Abstract

Metasurfaces, with their superior capability in manipulating the optical wavefront at the subwavelength scale and low manufacturing complexity, have shown great potential for planar photonics and novel optical devices. However, vector field simulation of metasurfaces is so far limited to periodic-structured metasurfaces containing a small number of meta-atoms in the unit cell by using full-wave numerical methods. Here, focusing on achiral meta-atoms only with electric polarizability and thickness far less than the wavelength of light, and ignoring the coupling between meta-atoms, we propose a general phenomenological method to analytically model the metasurfaces based on the assumption that the meta-atoms possess localized resonances with Lorentz-Drude forms, whose exact form can be retrieved from the full wave simulation of a single element. Applied to phase modulated geometric metasurfaces constituted by identical meta-atoms with different orientations, our analytical results show good agreement with full-wave numerical simulations. The proposed theory provides an efficient method to model and design optical devices based on metasurfaces.

© 2016 Optical Society of America

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References

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  28. A. Epstein and G. V. Eleftheriades, “Huygens’ metasurfaces via the equivalence principle: design and applications,” J. Opt. Soc. Am. B 33(2), A31 (2016).
    [Crossref]
  29. E. F. Kuester, M. A. Mohamed, M. Piket-May, and C. L. Holloway, “Averaged Transition Conditions for Electromagnetic Fields at a Metafilm,” IEEE Trans. Antenn. Propag. 51(10), 2641–2651 (2003).
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    [Crossref]

2016 (1)

2015 (1)

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref] [PubMed]

2014 (7)

C. Pfeiffer, C. Zhang, V. Ray, L. J. Guo, and A. Grbic, “High performance bianisotropic metasurfaces: Asymmetric transmission of light,” Phys. Rev. Lett. 113(2), 023902 (2014).
[Crossref] [PubMed]

A. Epstein and G. V. Eleftheriades, “Floquet-Bloch analysis of refracting Huygens metasurfaces,” Phys. Rev. B 90(23), 235127 (2014).
[Crossref]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014).
[Crossref]

S. Jiang, X. Xiong, Y. Hu, Y. Hu, G. Ma, R. Peng, C. Sun, and M. Wang, “Controlling the Polarization State of Light with a Dispersion-Free Metastructure,” Phys. Rev. X 4(2), 021026 (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(1), 225–230 (2014).
[Crossref] [PubMed]

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
[Crossref]

2013 (12)

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(3), e70 (2013).
[Crossref]

J. Lin, J. P. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[Crossref] [PubMed]

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

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. Pun, K. W. Cheah, and J. Li, “Spin-Enabled Plasmonic Metasurfaces for Manipulating Orbital Angular Momentum of Light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref] [PubMed]

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [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).
[Crossref] [PubMed]

B. Yang, W. M. Ye, X. D. Yuan, Z. H. Zhu, and C. Zeng, “Design of ultrathin plasmonic quarter-wave plate based on period coupling,” Opt. Lett. 38(5), 679–681 (2013).
[Crossref] [PubMed]

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet inverted plasmonic metalenses,” Light Sci. Appl. 2(4), e72 (2013).
[Crossref]

A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband Focusing Flat Mirrors Based on Plasmonic Gradient Metasurfaces,” Nano Lett. 13(2), 829–834 (2013).
[Crossref] [PubMed]

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13(9), 4269–4274 (2013).
[Crossref] [PubMed]

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

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar Photonics with Metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref] [PubMed]

2012 (4)

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012).
[Crossref]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012).
[Crossref] [PubMed]

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(5), 426–431 (2012).
[Crossref] [PubMed]

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A. 109(31), 12364–12368 (2012).
[Crossref]

2011 (4)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

A. M. Patel and A. Grbic, “A Printed Leaky-Wave Antenna Based on a Sinusoidally-Modulated Reactance Surface,” IEEE Trans. Antenn. Propag. 59(6), 2087–2096 (2011).
[Crossref]

Y. Zhao, N. Engheta, and A. Alù, “Homogenization of plasmonic metasurfaces modeled as transmission-line loads,” Metamaterials (Amst.) 5(2-3), 90–96 (2011).
[Crossref]

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84(20), 205428 (2011).
[Crossref]

2003 (1)

E. F. Kuester, M. A. Mohamed, M. Piket-May, and C. L. Holloway, “Averaged Transition Conditions for Electromagnetic Fields at a Metafilm,” IEEE Trans. Antenn. Propag. 51(10), 2641–2651 (2003).
[Crossref]

Aieta, F.

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A. 109(31), 12364–12368 (2012).
[Crossref]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Alù, A.

Y. Zhao, N. Engheta, and A. Alù, “Homogenization of plasmonic metasurfaces modeled as transmission-line loads,” Metamaterials (Amst.) 5(2-3), 90–96 (2011).
[Crossref]

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84(20), 205428 (2011).
[Crossref]

Antoniou, N.

J. Lin, J. P. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[Crossref] [PubMed]

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13(9), 4269–4274 (2013).
[Crossref] [PubMed]

Aoust, G.

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A. 109(31), 12364–12368 (2012).
[Crossref]

Bai, B.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. 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(3), e70 (2013).
[Crossref]

Barnes, W. L.

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014).
[Crossref]

Blanchard, R.

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A. 109(31), 12364–12368 (2012).
[Crossref]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012).
[Crossref]

Boltasseva, A.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar Photonics with Metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref] [PubMed]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012).
[Crossref] [PubMed]

Boyd, R. W.

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
[Crossref]

Bozhevolnyi, S. I.

A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband Focusing Flat Mirrors Based on Plasmonic Gradient Metasurfaces,” Nano Lett. 13(2), 829–834 (2013).
[Crossref] [PubMed]

Capasso, F.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13(9), 4269–4274 (2013).
[Crossref] [PubMed]

J. Lin, J. P. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[Crossref] [PubMed]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012).
[Crossref]

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A. 109(31), 12364–12368 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Cheah, K.

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

Cheah, K. W.

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. Pun, K. W. Cheah, and J. Li, “Spin-Enabled Plasmonic Metasurfaces for Manipulating Orbital Angular Momentum of Light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref] [PubMed]

Chen, S.

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. Pun, K. W. Cheah, and J. Li, “Spin-Enabled Plasmonic Metasurfaces for Manipulating Orbital Angular Momentum of Light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref] [PubMed]

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. 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, 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(1), 225–230 (2014).
[Crossref] [PubMed]

Chen, X.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. 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(3), e70 (2013).
[Crossref]

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(1), 225–230 (2014).
[Crossref] [PubMed]

De Leon, I.

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
[Crossref]

Eleftheriades, G. V.

A. Epstein and G. V. Eleftheriades, “Huygens’ metasurfaces via the equivalence principle: design and applications,” J. Opt. Soc. Am. B 33(2), A31 (2016).
[Crossref]

A. Epstein and G. V. Eleftheriades, “Floquet-Bloch analysis of refracting Huygens metasurfaces,” Phys. Rev. B 90(23), 235127 (2014).
[Crossref]

Emani, N. K.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012).
[Crossref] [PubMed]

Engheta, N.

Y. Zhao, N. Engheta, and A. Alù, “Homogenization of plasmonic metasurfaces modeled as transmission-line loads,” Metamaterials (Amst.) 5(2-3), 90–96 (2011).
[Crossref]

Epstein, A.

A. Epstein and G. V. Eleftheriades, “Huygens’ metasurfaces via the equivalence principle: design and applications,” J. Opt. Soc. Am. B 33(2), A31 (2016).
[Crossref]

A. Epstein and G. V. Eleftheriades, “Floquet-Bloch analysis of refracting Huygens metasurfaces,” Phys. Rev. B 90(23), 235127 (2014).
[Crossref]

Eriksen, R. L.

A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband Focusing Flat Mirrors Based on Plasmonic Gradient Metasurfaces,” Nano Lett. 13(2), 829–834 (2013).
[Crossref] [PubMed]

Gaburro, Z.

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012).
[Crossref]

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A. 109(31), 12364–12368 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Genevet, P.

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13(9), 4269–4274 (2013).
[Crossref] [PubMed]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012).
[Crossref]

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A. 109(31), 12364–12368 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Grbic, A.

C. Pfeiffer, C. Zhang, V. Ray, L. J. Guo, and A. Grbic, “High performance bianisotropic metasurfaces: Asymmetric transmission of light,” Phys. Rev. Lett. 113(2), 023902 (2014).
[Crossref] [PubMed]

A. M. Patel and A. Grbic, “A Printed Leaky-Wave Antenna Based on a Sinusoidally-Modulated Reactance Surface,” IEEE Trans. Antenn. Propag. 59(6), 2087–2096 (2011).
[Crossref]

Guo, L. J.

C. Pfeiffer, C. Zhang, V. Ray, L. J. Guo, and A. Grbic, “High performance bianisotropic metasurfaces: Asymmetric transmission of light,” Phys. Rev. Lett. 113(2), 023902 (2014).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

He, Q.

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(5), 426–431 (2012).
[Crossref] [PubMed]

Holloway, C. L.

E. F. Kuester, M. A. Mohamed, M. Piket-May, and C. L. Holloway, “Averaged Transition Conditions for Electromagnetic Fields at a Metafilm,” IEEE Trans. Antenn. Propag. 51(10), 2641–2651 (2003).
[Crossref]

Hooper, I. R.

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014).
[Crossref]

Hsu, W. L.

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(1), 225–230 (2014).
[Crossref] [PubMed]

Hu, Y.

S. Jiang, X. Xiong, Y. Hu, Y. Hu, G. Ma, R. Peng, C. Sun, and M. Wang, “Controlling the Polarization State of Light with a Dispersion-Free Metastructure,” Phys. Rev. X 4(2), 021026 (2014).
[Crossref]

S. Jiang, X. Xiong, Y. Hu, Y. Hu, G. Ma, R. Peng, C. Sun, and M. Wang, “Controlling the Polarization State of Light with a Dispersion-Free Metastructure,” Phys. Rev. X 4(2), 021026 (2014).
[Crossref]

Huang, L.

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(3), e70 (2013).
[Crossref]

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

Huang, Y. W.

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(1), 225–230 (2014).
[Crossref] [PubMed]

Ishii, S.

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet inverted plasmonic metalenses,” Light Sci. Appl. 2(4), e72 (2013).
[Crossref]

Jiang, S.

S. Jiang, X. Xiong, Y. Hu, Y. Hu, G. Ma, R. Peng, C. Sun, and M. Wang, “Controlling the Polarization State of Light with a Dispersion-Free Metastructure,” Phys. Rev. X 4(2), 021026 (2014).
[Crossref]

Jin, G.

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(3), e70 (2013).
[Crossref]

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

Kang, M.

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. Pun, K. W. Cheah, and J. Li, “Spin-Enabled Plasmonic Metasurfaces for Manipulating Orbital Angular Momentum of Light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref] [PubMed]

Karimi, E.

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
[Crossref]

Kats, M. A.

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13(9), 4269–4274 (2013).
[Crossref] [PubMed]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012).
[Crossref]

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A. 109(31), 12364–12368 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Kenney, M.

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref] [PubMed]

Kildishev, A. V.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar Photonics with Metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref] [PubMed]

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

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet inverted plasmonic metalenses,” Light Sci. Appl. 2(4), e72 (2013).
[Crossref]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012).
[Crossref] [PubMed]

Kleiner, V.

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).
[Crossref] [PubMed]

Kuester, E. F.

E. F. Kuester, M. A. Mohamed, M. Piket-May, and C. L. Holloway, “Averaged Transition Conditions for Electromagnetic Fields at a Metafilm,” IEEE Trans. Antenn. Propag. 51(10), 2641–2651 (2003).
[Crossref]

Li, G.

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref] [PubMed]

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. Pun, K. W. Cheah, and J. Li, “Spin-Enabled Plasmonic Metasurfaces for Manipulating Orbital Angular Momentum of Light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref] [PubMed]

Li, J.

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. Pun, K. W. Cheah, and J. Li, “Spin-Enabled Plasmonic Metasurfaces for Manipulating Orbital Angular Momentum of Light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref] [PubMed]

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

Li, X.

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(5), 426–431 (2012).
[Crossref] [PubMed]

Liao, C. Y.

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(1), 225–230 (2014).
[Crossref] [PubMed]

Lin, H. T.

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(1), 225–230 (2014).
[Crossref] [PubMed]

Lin, J.

J. Lin, J. P. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[Crossref] [PubMed]

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13(9), 4269–4274 (2013).
[Crossref] [PubMed]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012).
[Crossref]

Liu, A. Q.

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(1), 225–230 (2014).
[Crossref] [PubMed]

Ma, G.

S. Jiang, X. Xiong, Y. Hu, Y. Hu, G. Ma, R. Peng, C. Sun, and M. Wang, “Controlling the Polarization State of Light with a Dispersion-Free Metastructure,” Phys. Rev. X 4(2), 021026 (2014).
[Crossref]

Maguid, 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).
[Crossref] [PubMed]

Meinzer, N.

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014).
[Crossref]

Mohamed, M. A.

E. F. Kuester, M. A. Mohamed, M. Piket-May, and C. L. Holloway, “Averaged Transition Conditions for Electromagnetic Fields at a Metafilm,” IEEE Trans. Antenn. Propag. 51(10), 2641–2651 (2003).
[Crossref]

Mueller, J. P.

J. Lin, J. P. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[Crossref] [PubMed]

Mühlenbernd, H.

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref] [PubMed]

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

Ni, X.

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet inverted plasmonic metalenses,” Light Sci. Appl. 2(4), e72 (2013).
[Crossref]

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

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012).
[Crossref] [PubMed]

Nielsen, M. G.

A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband Focusing Flat Mirrors Based on Plasmonic Gradient Metasurfaces,” Nano Lett. 13(2), 829–834 (2013).
[Crossref] [PubMed]

Ozeri, 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).
[Crossref] [PubMed]

Patel, A. M.

A. M. Patel and A. Grbic, “A Printed Leaky-Wave Antenna Based on a Sinusoidally-Modulated Reactance Surface,” IEEE Trans. Antenn. Propag. 59(6), 2087–2096 (2011).
[Crossref]

Peng, R.

S. Jiang, X. Xiong, Y. Hu, Y. Hu, G. Ma, R. Peng, C. Sun, and M. Wang, “Controlling the Polarization State of Light with a Dispersion-Free Metastructure,” Phys. Rev. X 4(2), 021026 (2014).
[Crossref]

Pfeiffer, C.

C. Pfeiffer, C. Zhang, V. Ray, L. J. Guo, and A. Grbic, “High performance bianisotropic metasurfaces: Asymmetric transmission of light,” Phys. Rev. Lett. 113(2), 023902 (2014).
[Crossref] [PubMed]

Piket-May, M.

E. F. Kuester, M. A. Mohamed, M. Piket-May, and C. L. Holloway, “Averaged Transition Conditions for Electromagnetic Fields at a Metafilm,” IEEE Trans. Antenn. Propag. 51(10), 2641–2651 (2003).
[Crossref]

Pors, A.

A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband Focusing Flat Mirrors Based on Plasmonic Gradient Metasurfaces,” Nano Lett. 13(2), 829–834 (2013).
[Crossref] [PubMed]

Pun, E. Y.

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. Pun, K. W. Cheah, and J. Li, “Spin-Enabled Plasmonic Metasurfaces for Manipulating Orbital Angular Momentum of Light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref] [PubMed]

Qassim, H.

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
[Crossref]

Qiu, C.

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

Ray, V.

C. Pfeiffer, C. Zhang, V. Ray, L. J. Guo, and A. Grbic, “High performance bianisotropic metasurfaces: Asymmetric transmission of light,” Phys. Rev. Lett. 113(2), 023902 (2014).
[Crossref] [PubMed]

Rho, J.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

Schulz, S. A.

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
[Crossref]

Scully, M. O.

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012).
[Crossref]

Shalaev, V. M.

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

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet inverted plasmonic metalenses,” Light Sci. Appl. 2(4), e72 (2013).
[Crossref]

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar Photonics with Metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref] [PubMed]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Sun, C.

S. Jiang, X. Xiong, Y. Hu, Y. Hu, G. Ma, R. Peng, C. Sun, and M. Wang, “Controlling the Polarization State of Light with a Dispersion-Free Metastructure,” Phys. Rev. X 4(2), 021026 (2014).
[Crossref]

Sun, G.

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(1), 225–230 (2014).
[Crossref] [PubMed]

Sun, S.

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(1), 225–230 (2014).
[Crossref] [PubMed]

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(5), 426–431 (2012).
[Crossref] [PubMed]

Tan, Q.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. 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(3), e70 (2013).
[Crossref]

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).
[Crossref] [PubMed]

Tsai, D. P.

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(1), 225–230 (2014).
[Crossref] [PubMed]

Upham, J.

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
[Crossref]

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).
[Crossref] [PubMed]

Wang, C. M.

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(1), 225–230 (2014).
[Crossref] [PubMed]

Wang, M.

S. Jiang, X. Xiong, Y. Hu, Y. Hu, G. Ma, R. Peng, C. Sun, and M. Wang, “Controlling the Polarization State of Light with a Dispersion-Free Metastructure,” Phys. Rev. X 4(2), 021026 (2014).
[Crossref]

Wang, Q.

J. Lin, J. P. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[Crossref] [PubMed]

Wang, Y.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

Xiao, S.

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(5), 426–431 (2012).
[Crossref] [PubMed]

Xiong, X.

S. Jiang, X. Xiong, Y. Hu, Y. Hu, G. Ma, R. Peng, C. Sun, and M. Wang, “Controlling the Polarization State of Light with a Dispersion-Free Metastructure,” Phys. Rev. X 4(2), 021026 (2014).
[Crossref]

Xu, Q.

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(5), 426–431 (2012).
[Crossref] [PubMed]

Yang, B.

Yang, K. Y.

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(1), 225–230 (2014).
[Crossref] [PubMed]

Ye, W. M.

Ye, Z.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

Yin, X.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

Yu, N.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A. 109(31), 12364–12368 (2012).
[Crossref]

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Yuan, G.

J. Lin, J. P. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[Crossref] [PubMed]

Yuan, X. C.

J. Lin, J. P. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[Crossref] [PubMed]

Yuan, X. D.

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).
[Crossref] [PubMed]

Zeng, C.

Zentgraf, T.

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref] [PubMed]

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. 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(3), e70 (2013).
[Crossref]

Zhang, C.

C. Pfeiffer, C. Zhang, V. Ray, L. J. Guo, and A. Grbic, “High performance bianisotropic metasurfaces: Asymmetric transmission of light,” Phys. Rev. Lett. 113(2), 023902 (2014).
[Crossref] [PubMed]

Zhang, H.

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

Zhang, S.

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref] [PubMed]

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. Cheah, C. 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(3), e70 (2013).
[Crossref]

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. Pun, K. W. Cheah, and J. Li, “Spin-Enabled Plasmonic Metasurfaces for Manipulating Orbital Angular Momentum of Light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref] [PubMed]

Zhang, X.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

Zhao, Y.

Y. Zhao, N. Engheta, and A. Alù, “Homogenization of plasmonic metasurfaces modeled as transmission-line loads,” Metamaterials (Amst.) 5(2-3), 90–96 (2011).
[Crossref]

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84(20), 205428 (2011).
[Crossref]

Zheng, G.

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref] [PubMed]

Zhou, L.

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(1), 225–230 (2014).
[Crossref] [PubMed]

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(5), 426–431 (2012).
[Crossref] [PubMed]

Zhu, Z. H.

Appl. Phys. Lett. (1)

P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012).
[Crossref]

IEEE Trans. Antenn. Propag. (2)

E. F. Kuester, M. A. Mohamed, M. Piket-May, and C. L. Holloway, “Averaged Transition Conditions for Electromagnetic Fields at a Metafilm,” IEEE Trans. Antenn. Propag. 51(10), 2641–2651 (2003).
[Crossref]

A. M. Patel and A. Grbic, “A Printed Leaky-Wave Antenna Based on a Sinusoidally-Modulated Reactance Surface,” IEEE Trans. Antenn. Propag. 59(6), 2087–2096 (2011).
[Crossref]

J. Opt. Soc. Am. B (1)

Light Sci. Appl. (3)

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
[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(3), e70 (2013).
[Crossref]

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet inverted plasmonic metalenses,” Light Sci. Appl. 2(4), e72 (2013).
[Crossref]

Metamaterials (Amst.) (1)

Y. Zhao, N. Engheta, and A. Alù, “Homogenization of plasmonic metasurfaces modeled as transmission-line loads,” Metamaterials (Amst.) 5(2-3), 90–96 (2011).
[Crossref]

Nano Lett. (4)

A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband Focusing Flat Mirrors Based on Plasmonic Gradient Metasurfaces,” Nano Lett. 13(2), 829–834 (2013).
[Crossref] [PubMed]

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13(9), 4269–4274 (2013).
[Crossref] [PubMed]

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(1), 225–230 (2014).
[Crossref] [PubMed]

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. Pun, K. W. Cheah, and J. Li, “Spin-Enabled Plasmonic Metasurfaces for Manipulating Orbital Angular Momentum of Light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref] [PubMed]

Nat. Commun. (2)

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

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

Nat. Mater. (2)

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(5), 426–431 (2012).
[Crossref] [PubMed]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref] [PubMed]

Nat. Photonics (1)

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014).
[Crossref]

Opt. Lett. (1)

Phys. Rev. B (2)

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84(20), 205428 (2011).
[Crossref]

A. Epstein and G. V. Eleftheriades, “Floquet-Bloch analysis of refracting Huygens metasurfaces,” Phys. Rev. B 90(23), 235127 (2014).
[Crossref]

Phys. Rev. Lett. (1)

C. Pfeiffer, C. Zhang, V. Ray, L. J. Guo, and A. Grbic, “High performance bianisotropic metasurfaces: Asymmetric transmission of light,” Phys. Rev. Lett. 113(2), 023902 (2014).
[Crossref] [PubMed]

Phys. Rev. X (1)

S. Jiang, X. Xiong, Y. Hu, Y. Hu, G. Ma, R. Peng, C. Sun, and M. Wang, “Controlling the Polarization State of Light with a Dispersion-Free Metastructure,” Phys. Rev. X 4(2), 021026 (2014).
[Crossref]

Proc. Natl. Acad. Sci. U.S.A. (1)

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A. 109(31), 12364–12368 (2012).
[Crossref]

Science (6)

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar Photonics with Metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref] [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).
[Crossref] [PubMed]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012).
[Crossref] [PubMed]

J. Lin, J. P. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[Crossref] [PubMed]

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [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).
[Crossref] [PubMed]

Other (1)

D. J. Griffiths, Introduction to Electrodynamics, 3rd ed. (PrenticeHall International, New Jersey, 1999)

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Figures (8)

Fig. 1
Fig. 1

Schematic illustration of the model of metasurface.

Fig. 2
Fig. 2

Schematic of a metasurface consisting of gold nanorods with different orientations (a) arranged on an infinite substrate; (b) on top of SiO2/Au layers, where the thickness of SiO2 is d, and the thickness of Au is much greater than the skin depth such that no light can transmit through. The cover of the metasurface is air.

Fig. 3
Fig. 3

(a) Schematic illustration of a metasurface with periodic Au nanorods array on the SiO2 substrate with periodΔis 500 nm. The width, length and thickness of the nanorod is 80 nm, 320 nm, and 30 nm, respectively. Numerical simulations of the transmission amplitude (b,d) and phase (c,e) of X-polarized and Y-polarized light normally incident from cover onto the metasurface. The fitting is based on Eq. (5) and Eq. (16).

Fig. 4
Fig. 4

(a) Schematic illustration of a phase-gradient metasurface with a linear gradient in the orientations angle along the x axis on an infinite substrate. The nanorad is same as that in Fig. 3 (a). (b, c) The analytical and simulated reflectivity spectra (b) and transmittivity spectra (c) for both zero-order (RCP) and first-order (LCP) diffractions when a right circularly polarized light (RCP) light is normally incident from air onto the metasurface. In the insets, letter A and letter S denote results obtained from our analytical theory and CST simulation, respectively.

Fig. 5
Fig. 5

The analytical and simulated reflectivity spectra of zero-order (RCP) and first-order (LCP) for a RCP beam at an incident angle of 30° from air onto the metasurface shown in Fig. 4(a).

Fig. 6
Fig. 6

(a) Schematic illustration of a three layer metasurface design with periodic Au nanorods array on the SiO2 substrate with Au ground plane underneath. The nanorad is the same as that in Fig. 3 (a) and the thickness of the SiO2 is 182nm. (b) The corresponding analytical and simulated reflectivity spectra of co-polarization and cross polarization for a normally incident RCP beam. The polarization conversion efficiency could reach 85% for the three layer design.

Fig. 7
Fig. 7

(a) Schematic illustration of a phase-gradient three layer design with Au ground plane and an increased orientations angle along the x axis. The nanorad is same as that in Fig. 3 (a) and the thickness of the SiO2 is 182nm. (b) The corresponding analytical and simulated reflectivity curves of zero-order (RCP) and first-order (LCP) diffractive light for the normally incident RCP.

Fig. 8
Fig. 8

The analytical and simulated total reflectivity curves of different ordered diffractive light for the normally incident RCP onto the one-dimensional hologram metasurface ended with Au ground plate.

Equations (29)

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E C+ + E C = E S+ + E S = E
e z ×( H S+ + H S H C+ H C )=iω ε 0 χ E
χ(x,y) m,n δ( x x m )δ( y y n ) α mn
α mn = α mn+ + α mn [ cos2 φ mn sin2 φ mn sin2 φ mn cos2 φ mn ]; α mm± = α mn S ± α mn P 2
α mn S(P) ( ω )= c g mn S(P) γ mn S(P) ω 2 ω mn S(P)2 +iω γ mn S(P)
χ(x,y)= k x , k y e i k x x+i k y y α ¯ ( k x , k y ) ; α ¯ ( k x , k y )= S 1 m,n e i k x x m i k y y n α mn ; E S(C)± (x,y)= k x , k y e i k x x+i k y y E k x , k y S(C)±
E k x , k y C+ + E k x , k y C = E k x , k y S+ + E k x , k y S ;
Y S ( k x , k y )( E k x , k y S+ E k x , k y S ) Y C ( k x , k y )( E k x , k y C+ E k x , k y C ) =( iω ε 0 ) k x , k y α ¯ ( k x k x , k y k y ) ( E k x , k y S+ + E k x , k y S )
Y S ( k x , k y )= ε S / μ S k 0 n S k 0 2 n S 2 k x 2 k y 2 [ k 0 2 n S 2 k y 2 k x k y k x k y k 0 2 n S 2 k x 2 ]
[ [ E k x , k y S+ ] [ E k x , k y C ] ]= [ Π ( k x , k y ),( k x , k y ) (+) Γ ( k x , k y ),( k x , k y ) I I ] 1 [ Γ ( k x , k y ),( k x , k y ) Π ( k x , k y ),( k x , k y ) () I I ][ [ E k x , k y C+ ] [ E k x , k y S ] ]
Π ( k x , k y ),( k x , k y ) (±) = Y S ( k x , k y ) δ k x , k x δ k y , k y ±iω ε 0 α ¯ ( k x k x , k y k y ) Γ ( k x , k y ),( k x , k y ) = Y C ( k x , k y ) δ k x , k x δ k y , k y
E k x , k y C+ + E k x , k y C = E k x , k y S
Y ¯ S ( k x , k y ) E k x , k y S Y C ( k x , k y )( E k x , k y C+ E k x , k y C ) =( iω ε 0 ) k x , k y α ¯ ( k x k x , k y k y ) E k x , k y S
Y ¯ S ( k x , k y )= Y S ( k x , k y ) R 1 ( k x , k y )[ itan ψ k x , k y TE 0 0 itan ψ k x , k y TM ]R( k x , k y )
R( k x , k y )= 1 k k z [ k y k z k x k z k x k 0 n S k y k 0 n S ]; k z = k 0 2 n S 2 k x 2 k y 2 ; k = k x 2 + k y 2 ψ k x , k y TE(TM) = k z di ln( r ¯ k x , k y TE(TM) ) /2
Y ¯ S ( 0,0 )=i ε S / μ S tan( k 0 n S di ln( r ¯ 0,0 TE ) /2 )
ε r (Au)=1 ω p 2 ω(ω+i ω τ ) , ω p =1.37× 10 16 rad/s, ω τ =1.215× 10 14 rad/s
[ E 0x S+ E 0y S+ ]= 2 n C n ˜ 2 + ( k 0 α Δ 2 ) 2 [ n ˜ +i k 0 α Δ 2 cos2φ i k 0 α Δ 2 sin2φ i k 0 α Δ 2 sin2φ n ˜ i k 0 α Δ 2 cos2φ ][ E 0x C+ E 0y C+ ]; E 0 C = E 0 S+ E 0 C+
[ E 0R S+ E 0L S+ ]= 2 n C n ˜ 2 + ( k 0 α Δ 2 ) 2 [ n ˜ i k 0 α Δ 2 e i2φ i k 0 α Δ 2 e i2φ n ˜ ][ E 0R C+ E 0L C+ ]
g S =13.9 Δ 2 , ω S =1.492× 10 15 rad/s, γ S =6.0× 10 13 rad/s
g P =5 Δ 2 , ω P =3.5× 10 15 rad/s, γ P =3× 10 13 rad/s
χ= k x , k y e i k x x+i k y y α ¯ ( k x , k y ) α S + α P 2 Δ 2 I+ e i 2π NΔ x e 2i φ 0 α S α P 4 Δ 2 [ 1 i i 1 ]+ e i 2π NΔ x e 2i φ 0 α S α P 4 Δ 2 [ 1 i i 1 ]
E 1 C = E 1 S+ =( 2iω ε 0 ) Λ 1 1 α ¯ 1 Ξ 1 Y 0 C E 0 C+
E 0 S+ =2 Ξ 1 Y 0 C E 0 C+ ; E 0 C =( 2 Ξ 1 Y 0 C I ) E 0 C+
E 1 C = E 1 S+ =( 2iω ε 0 ) Λ +1 1 α ¯ +1 Ξ 1 Y 0 C E 0 C+
Y ±1 S/C = Y S/C ( k x in ± 2π NΔ , k y in ), Y 0 S/C = Y S/C ( k x in , k y in ); α ¯ ±1 = α ¯ ( ± 2π NΔ ,0 ), α ¯ 0 = α ¯ ( 0,0 )
Λ ±1 =( Y ±1 S + Y ±1 C +iω ε 0 α ¯ 0 ); Λ 0 =( Y 0 S + Y 0 C +iω ε 0 α ¯ 0 )
Ξ= Λ 0 + ( ω ε 0 ) 2 α ¯ +1 Λ 1 1 α ¯ 1 + ( ω ε 0 ) 2 α ¯ 1 Λ +1 1 α ¯ +1
Y ¯ S ( 0,0 )= Y S ( 0,0 )itan( k 0 n S di ln( r ¯ 0,0 Au ) /2 )

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