Abstract

A new method for realizing achromatic flat focusing based on all-dielectric silicon subwavelength metasurface is presented. The designed subwavelength silicon-air slits waveguide array with varied widths can provide desired phase shift of beam focusing and has the non-dispersive characteristic when the period of each unit cell is far less than the wavelength of incident electromagnetic wave (about λ/10) in mid-infrared and far-infrared spectral range. Numerical simulation of an achromatic flat focusing lens in wide spectral range from 8μm to 12μm is performed by the finite difference time domain method and the results show agreement with theory analysis results. This work indicates an effective solution for wide-band achromatic flat optical elements and potential application in integrated achromatic infrared optical systems.

© 2017 Optical Society of America

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  1. G. Vallerotto, M. Victoria, S. Askins, R. Herrero, C. Domínguez, I. Antón, and G. Sala, “Design and modeling of a cost-effective achromatic Fresnel lens for concentrating photovoltaics,” Opt. Express 24(18), A1245–A1256 (2016).
    [Crossref] [PubMed]
  2. J. H. Lee, J. Woong Yoon, M. Jin Jung, J. Kyun Hong, S. Ho Song, and R. Magnusson, “A semiconductor metasurface with multiple functionalities: a polarizing beam splitter with simultaneous focusing ability,” Appl. Phys. Lett. 104(23), 233505 (2014).
    [Crossref]
  3. D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
    [Crossref] [PubMed]
  4. S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
    [Crossref] [PubMed]
  5. Z. Sun and H. K. Kim, “Refractive transmission of light and beam shapingwith metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
    [Crossref]
  6. N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
    [Crossref] [PubMed]
  7. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
    [Crossref] [PubMed]
  8. A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
    [Crossref] [PubMed]
  9. H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express 13(18), 6815–6820 (2005).
    [Crossref] [PubMed]
  10. L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
    [Crossref] [PubMed]
  11. 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]
  12. L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12(11), 5750–5755 (2012).
    [Crossref] [PubMed]
  13. 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]
  14. T. Xu, C. Wang, C. Du, and X. Luo, “Plasmonic beam deflector,” Opt. Express 16(7), 4753–4759 (2008).
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    [Crossref] [PubMed]
  16. L. L. Huang, X. Z. Chen, H. Muhlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. F. Tan, G. F. Jin, K. W. Cheah, C. W. Qiu, J. S. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
    [Crossref]
  17. 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]
  18. M. Khorasaninejad, W. Zhu, and K. B. Crozier, “Efficient polarization beam splitter pixels based on a dielectric metasurface,” Optica 2(4), 376–382 (2015).
    [Crossref]
  19. J. Lin, J. P. B. 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]
  20. 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]
  21. 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]
  22. Z. L. Deng, S. Zhang, and G. P. Wang, “Wide-angled off-axis achromatic metasurfaces for visible light,” Opt. Express 24(20), 23118–23128 (2016).
    [Crossref] [PubMed]
  23. J. Ding, N. Xu, H. Ren, Y. Lin, W. Zhang, and H. Zhang, “Dual-wavelength terahertz metasurfaces with independent phase and amplitude control at each wavelength,” Sci. Rep. 6, 34020 (2016).
    [Crossref] [PubMed]
  24. 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]
  25. 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]
  26. 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]
  27. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004).
    [Crossref] [PubMed]

2016 (5)

J. Ding, N. Xu, H. Ren, Y. Lin, W. Zhang, and H. Zhang, “Dual-wavelength terahertz metasurfaces with independent phase and amplitude control at each wavelength,” Sci. Rep. 6, 34020 (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]

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]

G. Vallerotto, M. Victoria, S. Askins, R. Herrero, C. Domínguez, I. Antón, and G. Sala, “Design and modeling of a cost-effective achromatic Fresnel lens for concentrating photovoltaics,” Opt. Express 24(18), A1245–A1256 (2016).
[Crossref] [PubMed]

Z. L. Deng, S. Zhang, and G. P. Wang, “Wide-angled off-axis achromatic metasurfaces for visible light,” Opt. Express 24(20), 23118–23128 (2016).
[Crossref] [PubMed]

2015 (6)

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. Khorasaninejad, W. Zhu, and K. B. Crozier, “Efficient polarization beam splitter pixels based on a dielectric metasurface,” Optica 2(4), 376–382 (2015).
[Crossref]

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref] [PubMed]

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]

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]

2014 (5)

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]

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

J. H. Lee, J. Woong Yoon, M. Jin Jung, J. Kyun Hong, S. Ho Song, and R. Magnusson, “A semiconductor metasurface with multiple functionalities: a polarizing beam splitter with simultaneous focusing ability,” Appl. Phys. Lett. 104(23), 233505 (2014).
[Crossref]

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

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]

2013 (2)

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

J. Lin, J. P. B. 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]

2012 (3)

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12(11), 5750–5755 (2012).
[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]

S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[Crossref] [PubMed]

2011 (1)

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

2009 (1)

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[Crossref] [PubMed]

2008 (1)

2005 (1)

2004 (2)

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004).
[Crossref] [PubMed]

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shapingwith metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
[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]

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]

Almeida, V. R.

Antón, I.

Antoniou, N.

J. Lin, J. P. B. 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]

Arbabi, A.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref] [PubMed]

Askins, S.

Bagheri, M.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref] [PubMed]

Bai, B.

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12(11), 5750–5755 (2012).
[Crossref] [PubMed]

Bai, B. F.

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

Ball, A. J.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref] [PubMed]

Barnard, E. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[Crossref] [PubMed]

Barrios, C. A.

Boltasseva, A.

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]

Brongersma, M. L.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[Crossref] [PubMed]

Byren, R.

Capasso, 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]

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

J. Lin, J. P. B. 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]

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]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[Crossref] [PubMed]

Cheah, K. W.

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

Chen, J.

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]

Chen, S. M.

L. L. Huang, X. Z. Chen, H. Muhlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. F. Tan, G. F. Jin, K. W. Cheah, C. W. Qiu, J. S. 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]

S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[Crossref] [PubMed]

Chen, X.

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12(11), 5750–5755 (2012).
[Crossref] [PubMed]

Chen, X. Z.

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

Chu, W.

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]

Crozier, K. B.

Deng, Z. L.

Ding, J.

J. Ding, N. Xu, H. Ren, Y. Lin, W. Zhang, and H. Zhang, “Dual-wavelength terahertz metasurfaces with independent phase and amplitude control at each wavelength,” Sci. Rep. 6, 34020 (2016).
[Crossref] [PubMed]

Dodds, R. K.

Domínguez, C.

Dong, 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]

Dong, X.

Du, C.

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]

Fan, P.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[Crossref] [PubMed]

Faraon, A.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref] [PubMed]

Gaburro, Z.

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

Gao, H.

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S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
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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).
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Xu, L.

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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Xu, N.

J. Ding, N. Xu, H. Ren, Y. Lin, W. Zhang, and H. Zhang, “Dual-wavelength terahertz metasurfaces with independent phase and amplitude control at each wavelength,” Sci. Rep. 6, 34020 (2016).
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Xu, Q.

Xu, T.

Yang, D.

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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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).
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S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
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Yu, N.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
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N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
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L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
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Yuan, X. C.

J. Lin, J. P. B. 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).
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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).
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L. L. Huang, X. Z. Chen, H. Muhlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. F. Tan, G. F. Jin, K. W. Cheah, C. W. Qiu, J. S. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
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L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12(11), 5750–5755 (2012).
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J. Ding, N. Xu, H. Ren, Y. Lin, W. Zhang, and H. Zhang, “Dual-wavelength terahertz metasurfaces with independent phase and amplitude control at each wavelength,” Sci. Rep. 6, 34020 (2016).
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L. L. Huang, X. Z. Chen, H. Muhlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. F. Tan, G. F. Jin, K. W. Cheah, C. W. Qiu, J. S. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
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L. L. Huang, X. Z. Chen, H. Muhlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. F. Tan, G. F. Jin, K. W. Cheah, C. W. Qiu, J. S. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
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L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12(11), 5750–5755 (2012).
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J. Ding, N. Xu, H. Ren, Y. Lin, W. Zhang, and H. Zhang, “Dual-wavelength terahertz metasurfaces with independent phase and amplitude control at each wavelength,” Sci. Rep. 6, 34020 (2016).
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Zhao, Z.

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).
[Crossref] [PubMed]

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).
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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).
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S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
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S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012).
[Crossref] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
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L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12(11), 5750–5755 (2012).
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W. T. Chen, K. Y. Yang, C. M. Wang, Y. W. Huang, G. Sun, I. D. Chiang, C. Y. Liao, W. L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
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Nat. Commun. (2)

L. L. Huang, X. Z. Chen, H. Muhlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. F. Tan, G. F. Jin, K. W. Cheah, C. W. Qiu, J. S. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
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A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
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Nat. Mater. (1)

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

Opt. Express (5)

Opt. Lett. (1)

Optica (1)

Sci. Rep. (3)

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. 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]

J. Ding, N. Xu, H. Ren, Y. Lin, W. Zhang, and H. Zhang, “Dual-wavelength terahertz metasurfaces with independent phase and amplitude control at each wavelength,” Sci. Rep. 6, 34020 (2016).
[Crossref] [PubMed]

Science (5)

J. Lin, J. P. B. 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).
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F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015).
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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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D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
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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]

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Figures (8)

Fig. 1
Fig. 1 Schematic of achromatic flat focusing lens based on all-dielectric subwavelength metasurface.

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Fig. 2
Fig. 2 (a) Normalized electric field intensity distribution for slit waveguide with the period P = 1μm, the slit width w = 0.3μm, the length L = 15μm, at λ = 10μm. (b) Eeffective refractive index of unit cell with differernt slit widths in the spectral range from 5μm to 15μm.

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Fig. 3
Fig. 3 Effective refractive index of unit cell with different periods in the spectral range from 5μm to 15μm.

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Fig. 4
Fig. 4 Effective refractive index of unit cell vary as slit widths for the cell with non-uniform period of unit at different wavelengths of incident electromagnetic wave(a), and the cell with uniform period P = 1.0μm at different wavelengths of incident electromagnetic wave (b).

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Fig. 5
Fig. 5 (a) Phase shift of unit cell with differernt silt widths. (b) Phase shift of unit cell with differernt wavelengths of incident electromagnetic wave.

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Fig. 6
Fig. 6 (a) Achromatic phase shift of unit cell with differernt silt widths. (b) Achromatic phase shift of unit cell with differernt wavelengths of incident electromagnetic wave.

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Fig. 7
Fig. 7 (a) Slit widths distribution along x direction. (b) Phase shift distribution for different wavelengths along x direction. (c) Achromatic phase shift distribution for different wavelengths along x direction.

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Fig. 8
Fig. 8 (a-e) Normalized electric field intensity distribution for different wavelengths. (f) Cross section of focus spot in x direction for different wavelengths. (g) Focus position in spectral range from 8μm to 12μm.

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Equations (8)

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

tan[ κ H (P−w)−ϕ]= γ S n H 2 κ H n S 2 tanh( γ S w/2) k 0 2 n H 2 − κ H 2 = k 0 2 n S 2 + γ S 2 = β 2 n eff =β/ k 0 ϕ=arctan[ γ S n H 2 /( κ H n S 2 )]
φ= φ 0 + n eff k 0 L+Δ φ 1 +Δ φ 2 −θ
φ= φ 0 + n eff k 0 L
Δ φ 1,2 =2πL[ n eff ( w 2 , λ 1,2 )− n eff ( w 1 , λ 1,2 )]/ λ 1,2
Δ φ f =2π( f− f 2 + x 2 )/λ
Δ φ f 1,2 λ 1,2 /2π=( f− f 2 + x 2 )=const
Δ φ 1,2 λ 1,2 /2π=Δ φ f1,2 λ 1,2 /2π=[ n eff ( w 2 , λ 1,2 )− n eff ( w 1 , λ 1,2 )]L=const
[ n eff ( w 2 , λ 2 )− n eff ( w 1 , λ 2 )]L−[ n eff ( w 2 , λ 1 )− n eff ( w 1 , λ 1 )]L=0

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