Abstract

We report the experimental demonstration of a two-dimensional (2D) metasurface with ordered rotation of elements and show that it can be used to control the symmetry of light-matter interaction. A 2D lens is demonstrated in the visible region by transforming the rotational symmetry associated with the off-axis incident light to the translational symmetry, allowing an extraordinarily large field of view (FOV) as well as optical Fourier transformation. Furthermore, such a planar lens has a long focal depth, with polarization selectivity and subwavelength resolution. The scheme presented here may provide many new perspectives on the design of novel 2D optical devices.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Corrections

5 December 2017: A typographical correction was made to Fig. 3.

1. Introduction

The wide-angle view, as an elaborately evolved technique for arthropods and many vertebrates, is one of the most fascinating optical properties of animal visual systems. Owing to the spherical arrangement of ommatidia or spherically-shaped camera-type eyes [1], the FOV of these systems can be close or even larger than 180°. By analogy to these natural prototypes, a plethora of optical devices, such as the artificial lenses enabled by the elastomeric materials [2] have been developed. Unfortunately, the operating principle of these 3D lenses is based on the refractive optics, which cause them to be bulky and not easy to be implemented in 2D flat optical systems.

Recently, 2D metasurfaces have emerged as a promising alternative to traditional bulky components [3–7]. However, virtually all previous demonstrations of flat lenses are limited by the off-axis aberration [8,9]. Although multilayered metasurfaces have been demonstrated to be able to increase the FOV [10,11], the fabrication process becomes more complex. In a general theory, such angle-induced aberration could be considered as a direct result of the breaking of rotational symmetry of the light-lens configuration. As illustrated in Figs. 1(a) and 1(b), the pronounced Luneburg lens and compound eyes possess spherical symmetry in refractive index distribution, and therefore light rays coming from different orientation angles could be perfectly directed to predefined spherical focal surfaces. Nevertheless, the rotational symmetry of these near-optimal lenses make them to be not compatible with flat optics as well as current planar fabrication technologies [12,13]. Here, we present a conceptually new strategy that is able to control the symmetry of light-matter interaction in 2D structured media. We prove that an ultrathin flat lens with rapid phase gradient could enable almost perfect conversion from rotational symmetry to translational symmetry, resulting in superior wide-angle lensing performance.

 figure: Fig. 1

Fig. 1 Comparison of different wide-angle lenses. (a) Luneburg lens. The height h equals to the diameter. (b) Compound eyes composed of many ommatidia. (c) Wide-angle flat lens. The thickness t is far smaller than the wavelength. The red, blue and yellow lines represent the light rays with different incidence angles.

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2. Principle of design

The phase of the super-symmetric lens presented here follows a quadratic form. Therefore, the lens can be termed “quadratic lens”:

Φ(r)=k0r22f,
where k0 is the wavenumber in free space, f the corresponding focal length, and r∈[0,2f] the radial distance to the lens center. Interestingly, Eq. (1) is just the phase for a normal thin lens in the paraxial regime. Assuming that the incident collimated light beam lies in the xz plane with an arbitrary angle of θ to the normal axis of the lens, the phase carried by the outgoing light should be:
Φ(r)=k0r22f+k0xsinθ=k02f((x+fsinθ)2+y2)−fk0sin2θ2,
where k0xsinθ is the gradient phase induced by the oblique incidence. Since the last term in the right hand is independent of r and can be neglected, there is only a transversal shift of fsinθ in the x-direction with respect to normal incidence. In this regard, the rotational effect of the oblique incidence light is perfectly converted to the translational symmetry of the focusing beam (see Fig. 1(c)). As a result, this lens can be used in either wide-angle imaging or Fourier analysis. It is noteworthy that the symmetry transformation is also related to the transformation optics [14], but the quadratic lens is much thinner than that obtained with a direct coordinate transformation.

Although the theory of quadratic lens seems straightforward, such lens could not be easily realized with either the refractive or diffractive optics. The main challenge lies in the fact that the radial wavenumber induced by the phase gradient (kr = ∂Φ/∂r) is rather larger than that of conventional case. For instance, there are kr = k0 and 2k0 at r = f and 2f, respectively. At normal incidence, the light fields passing through region where r>f will become evanescent and therefore do not contribute to the focal spot. At oblique incidence with angle of θ, the evanescent zone would shift horizontally. This dynamical excitation of the evanescent wave demonstrates an interest phenomenon different from previous results of angle-selective transmission [15].

Besides the wide FOV resulted from the symmetry transformation and angle-dependent excitation of evanescent wave, the quadratic lens possesses an extraordinarily large depth of focus (DOF) compared to an ordinary lens. This fact can be clarified using the geometric optics view as shown in Figs. 2(a) and 2(b), where the propagation direction of the light ray is calculated using the metasurface-assisted law of refraction [16,17]. In contrast to the ordinary lens that focus all light rays into a single point, distinct parts of the quadratic lens contribute to slightly vertically shifted focal spots. Consequently, the formed light spots resemble a needle in 3D space, which are of particular importance in applications such as optical storage and nanolithography [18,19].

 figure: Fig. 2

Fig. 2 Flat lenses based on 2D quasi-crystal. (a) and (b) Schematic of the light rays for both an ordinary lens and a quadratic lens. (c) Array of the perforated elliptical apertures. The long and short axes are chosen as 180 nm and 60 nm. The lattice constant is p = 150 nm.

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As noted in above discussion, the quadratic lens needs a rapid phase variation at its periphery (kr = 2k0), which in turn requires that the period of the phase-changing unit cell to be p = λ/2N (N is the number of discrete levels within [0, 2π]). If we choose N = 2 and λ = 600 nm, the period should be as small as 150 nm, with the characteristic dimensions of the nanostructures to be much smaller. Besides the fabrication challenge, the deep-subwavelength patterns are less effective in energy efficiency because the electromagnetic resonances corresponding to the phase variation are tightly related with the dimension of these nanostructures [20].

To achieve a better phase modulation in the deep sub-wavelength scale, 2D quasi-crystal composed of elliptical nano-aperture array in an ultrathin metallic film are adopted (see Fig. 2(c)). By rotating theses apertures in a hexagonal lattice, the predefined phase profile can be realized accompanying with a strong spin-orbit interaction [21–23]. Different from the sparsely arranged nano-antennas [3,24], the nanoholes are compactly arrayed so that some of them are connected together, leading to a much wider bandwidth [25] (Note that the efficiency of single-layered metasurface has an upper limit of 25%, while the experimental efficiency is typically below 10%, which can be increased by using dielectric or reflective structures [26–28]).

3. Experimental validation

As a proof-of-concept, a sample was fabricated by defining quasi-continuous apertures in a 100 nm thick gold film using focus ion beam (FIB) milling following the approach shown in [25] (Fig. 3(a)). The radius of the sample is 20 μm and the predefined focal length f is chosen as 10 μm at λ = 532 nm (8.407 μm at 632.8 nm). To demonstrate the wide-angle performance, four plane waves with different orientation angles with respect to the x-axis are combined and used as the incident light. Finite difference time domain method and vectorial angular spectrum theory are adopted in the numerical simulations. In all the calculations, we assume that light is propagating along the + z direction. As can be seen in the simulated results at λ = 632.8 nm (Figs. 3(b) and 3(c)), the light fields for different plane waves are just the same except that there are some translational shifts corresponding to Δ = fsinθ. Owing to the long DOF, the maximal intensity shift to z = 7.5 μm. The values of Δ are −4.4, 5.9, and −8.3 μm for θ = −32°, 45°, and −80°, agreeing with the theoretical expectations. Using two He-Ne lasers and a home-made microscope, we measured the focusing behavior of the sample. While one laser beam illuminates at normal incidence, the incidence angle of the other laser beam was tuned at −32° and −80° successively. As shown in Figs. 3(d)-3(f), the measured results are in good agreement with the numerical ones.

 figure: Fig. 3

Fig. 3 Performance of the wide-angle flat lens. (a) Scanning electron microscope (SEM) image of one section of the fabricated 2D metalens. Scale bar, 2 μm. (b) and (c) Simulated light intensity distributed on the xz-plane (y = 0) and xy-plane (z = 7.5μm) at a wavelength of 632.8 nm. (d) and (e) Experimental results of the intensity distribution on the xz-plane (y = 0) for θ = 0°, −32° and θ = 0°, −80°. (f) Cross–section view (z = 7.5 μm) of the intensity distribution along the x-direction shown in (d) and (e). The full width at half maximum (FWHM) is about 427 nm.

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The “optical needles” formed by the quadratic lens do not maintain their width at different positions along the z-direction. Instead, both the intensity and the field distribution vary at each horizontal plane before and after approaching the focal plane, as a result of the interference of the complex electromagnetic fields. Such interference may provide a mean to break the diffraction limit in classic optics, although the large side lobes are still need to be suppressed [29,30]. Another important characteristic of the formula shown in Eq. (1) is that the phase can be simply scaled for different operating wavelengths. That is to say, when the wavelength of light is altered, the focal length changes in a linear way. Recalling the fact that the quadratic lens has a rather long DOF, we expect that such lens could operate at a constant image distance within a wide spectrum. Such property may help to overcome the chromatic dispersion in traditional flat lens [18]. To demonstrate this, three lasers operating at red (632.8 nm), green (532 nm) and blue (490 nm) wavelengths are used as the light sources, as shown in Fig. 4(a). The incidence angle for the three lasers are set as: (θ1, φ1) = (0, 0), (θ2, φ2) = (32°, 0), and (θ3, φ3) = (80°, 270°), where φ = atan(y, x) denotes azimuthal angle in the xy plane. Figures 4(b) and 4(c) show the cross-sections of the intensity distribution. It is clear that the centroids of the focused beam would shift to larger z when the wavelength is decreased from 632.8 to 532 nm. Nevertheless, the three focal spots can be clearly observed in a common cross plane at z = 7.5 μm (see Fig. 4(c)).

 figure: Fig. 4

Fig. 4 Multiwavelength behaviour of the quadratic lens. (a) Schematic of the measuring set-up. (b) Cross-section view of the intensity distribution in the xy (z = 0), xz (y = 0) and yz (x = 0) planes. (c) Intensity distribution in the focal plane (z = 7.5 μm).

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4. Flat lens for wide-angle beam steering

Besides the novel properties mentioned above, the translational symmetry of the quadratic lens also makes the flat lens suitable for lens antennas. As shown in Fig. 5, a proof-of-concept simulation shows that the radiation direction and side lobe of the output beams can be readily tuned by adjusting the horizontal position and the distance between the source and the flat lens. Again, the side lobe of the radiation is dependent on the distance between the lens and point source. Figure 5(a) shows the radiation patterns with side lobes below −20dB. By decreasing the distance from 50 μm to 46 μm, the side lobes increase to about −12dB, while the 3dB beam widths decreased from 1.1° to 0.6° for normal incidence. In principle, further reduction of the beam width is possible by increasing of the aperture, although it will be a bit larger than an ideal lens antenna since the quadratic lens has a long depth of focus. Compared with previous beam steering techniques such as Luneburg lens and rotational prisms, the current design provide great advantages such as low profile, easy implementation and dramatically reduced side lobe.

 figure: Fig. 5

Fig. 5 Performance of beam steering lens antenna. λ = 532 nm. R = 100 μm, f = 50 μm. (a) Far-field power patterns for θ = 0, 32, −45, 60, and −80°. The point sources are placed at 25sinθ, and z = 50 μm. Inset is the schematic of the operation set-up. (b) The point sources are placed at 25sinθ, and z = 46 μm. The power patterns are normalized with sinθ.

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5. Conclusion

In summary, we have presented the design principle and experimental validation of flat lenses with wide range of operation angles, which may find applications in many scenarios ranging from surveillance and security in the optical range to beam steering in the microwave regime, owing to its planar and ultrathin profile and outstanding wide-angle scanning ability. Moreover, the concept of symmetry transformation may provide a powerful tool for dealing with similar physical problems, leading to either improvement of the performance or completely new innovations in related areas associated with all kinds of waves.

Funding

973 Program of China (2013CBA01700); National Natural Science Foundation of China (61622508, 61575201).

References and links

1. L. P. Lee and R. Szema, “Inspirations from biological optics for advanced photonic systems,” Science 310(5751), 1148–1150 (2005). [PubMed]  

2. Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K.-J. Choi, Z. Liu, H. Park, C. Lu, R.-H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013). [PubMed]  

3. F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2(1), e1501168 (2016). [PubMed]  

4. M. Pu, X. Ma, X. Li, Y. Guo, and X. Luo, “Merging plasmonics and metamaterials by two-dimensional subwavelength structures,” J. Mater. Chem. C Mater. Opt. Electron. Devices 5, 4361 (2017).

5. S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1), 187 (2017). [PubMed]  

6. Q. Song, W. Zhang, P. C. Wu, W. Zhu, Z. X. Shen, P. H. J. Chong, Q. X. Liang, Z. C. Yang, Y. L. Hao, H. Cai, H. F. Zhou, Y. Gu, G.-Q. Lo, D. P. Tsai, T. Bourouina, Y. Leprince-Wang, and A.-Q. Liu, “Water-resonator-based metasurface: an ultrabroadband and near-unity absorption,” Adv. Opt. Mater. 5, 1601103 (2017).

7. H.-H. Hsiao, C. H. Chu, and D. P. Tsai, “Fundamentals and applications of metasurfaces,” Small Methods 1, 1600064 (2017).

8. F. Aieta, P. Genevet, M. Kats, and F. Capasso, “Aberrations of flat lenses and aplanatic metasurfaces,” Opt. Express 21(25), 31530–31539 (2013). [PubMed]  

9. 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, 7069 (2015). [PubMed]  

10. B. Groever, W. T. Chen, and F. Capasso, “Meta-lens doublet in the visible region,” Nano Lett. 17(8), 4902–4907 (2017). [PubMed]  

11. A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7, 13682 (2016). [PubMed]  

12. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010). [PubMed]  

13. H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010). [PubMed]  

14. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [PubMed]  

15. Y. Shen, D. Ye, I. Celanovic, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Optical broadband angular selectivity,” Science 343(6178), 1499–1501 (2014). [PubMed]  

16. 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). [PubMed]  

17. X. Luo, “Principles of electromagnetic waves in metasurfaces,” Sci. China Phys. Mech. Astron. 58, 594201 (2015).

18. F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5, 9977 (2015). [PubMed]  

19. L. Liu, P. Gao, K. Liu, W. Kong, Z. Zhao, M. Pu, C. Wang, and X. Luo, “Nanofocusing of circularly polarized Bessel-type plasmon polaritons with hyperbolic metamaterials,” Mater. Horiz. 4, 290–296 (2017).

20. A. Y. Nikitin, D. Zueco, F. J. Garcia-Vidal, and L. Martin-Moreno, “Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008).

21. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006). [PubMed]  

22. N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013). [PubMed]  

23. X. Luo, M. Pu, X. Li, and X. Ma, “Broadband spin Hall effect of light in single nanoapertures,” Light Sci. Appl. 6, e16276 (2017).

24. X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016). [PubMed]  

25. M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015). [PubMed]  

26. M. Pu, Z. Zhao, Y. Wang, X. Li, X. Ma, C. Hu, C. Wang, C. Huang, and X. Luo, “Spatially and spectrally engineered spin-orbit interaction for achromatic virtual shaping,” Sci. Rep. 5, 9822 (2015). [PubMed]  

27. 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). [PubMed]  

28. B. H. Chen, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, I. C. Lee, J.-W. Chen, Y. H. Chen, Y.-C. Lan, C.-H. Kuan, and D. P. Tsai, “GaN metalens for pixel-level full-color routing at visible light,” Nano Lett. 17(10), 6345–6352 (2017). [PubMed]  

29. 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). [PubMed]  

30. D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing,” Laser Photonics Rev. 9, 713–719 (2015).

References

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  • Author
  • |
  • Publication
  1. L. P. Lee and R. Szema, “Inspirations from biological optics for advanced photonic systems,” Science 310(5751), 1148–1150 (2005).
    [PubMed]
  2. Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K.-J. Choi, Z. Liu, H. Park, C. Lu, R.-H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
    [PubMed]
  3. F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2(1), e1501168 (2016).
    [PubMed]
  4. M. Pu, X. Ma, X. Li, Y. Guo, and X. Luo, “Merging plasmonics and metamaterials by two-dimensional subwavelength structures,” J. Mater. Chem. C Mater. Opt. Electron. Devices 5, 4361 (2017).
  5. S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1), 187 (2017).
    [PubMed]
  6. Q. Song, W. Zhang, P. C. Wu, W. Zhu, Z. X. Shen, P. H. J. Chong, Q. X. Liang, Z. C. Yang, Y. L. Hao, H. Cai, H. F. Zhou, Y. Gu, G.-Q. Lo, D. P. Tsai, T. Bourouina, Y. Leprince-Wang, and A.-Q. Liu, “Water-resonator-based metasurface: an ultrabroadband and near-unity absorption,” Adv. Opt. Mater. 5, 1601103 (2017).
  7. H.-H. Hsiao, C. H. Chu, and D. P. Tsai, “Fundamentals and applications of metasurfaces,” Small Methods 1, 1600064 (2017).
  8. F. Aieta, P. Genevet, M. Kats, and F. Capasso, “Aberrations of flat lenses and aplanatic metasurfaces,” Opt. Express 21(25), 31530–31539 (2013).
    [PubMed]
  9. 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, 7069 (2015).
    [PubMed]
  10. B. Groever, W. T. Chen, and F. Capasso, “Meta-lens doublet in the visible region,” Nano Lett. 17(8), 4902–4907 (2017).
    [PubMed]
  11. A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7, 13682 (2016).
    [PubMed]
  12. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
    [PubMed]
  13. H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
    [PubMed]
  14. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [PubMed]
  15. Y. Shen, D. Ye, I. Celanovic, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Optical broadband angular selectivity,” Science 343(6178), 1499–1501 (2014).
    [PubMed]
  16. 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).
    [PubMed]
  17. X. Luo, “Principles of electromagnetic waves in metasurfaces,” Sci. China Phys. Mech. Astron. 58, 594201 (2015).
  18. F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5, 9977 (2015).
    [PubMed]
  19. L. Liu, P. Gao, K. Liu, W. Kong, Z. Zhao, M. Pu, C. Wang, and X. Luo, “Nanofocusing of circularly polarized Bessel-type plasmon polaritons with hyperbolic metamaterials,” Mater. Horiz. 4, 290–296 (2017).
  20. A. Y. Nikitin, D. Zueco, F. J. Garcia-Vidal, and L. Martin-Moreno, “Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008).
  21. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
    [PubMed]
  22. N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
    [PubMed]
  23. X. Luo, M. Pu, X. Li, and X. Ma, “Broadband spin Hall effect of light in single nanoapertures,” Light Sci. Appl. 6, e16276 (2017).
  24. X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016).
    [PubMed]
  25. M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
    [PubMed]
  26. M. Pu, Z. Zhao, Y. Wang, X. Li, X. Ma, C. Hu, C. Wang, C. Huang, and X. Luo, “Spatially and spectrally engineered spin-orbit interaction for achromatic virtual shaping,” Sci. Rep. 5, 9822 (2015).
    [PubMed]
  27. 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).
    [PubMed]
  28. B. H. Chen, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, I. C. Lee, J.-W. Chen, Y. H. Chen, Y.-C. Lan, C.-H. Kuan, and D. P. Tsai, “GaN metalens for pixel-level full-color routing at visible light,” Nano Lett. 17(10), 6345–6352 (2017).
    [PubMed]
  29. 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).
    [PubMed]
  30. D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing,” Laser Photonics Rev. 9, 713–719 (2015).

2017 (8)

M. Pu, X. Ma, X. Li, Y. Guo, and X. Luo, “Merging plasmonics and metamaterials by two-dimensional subwavelength structures,” J. Mater. Chem. C Mater. Opt. Electron. Devices 5, 4361 (2017).

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1), 187 (2017).
[PubMed]

Q. Song, W. Zhang, P. C. Wu, W. Zhu, Z. X. Shen, P. H. J. Chong, Q. X. Liang, Z. C. Yang, Y. L. Hao, H. Cai, H. F. Zhou, Y. Gu, G.-Q. Lo, D. P. Tsai, T. Bourouina, Y. Leprince-Wang, and A.-Q. Liu, “Water-resonator-based metasurface: an ultrabroadband and near-unity absorption,” Adv. Opt. Mater. 5, 1601103 (2017).

H.-H. Hsiao, C. H. Chu, and D. P. Tsai, “Fundamentals and applications of metasurfaces,” Small Methods 1, 1600064 (2017).

B. Groever, W. T. Chen, and F. Capasso, “Meta-lens doublet in the visible region,” Nano Lett. 17(8), 4902–4907 (2017).
[PubMed]

X. Luo, M. Pu, X. Li, and X. Ma, “Broadband spin Hall effect of light in single nanoapertures,” Light Sci. Appl. 6, e16276 (2017).

L. Liu, P. Gao, K. Liu, W. Kong, Z. Zhao, M. Pu, C. Wang, and X. Luo, “Nanofocusing of circularly polarized Bessel-type plasmon polaritons with hyperbolic metamaterials,” Mater. Horiz. 4, 290–296 (2017).

B. H. Chen, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, I. C. Lee, J.-W. Chen, Y. H. Chen, Y.-C. Lan, C.-H. Kuan, and D. P. Tsai, “GaN metalens for pixel-level full-color routing at visible light,” Nano Lett. 17(10), 6345–6352 (2017).
[PubMed]

2016 (4)

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).
[PubMed]

X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016).
[PubMed]

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7, 13682 (2016).
[PubMed]

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2(1), e1501168 (2016).
[PubMed]

2015 (6)

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, 7069 (2015).
[PubMed]

X. Luo, “Principles of electromagnetic waves in metasurfaces,” Sci. China Phys. Mech. Astron. 58, 594201 (2015).

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5, 9977 (2015).
[PubMed]

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[PubMed]

M. Pu, Z. Zhao, Y. Wang, X. Li, X. Ma, C. Hu, C. Wang, C. Huang, and X. Luo, “Spatially and spectrally engineered spin-orbit interaction for achromatic virtual shaping,” Sci. Rep. 5, 9822 (2015).
[PubMed]

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing,” Laser Photonics Rev. 9, 713–719 (2015).

2014 (1)

Y. Shen, D. Ye, I. Celanovic, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Optical broadband angular selectivity,” Science 343(6178), 1499–1501 (2014).
[PubMed]

2013 (3)

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K.-J. Choi, Z. Liu, H. Park, C. Lu, R.-H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[PubMed]

F. Aieta, P. Genevet, M. Kats, and F. Capasso, “Aberrations of flat lenses and aplanatic metasurfaces,” Opt. Express 21(25), 31530–31539 (2013).
[PubMed]

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[PubMed]

2012 (1)

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).
[PubMed]

2011 (1)

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).
[PubMed]

2010 (2)

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[PubMed]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
[PubMed]

2008 (1)

A. Y. Nikitin, D. Zueco, F. J. Garcia-Vidal, and L. Martin-Moreno, “Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008).

2006 (2)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[PubMed]

2005 (1)

L. P. Lee and R. Szema, “Inspirations from biological optics for advanced photonic systems,” Science 310(5751), 1148–1150 (2005).
[PubMed]

Aieta, F.

F. Aieta, P. Genevet, M. Kats, and F. Capasso, “Aberrations of flat lenses and aplanatic metasurfaces,” Opt. Express 21(25), 31530–31539 (2013).
[PubMed]

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).
[PubMed]

Alù, A.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2(1), e1501168 (2016).
[PubMed]

Arbabi, A.

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7, 13682 (2016).
[PubMed]

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, 7069 (2015).
[PubMed]

Arbabi, E.

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7, 13682 (2016).
[PubMed]

Bagheri, M.

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, 7069 (2015).
[PubMed]

Ball, A. J.

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, 7069 (2015).
[PubMed]

Bourouina, T.

Q. Song, W. Zhang, P. C. Wu, W. Zhu, Z. X. Shen, P. H. J. Chong, Q. X. Liang, Z. C. Yang, Y. L. Hao, H. Cai, H. F. Zhou, Y. Gu, G.-Q. Lo, D. P. Tsai, T. Bourouina, Y. Leprince-Wang, and A.-Q. Liu, “Water-resonator-based metasurface: an ultrabroadband and near-unity absorption,” Adv. Opt. Mater. 5, 1601103 (2017).

Cai, H.

Q. Song, W. Zhang, P. C. Wu, W. Zhu, Z. X. Shen, P. H. J. Chong, Q. X. Liang, Z. C. Yang, Y. L. Hao, H. Cai, H. F. Zhou, Y. Gu, G.-Q. Lo, D. P. Tsai, T. Bourouina, Y. Leprince-Wang, and A.-Q. Liu, “Water-resonator-based metasurface: an ultrabroadband and near-unity absorption,” Adv. Opt. Mater. 5, 1601103 (2017).

Capasso, F.

B. Groever, W. T. Chen, and F. Capasso, “Meta-lens doublet in the visible region,” Nano Lett. 17(8), 4902–4907 (2017).
[PubMed]

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).
[PubMed]

F. Aieta, P. Genevet, M. Kats, and F. Capasso, “Aberrations of flat lenses and aplanatic metasurfaces,” Opt. Express 21(25), 31530–31539 (2013).
[PubMed]

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).
[PubMed]

Celanovic, I.

Y. Shen, D. Ye, I. Celanovic, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Optical broadband angular selectivity,” Science 343(6178), 1499–1501 (2014).
[PubMed]

Chad, J. E.

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).
[PubMed]

Chen, B. H.

B. H. Chen, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, I. C. Lee, J.-W. Chen, Y. H. Chen, Y.-C. Lan, C.-H. Kuan, and D. P. Tsai, “GaN metalens for pixel-level full-color routing at visible light,” Nano Lett. 17(10), 6345–6352 (2017).
[PubMed]

Chen, J.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1), 187 (2017).
[PubMed]

Chen, J.-W.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1), 187 (2017).
[PubMed]

B. H. Chen, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, I. C. Lee, J.-W. Chen, Y. H. Chen, Y.-C. Lan, C.-H. Kuan, and D. P. Tsai, “GaN metalens for pixel-level full-color routing at visible light,” Nano Lett. 17(10), 6345–6352 (2017).
[PubMed]

Chen, L.

X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016).
[PubMed]

Chen, W. T.

B. Groever, W. T. Chen, and F. Capasso, “Meta-lens doublet in the visible region,” Nano Lett. 17(8), 4902–4907 (2017).
[PubMed]

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).
[PubMed]

Chen, Y. H.

B. H. Chen, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, I. C. Lee, J.-W. Chen, Y. H. Chen, Y.-C. Lan, C.-H. Kuan, and D. P. Tsai, “GaN metalens for pixel-level full-color routing at visible light,” Nano Lett. 17(10), 6345–6352 (2017).
[PubMed]

Choi, K.-J.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K.-J. Choi, Z. Liu, H. Park, C. Lu, R.-H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[PubMed]

Chong, P. H. J.

Q. Song, W. Zhang, P. C. Wu, W. Zhu, Z. X. Shen, P. H. J. Chong, Q. X. Liang, Z. C. Yang, Y. L. Hao, H. Cai, H. F. Zhou, Y. Gu, G.-Q. Lo, D. P. Tsai, T. Bourouina, Y. Leprince-Wang, and A.-Q. Liu, “Water-resonator-based metasurface: an ultrabroadband and near-unity absorption,” Adv. Opt. Mater. 5, 1601103 (2017).

Chu, C. H.

H.-H. Hsiao, C. H. Chu, and D. P. Tsai, “Fundamentals and applications of metasurfaces,” Small Methods 1, 1600064 (2017).

B. H. Chen, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, I. C. Lee, J.-W. Chen, Y. H. Chen, Y.-C. Lan, C.-H. Kuan, and D. P. Tsai, “GaN metalens for pixel-level full-color routing at visible light,” Nano Lett. 17(10), 6345–6352 (2017).
[PubMed]

Chum, C. C.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2(1), e1501168 (2016).
[PubMed]

Crozier, K. B.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K.-J. Choi, Z. Liu, H. Park, C. Lu, R.-H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[PubMed]

Cui, T. J.

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
[PubMed]

Deng, J.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2(1), e1501168 (2016).
[PubMed]

Dennis, M. R.

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).
[PubMed]

Devlin, R. C.

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).
[PubMed]

Ding, L.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2(1), e1501168 (2016).
[PubMed]

Faraon, A.

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7, 13682 (2016).
[PubMed]

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, 7069 (2015).
[PubMed]

Gaburro, Z.

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).
[PubMed]

Gao, P.

L. Liu, P. Gao, K. Liu, W. Kong, Z. Zhao, M. Pu, C. Wang, and X. Luo, “Nanofocusing of circularly polarized Bessel-type plasmon polaritons with hyperbolic metamaterials,” Mater. Horiz. 4, 290–296 (2017).

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[PubMed]

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing,” Laser Photonics Rev. 9, 713–719 (2015).

Garcia-Vidal, F. J.

A. Y. Nikitin, D. Zueco, F. J. Garcia-Vidal, and L. Martin-Moreno, “Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008).

Genevet, P.

F. Aieta, P. Genevet, M. Kats, and F. Capasso, “Aberrations of flat lenses and aplanatic metasurfaces,” Opt. Express 21(25), 31530–31539 (2013).
[PubMed]

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).
[PubMed]

Groever, B.

B. Groever, W. T. Chen, and F. Capasso, “Meta-lens doublet in the visible region,” Nano Lett. 17(8), 4902–4907 (2017).
[PubMed]

Gu, M.

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[PubMed]

Gu, Y.

Q. Song, W. Zhang, P. C. Wu, W. Zhu, Z. X. Shen, P. H. J. Chong, Q. X. Liang, Z. C. Yang, Y. L. Hao, H. Cai, H. F. Zhou, Y. Gu, G.-Q. Lo, D. P. Tsai, T. Bourouina, Y. Leprince-Wang, and A.-Q. Liu, “Water-resonator-based metasurface: an ultrabroadband and near-unity absorption,” Adv. Opt. Mater. 5, 1601103 (2017).

Guo, Y.

M. Pu, X. Ma, X. Li, Y. Guo, and X. Luo, “Merging plasmonics and metamaterials by two-dimensional subwavelength structures,” J. Mater. Chem. C Mater. Opt. Electron. Devices 5, 4361 (2017).

Han, S.

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7, 13682 (2016).
[PubMed]

Hao, Y. L.

Q. Song, W. Zhang, P. C. Wu, W. Zhu, Z. X. Shen, P. H. J. Chong, Q. X. Liang, Z. C. Yang, Y. L. Hao, H. Cai, H. F. Zhou, Y. Gu, G.-Q. Lo, D. P. Tsai, T. Bourouina, Y. Leprince-Wang, and A.-Q. Liu, “Water-resonator-based metasurface: an ultrabroadband and near-unity absorption,” Adv. Opt. Mater. 5, 1601103 (2017).

Hasman, E.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[PubMed]

Hong, M.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2(1), e1501168 (2016).
[PubMed]

X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016).
[PubMed]

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[PubMed]

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5, 9977 (2015).
[PubMed]

Horie, Y.

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7, 13682 (2016).
[PubMed]

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, 7069 (2015).
[PubMed]

Hsiao, H.-H.

H.-H. Hsiao, C. H. Chu, and D. P. Tsai, “Fundamentals and applications of metasurfaces,” Small Methods 1, 1600064 (2017).

Hu, C.

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[PubMed]

M. Pu, Z. Zhao, Y. Wang, X. Li, X. Ma, C. Hu, C. Wang, C. Huang, and X. Luo, “Spatially and spectrally engineered spin-orbit interaction for achromatic virtual shaping,” Sci. Rep. 5, 9822 (2015).
[PubMed]

Huang, C.

M. Pu, Z. Zhao, Y. Wang, X. Li, X. Ma, C. Hu, C. Wang, C. Huang, and X. Luo, “Spatially and spectrally engineered spin-orbit interaction for achromatic virtual shaping,” Sci. Rep. 5, 9822 (2015).
[PubMed]

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[PubMed]

Huang, K.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5, 9977 (2015).
[PubMed]

Huang, Y.

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X. Luo, M. Pu, X. Li, and X. Ma, “Broadband spin Hall effect of light in single nanoapertures,” Light Sci. Appl. 6, e16276 (2017).

X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016).
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M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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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).
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Liu, K.

L. Liu, P. Gao, K. Liu, W. Kong, Z. Zhao, M. Pu, C. Wang, and X. Luo, “Nanofocusing of circularly polarized Bessel-type plasmon polaritons with hyperbolic metamaterials,” Mater. Horiz. 4, 290–296 (2017).

Liu, L.

L. Liu, P. Gao, K. Liu, W. Kong, Z. Zhao, M. Pu, C. Wang, and X. Luo, “Nanofocusing of circularly polarized Bessel-type plasmon polaritons with hyperbolic metamaterials,” Mater. Horiz. 4, 290–296 (2017).

Liu, Z.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K.-J. Choi, Z. Liu, H. Park, C. Lu, R.-H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
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Q. Song, W. Zhang, P. C. Wu, W. Zhu, Z. X. Shen, P. H. J. Chong, Q. X. Liang, Z. C. Yang, Y. L. Hao, H. Cai, H. F. Zhou, Y. Gu, G.-Q. Lo, D. P. Tsai, T. Bourouina, Y. Leprince-Wang, and A.-Q. Liu, “Water-resonator-based metasurface: an ultrabroadband and near-unity absorption,” Adv. Opt. Mater. 5, 1601103 (2017).

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Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K.-J. Choi, Z. Liu, H. Park, C. Lu, R.-H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
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S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1), 187 (2017).
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M. Pu, X. Ma, X. Li, Y. Guo, and X. Luo, “Merging plasmonics and metamaterials by two-dimensional subwavelength structures,” J. Mater. Chem. C Mater. Opt. Electron. Devices 5, 4361 (2017).

L. Liu, P. Gao, K. Liu, W. Kong, Z. Zhao, M. Pu, C. Wang, and X. Luo, “Nanofocusing of circularly polarized Bessel-type plasmon polaritons with hyperbolic metamaterials,” Mater. Horiz. 4, 290–296 (2017).

X. Luo, M. Pu, X. Li, and X. Ma, “Broadband spin Hall effect of light in single nanoapertures,” Light Sci. Appl. 6, e16276 (2017).

X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016).
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M. Pu, Z. Zhao, Y. Wang, X. Li, X. Ma, C. Hu, C. Wang, C. Huang, and X. Luo, “Spatially and spectrally engineered spin-orbit interaction for achromatic virtual shaping,” Sci. Rep. 5, 9822 (2015).
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D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing,” Laser Photonics Rev. 9, 713–719 (2015).

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5, 9977 (2015).
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X. Luo, M. Pu, X. Li, and X. Ma, “Broadband spin Hall effect of light in single nanoapertures,” Light Sci. Appl. 6, e16276 (2017).

M. Pu, X. Ma, X. Li, Y. Guo, and X. Luo, “Merging plasmonics and metamaterials by two-dimensional subwavelength structures,” J. Mater. Chem. C Mater. Opt. Electron. Devices 5, 4361 (2017).

X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016).
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M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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M. Pu, Z. Zhao, Y. Wang, X. Li, X. Ma, C. Hu, C. Wang, C. Huang, and X. Luo, “Spatially and spectrally engineered spin-orbit interaction for achromatic virtual shaping,” Sci. Rep. 5, 9822 (2015).
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N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
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Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K.-J. Choi, Z. Liu, H. Park, C. Lu, R.-H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
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F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2(1), e1501168 (2016).
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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).
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N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
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L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
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Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K.-J. Choi, Z. Liu, H. Park, C. Lu, R.-H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
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J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
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X. Luo, M. Pu, X. Li, and X. Ma, “Broadband spin Hall effect of light in single nanoapertures,” Light Sci. Appl. 6, e16276 (2017).

L. Liu, P. Gao, K. Liu, W. Kong, Z. Zhao, M. Pu, C. Wang, and X. Luo, “Nanofocusing of circularly polarized Bessel-type plasmon polaritons with hyperbolic metamaterials,” Mater. Horiz. 4, 290–296 (2017).

M. Pu, X. Ma, X. Li, Y. Guo, and X. Luo, “Merging plasmonics and metamaterials by two-dimensional subwavelength structures,” J. Mater. Chem. C Mater. Opt. Electron. Devices 5, 4361 (2017).

X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016).
[PubMed]

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[PubMed]

M. Pu, Z. Zhao, Y. Wang, X. Li, X. Ma, C. Hu, C. Wang, C. Huang, and X. Luo, “Spatially and spectrally engineered spin-orbit interaction for achromatic virtual shaping,” Sci. Rep. 5, 9822 (2015).
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D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing,” Laser Photonics Rev. 9, 713–719 (2015).

Qin, F.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2(1), e1501168 (2016).
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F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5, 9977 (2015).
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M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5, 9977 (2015).
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F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2(1), e1501168 (2016).
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Ren, H.

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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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).
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Rogers, J. A.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K.-J. Choi, Z. Liu, H. Park, C. Lu, R.-H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
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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).
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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).
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Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
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Shen, Y.

Y. Shen, D. Ye, I. Celanovic, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Optical broadband angular selectivity,” Science 343(6178), 1499–1501 (2014).
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Q. Song, W. Zhang, P. C. Wu, W. Zhu, Z. X. Shen, P. H. J. Chong, Q. X. Liang, Z. C. Yang, Y. L. Hao, H. Cai, H. F. Zhou, Y. Gu, G.-Q. Lo, D. P. Tsai, T. Bourouina, Y. Leprince-Wang, and A.-Q. Liu, “Water-resonator-based metasurface: an ultrabroadband and near-unity absorption,” Adv. Opt. Mater. 5, 1601103 (2017).

Shitrit, N.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[PubMed]

Smith, D. R.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[PubMed]

Soljacic, M.

Y. Shen, D. Ye, I. Celanovic, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Optical broadband angular selectivity,” Science 343(6178), 1499–1501 (2014).
[PubMed]

Song, Q.

Q. Song, W. Zhang, P. C. Wu, W. Zhu, Z. X. Shen, P. H. J. Chong, Q. X. Liang, Z. C. Yang, Y. L. Hao, H. Cai, H. F. Zhou, Y. Gu, G.-Q. Lo, D. P. Tsai, T. Bourouina, Y. Leprince-Wang, and A.-Q. Liu, “Water-resonator-based metasurface: an ultrabroadband and near-unity absorption,” Adv. Opt. Mater. 5, 1601103 (2017).

Song, Y. M.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K.-J. Choi, Z. Liu, H. Park, C. Lu, R.-H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[PubMed]

Su, V.-C.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1), 187 (2017).
[PubMed]

B. H. Chen, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, I. C. Lee, J.-W. Chen, Y. H. Chen, Y.-C. Lan, C.-H. Kuan, and D. P. Tsai, “GaN metalens for pixel-level full-color routing at visible light,” Nano Lett. 17(10), 6345–6352 (2017).
[PubMed]

Szema, R.

L. P. Lee and R. Szema, “Inspirations from biological optics for advanced photonic systems,” Science 310(5751), 1148–1150 (2005).
[PubMed]

Tang, D.

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing,” Laser Photonics Rev. 9, 713–719 (2015).

Teng, J.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2(1), e1501168 (2016).
[PubMed]

Tetienne, J.-P.

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).
[PubMed]

Tsai, D. P.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1), 187 (2017).
[PubMed]

Q. Song, W. Zhang, P. C. Wu, W. Zhu, Z. X. Shen, P. H. J. Chong, Q. X. Liang, Z. C. Yang, Y. L. Hao, H. Cai, H. F. Zhou, Y. Gu, G.-Q. Lo, D. P. Tsai, T. Bourouina, Y. Leprince-Wang, and A.-Q. Liu, “Water-resonator-based metasurface: an ultrabroadband and near-unity absorption,” Adv. Opt. Mater. 5, 1601103 (2017).

H.-H. Hsiao, C. H. Chu, and D. P. Tsai, “Fundamentals and applications of metasurfaces,” Small Methods 1, 1600064 (2017).

B. H. Chen, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, I. C. Lee, J.-W. Chen, Y. H. Chen, Y.-C. Lan, C.-H. Kuan, and D. P. Tsai, “GaN metalens for pixel-level full-color routing at visible light,” Nano Lett. 17(10), 6345–6352 (2017).
[PubMed]

Veksler, D.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[PubMed]

Wang, C.

L. Liu, P. Gao, K. Liu, W. Kong, Z. Zhao, M. Pu, C. Wang, and X. Luo, “Nanofocusing of circularly polarized Bessel-type plasmon polaritons with hyperbolic metamaterials,” Mater. Horiz. 4, 290–296 (2017).

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing,” Laser Photonics Rev. 9, 713–719 (2015).

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[PubMed]

M. Pu, Z. Zhao, Y. Wang, X. Li, X. Ma, C. Hu, C. Wang, C. Huang, and X. Luo, “Spatially and spectrally engineered spin-orbit interaction for achromatic virtual shaping,” Sci. Rep. 5, 9822 (2015).
[PubMed]

Wang, S.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1), 187 (2017).
[PubMed]

Wang, Y.

X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016).
[PubMed]

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[PubMed]

M. Pu, Z. Zhao, Y. Wang, X. Li, X. Ma, C. Hu, C. Wang, C. Huang, and X. Luo, “Spatially and spectrally engineered spin-orbit interaction for achromatic virtual shaping,” Sci. Rep. 5, 9822 (2015).
[PubMed]

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing,” Laser Photonics Rev. 9, 713–719 (2015).

Wu, J.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5, 9977 (2015).
[PubMed]

Wu, P. C.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1), 187 (2017).
[PubMed]

Q. Song, W. Zhang, P. C. Wu, W. Zhu, Z. X. Shen, P. H. J. Chong, Q. X. Liang, Z. C. Yang, Y. L. Hao, H. Cai, H. F. Zhou, Y. Gu, G.-Q. Lo, D. P. Tsai, T. Bourouina, Y. Leprince-Wang, and A.-Q. Liu, “Water-resonator-based metasurface: an ultrabroadband and near-unity absorption,” Adv. Opt. Mater. 5, 1601103 (2017).

B. H. Chen, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, I. C. Lee, J.-W. Chen, Y. H. Chen, Y.-C. Lan, C.-H. Kuan, and D. P. Tsai, “GaN metalens for pixel-level full-color routing at visible light,” Nano Lett. 17(10), 6345–6352 (2017).
[PubMed]

Xiao, J.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K.-J. Choi, Z. Liu, H. Park, C. Lu, R.-H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[PubMed]

Xie, Y.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K.-J. Choi, Z. Liu, H. Park, C. Lu, R.-H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[PubMed]

Xu, B.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1), 187 (2017).
[PubMed]

Yang, J.

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[PubMed]

Yang, Z. C.

Q. Song, W. Zhang, P. C. Wu, W. Zhu, Z. X. Shen, P. H. J. Chong, Q. X. Liang, Z. C. Yang, Y. L. Hao, H. Cai, H. F. Zhou, Y. Gu, G.-Q. Lo, D. P. Tsai, T. Bourouina, Y. Leprince-Wang, and A.-Q. Liu, “Water-resonator-based metasurface: an ultrabroadband and near-unity absorption,” Adv. Opt. Mater. 5, 1601103 (2017).

Ye, D.

Y. Shen, D. Ye, I. Celanovic, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Optical broadband angular selectivity,” Science 343(6178), 1499–1501 (2014).
[PubMed]

Yu, N.

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).
[PubMed]

Yulevich, I.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[PubMed]

Zhang, L.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2(1), e1501168 (2016).
[PubMed]

Zhang, S.

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2(1), e1501168 (2016).
[PubMed]

Zhang, W.

Q. Song, W. Zhang, P. C. Wu, W. Zhu, Z. X. Shen, P. H. J. Chong, Q. X. Liang, Z. C. Yang, Y. L. Hao, H. Cai, H. F. Zhou, Y. Gu, G.-Q. Lo, D. P. Tsai, T. Bourouina, Y. Leprince-Wang, and A.-Q. Liu, “Water-resonator-based metasurface: an ultrabroadband and near-unity absorption,” Adv. Opt. Mater. 5, 1601103 (2017).

Zhang, X.

X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016).
[PubMed]

Zhao, Z.

L. Liu, P. Gao, K. Liu, W. Kong, Z. Zhao, M. Pu, C. Wang, and X. Luo, “Nanofocusing of circularly polarized Bessel-type plasmon polaritons with hyperbolic metamaterials,” Mater. Horiz. 4, 290–296 (2017).

X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016).
[PubMed]

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[PubMed]

M. Pu, Z. Zhao, Y. Wang, X. Li, X. Ma, C. Hu, C. Wang, C. Huang, and X. Luo, “Spatially and spectrally engineered spin-orbit interaction for achromatic virtual shaping,” Sci. Rep. 5, 9822 (2015).
[PubMed]

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing,” Laser Photonics Rev. 9, 713–719 (2015).

Zheludev, N. I.

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).
[PubMed]

Zhou, H. F.

Q. Song, W. Zhang, P. C. Wu, W. Zhu, Z. X. Shen, P. H. J. Chong, Q. X. Liang, Z. C. Yang, Y. L. Hao, H. Cai, H. F. Zhou, Y. Gu, G.-Q. Lo, D. P. Tsai, T. Bourouina, Y. Leprince-Wang, and A.-Q. Liu, “Water-resonator-based metasurface: an ultrabroadband and near-unity absorption,” Adv. Opt. Mater. 5, 1601103 (2017).

Zhu, A. Y.

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).
[PubMed]

Zhu, S.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1), 187 (2017).
[PubMed]

Zhu, W.

Q. Song, W. Zhang, P. C. Wu, W. Zhu, Z. X. Shen, P. H. J. Chong, Q. X. Liang, Z. C. Yang, Y. L. Hao, H. Cai, H. F. Zhou, Y. Gu, G.-Q. Lo, D. P. Tsai, T. Bourouina, Y. Leprince-Wang, and A.-Q. Liu, “Water-resonator-based metasurface: an ultrabroadband and near-unity absorption,” Adv. Opt. Mater. 5, 1601103 (2017).

Zueco, D.

A. Y. Nikitin, D. Zueco, F. J. Garcia-Vidal, and L. Martin-Moreno, “Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008).

Adv. Opt. Mater. (1)

Q. Song, W. Zhang, P. C. Wu, W. Zhu, Z. X. Shen, P. H. J. Chong, Q. X. Liang, Z. C. Yang, Y. L. Hao, H. Cai, H. F. Zhou, Y. Gu, G.-Q. Lo, D. P. Tsai, T. Bourouina, Y. Leprince-Wang, and A.-Q. Liu, “Water-resonator-based metasurface: an ultrabroadband and near-unity absorption,” Adv. Opt. Mater. 5, 1601103 (2017).

J. Mater. Chem. C Mater. Opt. Electron. Devices (1)

M. Pu, X. Ma, X. Li, Y. Guo, and X. Luo, “Merging plasmonics and metamaterials by two-dimensional subwavelength structures,” J. Mater. Chem. C Mater. Opt. Electron. Devices 5, 4361 (2017).

Laser Photonics Rev. (1)

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing,” Laser Photonics Rev. 9, 713–719 (2015).

Light Sci. Appl. (1)

X. Luo, M. Pu, X. Li, and X. Ma, “Broadband spin Hall effect of light in single nanoapertures,” Light Sci. Appl. 6, e16276 (2017).

Mater. Horiz. (1)

L. Liu, P. Gao, K. Liu, W. Kong, Z. Zhao, M. Pu, C. Wang, and X. Luo, “Nanofocusing of circularly polarized Bessel-type plasmon polaritons with hyperbolic metamaterials,” Mater. Horiz. 4, 290–296 (2017).

Nano Lett. (2)

B. H. Chen, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, I. C. Lee, J.-W. Chen, Y. H. Chen, Y.-C. Lan, C.-H. Kuan, and D. P. Tsai, “GaN metalens for pixel-level full-color routing at visible light,” Nano Lett. 17(10), 6345–6352 (2017).
[PubMed]

B. Groever, W. T. Chen, and F. Capasso, “Meta-lens doublet in the visible region,” Nano Lett. 17(8), 4902–4907 (2017).
[PubMed]

Nat. Commun. (4)

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7, 13682 (2016).
[PubMed]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
[PubMed]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. Hung Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1), 187 (2017).
[PubMed]

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, 7069 (2015).
[PubMed]

Nat. Mater. (2)

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).
[PubMed]

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[PubMed]

Nature (1)

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K.-J. Choi, Z. Liu, H. Park, C. Lu, R.-H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[PubMed]

Opt. Express (1)

Phys. Rev. B (1)

A. Y. Nikitin, D. Zueco, F. J. Garcia-Vidal, and L. Martin-Moreno, “Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008).

Phys. Rev. Lett. (1)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[PubMed]

Sci. Adv. (3)

X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016).
[PubMed]

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[PubMed]

F. Qin, L. Ding, L. Zhang, F. Monticone, C. C. Chum, J. Deng, S. Mei, Y. Li, J. Teng, M. Hong, S. Zhang, A. Alù, and C.-W. Qiu, “Hybrid bilayer plasmonic metasurface efficiently manipulates visible light,” Sci. Adv. 2(1), e1501168 (2016).
[PubMed]

Sci. China Phys. Mech. Astron. (1)

X. Luo, “Principles of electromagnetic waves in metasurfaces,” Sci. China Phys. Mech. Astron. 58, 594201 (2015).

Sci. Rep. (2)

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light,” Sci. Rep. 5, 9977 (2015).
[PubMed]

M. Pu, Z. Zhao, Y. Wang, X. Li, X. Ma, C. Hu, C. Wang, C. Huang, and X. Luo, “Spatially and spectrally engineered spin-orbit interaction for achromatic virtual shaping,” Sci. Rep. 5, 9822 (2015).
[PubMed]

Science (6)

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).
[PubMed]

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[PubMed]

Y. Shen, D. Ye, I. Celanovic, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Optical broadband angular selectivity,” Science 343(6178), 1499–1501 (2014).
[PubMed]

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).
[PubMed]

L. P. Lee and R. Szema, “Inspirations from biological optics for advanced photonic systems,” Science 310(5751), 1148–1150 (2005).
[PubMed]

Small Methods (1)

H.-H. Hsiao, C. H. Chu, and D. P. Tsai, “Fundamentals and applications of metasurfaces,” Small Methods 1, 1600064 (2017).

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Figures (5)

Fig. 1
Fig. 1 Comparison of different wide-angle lenses. (a) Luneburg lens. The height h equals to the diameter. (b) Compound eyes composed of many ommatidia. (c) Wide-angle flat lens. The thickness t is far smaller than the wavelength. The red, blue and yellow lines represent the light rays with different incidence angles.

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Fig. 2
Fig. 2 Flat lenses based on 2D quasi-crystal. (a) and (b) Schematic of the light rays for both an ordinary lens and a quadratic lens. (c) Array of the perforated elliptical apertures. The long and short axes are chosen as 180 nm and 60 nm. The lattice constant is p = 150 nm.

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Fig. 3
Fig. 3 Performance of the wide-angle flat lens. (a) Scanning electron microscope (SEM) image of one section of the fabricated 2D metalens. Scale bar, 2 μm. (b) and (c) Simulated light intensity distributed on the xz-plane (y = 0) and xy-plane (z = 7.5μm) at a wavelength of 632.8 nm. (d) and (e) Experimental results of the intensity distribution on the xz-plane (y = 0) for θ = 0°, −32° and θ = 0°, −80°. (f) Cross–section view (z = 7.5 μm) of the intensity distribution along the x-direction shown in (d) and (e). The full width at half maximum (FWHM) is about 427 nm.

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Fig. 4
Fig. 4 Multiwavelength behaviour of the quadratic lens. (a) Schematic of the measuring set-up. (b) Cross-section view of the intensity distribution in the xy (z = 0), xz (y = 0) and yz (x = 0) planes. (c) Intensity distribution in the focal plane (z = 7.5 μm).

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Fig. 5
Fig. 5 Performance of beam steering lens antenna. λ = 532 nm. R = 100 μm, f = 50 μm. (a) Far-field power patterns for θ = 0, 32, −45, 60, and −80°. The point sources are placed at 25sinθ, and z = 50 μm. Inset is the schematic of the operation set-up. (b) The point sources are placed at 25sinθ, and z = 46 μm. The power patterns are normalized with sinθ.

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Equations (2)

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Φ ( r ) = k 0 r 2 2 f ,
Φ ( r ) = k 0 r 2 2 f + k 0 x sin θ = k 0 2 f ( ( x + f sin θ ) 2 + y 2 ) − f k 0 sin 2 θ 2 ,

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