Abstract

Dispersion management is crucial in constructing spectrometers, superprisms, and achromatic lens systems. Unfortunately, the dispersion of natural materials is determined by the molecular energy levels with limited tunability, and thus conventional methods of dispersion controlling are complex and need to trade off other aberration. Metasurface offers an alternative method to overcome those limits via utilizing dedicatedly designed nanostructures that response to special wavelength, which results in well-engineered dispersions. As proof of the concept, we design a series of flat dielectric metasurface lenses, which are able to steer the dispersion arbitrarily for three wavelengths at visible frequency (473, 532, and 632.8 nm). Based on the unique dispersion engineering ability of metasurface, the achromatic meta-lens and the super-dispersion meta-lenses are realized. Furthermore, the light of different wavelengths can be focused on any desired spatial positions.

© 2017 Optical Society of America

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References

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2017 (6)

M. B. Pu, X. L. Ma, X. Li, Y. H. Guo, and X. G. Luo, “Merging plasmonics and metamaterials by two-dimensional subwavelength structures,” J. Mater. Chem. C 5(18), 4361–4378 (2017).
[Crossref]

Y. Li, X. Li, L. Chen, M. B. Pu, J. J. Jin, M. Hong, and X. G. Luo, “Orbital angular momentum multiplexing and demultiplexing by a single metasurfaces,” Adv. Opt. Mater. 5(2), 1600502 (2017).
[Crossref]

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

P. C. Wu, W. Y. Tsai, W. T. Chen, Y. W. Huang, T. Y. Chen, J. W. Chen, C. Y. Liao, C. H. Chu, G. Sun, and D. P. Tsai, “Versatile polarization generation with an aluminum plasmonicmetasurface,” Nano Lett. 17(1), 445–452 (2017).
[Crossref] [PubMed]

P. C. Wu, W. Z. X. Zhu, Z. X. Shen, P. H. J. Chong, W. Ser, D. P. Tsai, and A.-Q. Liu, “Broadband wide-angle multifunctional polarization converter via liquid‐metal‐based metasurfaces,” Adv. Opt. Mater. 5(7), 1600938 (2017).
[Crossref]

H. H. Hsiao, C. H. Chu, and D. P. Tsai, “Fundamentals and applications of metasurfaces,” Small Methods 1(4), 1600064 (2017).
[Crossref]

2016 (8)

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. Rep. 6, 19885 (2016).
[Crossref] [PubMed]

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

B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
[Crossref] [PubMed]

E. Almeida, O. Bitton, and Y. Prior, “Nonlinear metamaterials for holography,” Nat. Commun. 7, 12533 (2016).
[Crossref] [PubMed]

M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Super-dispersive off-axis meta-lenses for compact high resolution spectroscopy,” Nano Lett. 16(6), 3732–3737 (2016).
[Crossref] [PubMed]

Y. H. Guo, M. B. Pu, Z. Y. Zhao, J. J. Jin, P. Gao, X. Li, X. L. Ma, and X. G. Luo, “Merging geometric phase and plasmon retardation phase in continuously shaped metasurfaces for arbitrary orbital angular momentum generation,” ACS Photonics 3(11), 2022–2029 (2016).
[Crossref]

D. Lin, A. L. Holsteen, E. Maguid, G. Wetzstein, P. G. Kik, E. Hasman, and M. L. Brongersma, “Photonic multitasking interleaved si nanoantenna phased array,” Nano Lett. 16(12), 7671–7676 (2016).
[Crossref] [PubMed]

2015 (11)

X. Luo, “Principles of electromagnetic waves in metasurfaces,” Sci. China: Phys., Mech. Astron. 58(9), 594201 (2015).
[Crossref] [PubMed]

M. Veysi, C. Guclu, O. Boyraz, and F. Capolino, “Thin anisotropic metasurfaces for simultaneous light focusing and polarization manipulation,” J. Opt. Soc. Am. B 32(2), 318–323 (2015).
[Crossref]

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

Y. Guo, Y. Wang, M. Pu, Z. Zhao, X. Wu, X. Ma, C. Wang, L. Yan, and X. Luo, “Dispersion management of anisotropic metamirror for super-octave bandwidth polarization conversion,” Sci. Rep. 5, 8434 (2015).
[Crossref] [PubMed]

F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015).
[Crossref] [PubMed]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano Lett. 15(8), 5358–5362 (2015).
[Crossref] [PubMed]

Q. Wang, X. Zhang, Y. Xu, Z. Tian, J. Gu, W. Yue, S. Zhang, J. Han, and W. Zhang, “A broadband metasurface-based terahertz flat-lens array,” Adv. Opt. Mater. 3(6), 779–785 (2015).
[Crossref]

Y. Guo, L. Yan, W. Pan, and B. Luo, “Achromatic polarization manipulation by dispersion management of anisotropic meta-mirror with dual-metasurface,” Opt. Express 23(21), 27566–27575 (2015).
[Crossref] [PubMed]

Z. Zhao, M. Pu, H. Gao, J. Jin, X. Li, X. Ma, Y. Wang, P. Gao, and X. Luo, “Multispectral optical metasurfaces enabled by achromatic phase transition,” Sci. Rep. 5, 15781 (2015).
[Crossref] [PubMed]

S. W. Qu, W. W. Wu, B. J. Chen, H. Yi, X. Bai, K. B. Ng, and C. H. Chan, “Controlling dispersion characteristics of terahertz metasurface,” Sci. Rep. 5, 9367 (2015).
[Crossref] [PubMed]

2014 (4)

Y. Wang and Z. Gao, “Design and test of imaging spectrometer’s dual dispersive prisms,” Infrared Laser Eng. 43(6), 1982–1987 (2014).

D. Hu, G. Moreno, X. Wang, J. He, A. Chahadih, Z. Xie, B. Wang, T. Akalin, and Y. Zhang, “Dispersion characteristic of ultrathin terahertz planar lenses based on metasurface,” Opt. Commun. 322, 164–168 (2014).
[Crossref]

P. R. West, J. L. Stewart, A. V. Kildishev, V. M. Shalaev, V. V. Shkunov, F. Strohkendl, Y. A. Zakharenkov, R. K. Dodds, and R. Byren, “All-dielectric subwavelength metasurface focusing lens,” Opt. Express 22(21), 26212–26221 (2014).
[Crossref] [PubMed]

C. Saeidi and D. van der Weide, “Wideband plasmonic focusing metasurfaces,” Appl. Phys. Lett. 105(5), 053107 (2014).
[Crossref]

2013 (4)

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

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. W. Cheah, and C. W. Qiu, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(7), 2808 (2013).

X. Y. Jiang, J. S. Ye, J. W. He, X. K. Wang, D. Hu, S. F. Feng, Q. Kan, and Y. Zhang, “An ultrathin terahertz lens with axial long focal depth based on metasurfaces,” Opt. Express 21(24), 30030–30038 (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, e72 (2013).
[Crossref]

2012 (3)

Q. Feng, M. Pu, C. Hu, and X. Luo, “Engineering the dispersion of metamaterial surface for broadband infrared absorption,” Opt. Lett. 37(11), 2133–2135 (2012).
[Crossref] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12(3), 1702–1706 (2012).
[Crossref] [PubMed]

2011 (2)

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]

M. Ozaki, J. Kato, and S. Kawata, “Surface-plasmon holography with white-light illumination,” Science 332(6026), 218–220 (2011).
[Crossref] [PubMed]

2010 (2)

Z. C. Chen, M. H. Hong, C. S. Lim, N. R. Han, L. P. Shi, and T. C. Chong, “Parallel laser microfabrication of large-area asymmetric split ring resonator metamaterials and its structural tuning for terahertz resonance,” Appl. Phys. Lett. 96(18), 181101 (2010).
[Crossref]

Z. C. Chen, M. H. Hong, H. Dong, Y. D. Gong, C. S. Lim, L. P. Shi, and T. C. Chong, “Parallel laser microfabrication of terahertz metamaterials and its polarization-dependent transmission property,” Appl. Phys., A Mater. Sci. Process. 101(1), 33–36 (2010).
[Crossref]

2000 (1)

Y. D. Gong, T. J. Li, and S. S. Jian, “Multi-channel fiber grating for DWDM,” Chin. J. Electron. 9(3), 292–295 (2000).

1999 (1)

P. Hariharan, “Superachromatic lens combinations,” Opt. Laser Technol. 31(2), 115–118 (1999).
[Crossref]

1993 (1)

C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photonic. Tech. Lett. 5(10), 1250–1253 (1993).
[Crossref]

Aieta, F.

F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015).
[Crossref] [PubMed]

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano Lett. 15(8), 5358–5362 (2015).
[Crossref] [PubMed]

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

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12(3), 1702–1706 (2012).
[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]

Akalin, T.

D. Hu, G. Moreno, X. Wang, J. He, A. Chahadih, Z. Xie, B. Wang, T. Akalin, and Y. Zhang, “Dispersion characteristic of ultrathin terahertz planar lenses based on metasurface,” Opt. Commun. 322, 164–168 (2014).
[Crossref]

Almeida, E.

E. Almeida, O. Bitton, and Y. Prior, “Nonlinear metamaterials for holography,” Nat. Commun. 7, 12533 (2016).
[Crossref] [PubMed]

Arbabi, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

Bagheri, M.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

Bai, B.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. W. Cheah, and C. W. Qiu, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(7), 2808 (2013).

Bai, X.

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M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
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M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Super-dispersive off-axis meta-lenses for compact high resolution spectroscopy,” Nano Lett. 16(6), 3732–3737 (2016).
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M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano Lett. 15(8), 5358–5362 (2015).
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D. Lin, A. L. Holsteen, E. Maguid, G. Wetzstein, P. G. Kik, E. Hasman, and M. L. Brongersma, “Photonic multitasking interleaved si nanoantenna phased array,” Nano Lett. 16(12), 7671–7676 (2016).
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M. B. Pu, X. L. Ma, X. Li, Y. H. Guo, and X. G. Luo, “Merging plasmonics and metamaterials by two-dimensional subwavelength structures,” J. Mater. Chem. C 5(18), 4361–4378 (2017).
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Y. Li, X. Li, L. Chen, M. B. Pu, J. J. Jin, M. Hong, and X. G. Luo, “Orbital angular momentum multiplexing and demultiplexing by a single metasurfaces,” Adv. Opt. Mater. 5(2), 1600502 (2017).
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X. G. Luo, M. B. Pu, X. Li, and X. L. Ma, “Broadband spin Hall effect of light in single nanoapertures,” Light Sci. Appl. 6, e16276 (2017).
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Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. Rep. 6, 19885 (2016).
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X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016).
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Y. H. Guo, M. B. Pu, Z. Y. Zhao, J. J. Jin, P. Gao, X. Li, X. L. Ma, and X. G. Luo, “Merging geometric phase and plasmon retardation phase in continuously shaped metasurfaces for arbitrary orbital angular momentum generation,” ACS Photonics 3(11), 2022–2029 (2016).
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M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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Z. Zhao, M. Pu, H. Gao, J. Jin, X. Li, X. Ma, Y. Wang, P. Gao, and X. Luo, “Multispectral optical metasurfaces enabled by achromatic phase transition,” Sci. Rep. 5, 15781 (2015).
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Y. Li, X. Li, L. Chen, M. B. Pu, J. J. Jin, M. Hong, and X. G. Luo, “Orbital angular momentum multiplexing and demultiplexing by a single metasurfaces,” Adv. Opt. Mater. 5(2), 1600502 (2017).
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X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016).
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Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. Rep. 6, 19885 (2016).
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P. C. Wu, W. Y. Tsai, W. T. Chen, Y. W. Huang, T. Y. Chen, J. W. Chen, C. Y. Liao, C. H. Chu, G. Sun, and D. P. Tsai, “Versatile polarization generation with an aluminum plasmonicmetasurface,” Nano Lett. 17(1), 445–452 (2017).
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Z. C. Chen, M. H. Hong, C. S. Lim, N. R. Han, L. P. Shi, and T. C. Chong, “Parallel laser microfabrication of large-area asymmetric split ring resonator metamaterials and its structural tuning for terahertz resonance,” Appl. Phys. Lett. 96(18), 181101 (2010).
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Z. C. Chen, M. H. Hong, H. Dong, Y. D. Gong, C. S. Lim, L. P. Shi, and T. C. Chong, “Parallel laser microfabrication of terahertz metamaterials and its polarization-dependent transmission property,” Appl. Phys., A Mater. Sci. Process. 101(1), 33–36 (2010).
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D. Lin, A. L. Holsteen, E. Maguid, G. Wetzstein, P. G. Kik, E. Hasman, and M. L. Brongersma, “Photonic multitasking interleaved si nanoantenna phased array,” Nano Lett. 16(12), 7671–7676 (2016).
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P. C. Wu, W. Z. X. Zhu, Z. X. Shen, P. H. J. Chong, W. Ser, D. P. Tsai, and A.-Q. Liu, “Broadband wide-angle multifunctional polarization converter via liquid‐metal‐based metasurfaces,” Adv. Opt. Mater. 5(7), 1600938 (2017).
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Luo, B.

Luo, X.

X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016).
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Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. Rep. 6, 19885 (2016).
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Z. Zhao, M. Pu, H. Gao, J. Jin, X. Li, X. Ma, Y. Wang, P. Gao, and X. Luo, “Multispectral optical metasurfaces enabled by achromatic phase transition,” Sci. Rep. 5, 15781 (2015).
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X. Luo, “Principles of electromagnetic waves in metasurfaces,” Sci. China: Phys., Mech. Astron. 58(9), 594201 (2015).
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Y. Guo, Y. Wang, M. Pu, Z. Zhao, X. Wu, X. Ma, C. Wang, L. Yan, and X. Luo, “Dispersion management of anisotropic metamirror for super-octave bandwidth polarization conversion,” Sci. Rep. 5, 8434 (2015).
[Crossref] [PubMed]

Q. Feng, M. Pu, C. Hu, and X. Luo, “Engineering the dispersion of metamaterial surface for broadband infrared absorption,” Opt. Lett. 37(11), 2133–2135 (2012).
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Luo, X. G.

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

M. B. Pu, X. L. Ma, X. Li, Y. H. Guo, and X. G. Luo, “Merging plasmonics and metamaterials by two-dimensional subwavelength structures,” J. Mater. Chem. C 5(18), 4361–4378 (2017).
[Crossref]

Y. Li, X. Li, L. Chen, M. B. Pu, J. J. Jin, M. Hong, and X. G. Luo, “Orbital angular momentum multiplexing and demultiplexing by a single metasurfaces,” Adv. Opt. Mater. 5(2), 1600502 (2017).
[Crossref]

Y. H. Guo, M. B. Pu, Z. Y. Zhao, J. J. Jin, P. Gao, X. Li, X. L. Ma, and X. G. Luo, “Merging geometric phase and plasmon retardation phase in continuously shaped metasurfaces for arbitrary orbital angular momentum generation,” ACS Photonics 3(11), 2022–2029 (2016).
[Crossref]

Ma, X.

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. Rep. 6, 19885 (2016).
[Crossref] [PubMed]

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

Z. Zhao, M. Pu, H. Gao, J. Jin, X. Li, X. Ma, Y. Wang, P. Gao, and X. Luo, “Multispectral optical metasurfaces enabled by achromatic phase transition,” Sci. Rep. 5, 15781 (2015).
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M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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Y. Guo, Y. Wang, M. Pu, Z. Zhao, X. Wu, X. Ma, C. Wang, L. Yan, and X. Luo, “Dispersion management of anisotropic metamirror for super-octave bandwidth polarization conversion,” Sci. Rep. 5, 8434 (2015).
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Ma, X. L.

M. B. Pu, X. L. Ma, X. Li, Y. H. Guo, and X. G. Luo, “Merging plasmonics and metamaterials by two-dimensional subwavelength structures,” J. Mater. Chem. C 5(18), 4361–4378 (2017).
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X. G. Luo, M. B. Pu, X. Li, and X. L. Ma, “Broadband spin Hall effect of light in single nanoapertures,” Light Sci. Appl. 6, e16276 (2017).
[Crossref]

Y. H. Guo, M. B. Pu, Z. Y. Zhao, J. J. Jin, P. Gao, X. Li, X. L. Ma, and X. G. Luo, “Merging geometric phase and plasmon retardation phase in continuously shaped metasurfaces for arbitrary orbital angular momentum generation,” ACS Photonics 3(11), 2022–2029 (2016).
[Crossref]

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D. Lin, A. L. Holsteen, E. Maguid, G. Wetzstein, P. G. Kik, E. Hasman, and M. L. Brongersma, “Photonic multitasking interleaved si nanoantenna phased array,” Nano Lett. 16(12), 7671–7676 (2016).
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D. Hu, G. Moreno, X. Wang, J. He, A. Chahadih, Z. Xie, B. Wang, T. Akalin, and Y. Zhang, “Dispersion characteristic of ultrathin terahertz planar lenses based on metasurface,” Opt. Commun. 322, 164–168 (2014).
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L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. W. Cheah, and C. W. Qiu, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(7), 2808 (2013).

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S. W. Qu, W. W. Wu, B. J. Chen, H. Yi, X. Bai, K. B. Ng, and C. H. Chan, “Controlling dispersion characteristics of terahertz metasurface,” Sci. Rep. 5, 9367 (2015).
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M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Super-dispersive off-axis meta-lenses for compact high resolution spectroscopy,” Nano Lett. 16(6), 3732–3737 (2016).
[Crossref] [PubMed]

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M. Ozaki, J. Kato, and S. Kawata, “Surface-plasmon holography with white-light illumination,” Science 332(6026), 218–220 (2011).
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X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016).
[Crossref] [PubMed]

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. Rep. 6, 19885 (2016).
[Crossref] [PubMed]

Z. Zhao, M. Pu, H. Gao, J. Jin, X. Li, X. Ma, Y. Wang, P. Gao, and X. Luo, “Multispectral optical metasurfaces enabled by achromatic phase transition,” Sci. Rep. 5, 15781 (2015).
[Crossref] [PubMed]

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

Y. Guo, Y. Wang, M. Pu, Z. Zhao, X. Wu, X. Ma, C. Wang, L. Yan, and X. Luo, “Dispersion management of anisotropic metamirror for super-octave bandwidth polarization conversion,” Sci. Rep. 5, 8434 (2015).
[Crossref] [PubMed]

Q. Feng, M. Pu, C. Hu, and X. Luo, “Engineering the dispersion of metamaterial surface for broadband infrared absorption,” Opt. Lett. 37(11), 2133–2135 (2012).
[Crossref] [PubMed]

Pu, M. B.

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

M. B. Pu, X. L. Ma, X. Li, Y. H. Guo, and X. G. Luo, “Merging plasmonics and metamaterials by two-dimensional subwavelength structures,” J. Mater. Chem. C 5(18), 4361–4378 (2017).
[Crossref]

Y. Li, X. Li, L. Chen, M. B. Pu, J. J. Jin, M. Hong, and X. G. Luo, “Orbital angular momentum multiplexing and demultiplexing by a single metasurfaces,” Adv. Opt. Mater. 5(2), 1600502 (2017).
[Crossref]

Y. H. Guo, M. B. Pu, Z. Y. Zhao, J. J. Jin, P. Gao, X. Li, X. L. Ma, and X. G. Luo, “Merging geometric phase and plasmon retardation phase in continuously shaped metasurfaces for arbitrary orbital angular momentum generation,” ACS Photonics 3(11), 2022–2029 (2016).
[Crossref]

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M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. W. Cheah, and C. W. Qiu, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(7), 2808 (2013).

Qu, S. W.

S. W. Qu, W. W. Wu, B. J. Chen, H. Yi, X. Bai, K. B. Ng, and C. H. Chan, “Controlling dispersion characteristics of terahertz metasurface,” Sci. Rep. 5, 9367 (2015).
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M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano Lett. 15(8), 5358–5362 (2015).
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C. Saeidi and D. van der Weide, “Wideband plasmonic focusing metasurfaces,” Appl. Phys. Lett. 105(5), 053107 (2014).
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P. C. Wu, W. Z. X. Zhu, Z. X. Shen, P. H. J. Chong, W. Ser, D. P. Tsai, and A.-Q. Liu, “Broadband wide-angle multifunctional polarization converter via liquid‐metal‐based metasurfaces,” Adv. Opt. Mater. 5(7), 1600938 (2017).
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Shen, Z. X.

P. C. Wu, W. Z. X. Zhu, Z. X. Shen, P. H. J. Chong, W. Ser, D. P. Tsai, and A.-Q. Liu, “Broadband wide-angle multifunctional polarization converter via liquid‐metal‐based metasurfaces,” Adv. Opt. Mater. 5(7), 1600938 (2017).
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Z. C. Chen, M. H. Hong, H. Dong, Y. D. Gong, C. S. Lim, L. P. Shi, and T. C. Chong, “Parallel laser microfabrication of terahertz metamaterials and its polarization-dependent transmission property,” Appl. Phys., A Mater. Sci. Process. 101(1), 33–36 (2010).
[Crossref]

Z. C. Chen, M. H. Hong, C. S. Lim, N. R. Han, L. P. Shi, and T. C. Chong, “Parallel laser microfabrication of large-area asymmetric split ring resonator metamaterials and its structural tuning for terahertz resonance,” Appl. Phys. Lett. 96(18), 181101 (2010).
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Song, Z.

B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
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Strohkendl, F.

Sun, C.

B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
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P. C. Wu, W. Y. Tsai, W. T. Chen, Y. W. Huang, T. Y. Chen, J. W. Chen, C. Y. Liao, C. H. Chu, G. Sun, and D. P. Tsai, “Versatile polarization generation with an aluminum plasmonicmetasurface,” Nano Lett. 17(1), 445–452 (2017).
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L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. W. Cheah, and C. W. Qiu, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(7), 2808 (2013).

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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(6054), 333–337 (2011).
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Q. Wang, X. Zhang, Y. Xu, Z. Tian, J. Gu, W. Yue, S. Zhang, J. Han, and W. Zhang, “A broadband metasurface-based terahertz flat-lens array,” Adv. Opt. Mater. 3(6), 779–785 (2015).
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P. C. Wu, W. Y. Tsai, W. T. Chen, Y. W. Huang, T. Y. Chen, J. W. Chen, C. Y. Liao, C. H. Chu, G. Sun, and D. P. Tsai, “Versatile polarization generation with an aluminum plasmonicmetasurface,” Nano Lett. 17(1), 445–452 (2017).
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P. C. Wu, W. Z. X. Zhu, Z. X. Shen, P. H. J. Chong, W. Ser, D. P. Tsai, and A.-Q. Liu, “Broadband wide-angle multifunctional polarization converter via liquid‐metal‐based metasurfaces,” Adv. Opt. Mater. 5(7), 1600938 (2017).
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P. C. Wu, W. Y. Tsai, W. T. Chen, Y. W. Huang, T. Y. Chen, J. W. Chen, C. Y. Liao, C. H. Chu, G. Sun, and D. P. Tsai, “Versatile polarization generation with an aluminum plasmonicmetasurface,” Nano Lett. 17(1), 445–452 (2017).
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C. Saeidi and D. van der Weide, “Wideband plasmonic focusing metasurfaces,” Appl. Phys. Lett. 105(5), 053107 (2014).
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Wang, B.

B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
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D. Hu, G. Moreno, X. Wang, J. He, A. Chahadih, Z. Xie, B. Wang, T. Akalin, and Y. Zhang, “Dispersion characteristic of ultrathin terahertz planar lenses based on metasurface,” Opt. Commun. 322, 164–168 (2014).
[Crossref]

Wang, C.

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

Y. Guo, Y. Wang, M. Pu, Z. Zhao, X. Wu, X. Ma, C. Wang, L. Yan, and X. Luo, “Dispersion management of anisotropic metamirror for super-octave bandwidth polarization conversion,” Sci. Rep. 5, 8434 (2015).
[Crossref] [PubMed]

Wang, Q.

Q. Wang, X. Zhang, Y. Xu, Z. Tian, J. Gu, W. Yue, S. Zhang, J. Han, and W. Zhang, “A broadband metasurface-based terahertz flat-lens array,” Adv. Opt. Mater. 3(6), 779–785 (2015).
[Crossref]

Wang, X.

D. Hu, G. Moreno, X. Wang, J. He, A. Chahadih, Z. Xie, B. Wang, T. Akalin, and Y. Zhang, “Dispersion characteristic of ultrathin terahertz planar lenses based on metasurface,” Opt. Commun. 322, 164–168 (2014).
[Crossref]

Wang, X. K.

Wang, Y.

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

Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. Rep. 6, 19885 (2016).
[Crossref] [PubMed]

Z. Zhao, M. Pu, H. Gao, J. Jin, X. Li, X. Ma, Y. Wang, P. Gao, and X. Luo, “Multispectral optical metasurfaces enabled by achromatic phase transition,” Sci. Rep. 5, 15781 (2015).
[Crossref] [PubMed]

Y. Guo, Y. Wang, M. Pu, Z. Zhao, X. Wu, X. Ma, C. Wang, L. Yan, and X. Luo, “Dispersion management of anisotropic metamirror for super-octave bandwidth polarization conversion,” Sci. Rep. 5, 8434 (2015).
[Crossref] [PubMed]

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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Y. Wang and Z. Gao, “Design and test of imaging spectrometer’s dual dispersive prisms,” Infrared Laser Eng. 43(6), 1982–1987 (2014).

West, P. R.

Wetzstein, G.

D. Lin, A. L. Holsteen, E. Maguid, G. Wetzstein, P. G. Kik, E. Hasman, and M. L. Brongersma, “Photonic multitasking interleaved si nanoantenna phased array,” Nano Lett. 16(12), 7671–7676 (2016).
[Crossref] [PubMed]

Wu, P. C.

P. C. Wu, W. Z. X. Zhu, Z. X. Shen, P. H. J. Chong, W. Ser, D. P. Tsai, and A.-Q. Liu, “Broadband wide-angle multifunctional polarization converter via liquid‐metal‐based metasurfaces,” Adv. Opt. Mater. 5(7), 1600938 (2017).
[Crossref]

P. C. Wu, W. Y. Tsai, W. T. Chen, Y. W. Huang, T. Y. Chen, J. W. Chen, C. Y. Liao, C. H. Chu, G. Sun, and D. P. Tsai, “Versatile polarization generation with an aluminum plasmonicmetasurface,” Nano Lett. 17(1), 445–452 (2017).
[Crossref] [PubMed]

Wu, W. W.

S. W. Qu, W. W. Wu, B. J. Chen, H. Yi, X. Bai, K. B. Ng, and C. H. Chan, “Controlling dispersion characteristics of terahertz metasurface,” Sci. Rep. 5, 9367 (2015).
[Crossref] [PubMed]

Wu, X.

Y. Guo, Y. Wang, M. Pu, Z. Zhao, X. Wu, X. Ma, C. Wang, L. Yan, and X. Luo, “Dispersion management of anisotropic metamirror for super-octave bandwidth polarization conversion,” Sci. Rep. 5, 8434 (2015).
[Crossref] [PubMed]

Xiao, Y. F.

B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
[Crossref] [PubMed]

Xie, Z.

D. Hu, G. Moreno, X. Wang, J. He, A. Chahadih, Z. Xie, B. Wang, T. Akalin, and Y. Zhang, “Dispersion characteristic of ultrathin terahertz planar lenses based on metasurface,” Opt. Commun. 322, 164–168 (2014).
[Crossref]

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B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
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Q. Wang, X. Zhang, Y. Xu, Z. Tian, J. Gu, W. Yue, S. Zhang, J. Han, and W. Zhang, “A broadband metasurface-based terahertz flat-lens array,” Adv. Opt. Mater. 3(6), 779–785 (2015).
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B. Wang, F. Dong, Q. T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y. F. Xiao, Q. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
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Ye, J. S.

Yi, H.

S. W. Qu, W. W. Wu, B. J. Chen, H. Yi, X. Bai, K. B. Ng, and C. H. Chan, “Controlling dispersion characteristics of terahertz metasurface,” Sci. Rep. 5, 9367 (2015).
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Yu, N.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
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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(6054), 333–337 (2011).
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Yue, W.

Q. Wang, X. Zhang, Y. Xu, Z. Tian, J. Gu, W. Yue, S. Zhang, J. Han, and W. Zhang, “A broadband metasurface-based terahertz flat-lens array,” Adv. Opt. Mater. 3(6), 779–785 (2015).
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Q. Wang, X. Zhang, Y. Xu, Z. Tian, J. Gu, W. Yue, S. Zhang, J. Han, and W. Zhang, “A broadband metasurface-based terahertz flat-lens array,” Adv. Opt. Mater. 3(6), 779–785 (2015).
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X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016).
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Q. Wang, X. Zhang, Y. Xu, Z. Tian, J. Gu, W. Yue, S. Zhang, J. Han, and W. Zhang, “A broadband metasurface-based terahertz flat-lens array,” Adv. Opt. Mater. 3(6), 779–785 (2015).
[Crossref]

Zhang, Y.

D. Hu, G. Moreno, X. Wang, J. He, A. Chahadih, Z. Xie, B. Wang, T. Akalin, and Y. Zhang, “Dispersion characteristic of ultrathin terahertz planar lenses based on metasurface,” Opt. Commun. 322, 164–168 (2014).
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X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016).
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[Crossref] [PubMed]

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[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

The basic unit cell. (a) 3D view of the basic unit cell. The pixels are arranged with a period of P = 200 nm and a height of h = 400 nm. (b) The simulation transmissions (conversion efficiency) results of three individual designed nanocuboids illuminated by a normally-incident LCP (left circularly polarized) light beam. (c) The transmission (conversion efficiency) coefficient and phase shift of transmitted light as a function of θ for three nanocuboids. (d) Top view of a small metasurfaces with a radius of 3 μm.

Fig. 2
Fig. 2

The design principle of meta-lenses and five dispersion controllable meta-lenses. (a) The sketch map is used for phase distribution analyzing and illustrating. The circular flat meta-lens with the focal point F lens converts plane wave into spherical wave, where incident light travels along the z-aixs. Green semi-spherical surface is the desired equiphase surface, and the straight line AF ¯ intersects with the equiphase surface at point B. (b) Schematic and (c) phase distribution of achromatic meta-lens M1. (d) Schematic and (e) phase distribution of super-dispersion meta-lens M2 designed to separate different wavelength light in order of normal dispersion. (f) Schematic and (g) phase distribution of super-dispersion flat meta-lens M3 with anomalous dispersion. The distribution of focal points is opposite to M3. (h) Schematic and (i) phase distribution of super-dispersion flat meta-lens M4 with off-axis colors separation. (j) Schematic and (k) phase distribution of super-dispersion flat meta-lens M5 with different off-axis colors separation.

Fig. 3
Fig. 3

The comparison of normal flat meta-lens and achromatic meta-lenses. (a)-(c) Simulative normalized intensities distribution of normal flat meta-lenses in xz-plane upon illumination with λ = 473 nm, 532 nm and 632.8 nm wavelength light, respectively. (d) Comparison of the normalized intensity curves of three light along the z-axis. (e)-(g) Simulative normalized intensities distribution of achromatic flat meta-lenses M1 in xz-plane and (inset) the intensity profiles across the focal plane. (h) Comparison of the normalized intensity curves of three light along the z-axis.

Fig. 4
Fig. 4

Simulation results of super-dispersion meta-lenses M2 and M3. (a)-(c) Simulative normalized intensities distribution of super-dispersion meta-lenses M2 in xz-plane and (inset) the intensity profiles across the focal plane upon illumination with λ = 473 nm, 532 nm and 632.8 nm, respectively. (d) Comparison of theoretical results (dotted line) and simulation results (solid line) the normalized intensity curves of three light along the z-axis. (e)-(g) Simulative normalized intensities distribution of super-dispersion meta-lenses M3 in xz-plane and (inset) the intensity profiles across the focal plane upon illumination with λ = 473 nm, 532 nm and 632.8 nm, respectively. (h) Comparison of theoretical results (dotted line) and simulation results (solid line) the normalized intensity curves of three light along the z-axis

Fig. 5
Fig. 5

The CST simulation results of off-axis super-dispersion meta-lenses M4 and M5. (a)-(c) and (e)-(g) Simulative normalized intensities distribution in xz-plane of M4 and M5 upon illumination with λ = 473 nm, 532 nm and 632.8 nm, respectively. (d) and (h) Overall images of M4 and M5.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

E s R/L = t o + t e 2 E i R/L + t o t e 2 exp(i2θ) E i L/R
Δ Ф tot ( r,λ )= Ф m ( r,λ )+ Ф c ( r,λ )
Ф m ( x,y,λ )= 2π λ ( ( x x f ) 2 + ( y y f ) 2 + ( z z f ) 2 z f )