Open Access
Add to BibSonomy
Abstract
The polarization dependent switchable structural coloration has shown a prominence for its unnecessity of changing the structure itself to achieve tunable color displays. Nevertheless, a chirality-selective structural color display has been rarely elucidated. Here, we suggest a chirality-selective reflective structural color display under perpendicularly incident light based on all-dielectric metasurfaces. We first investigate a chiral response of a subwavelength thickness two-dimensional (2D) amorphous silicon (Si) structure. The multipole decomposition followed by the electromagnetic field distribution analysis explained the chirality-selective response of the metasurface with the chirality-selective excitation of magnetic dipole (MD) and electric quadrupole (EQ). We then analyzed the structural dependence of MD and EQ, finding a group of metasurfaces which can span the entire visible spectrum under left circularly polarized (LCP) light and show dark, faded colors under right circularly polarized (RCP) light. Our result provides design criteria for chirality-selective all-dielectric structural color displays, applicable to energy and time efficient real-time color switching displays.
© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Composed of periodic subwavelength scale nanostructures, numerous research on metamaterials have allowed unexcavated degrees of freedom in electromagnetic wave manipulation [1–3]. Not only bridging the so called ‘terahertz gap’ [4–6], metamaterials operating at visible spectrum can also replace coloration of naturally occurring materials – organic dyes and pigments – with significant enhancement in brightness and resolution [7–9]. Also referred to as structural colors, recent approaches on structural colors have focused on tunable metamaterials which can change its color under external stimuli such as chemical exposures and electric signals [10–14]. Contrary to these approaches, polarization dependent switchable structural color displays do not require external stimuli devices, supporting time and energy efficient switchable color displays. Notably, designing chirality-selective metamaterials in visible spectrum can lead to realization of “ON-OFF” switchable color displays by simply changing the handedness of circularly polarized light.
Realization of chirality-selective structural color displays should undergo two fundamental procedures: 1) designing metamaterials showing strong chiral response in visible spectrum, 2) understanding the wavelength dependence of chiral response to span entire visible spectrum with a group of chiral metamaterials. While several types of metamaterials have been reported to show optical chirality in visible spectrum [15,16], it has been recently shown that the two-dimensional (2D) all-dielectric metasurface can also show optical chirality under perpendicularly incident visible light based on Mie-type nano-resonator [17]. Compared to the three-dimensional (3D) chiral metamaterial, 2D all-dielectric metasurface is advantageous for its simplicity in fabrication process as well as compatibility with complementary metal-oxide-semiconductor (CMOS) fabrication facilities. In addition, the dimensionality reduction to 2D structure also suggests a more intuitive framework when understanding the electromagnetic behaviors in the given structure followed by the wavelength dependence of chiral response. Therefore, 2D all-dielectric metasurface allows the realization of chirality-selective structural color displays.
Here, we suggested a group of 2D all-dielectric reflective chiral metasurfaces spanning visible spectrum, indicating a chirality-selective structural color display. With appropriate design criteria for the 2D all-dielectric chiral metasurfaces in visible spectrum, we firstly designed z-shaped all-dielectric chiral metasurfaces achieving strong circular dichroism (CD) in reflection with maximum value of ∼56% between 500 nm and 600 nm as a result of full-wave simulations. Therefore, distinct color contrast between left circularly polarized (LCP) light incidence and right circularly polarized (RCP) light incidence was shown, having a pair of color with green and violet respectively. Conducting multipole decomposition with induced electromagnetic fields in the metasurface to explain the origin of chiral response, we found the chirality-selective behaviors of magnetic dipole (MD) and electric quadrupole (EQ) moments are the dominant sources of chirality. The dependence of chirality-selective MD and EQ on wavelengths and structural parameters could be understood by analyzing the electromagnetic field distributions of these multipole moments. Based on these results, we obtained five additional all-dielectric chiral metasurfaces with distinctive colors, achieving rainbow color palettes at LCP light incidence and relatively dark colors at RCP light incidence. Combining those metasurfaces, we proposed a color switching Quick Response (QR) code which can only be recognized under LCP light, as an example of switchable color displays. Supporting real-time energy-efficient switching and high reproducibility, our proposed chirality-selective structural color displays will pave a way of achieving future generation display.
2. Metasurface design
For all-dielectric metamaterials to show optical chirality, the oscillating magnetic (m) and electric (p) multipole component which are perpendicular to incident wave vector k should be coupled, known as the Rosenfeld criterion: m · p ≠ 0 [18]. This states that non-parallel radiation of electric fields by m and p rotates the polarization of incident light, showing optical chirality. To make non-parallel electric fields, m and p perpendicular to k should not be perpendicular, therefore m · p ≠ 0. The Rosenfeld criterion can be easily satisfied in 3D metamaterials such as helical structure, as the spiral movement of electrons causes non-perpendicular arrangement of m and p [19]. As the opposing case of 3D all-dielectric metamaterials, several requirements exist for 2D all-dielectric metasurfaces with near zero thickness (planar metasurfaces) to satisfy the Rosenfeld criterion [20]. First, there should be no 2-fold rotation symmetry in the structure. Furthermore, the incident light should be oblique, while maintaining misalignment between the plane of incidence and the mirror line of 2D chiral structures. This is because only tangential current loops can be formed in planar metasurfaces due to the deep-subwavelength thickness of the structure. Therefore, p is always perpendicular to k, while m is always parallel to k for planar metasurfaces under perpendicularly incident light, resulting in m perpendicular to k and satisfying m · p = 0. Also, the partial m from two sides satisfying 2-fold rotation symmetry has opposite signs, resulting in no net m which can be coupled with p to elicit optical chirality in planar metasurfaces satisfying 2-fold rotation symmetry. In this context, a relatively simple but the surest way to meet the Rosenfeld criterion in 2D metasurface is to use high refractive index dielectric with subwavelength thickness [17]. Drastic reduction of effective wavelength in the structure compensates the significant mismatch between wavelength and the thickness of the structure occurred in conventional planar metasurfaces, allowing vertical current loops to be formed inside the structure [21]. Therefore, vertical current loop supports part of m that is parallel with p, satisfying the Rosenfeld criterion.
In this context, we selected amorphous silicon (Si), known to have high refractive index and relatively trivial intrinsic loss compared to its plasmonic counterparts at visible region [22]. Placing z-shaped Si nanostructure with 250 nm thickness above Al2O3 substrate [22], the periodicity of unit cell was set to 250 nm to avoid diffraction in visible region [Fig. 1(a)]. As a result of full wave simulations using the Lumerical finite-difference time-domain (FDTD) solution, proposed structure showed strong CD with respect to reflection between 500 nm and 600 nm under perpendicularly incident light [Fig. 1(b)] (maximum CD of 56% at λ = 520 nm). Here, CD for reflection is defined as
where RLCP (RRCP) represent the reflectance of LCP (RCP) light at given wavelengths. From the reflection spectrum for each polarization in Fig. 1(b), the reflected colors can be determined for the standard illuminant condition, showing distinctive structural colors in accordance with the handedness of circularly polarized light [Fig. 1(c)].
Fig. 1. An all-dielectric chirality-selective metasurface and its optical properties. (a) A schematic of all-dielectric metasurface consists of z-shaped Si nanostructure above Al2O3 substrate. System parameters are p = 250 nm, m = 40 nm, l1 = l2 = 90 nm, l3 = 200 nm, w = 40 nm and h = 250 nm. Si nanostructure is rotated counterclockwise by φ = 30° with respect to + z axis. (b) Calculated reflection spectrum of the metasurface under different handedness of circularly polarized light. As clearly shown, strong chiral response occurs in wavelength λ = 500 nm ∼ 600 nm. (c) CIE 1931 diagram and corresponding color for LCP light and RCP light. Simulation results are calculated by Lumerical FDTD Solutions.
As demonstrated in Fig. 1(b), reflection spectrum under LCP light is composed of superposition of two peaks in λ ∼ 520 nm and λ ∼ 600 nm, while these peaks show little reflection in RCP light. In subwavelength scale all-dielectric metamaterial, difference in reflection patterns can be understood as difference in resonant behavior of multipole moments developed in Si dielectric nano-scatterers [23–25].
3. Multipole decomposition results
As demonstrated in the previous sections, analyzing the multipole moments induced inside the nanostructure plays a critical role in understanding the optical chirality of the all-dielectric metamaterial. With calculated electric field distribution in the 2D z-shaped nanostructure using the Lumerical FDTD Solutions, the induced displacement current distribution can be obtained. From the induced displacement current density distribution inside Si nanostructure, electric, magnetic and toroidal multipole moments and their dependence on handedness of circularly polarized light can be numerically calculated [26]. We obtained far-field intensity for each multipole moment and compared with the actual reflection spectrum.
Figure 2 shows the result of multipole decomposition in both LCP light and RCP light corresponding to the designed metasurface in Fig. 1, considering higher order multipole terms up to electric and magnetic octupoles and toroidal quadrupole. Although it has been reported that several combinations of coupled electric and magnetic multipole moments can elicit optical chirality [17,27,28], MD and EQ were the two dominant multipole moments explaining the chirality-selective response of our metasurface. Due to the different chiral response of these two multipole moments, our metasurface can show strong chirality between 500 nm and 600 nm.
Fig. 2. Chirality-selective response of multipole moments. Far-field intensity of individual multipole components under (a) LCP light and (b) RCP light. The radiation intensities of electric (E), magnetic (M) and toroidal (T) multipole in accordance with their order dipole (D), quadrupole (Q) and octupole (O) are analyzed. Note that radiation intensity of MD and EQ show strong chirality-selective response at two dashed lines λ = 594 nm and λ = 549 nm respectively.
To analyze how MD and EQ are formed in our z-shaped Si nanostructure, electromagnetic field distributions at yz plane cutting the middle rod part in Fig. 1(a) are under consideration. For clear comparison of MD and EQ in LCP and RCP light, the field distributions at λ = 594 nm and λ = 549 nm are under analysis.
Figure 3 shows the electric and magnetic field distributions, indicating the chiral responses of MD and EQ at λ = 594 nm and λ = 549 nm respectively. The electric field (black arrows) and magnetic field (2D contour plots) distributions support that parallel MD moments are made at the center of Si nanostructures [Figs. 3(a)–3(b)]. As mentioned in the previous section, vertical current flow is possible in Si nanostructures with subwavelength thickness. These vertical current loops make parallel MD moments at the center of the Si nanostructures. In addition, the magnetic fields Hx in LCP light and RCP light are in opposite directions while stronger MD moment is made in LCP light.
Fig. 3. Chirality-selective field distribution at yz plane in Fig. 1(a). (a-b) Field distribution at λ = 594 nm. Stronger MD response is shown under LCP light. (c-d) Field distribution at λ = 549 nm. Note that electric quadrupole is shown only under LCP light. For all cases, the black arrows indicate in plane electric fields at given points. Simulation results are calculated by Lumerical FDTD Solutions.
At λ = 549 nm, EQ is the dominant multipole moment for LCP incidence (Fig. 2). Therefore, we can expect strong EQ moment would be shown under LCP light. Figures 3(c)–3(d) illustrate the in-plane electric fields E// = Ey + Ez at λ = 549 nm. The electric fields are either diverging from or converging into corners of the monitor plane in LCP light, indicating the electric field distribution of the simplest EQ form. On the contrary, the electric field distribution in RCP light implies no dominant multipole moment is shown, as indicated in Fig. 2(b). This result indicates the significant difference between planar metasurfaces and subwavelength thickness 2D metasurfaces, showing optical chirality even in the structure with 2-fold symmetry.
To confirm the importance of maintaining subwavelength thickness of Si nanostructure in supporting vertical electric fields for MD and EQ, we conducted additional multipole decomposition of the metasurfaces having different thickness of Si nanostructures [Fig. 4]. While the other length parameters remain the same as Fig. 1(a), chirality-selective responses of MD and EQ resonances are shown at different wavelength by changing the thickness of Si nanostructure. In addition, little optical chirality was shown when there exists strong mismatch between the effective wavelength and the thickness of Si nanostructure [Figs. 4(e)–4(f)], indicating the importance of maintaining subwavelength thickness of Si nanostructure. For Fig. 4(f), the size increase of Si nanostructure reduces the back scattering efficiency and the reflectance. Therefore, the structural parameter dependent behavior of multipole moments including MD and EQ clearly indicate the possibility of realizing chirality-selective structural color display with series of z-shaped nanostructures with different structural parameters, which will be discussed in the following section.
Fig. 4. Chirality-selective metasurfaces with different thickness. (a-b) Calculated reflection spectrum and the following reflection colors of metasurfaces with the thickness of (a) h = 200 nm (b) h = 300 nm. (c-d) Calculated far field intensity of MDs and EQs explaining the chirality-selective response of (a) and (b) respectively. Solid and dashed lines denote calculated far field intensity under LCP light and RCP light respectively. (e-f) Calculated reflection spectrum of the metasurface with the thickness of (e) h = 50 nm and (f) h = 800 nm, showing little optical chirality. For (a-f), all the other parameters except for the thickness h are remained as same as those in Fig. 1(a).
4. Chirality-selective structural color display
Although the thickness of Si nanostructures plays a key role when determining the vertical current flows and the following chirality-selective responses, the simplicity in fabrication process generally requires two system parameters—thickness h and periodicity p—to remain constant for every unit cell. Therefore, the dependence of multipole moments on horizontal length of the structure should be also under consideration for easier fabrication. While several parameters (m, l1,2, l3 and w) in Fig. 1(a) determine the horizontal length of Si nanostructures, the existence of MDs and EQs at the center of Si nanostructures indicates the importance of structure size of center rod part in overall chirality. In this context, we conducted additional analysis on how wavelength selectivity of MDs and EQs changes by altering the width w of the Si nanostructures. As shown in Fig. 5(a), the chirality-selective responses of MDs and EQs are shown in relatively longer wavelength as the w increases. This indicates the increase of horizontal size allows the general resonance peak shift of MDs and EQs to longer wavelength, showing chirality-selective responses at longer wavelength.
Fig. 5. Switchable structural color display. (a) Calculated far-field intensity of EQ (solid line) and MD (dashed line) with different thickness w = 40 nm (green), w = 60 nm (orange) and w = 80 nm (red). For all cases, p = 250 nm, m = 40 nm, l1 = l2 = 70 nm, l3 = 200 nm, and h = 250 nm. (b) Color palettes demonstrated on CIE 1931 diagram and actual color images. Under LCP light, rainbow colors are shown while these colors turn to relatively dark colors under RCP light. (c-e) Examples of switchable QR code displays under (c) unpolarized light (natural light), (d) LCP light and (e) RCP light. (c) The rainbow color pattern under the natural light becomes (d) vivid under LCP light and (e) faded under RCP light. Note that dark background color is the calculated reflection color of the Al2O3 substrate without any Si nanostructure above.
Primarily changing w to obtain different reflection colors, we found five additional structures, as described in Table 1. Comparing the reflection colors of metasurfaces in Table 1, it was possible to get rainbow colors under LCP light and relatively dark colors under RCP light [Fig. 5(b)]. While the chirality-selective structural colors in Fig. 1 indicated switching between two distinctive colors (green and violet), the results in Fig. 5(b) highlight the “ON-OFF” behavior of overall color pixels in display as the colors become dark and faded under RCP light.
Table 1. System parameters of five chirality-selective structures. The structure numbers in the table corresponds to the numbers in Fig. 5(b).
With these results, we could design a QR code showing different color patterns under differently polarized light as demonstrated in Figs. 5(c)–5(e). Combining the individual color patterns obtained in Fig. 5(b), the expected color pattern of 355 × 355 metasurface arrays show a rainbow QR pattern under the natural light [Fig. 5(c)]. Under LCP light, this rainbow pattern becomes more vivid while these colors become dark and faded under RCP light [Figs. 5(d)–5(e)]. Therefore, unlike QR code in LCP light which shows clear distinction between the frame and inside patterns, the ambiguousness of overall patterns and background colors in RCP light results in image recognition failure. In addition, as the finder patterns locating at the corners except for the bottom right play a key role in recognizing the size and location of QR codes, the ambiguousness of colors between the background color and finder patterns colors in RCP light would impede the image recognition [29].
5. Conclusions
In conclusion, we proposed chirality-selective all-dielectric metasurfaces and their expected application to switchable structural color displays. The subwavelength thickness 2D z-shaped nanostructure showed strong chiral response under perpendicularly incident circularly polarized light. The multipole decomposition results followed by the electromagnetic field pattern analysis in the Si nanostructure have provided the microscopic explanation of reflection spectrum of our all-dielectric metasurfaces. With the geometric parameter sweep of Si nanostructure, we could find a set of metasurfaces which reflect rainbow color palettes under LCP light and dark, faded colors under RCP light. With those metasurfaces, we could emulate color display which can switch its image depending on the handedness of circularly polarized light. Although we employed perpendicularly incident circularly polarized light, the tolerance range of colors perceived by human eyes support that our chirality-selective structural color display is still valid under small perturbation on structural parameters and incident angle [30,31]. In addition, as the oblique incidence of light will still ensure the satisfaction of the Rosenfeld criterion, various chirality-selective structural colors would be also shown under obliquely incident light.
To further improve the performance of chirality-selective structural color displays, increasing the reflectance and reducing the full width at half maximum (FWHM) of reflection spectrum is important. Both of the factors are affected by the loss of dielectric media, which can be generally found in high-refractive dielectrics including Si [21]. Still, the relatively low loss and high compatibility with CMOS facilities of all-dielectric metasurfaces compared to the plasmonic counterparts is the surest advantage of our chirality-selective display. Meanwhile, using optimization method including inverse design technology will allow further improvements in the performance of chirality-selective structural color displays [32].
We expect our chirality-selective all-dielectric metasurfaces is applicable not only to switchable color display but also to other cases such as image encryption [33] and polarization detection devices [34,35]. Especially, anisotropic Si nanostructures have been widely studied in the context of Pancharatnam-Berry metamaterials [36,37], so we also expect our chirality-selective metasurfaces can support both wavefront and color manipulation with the gradual change in orientation of Si nanostructures.
Funding
National Research Foundation of Korea (2020R1A2B5B02002730).
Disclosures
The authors declare no conflicts of interests
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. J. Hong, H. Son, C. Kim, S. E. Mun, J. Sung, and B. Lee, “Absorptive metasurface color filters based on hyperbolic metamaterials for a CMOS image sensor,” Opt. Express 29(3), 3643–3658 (2021). [CrossRef]
2. C. Choi, S. E. Mun, J. Sung, K. Choi, S. Y. Lee, and B. Lee, “Hybrid state engineering of phase-change metasurface for all-optical cryptography,” Adv. Funct. Mater. 31(4), 2007210 (2021). [CrossRef]
3. J. Sung, G. Y. Lee, C. Choi, J. Hong, and B. Lee, “Polarization-dependent asymmetric transmission using a bifacial metasurface,” Nanoscale Horiz. 5(11), 1487–1495 (2020). [CrossRef]
4. W. Withayachumnankul and D. Abbott, “Metamaterials in the terahertz regime,” IEEE Photonics J. 1(2), 99–118 (2009). [CrossRef]
5. H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006). [CrossRef]
6. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000). [CrossRef]
7. A. Kristensen, J. K. W. Yang, S. I. Bozhevolnyi, S. Link, P. Nordlander, N. J. Halas, and N. A. Mortensen, “Plasmonic colour generation,” Nat. Rev. Mater. 2(1), 16088 (2017). [CrossRef]
8. T. Xu, H. Shi, Y. K. Wu, A. F. Kaplan, J. G. Ok, and L. J. Guo, “Structural colors: from plasmonic to carbon nanostructures,” Small 7(22), 3128–3136 (2011). [CrossRef]
9. M. K. Hedayati and M. Elbahri, “Review of metasurface plasmonic structural color,” Plasmonics 12(5), 1463–1479 (2017). [CrossRef]
10. X. Duan, S. Kamin, and N. Liu, “Dynamic plasmonic colour display,” Nat. Commun. 8(1), 14606 (2017). [CrossRef]
11. D. Franklin, Y. Chen, A. Vazquez-Guardado, S. Modak, J. Boroumand, D. Xu, S. T. Wu, and D. Chanda, “Polarization-independent actively tunable colour generation on imprinted plasmonic surfaces,” Nat. Commun. 6(1), 7337 (2015). [CrossRef]
12. F. Z. Shu, F. F. Yu, R. W. Peng, Y. Y. Zhu, B. Xiong, R. H. Fan, Z. H. Wang, Y. Liu, and M. Wang, “Dynamic plasmonic color generation based on phase transition of vanadium dioxide,” Adv. Opt. Mater. 6(7), 1700939 (2018). [CrossRef]
13. K. Gansel Justyna, M. Thiel, S. Rill Michael, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009). [CrossRef]
14. E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009). [CrossRef]
15. M. V. Gorkunov, O. Y. Rogov, A. V. Kondratov, V. V. Artemov, R. V. Gainutdinov, and A. A. Ezhov, “Chiral visible light metasurface patterned in monocrystalline silicon by focused ion beam,” Sci. Rep. 8(1), 11623 (2018). [CrossRef]
16. B. Tang, Z. Li, E. Palacios, Z. Liu, S. Butun, and K. Aydin, “Chiral-selective plasmonic metasurface absorbers operating at visible frequencies,” IEEE Photonics Technol. Lett. 29(3), 295–298 (2017). [CrossRef]
17. A. Y. Zhu, W. T. Chen, A. Zaidi, Y. W. Huang, M. Khorasaninejad, V. Sanjeev, C. W. Qiu, and F. Capasso, “Giant intrinsic chiro-optical activity in planar dielectric nanostructures,” Light Sci. Appl. 7(2), 17158 (2018). [CrossRef]
18. L. Rosenfeld, “Quantenmechanische theorie der natürlichen optischen aktivität von flüssigkeiten und gasen,” Z,” Phys. 52(3-4), 161–174 (1929). [CrossRef]
19. M. Schäferling, Chiral Nanophotonics : Chiral Optical Properties of Plasmonic Systems (Springer, 2016).
20. E. Plum, Chirality and metamaterials, Ph.D. thesis, University of Southampton, 2010.
21. I. Kuznetsov Arseniy, E. Miroshnichenko Andrey, L. Brongersma Mark, S. Kivshar Yuri, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354(6314), aag2472 (2016). [CrossRef]
22. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998).
23. P. D. Terekhov, K. V. Baryshnikova, Y. Greenberg, Y. H. Fu, A. B. Evlyukhin, A. S. Shalin, and A. Karabchevsky, “Enhanced absorption in all-dielectric metasurfaces due to magnetic dipole excitation,” Sci. Rep. 9(1), 3438 (2019). [CrossRef]
24. A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015). [CrossRef]
25. I. V. Stenishchev and A. A. Basharin, “Toroidal response in all-dielectric metamaterials based on water,” Sci. Rep. 7(1), 9468 (2017). [CrossRef]
26. V. Savinov, V. A. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Phys. Rev. B 89(20), 205112 (2014). [CrossRef]
27. S. Li, K. Chen, D. Zhang, Y. Chen, Y. Xu, J. Liu, X. Wang, and S. Zhuang, “Reconfigurable metamaterial for chirality switching and selective intensity modulation,” Opt. Express 28(23), 34804–34811 (2020). [CrossRef]
28. S. Yang, Z. Liu, H. Yang, A. Jin, S. Zhang, J. Li, and C. Gu, “Intrinsic Chirality and Multispectral Spin-Selective Transmission in Folded Eta-Shaped Metamaterials,” Adv. Opt. Mater. 8(4), 1901448 (2020). [CrossRef]
29. L. Yue, Y. Ju, and L. Mingjun, “Recognition of qr code with mobile phones,” in 2008 Chinese Control and Decision Conference (IEEE, 2008), pp. 203–206.
30. D. L. MacAdam, “Visual Sensitivities to Color Differences in Daylight,” J. Opt. Soc. Am. 32(5), 247–274 (1942). [CrossRef]
31. J. Dong, Y. Zhang, and Y. Zhu, “Convex relaxation for illumination control of multi-color multiple-input-multiple-output visible light communications with linear minimum mean square error detection,” Appl. Opt. 56(23), 6587–6595 (2017). [CrossRef]
32. J. Jiang, M. Chen, and J. A. Fan, “Deep neural networks for the evaluation and design of photonic devices,” Nat. Rev. Mater. 6(8), 679–700 (2021). [CrossRef]
33. M. Song, X. Li, M. Pu, Y. Guo, K. Liu, H. Yu, X. Ma, and X. Luo, “Color display and encryption with a plasmonic polarizing metamirror,” Nanophotonics 7(1), 323–331 (2018). [CrossRef]
34. D. Wen, F. Yue, S. Kumar, Y. Ma, M. Chen, X. Ren, P. E. Kremer, B. D. Gerardot, M. R. Taghizadeh, G. S. Buller, and X. Chen, “Metasurface for characterization of the polarization state of light,” Opt. Express 23(8), 10272–10281 (2015). [CrossRef]
35. E. Arbabi, S. M. Kamali, A. Arbabi, and A. Faraon, “Full-stokes imaging polarimetry using dielectric metasurfaces,” ACS Photonics 5(8), 3132–3140 (2018). [CrossRef]
36. G. Ruffato, P. Capaldo, M. Massari, E. Mafakheri, and F. Romanato, “Total angular momentum sorting in the telecom infrared with silicon Pancharatnam-Berry transformation optics,” Opt. Express 27(11), 15750–15764 (2019). [CrossRef]
37. P. Capaldo, A. Mezzadrelli, A. Pozzato, G. Ruffato, M. Massari, and F. Romanato, “Nano-fabrication and characterization of silicon meta-surfaces provided with Pancharatnam-Berry effect,” Opt. Mater. Express 9(3), 1015–1032 (2019). [CrossRef]
