. (b)–(j) Focusing intensity of MAPbCl3, MAPbBr3, and MAPbI3 metasurfaces at different incident wavelengths (450, 550, and 740 nm).
The above results confirm that halogen perovskites can well realize the functions of traditional metasurfaces. Further, we design halogen-perovskite holographic metasurfaces to explore their applications in imaging. The Gerchberg–Saxton (GS) algorithm (Fresnel holography) is used to obtain the phase distribution (Fig. 5(b), take the phase distribution under 450 nm as an example) of the target image (Fig. 5(a)) at different incident wavelengths. We use MAPbCl3, MAPbBr3, and MAPbI3 to design holographic metasurfaces corresponding to 450 nm, 550 nm, and 740 nm image phase distributions, respectively. The size of the metasurfaces was determined by the number of phase pixels obtained. The target image is shown in Fig. 5(a). It contains 300 × 300 pixels, and the size of the corresponding holographic metasurface is 109.5 µm × 109.5 µm. The imaging effects of the three holographic metasurfaces are calculated at different incident wavelengths. The theoretical results for the three perovskites are shown in Figs. 5(d) and (e) (MAPbCl3), Fig. 5(g) and 5(h) (MAPbBr3), and Fig. 5(j) and 5(l) (MAPbI3). The imaging results are consistent with the results in Fig. 4. In addition, the working distance from the sample to the image plane is 10 cm during the algorithm calculations.
Fig. 5. (a) and (b) Target image and its holographic phase distribution. (c) Schematic of holographic metasurfaces. Light of different wavelengths (450, 550, and 740 nm) is incident on MAPbX3 (X = Cl, Br, and I) holographic metasurfaces. (d)–(i) Theoretical imaging results of MAPbX3 (X = Cl, Br, and I) holographic metasurfaces at different wavelengths (450, 550, and 740 nm).
Halogen perovskites realize the basic functions of traditional metasurfaces, and their dynamic tunable characteristics make them suitable for many interesting applications. Related studies have shown that anions in halogen perovskites can be exchanged by CVD [41]. MAPbX3 can be reversibly transformed among MAPbCl3, MAPbBr3, and MAPbI3. With anion exchange, the real refractive index n of the material can maintain a high value, and the absorption coefficient k changes accordingly (Fig. 2(b)–2(d)). Halogen perovskites with different halogens exhibit different optical properties. In this case, metasurfaces based on halogen perovskites can also be dynamically tuned.
Owing to the tunable bandgap of halogen perovskites, we propose their applications in dynamically tunable metasurfaces. The grayscale map of the school badge of Jiangnan University is shown in the left picture of Fig. 6(a). The right picture of Fig. 6(a) shows the corresponding phase distribution map (240 × 240 pixels) of the school badge reproduced by the GS algorithm. According to the phase distribution map, we used MAPbBr3 to design the holographic metasurface. According to the target image size, the metasurface should be 87.6 µm × 87.6 µm. When incident by the light of 550 nm wavelength, MAPbBr3 metasurface could produce a clear image. When the MAPbBr3 metasurface is converted to MAPbCl3 or MAPbI3 metasurface by anion exchange, the metasurface could not form a clear image (the incident wavelength was 550 nm). The theoretical imaging effect is shown in Fig. 6(b). The imaging state is defined as “ON” state, and the non-imaging state is defined as “OFF” state. Because of the good reversible tuning of halogen perovskites, the metasurface in the “OFF” state could also be restored to the metasurface in the “ON” state.
Fig. 6. (a) Target image and its holographic phase distribution. (b) Light of 550-nm wavelength is incident on a MAPbBr3 holographic metasurface. When the metasurface is converted by CVD, the imaging results change accordingly (MAPbBr3: imaging; MAPbCl3 and MAPbI3: not imaging). (c) Target image: letters “J,” “N,” and “U”. (d) Metasurface containing phases of the three images. The metasurface can be converted to MAPbCl3, MAPbBr3, or MAPbI3 by CVD. Light of different incident wavelengths was incident on different metasurfaces produces different images.
The three halogen-perovskite metasurfaces considered herein show high transmission at different wavelengths. Therefore, we propose another application of tunable metasurface. We employ the GS algorithm to reproduce the phase distributions of the letters “J,” “N,” and “U” (Fig. 6(c)) corresponding to the incident wavelengths of 450, 550, and 740 nm. In the phase distribution of the three letters, we consider pixel units that do not overlap (each phase distribution extracts 1/3 of the total pixels) to synthesize a new holographic phase map. According to the final synthesized phase distribution, we use MAPbCl3 to design a metasurface. The blue letter “J” is imaged when incident by 450-nm light. Then, MAPbCl3 was converted to MAPbBr3 by CVD with 550-nm incident light, and the image is a green letter “N”. Similarly, when the metasurface is converted to MAPbI3 with 740-nm incident light, the image is a red letter “U”. The designed process of metasurface and theoretical results of imaging are shown in Fig. 6(d). We could flexibly and reversibly control the pattern and color of the holographic metasurface imaging by changing the incident wavelength and halogen-perovskite bandgap.
In addition to the applications of tunable metasurfaces, owing to the monochromatic permeability of the three halogen perovskites, they have great potential in color holographic metasurfaces. Since the transmission wavelengths of the three halogen perovskites are 450 nm, 550 nm, and 740 nm, respectively, we divide the phase information of the color image (as shown in Fig. 7(a)) into the R, G, and B channels. In order to reduce the color distortions caused by the different transmission efficiencies of the materials, we normalize the RGB channels of the original image according to the transmission efficiencies of the three materials. The change of the original image is shown in the left of Fig. 7(a). We employ the GS algorithm to obtain the phase information about the R, G, and B channels of the color image (the size of the target color image is 290 × 290 pixels), and 1/3 of the pixels is taken from the phase information of each channel to form a new phase distribution map. Three halogen perovskites are designed on the corresponding 1/3 pixel positions (Fig. 7(a)). The metasurface is 105.85 µm × 105.85 µm. The three halogen perovskites are evenly distributed in the metasurfaces array to ensure imaging. Due to the good monochromatic transmittance of three halogen perovskites, the three primary color holograms could be perfectly imaged in three completely independent channels with almost no interference, and a good color image is obtained. Figure 7(b) shows the theoretical imaging of the designed color holographic metasurface. Compared with other color holographic metasurfaces, the halogen-perovskite metasurface could effectively reduce the crosstalk between imaging channels due to its monochromatic permeability. To reproduce the phase distribution of the three primary colors, we can consider the chromatic aberration factor and compensate the imaging work lengths of the three channels to achieve achromatic imaging.
Fig. 7. (a) Phase information of the three primary colors of the target image is placed in three independent color channels. The three primary color channels correspond to three halogen-perovskite metasurfaces. The monochromatic transmittance of halogen perovskite can reduce the crosstalk between the imaging channels and form an excellent color holographic image. (b) Theoretical color holographic image results.
4. Conclusion
In summary, we qualitatively analyze the polarization conversion of halogen-perovskite-based metasurfaces and verified the monochromatic transmittance of the halogen perovskites (MAPbCl3, MAPbBr3, and MAPbI3). We screen out halogen-perovskite units that can produce a 2π phase change and designed metalenses using MAPbCl3, MAPbBr3, and MAPbI3. Next, we calculate the imaging ability of three perovskite metasurfaces at different incident wavelengths, which confirmed that different halogen perovskites can only be imaged at specific wavelengths. After that, considering the tunability of the halogen-perovskite bandgap, we propose two applications of the tunable holographic metasurface. Finally, based on the monochromatic permeability of the three halogen perovskites, we design a hybrid metasurface containing the three halogen perovskites. We put the phase information of the trichromatic (RGB) of the color picture into the imaging channels corresponding to three halogen perovskites. Owing to the excellent independence of the three monochromatic imaging channels, good color holographic imaging is ensured. With the recent rapid development of halogen-perovskite manufacturing technology, the production cost of halogen-perovskite-based metasurfaces can be reduced, which will provide promote the development of halogen-perovskite metasurfaces.
Funding
National Natural Science Foundation of China (11811530052); Intergovernmental Science and Technology Regular Meeting Exchange Project of Ministry of Science and Technology of China (CB02-20); State Key Laboratory of Millimeter Waves (K202238); Open Foundation for CAS Key Laboratory of Quantum Information (KQI201); Graduate Research and Innovation Projects of Jiangsu Province (SJCX20_0763).
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
1. S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated emission-depletion fluorescence microscopy,” Opt. Lett. 19(11), 780–782 (1994). [CrossRef]
2. M. J. Rust, M. Bates, and X. W. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006). [CrossRef]
3. E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006). [CrossRef]
4. M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000). [CrossRef]
5. M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U. S. A. 102(37), 13081–13086 (2005). [CrossRef]
6. E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6(5), 312–315 (2012). [CrossRef]
7. U. Dürig, D. W. Pohl, and F. Rohner, “Near-field optical-scanning microscopy,” J. Appl. Phys. 59(10), 3318–3327 (1986). [CrossRef]
8. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub–diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005). [CrossRef]
9. T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313(5793), 1595 (2006). [CrossRef]
10. M. V. Berry, “Evanescent and real waves in quantum billiards and Gaussian beams,” J. Phys. A: Math. Gen. 27(11), L391–L398 (1994). [CrossRef]
11. M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. A: Math. Gen. 39(22), 6965–6977 (2006). [CrossRef]
12. E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012). [CrossRef]
13. G. Chen, K. Zhang, A. Yu, X. Wang, Z. Zhang, Y. Li, Z. Wen, C. Li, L. Dai, S. Jiang, and F. Lin, “Far-field sub-diffraction focusing lens based on binary amplitude-phase mask for linearly polarized light,” Opt. Express 24(10), 11002–11008 (2016). [CrossRef]
14. Z. Wu, Q. Jin, S. Zhang, K. Zhang, L. Wang, L. Dai, Z. Wen, Z. Zhang, G. Liang, Y. Liu, and G. Chen, “Generating a three-dimensional hollow spot with sub-diffraction transverse size by a focused cylindrical vector wave,” Opt. Express 26(7), 7866–7875 (2018). [CrossRef]
15. K. S. Rogers, K. N. Bourdakos, G. H. Yuan, S. Mahajan, and E. T. F. Rogers, “Optimising superoscillatory spots for far-field super-resolution imaging,” Opt. Express 26(7), 8095–8112 (2018). [CrossRef]
16. Y. Kozawa, D. Matsunaga, and S. Sato, “Superresolution imaging via superoscillation focusing of a radially polarized beam,” Optica 5(2), 86–92 (2018). [CrossRef]
17. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011). [CrossRef]
18. N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014). [CrossRef]
19. 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]
20. X. Z. Chen, L. L. Huang, H. Muhlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, C. W. Qiu, S. Zhuang, and T. Zentgraf, “Dual-polarity plasmonic metaLlens for visible light,” Nat. Commun. 3(1), 1198 (2012). [CrossRef]
21. C. Zhang, S. Divitt, Q. Fan, W. Zhu, A. Agrawal, Y. Lu, T. Xu, and H. J. Lezec, “Low-loss metasurface optics down to the deep ultraviolet region,” Light: Sci. Appl. 9(1), 55 (2020). [CrossRef]
22. L. Huang, X. Chen, H. Mühlenbernd, Z. Hao, S. Chen, B. Bai, Q. Tan, G. Jin, K. W. Cheah, and C. W. Qiu, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013). [CrossRef]
23. X. Li, F. Zhang, H. He, J. J. Berry, K. Zhu, and T. Xu, “On-device lead sequestration for perovskite solar cells,” Nature 578(7796), 555–558 (2020). [CrossRef]
24. J. Burch, J. Ma, R. I. Hunter, S. A. Schulz, and A. D. Falco, “Flexible patches for mm-wave holography,” Appl. Phys. Lett. 115(2), 021104 (2019). [CrossRef]
25. J. Guo, T. Wang, H. Zhao, X. Wang, S. Feng, P. Han, and Y. Zhang, “Reconfigurable terahertz metasurface pure phase holograms,” Adv. Opt. Mater. 7(10), 1801696 (2019). [CrossRef]
26. F. Y. Yue, D. D. Wen, J. T. Xin, B. D. Gerardot, J. S. Li, and X. Z. Chen, “Vector vortex beam generation with a single plasmonic metasurface,” ACS Photonics 3(9), 1558–1563 (2016). [CrossRef]
27. J. Y. Guo, X. K. Wang, J. W. He, H. Zhao, S. F. Feng, P. Han, J. S. Ye, W. F. Sun, G. H. Situ, and Y. Zhang, “Generation of radial polarized lorentz beam with single layer metasurface,” Adv. Opt. Mater. 6(1), 1700925 (2018). [CrossRef]
28. Y. Bao, J. Ni, and C. Qiu, “A minimalist single-layer metasurface for arbitrary and full control of vector vortex beams,” Adv. Mater. 32(6), 1905659 (2020). [CrossRef]
29. J. W. He, X. K. Wang, D. Hu, J. S. Ye, S. F. Feng, Q. Kan, and Y. Zhang, “Generation and evolution of the terahertz vortex beam,” Opt. Express 21(17), 20230–20239 (2013). [CrossRef]
30. P. Huo, C. Zhang, W. Zhu, M. Liu, S. Zhang, S. Zhang, L. Chen, H. J. Lezec, A. Agrawal, Y. Lu, and T. Xu, “Photonic spin-multiplexing metasurface for switchable spiral phase contrast imaging,” Nano Lett. 20(4), 2791–2798 (2020). [CrossRef]
31. K. X. Cheng, Z. D. Hu, Y. Q. Wang, J. Ma, and J. Wang, “High-performance terahertz vortex beam generator based on square-split-ring metasurfaces,” Opt. Lett. 45(21), 6054–6057 (2020). [CrossRef]
32. G. Yuan, K. S. Rogers, E. T. F. Rogers, and N. I. Zheludev, “Far-Field superoscillatory metamaterial superlens,” Phys. Rev. Appl. 11(6), 064016 (2019). [CrossRef]
33. Z. Li, T. Zhang, Y. Wang, W. Kong, J. Zhang, Y. Huang, C. Wang, X. Li, M. Pu, and X. Luo, “Achromatic broadband super-resolution imaging by superoscillatory metasurface,” Laser Photonics Rev. 12(10), 1800064 (2018). [CrossRef]
34. X. Dai, F. Dong, K. Zhang, D. Liao, S. Li, Z. Shang, Y. Zhou, G. Liang, Z. Zhang, Z. Wen, G. Chen, L. Dai, and W. Chu, “Holographic super-resolution metalens for achromatic sub-wavelength focusing,” ACS Photonics 8(8), 2294–2303 (2021). [CrossRef]
35. R. Zuo, W. i. Liu, H. Cheng, S. Chen, and J. Tian, “Breaking the diffraction limit with radially polarized light based on dielectric metalenses,” Adv. Opt. Mater. 6(21), 1800795 (2018). [CrossRef]
36. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000). [CrossRef]
37. Y. Kozawa and S. Sato, “Sharper focal spot formed by higher-order radially polarized laser beams,” J. Opt. Soc. Am. A 24(6), 1793–1798 (2007). [CrossRef]
38. M. R. Foreman and P. Török, “Computational methods in vectorial imaging,” J. Mod. Opt. 58(5-6), 339–364 (2011). [CrossRef]
39. P. D. Higdon, P. Török, and T. Wilson, “Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes,” J. Microsc. 193(2), 127–141 (1999). [CrossRef]
40. W. Wang, B. Zhang, B. Wu, X. Li, J. Ma, P. Sun, S. Zheng, and J. Tan, “Image scanning microscopy with a long depth of focus generated by an annular radially polarized beam,” Opt. Express 28(26), 39288–39298 (2020). [CrossRef]
41. C. Zhang, S. Xiao, Y. Wang, Y. Gao, Y. Fan, C. Huang, N. Zhang, W. Yang, and Q. Song, “Lead Halide Perovskite-Based Dynamic Metasurfaces,” Laser Photonics Rev. 13(7), 1900079 (2019). [CrossRef]
42. R. Zhao, B. Sain, Q. Wei, C. Tang, X. Li, T. Weiss, L. Huang, Y. Wang, and T. Zentgraf, “Multichannel vectorial holographic display and encryption,” Light: Sci. Appl. 7(1), 95 (2018). [CrossRef]
43. H. Zhou, B. Sain, Y. Wang, C. Schlickriede, R. Zhao, X. Zhang, Q. Wei, X. Li, L. Huang, and T. Zentgraf, “Polarization-Encrypted Orbital Angular Momentum Multiplexed Metasurface Holography,” ACS Nano 14(5), 5553–5559 (2020). [CrossRef]
44. D. Penninckx and V. Morénas, “Jones matrix of polarization mode dispersion,” Opt. Lett. 24(13), 875 (1999). [CrossRef]
45. S. Brittman and E. C. Garnett, “Measuringn and k at the Microscale in Single Crystals of CH3NH3PbBr3 Perovskite,” J. Phys. Chem. C 120(1), 616–620 (2016). [CrossRef]
46. P. Löper, M. Stuckelberger, B. Niesen, J. Werner, M. Filipič, S. Moon, J. Yum, M. Topič, S. De Wolf, and C. Ballif, “Complex Refractive Index Spectra of CH3NH3PbI3 Perovskite Thin Films Determined by Spectroscopic Ellipsometry and Spectrophotometry,” J. Phys. Chem. Lett. 6(1), 66–71 (2015). [CrossRef]
47. A. M. A. Leguy, P. Azarhoosh, M. I. Alonso, M. Campoy-Quiles, O. J. Weber, J. Yao, D. Bryant, M. T. Weller, J. Nelson, A. Walsh, M. van Schilfgaarde, and P. R. F. Barnes, “Experimental and theoretical optical properties of methylammonium lead halide perovskites,” Nanoscale 8(12), 6317–6327 (2016). [CrossRef]
