Abstract

We propose and numerically investigate an efficient transmission-mode metasurface that consists of quasi-continuous trapezoid-shaped crystalline silicon nanoantennas on a quartz substrate. This metasurface provides a linear phase gradient and realizes both full 2π phase shift and high transmission efficiency in the operating wavelength range from 740 to 780 nm. At the central wavelength around 751 nm, the total transmission efficiency is up to 88.0% and the section of the desired anomalous refraction is 80.4%. The anomalous refraction angle is 29.62°, and larger refraction angle can be achieved by changing the period of the super cell. We demonstrate a refraction angle as large as 38.59°, and the anomalous transmission efficiency reaches 76.6% at wavelength of 741 nm. It is worth mentioning that the structure is much simpler than conventional metasurfaces based on arrays of discrete nanoantennas. Our research may pave the way for designing efficient all-dielectric phase-gradient metasurfaces and applying them in integrated optical devices for wavefront control.

© 2018 Chinese Laser Press

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References

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2017 (8)

Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, and T. F. Krauss, “Efficient silicon metasurfaces for visible light,” ACS Photon. 4, 544–551 (2017).
[Crossref]

T. Li, L. Huang, J. Liu, Y. Wang, and T. Zentgraf, “Tunable wave plate based on active plasmonic metasurfaces,” Opt. Express 25, 4216–4226 (2017).
[Crossref]

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-dielectric full-color printing with TiO2 metasurfaces,” ACS Nano 11, 4445–4452 (2017).
[Crossref]

S. Wang, J. Lai, T. Wu, C. Chen, and J. Sun, “Wide-band achromatic flat focusing lens based on all-dielectric subwavelength metasurface,” Opt. Express 25, 7121–7130 (2017).
[Crossref]

S. Gao, W. Yue, C. S. Park, S. S. Lee, E. S. Kim, and D. Y. Choi, “Aluminum plasmonic metasurface enabling a wavelength-insensitive phase gradient for linearly polarized visible light,” ACS Photon. 4, 322–328 (2017).
[Crossref]

Z. Y. Li, M. H. Kim, C. Wang, Z. H. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. F. Yu, “Controlling propagation and coupling of waveguide modes using phase-gradient metasurfaces,” Nat. Nanotechnol. 12, 675–683 (2017).
[Crossref]

M. A. Otte, A. Garcia-Martin, X. Borrise, and B. Sepulveda, “Metamirrors based on arrays of silicon nanowires with height gradients,” Adv. Opt. Mater. 5, 1600933 (2017).
[Crossref]

D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, “Large-angle, multifunctional metagratings based on freeform multimode geometries,” Nano Lett. 17, 3752–3757 (2017).
[Crossref]

2016 (14)

X. Chen, H. Zhou, M. Liu, and J. Dong, “Measurement of orbital angular momentum by self-interference using a plasmonic metasurface,” IEEE Photon. J. 8, 4800308 (2016).
[Crossref]

D. Sell, J. Yang, S. Doshay, K. Zhang, and J. A. Fan, “Visible light metasurfaces based on single-crystal silicon,” ACS Photon. 3, 1919–1925 (2016).
[Crossref]

M. Chen, J. Cai, W. Sun, L. Chang, and X. Xiao, “High-efficiency all-dielectric metasurfaces for broadband polarization conversion,” Plasmonics 13, 21–29 (2016).
[Crossref]

H. S. Ee and R. Agarwal, “Tunable metasurface and flat optical zoom lens on a stretchable substrate,” Nano Lett. 16, 2818–2823 (2016).
[Crossref]

Z. Li, E. Palacios, S. Butun, and K. Aydin, “Ultrawide angle, directional spectrum splitting with visible-frequency versatile metasurfaces,” Adv. Opt. Mater. 4, 953–958 (2016).
[Crossref]

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-insensitive metalenses at visible wavelengths,” Nano Lett. 16, 7229–7234 (2016).
[Crossref]

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, 1190–1194 (2016).
[Crossref]

A. Zhan, S. Colburn, R. Trivedi, T. K. Fryett, C. M. Dodson, and A. Majumdar, “Low-contrast dielectric metasurface optics,” ACS Photon. 3, 209–214 (2016).
[Crossref]

M. Khorasaninejad, A. Ambrosio, P. Kanhaiya, and F. Capasso, “Broadband and chiral binary dielectric meta-holograms,” Sci. Adv. 2, e1501258 (2016).
[Crossref]

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

Y. Zhao, X. Cao, J. Gao, X. Liu, and S. Li, “Jigsaw puzzle metasurface for multiple functions: polarization conversion, anomalous reflection and diffusion,” Opt. Express 24, 11208–11217 (2016).
[Crossref]

W. Zhu, F. Xiao, M. Kang, and M. Premaratne, “Coherent perfect absorption in an all-dielectric metasurface,” Appl. Phys. Lett. 108, 121901 (2016).
[Crossref]

L. Zhang, S. Mei, K. Huang, and C. W. Qiu, “Advances in full control of electromagnetic waves with metasurfaces,” Adv. Opt. Mater. 4, 818–833 (2016).
[Crossref]

Z. Liu, Q. Wang, Y. Xie, and Y. Zhu, “High-efficiency control of transmitted light with a three-layered plasmonic metasurface,” J. Phys. D 49, 475101 (2016).
[Crossref]

2015 (6)

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15, 6261–6266 (2015).
[Crossref]

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, and I. Brener, “Polarization-independent silicon metadevices for efficient optical wavefront control,” Nano Lett. 15, 5369–5374 (2015).
[Crossref]

Z. Li and K. Aydin, “Broadband metasurfaces for anomalous transmission and spectrum splitting at visible frequencies,” EPJ Appl. Metamater. 2, 2 (2015).
[Crossref]

Z. Li, E. Palacios, S. Butun, and K. Aydin, “Visible-frequency metasurfaces for broadband anomalous reflection and high-efficiency spectrum splitting,” Nano Lett. 15, 1615–1621 (2015).
[Crossref]

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

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

2014 (2)

Z. Li, L. Huang, K. Lu, Y. Sun, and L. Min, “Continuous metasurface for high-performance anomalous reflection,” Appl. Phys. Express 7, 112001 (2014).
[Crossref]

A. B. Evlyukhin, R. L. Eriksen, W. Cheng, J. Beermann, C. Reinhardt, A. Petrov, S. Prorok, M. Eich, B. N. Chichkov, and S. I. Bozhevolnyi, “Optical spectroscopy of single Si nanocylinders with magnetic and electric resonances,” Sci. Rep. 4, 4126 (2014).
[Crossref]

2013 (2)

C. Pfeiffer and G. Anthony, “Metamaterial Huygens’ surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 197401 (2013).
[Crossref]

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

2012 (5)

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (2012).
[Crossref]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

Y. Sun, G. C. Welch, W. L. Leong, C. J. Takacs, G. C. Bazan, and A. J. Heeger, “Solution-processed small-molecule solar cells with 6.7% efficiency,” Nat. Mater. 11, 44–48 (2012).
[Crossref]

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, and L. Zhou, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12, 6223–6229 (2012).
[Crossref]

S. Larouche and D. R. Smith, “Reconciliation of generalized refraction with diffraction theory,” Opt. Lett. 37, 2391–2393 (2012).
[Crossref]

2011 (1)

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

Agarwal, A. M.

Z. Y. Li, M. H. Kim, C. Wang, Z. H. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. F. Yu, “Controlling propagation and coupling of waveguide modes using phase-gradient metasurfaces,” Nat. Nanotechnol. 12, 675–683 (2017).
[Crossref]

Agarwal, R.

H. S. Ee and R. Agarwal, “Tunable metasurface and flat optical zoom lens on a stretchable substrate,” Nano Lett. 16, 2818–2823 (2016).
[Crossref]

Aieta, F.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (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, 333–337 (2011).
[Crossref]

Ambrosio, A.

M. Khorasaninejad, A. Ambrosio, P. Kanhaiya, and F. Capasso, “Broadband and chiral binary dielectric meta-holograms,” Sci. Adv. 2, e1501258 (2016).
[Crossref]

Anthony, G.

C. Pfeiffer and G. Anthony, “Metamaterial Huygens’ surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 197401 (2013).
[Crossref]

Aydin, K.

Z. Li, E. Palacios, S. Butun, and K. Aydin, “Ultrawide angle, directional spectrum splitting with visible-frequency versatile metasurfaces,” Adv. Opt. Mater. 4, 953–958 (2016).
[Crossref]

Z. Li and K. Aydin, “Broadband metasurfaces for anomalous transmission and spectrum splitting at visible frequencies,” EPJ Appl. Metamater. 2, 2 (2015).
[Crossref]

Z. Li, E. Palacios, S. Butun, and K. Aydin, “Visible-frequency metasurfaces for broadband anomalous reflection and high-efficiency spectrum splitting,” Nano Lett. 15, 1615–1621 (2015).
[Crossref]

Bazan, G. C.

Y. Sun, G. C. Welch, W. L. Leong, C. J. Takacs, G. C. Bazan, and A. J. Heeger, “Solution-processed small-molecule solar cells with 6.7% efficiency,” Nat. Mater. 11, 44–48 (2012).
[Crossref]

Beermann, J.

A. B. Evlyukhin, R. L. Eriksen, W. Cheng, J. Beermann, C. Reinhardt, A. Petrov, S. Prorok, M. Eich, B. N. Chichkov, and S. I. Bozhevolnyi, “Optical spectroscopy of single Si nanocylinders with magnetic and electric resonances,” Sci. Rep. 4, 4126 (2014).
[Crossref]

Boltasseva, A.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

Borrise, X.

M. A. Otte, A. Garcia-Martin, X. Borrise, and B. Sepulveda, “Metamirrors based on arrays of silicon nanowires with height gradients,” Adv. Opt. Mater. 5, 1600933 (2017).
[Crossref]

Bozhevolnyi, S. I.

A. B. Evlyukhin, R. L. Eriksen, W. Cheng, J. Beermann, C. Reinhardt, A. Petrov, S. Prorok, M. Eich, B. N. Chichkov, and S. I. Bozhevolnyi, “Optical spectroscopy of single Si nanocylinders with magnetic and electric resonances,” Sci. Rep. 4, 4126 (2014).
[Crossref]

Brener, I.

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, and I. Brener, “Polarization-independent silicon metadevices for efficient optical wavefront control,” Nano Lett. 15, 5369–5374 (2015).
[Crossref]

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

Butun, S.

Z. Li, E. Palacios, S. Butun, and K. Aydin, “Ultrawide angle, directional spectrum splitting with visible-frequency versatile metasurfaces,” Adv. Opt. Mater. 4, 953–958 (2016).
[Crossref]

Z. Li, E. Palacios, S. Butun, and K. Aydin, “Visible-frequency metasurfaces for broadband anomalous reflection and high-efficiency spectrum splitting,” Nano Lett. 15, 1615–1621 (2015).
[Crossref]

Cai, J.

M. Chen, J. Cai, W. Sun, L. Chang, and X. Xiao, “High-efficiency all-dielectric metasurfaces for broadband polarization conversion,” Plasmonics 13, 21–29 (2016).
[Crossref]

Campione, S.

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, and I. Brener, “Polarization-independent silicon metadevices for efficient optical wavefront control,” Nano Lett. 15, 5369–5374 (2015).
[Crossref]

Cao, X.

Capasso, F.

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-insensitive metalenses at visible wavelengths,” Nano Lett. 16, 7229–7234 (2016).
[Crossref]

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, 1190–1194 (2016).
[Crossref]

M. Khorasaninejad, A. Ambrosio, P. Kanhaiya, and F. Capasso, “Broadband and chiral binary dielectric meta-holograms,” Sci. Adv. 2, e1501258 (2016).
[Crossref]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (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, 333–337 (2011).
[Crossref]

Chang, L.

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D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, “Large-angle, multifunctional metagratings based on freeform multimode geometries,” Nano Lett. 17, 3752–3757 (2017).
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M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15, 6261–6266 (2015).
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X. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4, 2807 (2013).
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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, 427 (2012).
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F. Ding, Z. Wang, V. M. Shalaev, and A. V. Kildishev, “Broadband high-efficiency half-wave plate using plasmonic metasurface,” in CLEO: QELS_Fundamental Science (Optical Society of America, 2015), paper FTu1C.6.

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Z. Y. Li, M. H. Kim, C. Wang, Z. H. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. F. Yu, “Controlling propagation and coupling of waveguide modes using phase-gradient metasurfaces,” Nat. Nanotechnol. 12, 675–683 (2017).
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Song, Q.

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Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, and T. F. Krauss, “Efficient silicon metasurfaces for visible light,” ACS Photon. 4, 544–551 (2017).
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Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, and T. F. Krauss, “Efficient silicon metasurfaces for visible light,” ACS Photon. 4, 544–551 (2017).
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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, and Q. Gong, “Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms,” Nano Lett. 16, 5235–5240 (2016).
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Sun, S.

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-dielectric full-color printing with TiO2 metasurfaces,” ACS Nano 11, 4445–4452 (2017).
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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, and L. Zhou, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12, 6223–6229 (2012).
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M. Chen, J. Cai, W. Sun, L. Chang, and X. Xiao, “High-efficiency all-dielectric metasurfaces for broadband polarization conversion,” Plasmonics 13, 21–29 (2016).
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Y. Sun, G. C. Welch, W. L. Leong, C. J. Takacs, G. C. Bazan, and A. J. Heeger, “Solution-processed small-molecule solar cells with 6.7% efficiency,” Nat. Mater. 11, 44–48 (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, 333–337 (2011).
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A. Zhan, S. Colburn, R. Trivedi, T. K. Fryett, C. M. Dodson, and A. Majumdar, “Low-contrast dielectric metasurface optics,” ACS Photon. 3, 209–214 (2016).
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M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15, 6261–6266 (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, and Q. Gong, “Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms,” Nano Lett. 16, 5235–5240 (2016).
[Crossref]

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Z. Y. Li, M. H. Kim, C. Wang, Z. H. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. F. Yu, “Controlling propagation and coupling of waveguide modes using phase-gradient metasurfaces,” Nat. Nanotechnol. 12, 675–683 (2017).
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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, and L. Zhou, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12, 6223–6229 (2012).
[Crossref]

Wang, Q.

Z. Liu, Q. Wang, Y. Xie, and Y. Zhu, “High-efficiency control of transmitted light with a three-layered plasmonic metasurface,” J. Phys. D 49, 475101 (2016).
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Wang, Y.

Wang, Z.

F. Ding, Z. Wang, V. M. Shalaev, and A. V. Kildishev, “Broadband high-efficiency half-wave plate using plasmonic metasurface,” in CLEO: QELS_Fundamental Science (Optical Society of America, 2015), paper FTu1C.6.

Welch, G. C.

Y. Sun, G. C. Welch, W. L. Leong, C. J. Takacs, G. C. Bazan, and A. J. Heeger, “Solution-processed small-molecule solar cells with 6.7% efficiency,” Nat. Mater. 11, 44–48 (2012).
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Xiao, F.

W. Zhu, F. Xiao, M. Kang, and M. Premaratne, “Coherent perfect absorption in an all-dielectric metasurface,” Appl. Phys. Lett. 108, 121901 (2016).
[Crossref]

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S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-dielectric full-color printing with TiO2 metasurfaces,” ACS Nano 11, 4445–4452 (2017).
[Crossref]

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, and L. Zhou, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12, 6223–6229 (2012).
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Xiao, X.

M. Chen, J. Cai, W. Sun, L. Chang, and X. Xiao, “High-efficiency all-dielectric metasurfaces for broadband polarization conversion,” Plasmonics 13, 21–29 (2016).
[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, and Q. Gong, “Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms,” Nano Lett. 16, 5235–5240 (2016).
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Z. Liu, Q. Wang, Y. Xie, and Y. Zhu, “High-efficiency control of transmitted light with a three-layered plasmonic metasurface,” J. Phys. D 49, 475101 (2016).
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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, and Q. Gong, “Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms,” Nano Lett. 16, 5235–5240 (2016).
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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, and Q. Gong, “Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms,” Nano Lett. 16, 5235–5240 (2016).
[Crossref]

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D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, “Large-angle, multifunctional metagratings based on freeform multimode geometries,” Nano Lett. 17, 3752–3757 (2017).
[Crossref]

D. Sell, J. Yang, S. Doshay, K. Zhang, and J. A. Fan, “Visible light metasurfaces based on single-crystal silicon,” ACS Photon. 3, 1919–1925 (2016).
[Crossref]

Yang, K. Y.

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

Yang, R.

D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, “Large-angle, multifunctional metagratings based on freeform multimode geometries,” Nano Lett. 17, 3752–3757 (2017).
[Crossref]

Yao, B.

Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, and T. F. Krauss, “Efficient silicon metasurfaces for visible light,” ACS Photon. 4, 544–551 (2017).
[Crossref]

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N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (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, 333–337 (2011).
[Crossref]

Yu, N. F.

Z. Y. Li, M. H. Kim, C. Wang, Z. H. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. F. Yu, “Controlling propagation and coupling of waveguide modes using phase-gradient metasurfaces,” Nat. Nanotechnol. 12, 675–683 (2017).
[Crossref]

Yue, W.

S. Gao, W. Yue, C. S. Park, S. S. Lee, E. S. Kim, and D. Y. Choi, “Aluminum plasmonic metasurface enabling a wavelength-insensitive phase gradient for linearly polarized visible light,” ACS Photon. 4, 322–328 (2017).
[Crossref]

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

Zhan, A.

A. Zhan, S. Colburn, R. Trivedi, T. K. Fryett, C. M. Dodson, and A. Majumdar, “Low-contrast dielectric metasurface optics,” ACS Photon. 3, 209–214 (2016).
[Crossref]

Zhang, C.

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-dielectric full-color printing with TiO2 metasurfaces,” ACS Nano 11, 4445–4452 (2017).
[Crossref]

Zhang, K.

D. Sell, J. Yang, S. Doshay, K. Zhang, and J. A. Fan, “Visible light metasurfaces based on single-crystal silicon,” ACS Photon. 3, 1919–1925 (2016).
[Crossref]

Zhang, L.

L. Zhang, S. Mei, K. Huang, and C. W. Qiu, “Advances in full control of electromagnetic waves with metasurfaces,” Adv. Opt. Mater. 4, 818–833 (2016).
[Crossref]

Zhang, S.

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

Zhao, Y.

Zheng, G.

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10, 308–312 (2015).
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X. Chen, H. Zhou, M. Liu, and J. Dong, “Measurement of orbital angular momentum by self-interference using a plasmonic metasurface,” IEEE Photon. J. 8, 4800308 (2016).
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Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, and T. F. Krauss, “Efficient silicon metasurfaces for visible light,” ACS Photon. 4, 544–551 (2017).
[Crossref]

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, and L. Zhou, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12, 6223–6229 (2012).
[Crossref]

Zhou, Z.

Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, and T. F. Krauss, “Efficient silicon metasurfaces for visible light,” ACS Photon. 4, 544–551 (2017).
[Crossref]

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-dielectric full-color printing with TiO2 metasurfaces,” ACS Nano 11, 4445–4452 (2017).
[Crossref]

Zhu, A. Y.

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-insensitive metalenses at visible wavelengths,” Nano Lett. 16, 7229–7234 (2016).
[Crossref]

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, 1190–1194 (2016).
[Crossref]

Zhu, W.

W. Zhu, F. Xiao, M. Kang, and M. Premaratne, “Coherent perfect absorption in an all-dielectric metasurface,” Appl. Phys. Lett. 108, 121901 (2016).
[Crossref]

Zhu, Y.

Z. Liu, Q. Wang, Y. Xie, and Y. Zhu, “High-efficiency control of transmitted light with a three-layered plasmonic metasurface,” J. Phys. D 49, 475101 (2016).
[Crossref]

ACS Nano (1)

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-dielectric full-color printing with TiO2 metasurfaces,” ACS Nano 11, 4445–4452 (2017).
[Crossref]

ACS Photon. (4)

Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, C. P. Reardon, and T. F. Krauss, “Efficient silicon metasurfaces for visible light,” ACS Photon. 4, 544–551 (2017).
[Crossref]

A. Zhan, S. Colburn, R. Trivedi, T. K. Fryett, C. M. Dodson, and A. Majumdar, “Low-contrast dielectric metasurface optics,” ACS Photon. 3, 209–214 (2016).
[Crossref]

S. Gao, W. Yue, C. S. Park, S. S. Lee, E. S. Kim, and D. Y. Choi, “Aluminum plasmonic metasurface enabling a wavelength-insensitive phase gradient for linearly polarized visible light,” ACS Photon. 4, 322–328 (2017).
[Crossref]

D. Sell, J. Yang, S. Doshay, K. Zhang, and J. A. Fan, “Visible light metasurfaces based on single-crystal silicon,” ACS Photon. 3, 1919–1925 (2016).
[Crossref]

Adv. Opt. Mater. (4)

M. A. Otte, A. Garcia-Martin, X. Borrise, and B. Sepulveda, “Metamirrors based on arrays of silicon nanowires with height gradients,” Adv. Opt. Mater. 5, 1600933 (2017).
[Crossref]

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Appl. Phys. Express (1)

Z. Li, L. Huang, K. Lu, Y. Sun, and L. Min, “Continuous metasurface for high-performance anomalous reflection,” Appl. Phys. Express 7, 112001 (2014).
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Appl. Phys. Lett. (1)

W. Zhu, F. Xiao, M. Kang, and M. Premaratne, “Coherent perfect absorption in an all-dielectric metasurface,” Appl. Phys. Lett. 108, 121901 (2016).
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Z. Li and K. Aydin, “Broadband metasurfaces for anomalous transmission and spectrum splitting at visible frequencies,” EPJ Appl. Metamater. 2, 2 (2015).
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IEEE Photon. J. (1)

X. Chen, H. Zhou, M. Liu, and J. Dong, “Measurement of orbital angular momentum by self-interference using a plasmonic metasurface,” IEEE Photon. J. 8, 4800308 (2016).
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Z. Liu, Q. Wang, Y. Xie, and Y. Zhu, “High-efficiency control of transmitted light with a three-layered plasmonic metasurface,” J. Phys. D 49, 475101 (2016).
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Figures (8)

Fig. 1.
Fig. 1. Schematic of the homogeneous metasurface composed of rectangular crystalline silicon posts based on silica film.
Fig. 2.
Fig. 2. (a) Transmission and phase of the periodic c-silicon posts with 190 nm unit cell size and 220 nm height for different cross-section lengths at the wavelength of 751 nm. (b) Magnetic field amplitudes in the xz plane (Hxz) for w=120  nm and w=180  nm at wavelength of 751 nm. (c) Vertical view of the compactly arranged silicon posts. (d) Vertical view of the period formed by filling the gaps between the silicon posts.
Fig. 3.
Fig. 3. Schematic of the proposed silicon phase-gradient metasurface composed of trapezoidal antenna arrays on a quartz substrate.
Fig. 4.
Fig. 4. Simulated phase and the electric field amplitude variation for silicon nanoantenna thickness h=290  nm. (a) Simulated phase variation along the x direction of the super cell for wavelengths of 740–780 nm; (b) full 2π phase shift along the x direction of the super cell for typical wavelengths of 740, 751, 760, and 770 nm; (c) intensity of the transmission, reflection, and absorption; and (d) the transmission of every layer of the metasurface.
Fig. 5.
Fig. 5. (a) Simulated transmission efficiency normalized to input energy and the transmission energy of the quartz substrate for wavelengths of 740–780 nm. (b) Far-field transmission efficiency (normalized to input energy) for different anomalous refraction angles (θr) at wavelength of 751 nm, where the inset shows the E-field (Ey) distribution for the refracted light with the propagation being signified by a red arrow at wavelength of 751 nm.
Fig. 6.
Fig. 6. (a) Schematic of assumptive unit cell composed of rectangular silicon post arrays on quartz substrate. (b), (c) Simulated transmission and reflection of the unit cell with various thickness h of silicon posts for wavelengths of 720–780 nm (the marked dashed lines indicate the variation of transmission and reflection at wavelength of 751 nm). (d) Transmission, reflection, and absorption of the unit cell at wavelength of 751 nm.
Fig. 7.
Fig. 7. Transmission efficiency with the fixed geometric parameters of the silicon trapezoidal antennas. (a) Simulated transmission efficiency normalized to input energy and the transmission energy of the quartz substrate for wavelengths of 720–780 nm, and (b) far-field transmission efficiency (normalized to input energy) for different anomalous refraction angles (θr).
Fig. 8.
Fig. 8. (a) Calculated total transmission at different values of w1. (b) Calculated desired anomalous refraction efficiency at different values of w1.

Tables (3)

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Table 1. Cross-Section Lengths of the Silicon Posts

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Table 2. Geometrical Parameters of the Designed Super Cell

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Table 3. Calculation and Simulation Angles for All Diffraction Orders without 0 Order and Negative Angle of Symmetry

Equations (8)

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

nrsinθrnisinθi=λ02πdϕdx,
sinθr=λ02πdϕdx=λ0Px,
sinθr=m0λ0Px+λ02πdϕdx=(m0+1)λ0Px,
Tout=Iout/Is,
Tq=Itq/Is,
ηr1=(Ir/Is)×100%,
ηr2=(Ir/Itd)×100%,
θr=arcsin[(m0+1)λ0Px].

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