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Abstract
The application of metasurfaces requires the reduction or elimination of their chromatic aberration while maintaining a high efficiency. We propose a method for the design of dual-wavelength operating achromatic metalenses, which can focus two different wavelengths at the same position. Phase manipulation was achieved by crossing two crystalline Si nanorods on each pixel carrying phase information for wavelengths of 780 and 660 nm based on the principal of Pancharatnam-Berry (PB) phase. At 660 nm, chromatic aberration was reduced from 1.28 to 0.46 μm in numerical experiments. The focusing efficiency of the circularly polarized light reached 90.2% for 780 nm and 49.7% for 660 nm. This method can be extended to other wavelengths.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurfaces, which are ultra-thin planar optical structures consisting of two-dimensional sub-wavelength rationally-arranged optical scatters that control the basic properties of light (i.e., phase, polarization, and intensity), have received significant interest in recent years due to their ability to replace bulky optical components [1–5]. Unlike conventional optical components, which shape light beams by accumulating gradual phase shifts during light propagation, metasurfaces can provide abrupt phase changes covering 2π over the sub-wavelength scale. They have found widespread applications in vortex beam generation [6], light bending [7], focusing [8], and holograms [9], among others. More specifically, one particular device that has attracted a large amount of attention is the planar metalens.
However, the efficiency of metal-based metalenses is limited to 25% as they suffer from material absorption [10,11]. Various metalenses have therefore been prepared using low-loss dielectric materials, such as TiO2 [12,13] or Si [4,14]. In addition, for multiple wavelength operated metalenses, chromatic aberration is a significant issue, and so numerous studies have been carried out in this area [15–20].
Conventionally, the elimination or reduction of chromatic aberrations has been achieved by straightforward means, such as using the cascading multiple lens [15]. However, this is a bulky option, and requires a complex design to achieve optimum performances. In this context, planar metasurfaces have exhibited potential to overcome this issue, with significant progress having been made to date [16–20]. However, the majority of these studies utilize an area-division method to realize achromatic aberration [16,17], in which the metasurface is divided into several regions and each region corresponds to a single wavelength. Consequently, the efficiency is low, as only one part of the effective area is valid when light of a certain wavelength illuminates the metasurface.
Thus, we herein propose a method for the reduction of chromatic aberration at two wavelengths through use of the full effective area of the metasurface. A metalens will be built where wavelengths of 780 and 660 nm can be used as examples to achieve focusing. Our design will begin by analyzing the intensity distribution with each meta-atom-carrying phase and the amplitude information for the two different wavelengths. A phase reference, which should not influence the overall shape of the wavefront, will be added to one of the phase distributions to eliminate chromatic aberration. The principle of the Pancharatnam-Berry (PB) phase will then be applied to obtain the theoretical design. Two crystalline Si [21] nanorods of different sizes, each corresponding to an operating wavelength, will be superposed to form the meta-atom of the metalens, and the introduction of a reference phase by rotating the smaller nanorod (corresponding to 660 nm) should reduce chromatic aberration in addition to alleviating the influence of the larger nanorod. The feasibility of the method will be confirmed by numerical simulations, and we will examine the extension of our approach to other operating bands.
2. Theory
To focus collimated light at a focal distance of f, the required phase distribution φ(x,y) on the metalens is given by:
The phase is dependent on the wavelength λ, and the light field E at each point (x, y) can be expressed by:where I represents the amplitude of incident light. If light with two different wavelengths λ1 and λ2 are incident on the metalens with the same phase distribution given by Eq. (1), they will be focused at different positions, i.e., chromatic aberration appears. However, if we build a metalens with the light field Eʹ carrying information for both wavelengths as below, in which A and B represent the amplitude and are dependent on the incident wavelength, the incident light at wavelengths λ1 and λ2 can be focused around f. In addition, when B = 0 (A = 0) or B << A (B >> A), the light at wavelength λ1 (λ2) can be focused precisely at f. When B (A) is only slightly lower than A (B), then B (A) becomes a disturbance to A (B).Thus, we selected two typical wavelengths, i.e., λ1 = 780 nm and λ2 = 660 nm, to investigate the influence of the disturbance on the focal length. The pixel (square) spacing P and the value of f were set to 300 nm and 6 μm, respectively. To ensure consistency with a normal focusing lens, the shape of the phase map was set as circular with a radius of 5 μm. Without loss of generality, a disturbance of 1/3 was selected, i.e., A:B = 2:1 or A:B = 1:2. The distribution of the light field Eʹ carries information relating to both the phase and the amplitude. Figure 1 illustrates the intensity distribution along the optic axis (Z-axis) at wavelengths of 780 and 660 nm for disturbances of 1/3 and 0. As shown, the focal length deviated from 6 to 5.95 μm at λ1 = 780 nm and to 6.65 μm at λ2 = 660 nm. These slight deviations indicate that it is possible to obtain a single structure that allows significant alleviation of the chromatic aberration issue if it can carry phase information for two wavelengths, and simultaneously give A>B for λ1 and A<B for λ2.
Fig. 1 The light intensity distribution along the optic axis for the field map at the metalens under different parameters. When there is no disturbance, the focal length is 6 μm as designed. Upon the addition of a disturbance, A:B = 2:1 or A:B = 1:2, the focal length f deviates to 5.95 μm at λ1 = 780 nm (blue line) and 6.65 μm at λ2 = 660 nm (magenta line).
As shifting the whole wavefront forward or backward does not affect its shape, we can add a reference phase C into φ2, as shown in Eqs. (6) and (7):
In this case, light at λ2 can still be focused at f through the metalens with a field distribution of E2ʹ. If the second expression B(λ) of Eq. (5) is replaced by E2ʹ, Eʹ is affected, and the corresponding focal length deviates and oscillates with C. As the influence of C is dependent on the wavelength, the oscillation is different for different wavelengths. Figure 2(a) shows the relationship between the focal length f and the reference phase C, where it is apparent that the focal lengths at 780 and 660 nm oscillate asynchronously with C. It is therefore possible for us to find some crossed points, such as at C1 = 189° and C2 = 331° in Fig. 2(a), to focus light of the two wavelengths at the same position. Indeed, Fig. 2(b) confirms that both wavelengths can be focused at a position of 6.01 μm for C1 = 189°, thereby demonstrating that the metalens is theoretically achromatic at both wavelengths.Fig. 2 (a) and (c) The influence of reference phase C on the focal length at 780 nm (magenta line) and 660 nm (blue line) for the combined (solid lines) and single phase information (dashed lines). (b) and (d) The distribution of the intensity along the Z-axis when C = 189°/C = 180° is added to phase φ2 for different values of A:B.
In practice, it is difficult to find an ideal structure that fully satisfies the above conditions for both wavelengths. However, chromatic aberration can still be alleviated even when the two curves do not cross one another. This indicates that there is a remarkable tolerance for the light field distribution Eʹ. We therefore consider an extreme case, in which the amplitude A is always larger than B at both λ1 and λ2, as shown in Fig. 2(c), where the two dashed lines represent the focus position for a metalens that carries only one type of phase information (i.e., φ1). Naturally, these lines are straight, since a total shift induced by the reference phase cannot affect the shape of the wavefront. For a wavelength of 780 nm, the light is focused at 6.07 μm, which is a slight deviation from the designed value of 6 μm due to the shape mismatch between the phase map and the pixel. At 660 nm, an obvious deviation as large as 1.43 μm can be observed due to chromatic aberration. When a disturbance B (A:B = 1:0.2) is introduced into the structure, the focus positions for a wavelength of 780 nm begin to oscillate. In the case of a wavelength of 660 nm, A:B = 1:0.9 indicates that the disturbance is larger than the signal, and thus we can observe an oscillation with a large amplitude. In this extreme case, in a reference phase such as C = 180°, chromatic aberration can also be reduced to 0.79 μm. Based on these results, we built a field map carrying information for the two phases, and demonstrate the intensity distribution along the Z-axis direction as shown in Fig. 2(d). The differences of the focal lengths at both wavelengths were only 0.79 μm, and are consistent with those shown in Fig. 2(c).
In the next part, we will try to find a specific structure to carry phase information for two wavelengths and achieve chromatic aberration alleviation.
3. Design of the metalens
Several phase manipulation methods based on metasurfaces exist, which are themselves based on principles such as surface plasmon waveguiding [22–24], dielectric effective refracting [25,26], and metamaterial huygens’ surfaces [27–29]. In this context, the geometric phase, or the Pancharatnam-Berry (PB) phase has attracted significant attention due to its independence from the wavelength [30,31]. The PB phase is commonly controlled by a dielectric or plasmonic rectangular nanorod [13]. More specifically, when a circularly polarized light beam is normally incident onto a nanorod having an in-plane angle θ, the transmitted light is generally composed of two parts, namely the same-handedness part with no phase delay, and the opposite part with a phase delay of ± 2θ, there the sign “±” is determined by the handedness of the incident beam. If two differently sized nanorods with θ1 and θ2 are superposed to form an X-shaped meta-atom, they can be utilized to control the phase at two different wavelengths. For example, as shown in Fig. 3(a), under the illumination of left circular polarization, the transmitted intensity after the X-shaped meta-atom can be regarded as the superposition from two independent nanorods [32]:
where σ represents the chirality of the circular polarization, , and A and B correspond to the converting efficiencies of the nanorods. Upon comparison of Eqs. (8) and (5), a metalens consisting of X-shaped meta-atoms can be designed to control the phase and amplitude for two different wavelengths, in which the converting efficiency A represents the amplitude at λ1 while B at λ2.Fig. 3 (a) Schematic representation of the operating mechanism of the X-shaped meta-atom, which is formed by the superposition of two differently sized nanorods. The rotation of a nanorod with an in-plane angle θ1/θ2 can induce a phase change 2σθ1/2σθ2 in the oppositely-polarized component of the transmitted light according to the PB phase. (b) Definition of the geometric parameters for a unit cell of the metalens. The period P = 300 nm, height H = 400 nm, and width W = 72 nm. The length L is 250 nm for Rod 1 and 150 nm for Rod 2. (c) Schematic representation of the proposed metalens.
When combining two nanorods together to form the X-shaped meta-atom, the interaction between them will be very strong. Therefore, the converting efficiency must be optimized carefully at two wavelengths to satisfy A>B at λ1 while A<B at λ2. If the function of the nanorod is similar to a half-wave plate, i.e., it can induce the phase difference Δφ between the x- and y-polarizations to be approximately π, conversion of the right or left circular polarization to the opposite polarization will be possible with a particularly high efficiency. Similarly, where Δφ is close to 0, a low efficiency will be expected. As the induced Δφ is dependent on the geometric parameters of the nanorod, these parameters must be carefully selected to meet the requirements for A:B. Furthermore, the interaction between the two crossly-superposed nanorods should also be considered, and so based on these two factors, we selected a length L1 of 250 nm and a width W1 of 72 nm for Rod 1, while for Rod 2, L2 = 150 nm and W2 = 72 nm. The height H of both nanorods was set at 400 nm and the period P was set at 300 nm. The in-plane angle of the two nanorods is utilized to control the phase, and so Rod 1 carries phase information φ1 and Rod 2 carries φ2. According to the phase map obtained in the Theory section (part 3), a metalens was built as shown in Fig. 3(c). Moreover, the commercially available software finite difference time domain (FDTD) solution (Lumerical) was employed to conduct the numerical experiments, while the selected material was crystalline Si as suggested in the literature [21].
As mentioned above, the two superposed nanorods interact with one another, where the introduction of the second nanorod exerts an influence on the first nanorod at its corresponding wavelength. The effect of the cross-angle β on the intensity distribution for wavelengths of 780 and 660 nm should therefore be discussed. As shown in Figs. 4(a) and 4(b), in the case of right circular polarization, the energy is mainly concentrated on the two ends of the larger Rod 1 for both wavelengths when β < 90°, suggesting that the nanorod designed to control the PB phase of 780 nm plays the leading role. When β>90°, the smaller Rod 2 designed to control the phase for a wavelength of 660 nm starts to take effect. This tells us that to increase the effect of the smaller nanorod at its corresponding wavelength, the cross-angle must be larger than 90°. Although the intensity is mainly concentrated on the two ends of the larger Rod 1 at 660 nm, the converting efficiency of the smaller Rod 2 is higher due to its geometric parameters. Therefore, B>A can still be achieved at 660 nm.
Fig. 4 The near-field intensity distribution of the X-shaped meta-atoms with different cross-angles upon illumination using left circular polarized light at (a) 780 nm and (b) 660 nm.
According to the above analyses, a metalens with a radius R = 5 μm and a numerical aperture NA = 0.64 was designed to achieve focusing at 6 μm for both wavelengths (i.e., 780 and 660 nm), as shown in Fig. 3(c). In addition, Figs. 5(a) and 5(b) demonstrate that the wavelengths of 780 and 660 nm were focused at 6.09 and 7.37 μm, respectively, using the PB metalens designed for a wavelength of 780 nm. Upon combination of the two nanorods, the smaller nanorod must be rotated by an additional angle to increase their cross-angle β and reduce the influence of the larger nanorod. We tried different additionally rotated angles numerically and found that 90° was an appropriate value to satisfy the conditions where the focal length is ~6 μm and a greater number of cross-angles (β) are >90°. On the other hand, this additionally rotated angle leads to a phase change of 180° and corresponds to a reference phase C = 180° as described in the theoretic part.
Fig. 5 The electric field intensity distribution after passing through the metalens. Using (a) 780 nm and (b) 660 nm light incident on the metalens designed for a wavelength of 780 nm with a 6 μm focal length. The focal lengths were measured to be 6.09 and 7.37 μm respectively. Using (c) 780 nm and (d) 660 nm light incident on the metalens with X-shaped meta-atoms designed for a focal length of 6 μm. The reference phase C = 180° is included. The focal lengths were 5.75 and 6.21 μm, respectively. The white circle in each image indicates the position with the strongest intensity. The inset on the lower-left corner of each figure represents the field intensity distribution at focus on the x-y plane. The vertical (horizontal) cuts of focal spots have a full width at half-maximum (FWHM) of (a) 0.56 μm (0.56 μm), (b) 0.56 μm (0.56 μm), (c) 0.56 μm (0.56 μm), and (d) 0.48 μm (0.48 μm), respectively. Values of FWHMs from vertical and horizontal cuts are very close revealing the symmetry of the focal spots.
As shown in Figs. 5(c) and 5(d), chromatic aberration between the two wavelengths is reduced from 1.28 to 0.46 μm by the metalens composed of X-shaped atoms at each pixel where C = 180°. Furthermore, both wavelengths are focused at positions close to their ideal value of 6 μm. Thus, if the geometric parameters (i.e., the width, length, height, and period) were to be optimized further, the focal length would be expected to be closer to the designed value and chromatic aberration could be fully eliminated as indicated in the Theory section. However, in this case, we simply wished to verify the effectiveness of the proposed approach.
The focusing efficiency, which is defined by the ratio between the intensity at the focus and that of the incident beam, was calculated to be 90.2% for a wavelength of 780 nm and 49.7% for a wavelength of 660 nm for the metalens consisting of X-shaped meta-atoms. The efficiency difference between the two wavelengths can be attributed to two factors. One is that the energy is mainly concentrated on the two ends of the larger Rod 1, which was designed for 780 nm, even when the incident wavelength is 660 nm. The other one is that the transmission at 660 nm is lower than that at 780 nm. Compared to the results obtained from the area-division method, which utilizes only part of the metalens, the efficiency here is clearly higher at both wavelengths [16].
If we combine more nanorods into the meta-atom of the metalens, it is possible for us to realize achromatic aberration at more wavelengths. For example, we can combine three nanorods into one meta-atom to achieve three-wavelength achromatic aberration device which could pave the way to broaden applications such as RGB displays. However, the interaction between these combined nanorods could be very complicated and a proper way to optimize the device performance has to be set up.
4. Conclusions
We theoretically designed a dual-wavelength achromatic metalens for focusing both 780 and 660 nm wavelengths of light at the same position. The intensity at each meta-atom carries phase information for the two wavelengths to maximize the effective area of the metalens. Phase manipulation was achieved by crossing two Si nanorods on each pixel based on the principle of the Pancharatnam-Berry phase. The converting efficiency was controlled by the geometric parameters of each rod. In addition, the introduction of a reference phase by rotating one of the nanorods by 90° was found to not only reduce chromatic aberration, but also to decrease the influence of the larger nanorod on the smaller one. Due to the full use of the effective area, the efficiency of the designed metalens reached 90.2 and 49.7% for wavelengths of 780 and 660 nm, respectively. We propose that our method should be easily extendible to other operating wavelengths. These results are of importance as the application of metasurfaces requires the reduction or elimination of their chromatic aberration while maintaining a high efficiency.
Funding
National Natural Science Foundation of China (NSFC) (Grant Nos. 61675070, 61378082, and 11704133).
References
1. D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466 (2010). [CrossRef]
2. S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol. 11(1), 23–36 (2016). [CrossRef] [PubMed]
3. A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013). [CrossRef] [PubMed]
4. D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014). [CrossRef] [PubMed]
5. N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014). [CrossRef] [PubMed]
6. M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15(9), 6261–6266 (2015). [CrossRef] [PubMed]
7. 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] [PubMed]
8. D. Hu, G. Moreno, X. Wang, J. He, A. Chahadih, Z. Xie, B. Wang, T. Akalin, and Y. Zhang, “Dispersion characteristic of ultrathin terahertz planar lenses based on metasurface,” Opt. Commun. 322(322), 164–168 (2014). [CrossRef]
9. B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016). [CrossRef] [PubMed]
10. F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013). [CrossRef] [PubMed]
11. A. Arbabi and A. Faraon, “Fundamental limits of ultrathin metasurfaces,” Sci. Rep. 7(1), 43722 (2017), doi:. [CrossRef] [PubMed]
12. M. Khorasaninejad, Z. Shi, A. Y. Zhu, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60 nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17(3), 1819–1824 (2017). [CrossRef] [PubMed]
13. 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] [PubMed]
14. A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6(1), 7069 (2015). [CrossRef] [PubMed]
15. P. Hariharan, “Superachromatic lens combinations,” Opt. Laser Technol. 31(2), 115–118 (1999). [CrossRef]
16. E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Multiwavelength metasurfaces through spatial multiplexing,” Sci. Rep. 6(1), 32803 (2016), doi:. [CrossRef] [PubMed]
17. K. Li, Y. Guo, M. Pu, X. Li, X. Ma, Z. Zhao, and X. Luo, “Dispersion controlling meta-lens at visible frequency,” Opt. Express 25(18), 21419–21427 (2017). [CrossRef] [PubMed]
18. M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano Lett. 15(8), 5358–5362 (2015). [CrossRef] [PubMed]
19. M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Super-dispersive off-axis meta-lenses for compact high resolution spectroscopy,” Nano Lett. 16(6), 3732–3737 (2016). [CrossRef] [PubMed]
20. D. Lin, A. L. Holsteen, E. Maguid, G. Wetzstein, P. G. Kik, E. Hasman, and M. L. Brongersma, “Photonic multitasking interleaved si nanoantenna phased array,” Nano Lett. 16(12), 7671–7676 (2016). [CrossRef] [PubMed]
21. Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, T. F. Krauss, and X. Wang, “Efficient silicon metasurfaces for visible light,” ACS Photonics 4(3), 544–551 (2017). [CrossRef]
22. X. Luo, M. Pu, X. Ma, and X. Li, “Taming the electromagnetic boundaries via metasurfaces: From theory and fabrication to functional devices,” Int. J. Antennas Propag. 2015(16), 204127 (2015). [CrossRef]
23. X. G. Luo, “Principles of electromagnetic waves in metasurfaces,” Sci. China Phys. Mech. 58(9), 594201 (2015). [CrossRef]
24. T. Xu, C. Du, C. Wang, and X. Luo, “Subwavelength imaging by metallic slab lens with nanoslits,” Appl. Phys. Lett. 91(20), 3966 (2007). [CrossRef]
25. M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-insensitive metalenses at visible wavelengths,” Nano Lett. 16(11), 7229–7234 (2016). [CrossRef] [PubMed]
26. Z. Shi, M. Khorasaninejad, Y. W. Huang, C. Roques-Carmes, A. Y. Zhu, W. T. Chen, V. Sanjeev, Z. W. Ding, M. Tamagnone, K. Chaudhary, R. C. Devlin, C. W. Qiu, and F. Capasso, “Single-layer metasurface with controllable multiwavelength functions,” Nano Lett. 18(4), 2420–2427 (2018). [CrossRef] [PubMed]
27. C. Pfeiffer, N. K. Emani, A. M. Shaltout, A. Boltasseva, V. M. Shalaev, and A. Grbic, “Efficient light bending with isotropic metamaterial Huygens’ surfaces,” Nano Lett. 14(5), 2491–2497 (2014). [CrossRef] [PubMed]
28. C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110(19), 197401 (2013). [CrossRef] [PubMed]
29. C. Pfeiffer and A. Grbic, “Millimeter-wave transmitarrays for wavefront and polarization control,” IEEE Trans. Microw. Theory Tech. 61(12), 4407–4417 (2013). [CrossRef]
30. M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. Lond. 392(1802), 45–57 (1984). [CrossRef]
31. S. Pancharatnam, “Generalized theory of interference and its applications,” Proc. Indian Acad. Sci. A 44(6), 398–417 (1956). [CrossRef]
32. G. Y. Lee, G. Yoon, S. Y. Lee, H. Yun, J. Cho, K. Lee, H. Kim, J. Rho, and B. Lee, “Complete amplitude and phase control of light using broadband holographic metasurfaces,” Nanoscale 10(9), 4237–4245 (2018). [CrossRef] [PubMed]
