Abstract

Polarization, which represents the vector nature of electromagnetic waves, plays a fundamental role in optics. Fast, simple, and broadband polarization state characterization is required by applications such as polarization communication, polarimetry, and remote sensing. However, conventional polarization detection methods face great difficulty in determining the phase difference between orthogonal polarization states and often require a series of measurements. Here, we demonstrate how polarization-dependent holography enables direct polarization detection in a single measurement. Using a multiplexed Pancharatnam–Berry phase metasurface, we generate orthogonally polarized holograms that partially overlap with a spatially varying phase difference. Both amplitude and phase difference can be read from the holographic image in the circular polarization basis, facilitating the extraction of all Stokes parameters for polarized light. The metahologram detects polarization reliably at several near-infrared to visible wavelengths, and simulations predict broadband operation in the 580–940 nm spectral range. This method enables fast and compact polarization analyzing devices, e.g., for spectroscopy, sensing, and communications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (1)

L. Cong, P. Pitchappa, N. Wang, and R. Singh, “Electrically programmable terahertz diatomic metamolecules for chiral optical control,” Research 2019, 7084251 (2019).
[Crossref]

2018 (10)

Z.-L. Deng, J. Deng, X. Zhuang, S. Wang, T. Shi, G. P. Wang, Y. Wang, J. Xu, Y. Cao, X. Wang, X. Cheng, G. Li, and X. Li, “Facile metagrating holograms with broadband and extreme angle tolerance,” Light Sci. Appl. 7, 78 (2018).
[Crossref]

Z.-L. Deng, J. Deng, X. Zhuang, S. Wang, K. Li, Y. Wang, Y. Chi, X. Ye, J. Xu, G. P. Wang, R. Zhao, X. Wang, Y. Cao, X. Cheng, G. Li, and X. Li, “Diatomic metasurface for vectorial holography,” Nano Lett. 18, 2885–2892 (2018).
[Crossref]

L. Huang, S. Zhang, and T. Zentgraf, “Metasurface holography: from fundamentals to applications,” Nanophotonics 7, 1169–1190 (2018).
[Crossref]

L. Cong, Y. K. Srivastava, H. Zhang, X. Zhang, J. Han, and R. Singh, “All-optical active THz metasurfaces for ultrafast polarization switching and dynamic beam splitting,” Light Sci. Appl. 7, 28 (2018).
[Crossref]

Q. Wang, E. Plum, Q. Yang, X. Zhang, Q. Xu, Y. Xu, J. Han, and W. Zhang, “Reflective chiral meta-holography: multiplexing holograms for circularly polarized waves,” Light Sci. Appl. 7, 25 (2018).
[Crossref]

Y. Chen, X. Yang, and J. Gao, “Spin-controlled wavefront shaping with plasmonic chiral geometric metasurfaces,” Light Sci. Appl. 7, 84 (2018).
[Crossref]

J. Li, S. Kamin, G. Zheng, F. Neubrech, S. Zhang, and N. Liu, “Addressable metasurfaces for dynamic holography and optical information encryption,” Sci. Adv. 4, eaar6768 (2018).
[Crossref]

P. C. Wu, J.-W. Chen, C.-W. Yin, Y.-C. Lai, T. L. Chung, C. Y. Liao, B. H. Chen, K.-W. Lee, C.-J. Chuang, C.-M. Wang, and D. P. Tsai, “Visible metasurfaces for on-chip polarimetry,” ACS Photon. 5, 2568–2573 (2018).
[Crossref]

Q. He, S. Sun, S. Xiao, and L. Zhou, “High-efficiency metasurfaces: principles, realizations, and applications,” Adv. Opt. Mater. 6, 1800415 (2018).
[Crossref]

H. Zhang, X. Zhang, Q. Xu, Q. Wang, Y. Xu, M. Wei, Y. Li, J. Gu, Z. Tian, C. Ouyang, X. Zhang, C. Hu, J. Han, and W. Zhang, “Polarization-independent all-silicon dielectric metasurfaces in the terahertz regime,” Photon. Res. 6, 24–29 (2018).
[Crossref]

2017 (14)

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4, 139–152 (2017).
[Crossref]

S. Wei, Z. Yang, and M. Zhao, “Design of ultracompact polarimeters based on dielectric metasurfaces,” Opt. Lett. 42, 1580–1583 (2017).
[Crossref]

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Controlling the sign of chromatic dispersion in diffractive optics with dielectric metasurfaces,” Optica 4, 625–632 (2017).
[Crossref]

A. Arbabi and A. Faraon, “Fundamental limits of ultrathin metasurfaces,” Sci. Rep. 7, 43722 (2017).
[Crossref]

H. Zhang, M. Kang, X. Zhang, W. Guo, C. Lv, Y. Li, W. Zhang, and J. Han, “Coherent control of optical spin-to-orbital angular momentum conversion in metasurface,” Adv. Mater. 29, 1604252 (2017).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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, 187(2017).
[Crossref]

W. T. Chen, M. Khorasaninejad, A. Y. Zhu, J. Oh, R. C. Devlin, A. Zaidi, and F. Capasso, “Generation of wavelength-independent subwavelength Bessel beams using metasurfaces,” Light Sci. Appl. 6, e16259 (2017).
[Crossref]

W. Wan, J. Gao, and X. Yang, “Metasurface holograms for holographic imaging,” Adv. Opt. Mater. 5, 1700541 (2017).
[Crossref]

L. Cong, P. Pitchappa, Y. Wu, L. Ke, C. Lee, N. Singh, H. Yang, and R. Singh, “Active multifunctional microelectromechanical system metadevices: applications in polarization control, wavefront deflection, and holograms,” Adv. Opt. Mater. 5, 1600716 (2017).
[Crossref]

L. Li, T. J. Cui, W. Ji, S. Liu, J. Ding, X. Wan, Y. B. Li, M. Jiang, C.-W. Qiu, and S. Zhang, “Electromagnetic reprogrammable coding-metasurface holograms,” Nat. Commun. 8, 197 (2017).
[Crossref]

H.-C. Liu, B. Yang, Q. Guo, J. Shi, C. Guan, G. Zheng, H. Mühlenbernd, G. Li, T. Zentgraf, and S. Zhang, “Single-pixel computational ghost imaging with helicity-dependent metasurface hologram,” Sci. Adv. 3, e1701477 (2017).
[Crossref]

Z. Xie, T. Lei, G. Si, X. Wang, J. Lin, C. Min, and X. Yuan, “Meta-holograms with full parameter control of wavefront over a 1000  nm bandwidth,” ACS Photon. 4, 2158–2164 (2017).
[Crossref]

J. P. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).
[Crossref]

Q. Xu, X. Zhang, Y. Xu, C. Ouyang, Z. Tian, J. Gu, J. Li, S. Zhang, J. Han, and W. Zhang, “Polarization-controlled surface plasmon holography,” Laser Photon. Rev. 11, 1600212 (2017).
[Crossref]

2016 (5)

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, e1601102 (2016).
[Crossref]

H.-T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep. Prog. Phys. 79, 076401 (2016).
[Crossref]

E. Maguid, I. Yulevich, D. Veksler, V. Kleiner, M. L. Brongersma, and E. Hasman, “Photonic spin-controlled multifunctional shared-aperture antenna array,” Science 352, 1202–1206 (2016).
[Crossref]

A. Pors and S. I. Bozhevolnyi, “Waveguide metacouplers for in-plane polarimetry,” Phys. Rev. Appl. 5, 064015 (2016).
[Crossref]

J. P. B. Mueller, K. Leosson, and F. Capasso, “Ultracompact metasurface in-line polarimeter,” Optica 3, 42–47 (2016).
[Crossref]

2015 (6)

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Plasmonic metagratings for simultaneous determination of Stokes parameters,” Optica 2, 716–723 (2015).
[Crossref]

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).
[Crossref]

S. Xiao, F. Zhong, H. Liu, S. Zhu, and J. Li, “Flexible coherent control of plasmonic spin-Hall effect,” Nat. Commun. 6, 8360 (2015).
[Crossref]

D. Wen, F. Yue, G. Li, G. Zheng, K. Chan, S. Chen, M. Chen, K. F. Li, P. W. H. Wong, K. W. Cheah, E. Y. B. Pun, S. Zhang, and X. Chen, “Helicity multiplexed broadband metasurface holograms,” Nat. Commun. 6, 8241 (2015).
[Crossref]

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10, 308–312 (2015).
[Crossref]

X. Zhang, Y. Xu, W. Yue, Z. Tian, J. Gu, Y. Li, R. Singh, S. Zhang, J. Han, and W. Zhang, “Anomalous surface wave launching by handedness phase control,” Adv. Mater. 27, 7123–7129 (2015).
[Crossref]

2014 (4)

Y. Montelongo, J. O. Tenorio-Pearl, W. I. Milne, and T. D. Wilkinson, “Polarization switchable diffraction based on subwavelength plasmonic nanoantennas,” Nano Lett. 14, 294–298 (2014).
[Crossref]

Y. Yifat, M. Eitan, Z. Iluz, Y. Hanein, A. Boag, and J. Scheuer, “Highly efficient and broadband wide-angle holography using patch-dipole nanoantenna reflectarrays,” Nano Lett. 14, 2485–2490 (2014).
[Crossref]

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W.-L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14, 225–230 (2014).
[Crossref]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
[Crossref]

2013 (5)

L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light Sci. Appl. 2, e70 (2013).
[Crossref]

X. Zhang, Z. Tian, W. Yue, J. Gu, S. Zhang, J. Han, and W. Zhang, “Broadband terahertz wave deflections based on C-shape complex metamaterials with phase discontinuities,” Adv. Mater. 25, 4567–4572 (2013).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
[Crossref]

X. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4, 2807 (2013).
[Crossref]

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013).
[Crossref]

2012 (5)

F. Afshinmanesh, J. S. White, W. Cai, and M. L. Brongersma, “Measurement of the polarization state of light using an integrated plasmonic polarimeter,” Nanophotonics 1, 125–129 (2012).
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L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
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S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12, 6223–6229 (2012).
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X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012).
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S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11, 426–431 (2012).
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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, 333–337 (2011).
[Crossref]

2006 (1)

2000 (1)

C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature 404, 247–255 (2000).
[Crossref]

1982 (1)

R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta 29, 685–689 (1982).
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1977 (1)

Afshinmanesh, F.

F. Afshinmanesh, J. S. White, W. Cai, and M. L. Brongersma, “Measurement of the polarization state of light using an integrated plasmonic polarimeter,” Nanophotonics 1, 125–129 (2012).
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Aieta, F.

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4, 139–152 (2017).
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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, 333–337 (2011).
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Alù, A.

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013).
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Arbabi, A.

A. Arbabi and A. Faraon, “Fundamental limits of ultrathin metasurfaces,” Sci. Rep. 7, 43722 (2017).
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E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Controlling the sign of chromatic dispersion in diffractive optics with dielectric metasurfaces,” Optica 4, 625–632 (2017).
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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).
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Arbabi, E.

Azzam, R. M. A.

R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta 29, 685–689 (1982).
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R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

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).
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Bai, B.

L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light Sci. Appl. 2, e70 (2013).
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L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
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X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012).
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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).
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Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Bennett, C. H.

C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature 404, 247–255 (2000).
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Berry, H. G.

Boag, A.

Y. Yifat, M. Eitan, Z. Iluz, Y. Hanein, A. Boag, and J. Scheuer, “Highly efficient and broadband wide-angle holography using patch-dipole nanoantenna reflectarrays,” Nano Lett. 14, 2485–2490 (2014).
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Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

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A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Plasmonic metagratings for simultaneous determination of Stokes parameters,” Optica 2, 716–723 (2015).
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F. Afshinmanesh, J. S. White, W. Cai, and M. L. Brongersma, “Measurement of the polarization state of light using an integrated plasmonic polarimeter,” Nanophotonics 1, 125–129 (2012).
[Crossref]

Cai, W.

F. Afshinmanesh, J. S. White, W. Cai, and M. L. Brongersma, “Measurement of the polarization state of light using an integrated plasmonic polarimeter,” Nanophotonics 1, 125–129 (2012).
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Cao, Y.

Z.-L. Deng, J. Deng, X. Zhuang, S. Wang, T. Shi, G. P. Wang, Y. Wang, J. Xu, Y. Cao, X. Wang, X. Cheng, G. Li, and X. Li, “Facile metagrating holograms with broadband and extreme angle tolerance,” Light Sci. Appl. 7, 78 (2018).
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Z.-L. Deng, J. Deng, X. Zhuang, S. Wang, K. Li, Y. Wang, Y. Chi, X. Ye, J. Xu, G. P. Wang, R. Zhao, X. Wang, Y. Cao, X. Cheng, G. Li, and X. Li, “Diatomic metasurface for vectorial holography,” Nano Lett. 18, 2885–2892 (2018).
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Capasso, F.

J. P. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).
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W. T. Chen, M. Khorasaninejad, A. Y. Zhu, J. Oh, R. C. Devlin, A. Zaidi, and F. Capasso, “Generation of wavelength-independent subwavelength Bessel beams using metasurfaces,” Light Sci. Appl. 6, e16259 (2017).
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P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4, 139–152 (2017).
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J. P. B. Mueller, K. Leosson, and F. Capasso, “Ultracompact metasurface in-line polarimeter,” Optica 3, 42–47 (2016).
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N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
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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, 333–337 (2011).
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Chan, K.

D. Wen, F. Yue, G. Li, G. Zheng, K. Chan, S. Chen, M. Chen, K. F. Li, P. W. H. Wong, K. W. Cheah, E. Y. B. Pun, S. Zhang, and X. Chen, “Helicity multiplexed broadband metasurface holograms,” Nat. Commun. 6, 8241 (2015).
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Cheah, K. W.

D. Wen, F. Yue, G. Li, G. Zheng, K. Chan, S. Chen, M. Chen, K. F. Li, P. W. H. Wong, K. W. Cheah, E. Y. B. Pun, S. Zhang, and X. Chen, “Helicity multiplexed broadband metasurface holograms,” Nat. Commun. 6, 8241 (2015).
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Cheah, K.-W.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
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Chen, B. H.

P. C. Wu, J.-W. Chen, C.-W. Yin, Y.-C. Lai, T. L. Chung, C. Y. Liao, B. H. Chen, K.-W. Lee, C.-J. Chuang, C.-M. Wang, and D. P. Tsai, “Visible metasurfaces for on-chip polarimetry,” ACS Photon. 5, 2568–2573 (2018).
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Chen, H.-T.

H.-T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep. Prog. Phys. 79, 076401 (2016).
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Chen, J.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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, 187(2017).
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Chen, J.-W.

P. C. Wu, J.-W. Chen, C.-W. Yin, Y.-C. Lai, T. L. Chung, C. Y. Liao, B. H. Chen, K.-W. Lee, C.-J. Chuang, C.-M. Wang, and D. P. Tsai, “Visible metasurfaces for on-chip polarimetry,” ACS Photon. 5, 2568–2573 (2018).
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S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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, 187(2017).
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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, e1601102 (2016).
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Chen, M.

D. Wen, F. Yue, G. Li, G. Zheng, K. Chan, S. Chen, M. Chen, K. F. Li, P. W. H. Wong, K. W. Cheah, E. Y. B. Pun, S. Zhang, and X. Chen, “Helicity multiplexed broadband metasurface holograms,” Nat. Commun. 6, 8241 (2015).
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Chen, S.

D. Wen, F. Yue, G. Li, G. Zheng, K. Chan, S. Chen, M. Chen, K. F. Li, P. W. H. Wong, K. W. Cheah, E. Y. B. Pun, S. Zhang, and X. Chen, “Helicity multiplexed broadband metasurface holograms,” Nat. Commun. 6, 8241 (2015).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
[Crossref]

Chen, W. T.

W. T. Chen, M. Khorasaninejad, A. Y. Zhu, J. Oh, R. C. Devlin, A. Zaidi, and F. Capasso, “Generation of wavelength-independent subwavelength Bessel beams using metasurfaces,” Light Sci. Appl. 6, e16259 (2017).
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W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W.-L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14, 225–230 (2014).
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S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12, 6223–6229 (2012).
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Chen, X.

D. Wen, F. Yue, G. Li, G. Zheng, K. Chan, S. Chen, M. Chen, K. F. Li, P. W. H. Wong, K. W. Cheah, E. Y. B. Pun, S. Zhang, and X. Chen, “Helicity multiplexed broadband metasurface holograms,” Nat. Commun. 6, 8241 (2015).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
[Crossref]

L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light Sci. Appl. 2, e70 (2013).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
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X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012).
[Crossref]

Chen, Y.

Y. Chen, X. Yang, and J. Gao, “Spin-controlled wavefront shaping with plasmonic chiral geometric metasurfaces,” Light Sci. Appl. 7, 84 (2018).
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Chenault, D. B.

Cheng, X.

Z.-L. Deng, J. Deng, X. Zhuang, S. Wang, K. Li, Y. Wang, Y. Chi, X. Ye, J. Xu, G. P. Wang, R. Zhao, X. Wang, Y. Cao, X. Cheng, G. Li, and X. Li, “Diatomic metasurface for vectorial holography,” Nano Lett. 18, 2885–2892 (2018).
[Crossref]

Z.-L. Deng, J. Deng, X. Zhuang, S. Wang, T. Shi, G. P. Wang, Y. Wang, J. Xu, Y. Cao, X. Wang, X. Cheng, G. Li, and X. Li, “Facile metagrating holograms with broadband and extreme angle tolerance,” Light Sci. Appl. 7, 78 (2018).
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Chi, Y.

Z.-L. Deng, J. Deng, X. Zhuang, S. Wang, K. Li, Y. Wang, Y. Chi, X. Ye, J. Xu, G. P. Wang, R. Zhao, X. Wang, Y. Cao, X. Cheng, G. Li, and X. Li, “Diatomic metasurface for vectorial holography,” Nano Lett. 18, 2885–2892 (2018).
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Chiang, I.-D.

W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W.-L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14, 225–230 (2014).
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S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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, 187(2017).
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Chuang, C.-J.

P. C. Wu, J.-W. Chen, C.-W. Yin, Y.-C. Lai, T. L. Chung, C. Y. Liao, B. H. Chen, K.-W. Lee, C.-J. Chuang, C.-M. Wang, and D. P. Tsai, “Visible metasurfaces for on-chip polarimetry,” ACS Photon. 5, 2568–2573 (2018).
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Chung, T. L.

P. C. Wu, J.-W. Chen, C.-W. Yin, Y.-C. Lai, T. L. Chung, C. Y. Liao, B. H. Chen, K.-W. Lee, C.-J. Chuang, C.-M. Wang, and D. P. Tsai, “Visible metasurfaces for on-chip polarimetry,” ACS Photon. 5, 2568–2573 (2018).
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L. Cong, P. Pitchappa, N. Wang, and R. Singh, “Electrically programmable terahertz diatomic metamolecules for chiral optical control,” Research 2019, 7084251 (2019).
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L. Cong, Y. K. Srivastava, H. Zhang, X. Zhang, J. Han, and R. Singh, “All-optical active THz metasurfaces for ultrafast polarization switching and dynamic beam splitting,” Light Sci. Appl. 7, 28 (2018).
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L. Cong, P. Pitchappa, Y. Wu, L. Ke, C. Lee, N. Singh, H. Yang, and R. Singh, “Active multifunctional microelectromechanical system metadevices: applications in polarization control, wavefront deflection, and holograms,” Adv. Opt. Mater. 5, 1600716 (2017).
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L. Li, T. J. Cui, W. Ji, S. Liu, J. Ding, X. Wan, Y. B. Li, M. Jiang, C.-W. Qiu, and S. Zhang, “Electromagnetic reprogrammable coding-metasurface holograms,” Nat. Commun. 8, 197 (2017).
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[Crossref]

Z.-L. Deng, J. Deng, X. Zhuang, S. Wang, T. Shi, G. P. Wang, Y. Wang, J. Xu, Y. Cao, X. Wang, X. Cheng, G. Li, and X. Li, “Facile metagrating holograms with broadband and extreme angle tolerance,” Light Sci. Appl. 7, 78 (2018).
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Deng, Z.-L.

Z.-L. Deng, J. Deng, X. Zhuang, S. Wang, T. Shi, G. P. Wang, Y. Wang, J. Xu, Y. Cao, X. Wang, X. Cheng, G. Li, and X. Li, “Facile metagrating holograms with broadband and extreme angle tolerance,” Light Sci. Appl. 7, 78 (2018).
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Z.-L. Deng, J. Deng, X. Zhuang, S. Wang, K. Li, Y. Wang, Y. Chi, X. Ye, J. Xu, G. P. Wang, R. Zhao, X. Wang, Y. Cao, X. Cheng, G. Li, and X. Li, “Diatomic metasurface for vectorial holography,” Nano Lett. 18, 2885–2892 (2018).
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Devlin, R.

Devlin, R. C.

W. T. Chen, M. Khorasaninejad, A. Y. Zhu, J. Oh, R. C. Devlin, A. Zaidi, and F. Capasso, “Generation of wavelength-independent subwavelength Bessel beams using metasurfaces,” Light Sci. Appl. 6, e16259 (2017).
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J. P. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).
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Ding, J.

L. Li, T. J. Cui, W. Ji, S. Liu, J. Ding, X. Wan, Y. B. Li, M. Jiang, C.-W. Qiu, and S. Zhang, “Electromagnetic reprogrammable coding-metasurface holograms,” Nat. Commun. 8, 197 (2017).
[Crossref]

DiVincenzo, D. P.

C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature 404, 247–255 (2000).
[Crossref]

Eitan, M.

Y. Yifat, M. Eitan, Z. Iluz, Y. Hanein, A. Boag, and J. Scheuer, “Highly efficient and broadband wide-angle holography using patch-dipole nanoantenna reflectarrays,” Nano Lett. 14, 2485–2490 (2014).
[Crossref]

Estakhri, N. M.

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013).
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Faraon, A.

A. Arbabi and A. Faraon, “Fundamental limits of ultrathin metasurfaces,” Sci. Rep. 7, 43722 (2017).
[Crossref]

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Controlling the sign of chromatic dispersion in diffractive optics with dielectric metasurfaces,” Optica 4, 625–632 (2017).
[Crossref]

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).
[Crossref]

Gabrielse, G.

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, 333–337 (2011).
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Gao, J.

Y. Chen, X. Yang, and J. Gao, “Spin-controlled wavefront shaping with plasmonic chiral geometric metasurfaces,” Light Sci. Appl. 7, 84 (2018).
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W. Wan, J. Gao, and X. Yang, “Metasurface holograms for holographic imaging,” Adv. Opt. Mater. 5, 1700541 (2017).
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Genevet, P.

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4, 139–152 (2017).
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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, 333–337 (2011).
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Goldstein, D. L.

Groever, B.

J. P. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).
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Gu, J.

H. Zhang, X. Zhang, Q. Xu, Q. Wang, Y. Xu, M. Wei, Y. Li, J. Gu, Z. Tian, C. Ouyang, X. Zhang, C. Hu, J. Han, and W. Zhang, “Polarization-independent all-silicon dielectric metasurfaces in the terahertz regime,” Photon. Res. 6, 24–29 (2018).
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Q. Xu, X. Zhang, Y. Xu, C. Ouyang, Z. Tian, J. Gu, J. Li, S. Zhang, J. Han, and W. Zhang, “Polarization-controlled surface plasmon holography,” Laser Photon. Rev. 11, 1600212 (2017).
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X. Zhang, Z. Tian, W. Yue, J. Gu, S. Zhang, J. Han, and W. Zhang, “Broadband terahertz wave deflections based on C-shape complex metamaterials with phase discontinuities,” Adv. Mater. 25, 4567–4572 (2013).
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Guan, C.

H.-C. Liu, B. Yang, Q. Guo, J. Shi, C. Guan, G. Zheng, H. Mühlenbernd, G. Li, T. Zentgraf, and S. Zhang, “Single-pixel computational ghost imaging with helicity-dependent metasurface hologram,” Sci. Adv. 3, e1701477 (2017).
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Guo, G.-Y.

S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12, 6223–6229 (2012).
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X. Zhang, Z. Tian, W. Yue, J. Gu, S. Zhang, J. Han, and W. Zhang, “Broadband terahertz wave deflections based on C-shape complex metamaterials with phase discontinuities,” Adv. Mater. 25, 4567–4572 (2013).
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L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
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X. Zhang, Z. Tian, W. Yue, J. Gu, S. Zhang, J. Han, and W. Zhang, “Broadband terahertz wave deflections based on C-shape complex metamaterials with phase discontinuities,” Adv. Mater. 25, 4567–4572 (2013).
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L. Cong, Y. K. Srivastava, H. Zhang, X. Zhang, J. Han, and R. Singh, “All-optical active THz metasurfaces for ultrafast polarization switching and dynamic beam splitting,” Light Sci. Appl. 7, 28 (2018).
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Q. Wang, E. Plum, Q. Yang, X. Zhang, Q. Xu, Y. Xu, J. Han, and W. Zhang, “Reflective chiral meta-holography: multiplexing holograms for circularly polarized waves,” Light Sci. Appl. 7, 25 (2018).
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H. Zhang, X. Zhang, Q. Xu, Q. Wang, Y. Xu, M. Wei, Y. Li, J. Gu, Z. Tian, C. Ouyang, X. Zhang, C. Hu, J. Han, and W. Zhang, “Polarization-independent all-silicon dielectric metasurfaces in the terahertz regime,” Photon. Res. 6, 24–29 (2018).
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X. Zhang, Z. Tian, W. Yue, J. Gu, S. Zhang, J. Han, and W. Zhang, “Broadband terahertz wave deflections based on C-shape complex metamaterials with phase discontinuities,” Adv. Mater. 25, 4567–4572 (2013).
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[Crossref]

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10, 308–312 (2015).
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S. Xiao, F. Zhong, H. Liu, S. Zhu, and J. Li, “Flexible coherent control of plasmonic spin-Hall effect,” Nat. Commun. 6, 8360 (2015).
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Q. He, S. Sun, S. Xiao, and L. Zhou, “High-efficiency metasurfaces: principles, realizations, and applications,” Adv. Opt. Mater. 6, 1800415 (2018).
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W. T. Chen, M. Khorasaninejad, A. Y. Zhu, J. Oh, R. C. Devlin, A. Zaidi, and F. Capasso, “Generation of wavelength-independent subwavelength Bessel beams using metasurfaces,” Light Sci. Appl. 6, e16259 (2017).
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S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. 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, 187(2017).
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Z.-L. Deng, J. Deng, X. Zhuang, S. Wang, T. Shi, G. P. Wang, Y. Wang, J. Xu, Y. Cao, X. Wang, X. Cheng, G. Li, and X. Li, “Facile metagrating holograms with broadband and extreme angle tolerance,” Light Sci. Appl. 7, 78 (2018).
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Z.-L. Deng, J. Deng, X. Zhuang, S. Wang, K. Li, Y. Wang, Y. Chi, X. Ye, J. Xu, G. P. Wang, R. Zhao, X. Wang, Y. Cao, X. Cheng, G. Li, and X. Li, “Diatomic metasurface for vectorial holography,” Nano Lett. 18, 2885–2892 (2018).
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ACS Photon. (2)

Z. Xie, T. Lei, G. Si, X. Wang, J. Lin, C. Min, and X. Yuan, “Meta-holograms with full parameter control of wavefront over a 1000  nm bandwidth,” ACS Photon. 4, 2158–2164 (2017).
[Crossref]

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[Crossref]

Adv. Mater. (3)

X. Zhang, Y. Xu, W. Yue, Z. Tian, J. Gu, Y. Li, R. Singh, S. Zhang, J. Han, and W. Zhang, “Anomalous surface wave launching by handedness phase control,” Adv. Mater. 27, 7123–7129 (2015).
[Crossref]

X. Zhang, Z. Tian, W. Yue, J. Gu, S. Zhang, J. Han, and W. Zhang, “Broadband terahertz wave deflections based on C-shape complex metamaterials with phase discontinuities,” Adv. Mater. 25, 4567–4572 (2013).
[Crossref]

H. Zhang, M. Kang, X. Zhang, W. Guo, C. Lv, Y. Li, W. Zhang, and J. Han, “Coherent control of optical spin-to-orbital angular momentum conversion in metasurface,” Adv. Mater. 29, 1604252 (2017).
[Crossref]

Adv. Opt. Mater. (3)

W. Wan, J. Gao, and X. Yang, “Metasurface holograms for holographic imaging,” Adv. Opt. Mater. 5, 1700541 (2017).
[Crossref]

Q. He, S. Sun, S. Xiao, and L. Zhou, “High-efficiency metasurfaces: principles, realizations, and applications,” Adv. Opt. Mater. 6, 1800415 (2018).
[Crossref]

L. Cong, P. Pitchappa, Y. Wu, L. Ke, C. Lee, N. Singh, H. Yang, and R. Singh, “Active multifunctional microelectromechanical system metadevices: applications in polarization control, wavefront deflection, and holograms,” Adv. Opt. Mater. 5, 1600716 (2017).
[Crossref]

Appl. Opt. (2)

Laser Photon. Rev. (1)

Q. Xu, X. Zhang, Y. Xu, C. Ouyang, Z. Tian, J. Gu, J. Li, S. Zhang, J. Han, and W. Zhang, “Polarization-controlled surface plasmon holography,” Laser Photon. Rev. 11, 1600212 (2017).
[Crossref]

Light Sci. Appl. (6)

L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light Sci. Appl. 2, e70 (2013).
[Crossref]

Q. Wang, E. Plum, Q. Yang, X. Zhang, Q. Xu, Y. Xu, J. Han, and W. Zhang, “Reflective chiral meta-holography: multiplexing holograms for circularly polarized waves,” Light Sci. Appl. 7, 25 (2018).
[Crossref]

Y. Chen, X. Yang, and J. Gao, “Spin-controlled wavefront shaping with plasmonic chiral geometric metasurfaces,” Light Sci. Appl. 7, 84 (2018).
[Crossref]

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Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1. Holographic polarimetry concept. (a), (b) Circular-polarization-dependent metahologram for generating RCP and LCP images of a ring containing an upper or lower circular disk under LCP and RCP illumination, respectively. (c), (d) For illustration of the working mechanism, helical phase distributions φRL and φLR with 1 and +1 topological charges are assigned to the holographic rings generated by LCP and RCP illumination, respectively. (e) Phase difference distribution φRLφLR+Δφ, where Δφ is the chiral phase difference between the incident LCP and RCP components of the light. By comparing the intensities of the top and bottom circular disks, the chiral amplitude contrast can be obtained. The polarization state can thus be determined by combining the chiral phase difference and chiral amplitude contrast.
Fig. 2.
Fig. 2. Numerical demonstration of holographic polarimetry. (a)–(d) Ideal calculated x-polarized image components for illumination of the metahologram by waves with (a) RCP, (b) +45° linear, (c) left-handed elliptical, and (d) right-handed elliptical polarization, as indicated by the corresponding inset arrows. Here, the radial intensity distributions within the rings in (a)–(d) are uniform. (e) Schematic of a polarization ellipse, where ψ and χ represent the polarization orientation angle and ellipticity, respectively. For the four incident polarizations in (a)–(d), we set (ψ,χ)=(arbitrary value,45°), (45°, 0°), (60°, 15°), and (60°, 15°), respectively. (f) Normalized intensity distributions along the rings (dashed circle in a) in (a)–(d) as a function of azimuth angle θ, respectively. The arrows point to the first maximum, whose θ corresponds to half of the chiral phase difference. (g), (h) Theoretical relationships between (g) polarization orientation angle as a function of chiral phase difference: ψ=Δφ/2, and (h) polarization ellipticity as a function of s3 as defined in Eq. (4): χ=atan[s3/(1s32)1/2]/2, s3[1,1]. Here, s3=1, 0, 1 (corresponding to a=, 1, 0) represent LCP, linear polarization, RCP, respectively. The color markers in (g), (h) show the chiral phase difference and chiral amplitude contrast extracted from the holographic images in (a)–(d) using corresponding colors for markers and polarization arrows. (i) Schematic of a unit Poincaré sphere in 3D Cartesian coordinates formed by the Stokes parameters s1, s2, s3. The green and blue circles are the s3 latitude and Δφ meridian on the sphere, whose intersection point represents the polarization state.
Fig. 3.
Fig. 3. Metahologram design for broadband polarimetry. (a), (b) Designed holographic images generated under the LCP and RCP illumination, respectively, where the target ring and disk patterns are placed in the left-top corners. (c), (d) The corresponding calculated phase distributions of the holograms for LCP and RCP illumination based on the modified Gerchberg–Saxton algorithm, respectively. (e) Simulated copolarized and cross-polarized transmittance spectra of the metasurface’s bar resonators in the circular polarization basis. (f) Scanning electron microscopy image of a part of the fabricated metahologram, where resonators generating the holograms in panels (a) and (b) are colored green and orange, respectively.
Fig. 4.
Fig. 4. Experimental demonstration of holographic polarimetry. (a) Schematic of the experimental setup. LP, linear polarizer; WP, wave plate; F, space filter. Green arrows indicate the polarization state after LP1 and LP2. The orientation angle of wave plate’s fast axis is measured from the positive y axis, increasing towards the negative x axis as illustrated by the inset. (b)–(e), (j)–(m) Holographic images captured by the CCD camera for orientation angles of the half-wave plate’s fast axis of αHWP=0°, 30°, 60°, 90°, and orientation angles of the quarter-wave plate’s fast axis of αQWP=45°, 15°, 15°, 45°, respectively. The inset arrows schematically indicate the corresponding theoretical polarization state. (f), (n) Theoretical, experimental, and simulated chiral phase differences when rotating the half-wave plate and the quarter-wave plate, respectively. (g)–(i), (o)–(q) Theoretical, experimental, and simulated Stokes parameters s1, s2, and s3 when rotating the half-wave plate and the quarter-wave plate, respectively.

Equations (6)

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P=l0eiφLinL+r0eiφRinR=r0eiφRin[aeiΔφL+R],
PD(θ)=l0eiφLineiφRLR+r0eiφRineiφLRL=22ei(φLR+φRin){l0ei(Δφ2θ)[1i]+r0[1i]},
|PDx(θ)|2=12r02+12l02+l0r0cos(2θΔφ).
s3=IRILIR+IL=1a21+a2.
s1=1s32cosΔφ,
s2=1s32sinΔφ.

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