Abstract

Vortex beam has attracted growing attention in recent years due to its remarkable abilities in the communication system since it is believed to be an effective way to improve the channel capacity efficiency. However, available vortex beam generators suffer from the issues of complex configurations, low efficiency as well as narrow bandwidths, especially for the transmissive case. Here, we proposed a broadband transmissive metasurface to generate vortex beam with l=1 in a broad band ranging from 8GHz to 13 GHz. We enhance the working bandwidth by carefully designing the meta-atoms which provide high transmittances along with similar slopes of the phase responses within a large frequency interval. More importantly, the designed vortex beam generator exhibits very high working efficiencies (more than 83% within the whole working band). Our finding opens a door for the design of high-efficiency broadband transmissive vortex beam generators and operating at other frequency domains.

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

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References

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  49. Y. W. Wang, G. M. Wang, and B. F. Zong, “Directivity Improvement of Vivaldi Antenna Using Double-Slot Structure,” IEEE Antenn. Wirel. Pr. 12(3), 1380–1383 (2013).
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2018 (3)

Y. Ran, J. Liang, T. Cai, and H. Li, “High-performance broadband vortex beam generator using reflective Pancharatnam–Berry metasurface,” Opt. Commun. 427, 101–106 (2018).
[Crossref]

Z. Wang, S. Dong, W. Luo, M. Jia, Z. Liang, Q. He, S. Sun, and L. Zhou, “High-efficiency generation of Bessel beams with transmissive metasurfaces,” Appl. Phys. Lett. 112(19), 191901 (2018).
[Crossref]

Y. Ran, J. Liang, T. Cai, W. Ji, and G. Wang, “High-performance broadband vortex beam generator based on double-layered reflective metasurface,” AIP Adv. 8(9), 095201 (2018).
[Crossref]

2017 (5)

T. Cai, S. Tang, G. Wang, H. Xu, S. Sun, Q. He, and L. Zhou, “High‐performance bifunctional metasurfaces in transmission and reflection geometries,” Adv. Opt. Mater. 5(2), 1600506 (2017).
[Crossref]

W. Luo, S. Sun, H. Xu, Q. He, and L. Zhou, “Transmissive ultrathin Pancharatnam-Berry metasurfaces with nearly 100% efficiency,” Phys. Rev. Appl. 7(4), 044033 (2017).
[Crossref]

H. X. Xu, H. Liu, X. Ling, Y. Sun, and F. Yuan, “Broadband Vortex Beam Generation Using Multimode Pancharatnam–Berry Metasurface,” IEEE Trans. Antenn. Propag. 65(12), 7378–7382 (2017).
[Crossref]

T. Cai, G. M. Wang, S. W. Tang, H. X. Xu, J. W. Duan, H. J. Guo, F. X. Guan, S. L. Sun, Q. He, and L. Zhou, “High-Efficiency and Full-Space Manipulation of Electromagnetic Wave Fronts with Metasurfaces,” Phys. Rev. Appl. 8(3), 034033 (2017).
[Crossref]

X. Y. Lei and Y. J. Cheng, “High-Efficiency and High-Polarization Separation Reflectarray Element for OAM-Folded Antenna Application,” IEEE Antenn. Wirel. Pr. 16(99), 1357–1360 (2017).
[Crossref]

2016 (8)

S. Yu, L. Li, G. Shi, C. Zhu, and Y. Shi, “Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain,” Appl. Phys. Lett. 108(24), 241901 (2016).
[Crossref]

S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurface for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).
[Crossref]

M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C. W. Qiu, “Visible-Frequency Metasurface for Structuring and Spatially Multiplexing Optical Vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
[Crossref] [PubMed]

J. Jin, J. Luo, X. Zhang, H. Gao, X. Li, M. Pu, P. Gao, Z. Zhao, and X. Luo, “Generation and detection of orbital angular momentum via metasurface,” Sci. Rep. 6(1), 24286 (2016).
[Crossref] [PubMed]

Y. Guo, L. Yan, W. Pan, and B. Luo, “Generation and Manipulation of Orbital Angular Momentum by All-Dielectric Metasurfaces,” Plasmonics 11(1), 337–344 (2016).
[Crossref]

H. X. Xu, S. Tang, S. Ma, W. Luo, T. Cai, S. Sun, Q. He, and L. Zhou, “Tunable microwave metasurfaces for high-performance operations: dispersion compensation and dynamical switch,” Sci. Rep. 6(1), 38255 (2016).
[Crossref] [PubMed]

W. Sun, Q. He, S. Sun, and L. Zhou, “High-efficiency surface plasmon meta-couplers: concept and microwave-regime realizations,” Light Sci. Appl. 5(1), e16003 (2016).
[Crossref] [PubMed]

Z. Li, J. Hao, L. Huang, H. Li, H. Xu, Y. Sun, and N. Dai, “Manipulating the wavefront of light by plasmonic metasurfaces operating in high order modes,” Opt. Express 24(8), 8788–8796 (2016).
[Crossref] [PubMed]

2015 (3)

F. Ding, Z. Wang, S. He, V. M. Shalaev, and A. V. Kildishev, “Broadband high-efficiency half-wave plate: a supercell-based plasmonic metasurface approach,” ACS Nano 9(4), 4111–4119 (2015).
[Crossref] [PubMed]

T. Cai, G. Wang, X. Zhang, J. Liang, Y. Zhuang, D. Liu, and H. Xu, “Ultra-thin polarization beam splitter using 2-D transmissive phase gradient metasurface,” IEEE Trans. Antenn. Propag. 63(12), 5629–5636 (2015).
[Crossref]

A. E. Willner, H Huang, Y Yan, Y. Ren, N Ahmed, G Xie, C Bao, L Li, Y Cao, Z Zhao, J. Wang, M. P. J. Lavery, M Tur, S Ramachandran, A. F Molisch, N Ashrafi, and S Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

2014 (6)

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

L. Cheng, W. Hong, and Z. C. Hao, “Generation of electromagnetic waves with arbitrary orbital angular momentum modes,” Sci. Rep. 4(1), 4814 (2014).
[Crossref] [PubMed]

C. Pfeiffer and A. Grbic, “Controlling Vector Bessel Beams with Metasurfaces,” Phys. Rev. Appl. 2(4), 044012 (2014).
[Crossref]

L. Liu, X. Zhang, M. Kenney, X. Su, N. Xu, C. Ouyang, Y. Shi, J. Han, W. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26(29), 5031–5036 (2014).
[Crossref] [PubMed]

Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
[Crossref] [PubMed]

R. Niemiec, C. Brousseau, K. Mahdjoubi, O. Emile, and A. Ménard, “Characterization of an OAM Flat-Plate Antenna in the Millimeter Frequency Band,” IEEE Antenn. Wirel. Pr. 13(1), 1011–1014 (2014).
[Crossref]

2013 (5)

Y. W. Wang, G. M. Wang, and B. F. Zong, “Directivity Improvement of Vivaldi Antenna Using Double-Slot Structure,” IEEE Antenn. Wirel. Pr. 12(3), 1380–1383 (2013).
[Crossref]

Z. Zhao, J. Wang, S. Li, and A. E. Willner, “Metamaterials-based broadband generation of orbital angular momentum carrying vector beams,” Opt. Lett. 38(6), 932–934 (2013).
[Crossref] [PubMed]

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

Y. J. Chiang and T. J. Yen, “A composite-metamaterial-based terahertz-wave polarization rotator with an ultrathin thickness, an excellent conversion ratio, and enhanced transmission,” Appl. Phys. Lett. 102(1), 011129 (2013).
[Crossref]

D. Zelenchuk and V. Fusco, “Split-Ring FSS Spiral Phase Plate,” IEEE Antenn. Wirel. Pr. 12(3), 284–287 (2013).
[Crossref]

2012 (6)

P. Genevet, J. Lin, M. A. Kats, and F. Capasso, “Holographic detection of the orbital angular momentum of light with plasmonic photodiodes,” Nat. Commun. 3(1), 1278 (2012).
[Crossref] [PubMed]

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

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(12), 6328–6333 (2012).
[Crossref] [PubMed]

J. Wang, S. Qu, H. Ma, Z. Xu, A. Zhang, H. Zhou, H. Chen, and Y. Li, “High-efficiency spoof plasmon polariton coupler mediated by gradient metasurfaces,” Appl. Phys. Lett. 101(20), 201104 (2012).
[Crossref]

S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012).
[Crossref] [PubMed]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

2011 (4)

H. Chen, J. Hao, B. F. Zhang, J. Xu, J. Ding, and H. T. Wang, “Generation of vector beam with space-variant distribution of both polarization and phase,” Opt. Lett. 36(16), 3179–3181 (2011).
[Crossref] [PubMed]

Z. Wei, C. Yang, Y. Fan, Y. Xing, and H. Li, “Broadband polarization transformation via enhanced asymmetric transmission through arrays of twisted complementary split-ring resonators,” Appl. Phys. Lett. 99(22), 221907 (2011).
[Crossref]

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

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

2010 (2)

M. Uchida and A. Tonomura, “Generation of electron beams carrying orbital angular momentum,” Nature 464(7289), 737–739 (2010).
[Crossref] [PubMed]

C. Menzel, C. Rockstuhl, and F. Lederer, “Advanced Jones calculus for the classification of periodic metamaterials,” Phys. Rev. A 82(5), 053811 (2010).
[Crossref]

2007 (1)

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

2004 (2)

1997 (1)

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5-6), 321–327 (1994).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Ahmed, N

A. E. Willner, H Huang, Y Yan, Y. Ren, N Ahmed, G Xie, C Bao, L Li, Y Cao, Z Zhao, J. Wang, M. P. J. Lavery, M Tur, S Ramachandran, A. F Molisch, N Ashrafi, and S Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Ahmed, N.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Aieta, F.

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

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Ashrafi, S

A. E. Willner, H Huang, Y Yan, Y. Ren, N Ahmed, G Xie, C Bao, L Li, Y Cao, Z Zhao, J. Wang, M. P. J. Lavery, M Tur, S Ramachandran, A. F Molisch, N Ashrafi, and S Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

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N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
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P. Genevet, J. Lin, M. A. Kats, and F. Capasso, “Holographic detection of the orbital angular momentum of light with plasmonic photodiodes,” Nat. Commun. 3(1), 1278 (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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B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
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Dai, N.

Dalvit, D. A.

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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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J. Jin, J. Luo, X. Zhang, H. Gao, X. Li, M. Pu, P. Gao, Z. Zhao, and X. Luo, “Generation and detection of orbital angular momentum via metasurface,” Sci. Rep. 6(1), 24286 (2016).
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J. Jin, J. Luo, X. Zhang, H. Gao, X. Li, M. Pu, P. Gao, Z. Zhao, and X. Luo, “Generation and detection of orbital angular momentum via metasurface,” Sci. Rep. 6(1), 24286 (2016).
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P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012).
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P. Genevet, J. Lin, M. A. Kats, and F. Capasso, “Holographic detection of the orbital angular momentum of light with plasmonic photodiodes,” Nat. Commun. 3(1), 1278 (2012).
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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(12), 6328–6333 (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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J. Li, R. Jin, J. Geng, X. Liang, K. Wang, M. Premaratne, and W. Zhu, “Design of a Broadband Metasurface Luneburg Lens for Full-Angle Operation,” IEEE T. Antenn. Propag., doi: (2018).
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Hao, Z. C.

L. Cheng, W. Hong, and Z. C. Hao, “Generation of electromagnetic waves with arbitrary orbital angular momentum modes,” Sci. Rep. 4(1), 4814 (2014).
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Z. Wang, S. Dong, W. Luo, M. Jia, Z. Liang, Q. He, S. Sun, and L. Zhou, “High-efficiency generation of Bessel beams with transmissive metasurfaces,” Appl. Phys. Lett. 112(19), 191901 (2018).
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T. Cai, S. Tang, G. Wang, H. Xu, S. Sun, Q. He, and L. Zhou, “High‐performance bifunctional metasurfaces in transmission and reflection geometries,” Adv. Opt. Mater. 5(2), 1600506 (2017).
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H. X. Xu, S. Tang, S. Ma, W. Luo, T. Cai, S. Sun, Q. He, and L. Zhou, “Tunable microwave metasurfaces for high-performance operations: dispersion compensation and dynamical switch,” Sci. Rep. 6(1), 38255 (2016).
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F. Ding, Z. Wang, S. He, V. M. Shalaev, and A. V. Kildishev, “Broadband high-efficiency half-wave plate: a supercell-based plasmonic metasurface approach,” ACS Nano 9(4), 4111–4119 (2015).
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N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
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L. Cheng, W. Hong, and Z. C. Hao, “Generation of electromagnetic waves with arbitrary orbital angular momentum modes,” Sci. Rep. 4(1), 4814 (2014).
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A. E. Willner, H Huang, Y Yan, Y. Ren, N Ahmed, G Xie, C Bao, L Li, Y Cao, Z Zhao, J. Wang, M. P. J. Lavery, M Tur, S Ramachandran, A. F Molisch, N Ashrafi, and S Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Huang, H.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C. W. Qiu, “Visible-Frequency Metasurface for Structuring and Spatially Multiplexing Optical Vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
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B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
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B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
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Jeon, J. H.

Ji, W.

Y. Ran, J. Liang, T. Cai, W. Ji, and G. Wang, “High-performance broadband vortex beam generator based on double-layered reflective metasurface,” AIP Adv. 8(9), 095201 (2018).
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Z. Wang, S. Dong, W. Luo, M. Jia, Z. Liang, Q. He, S. Sun, and L. Zhou, “High-efficiency generation of Bessel beams with transmissive metasurfaces,” Appl. Phys. Lett. 112(19), 191901 (2018).
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J. Jin, J. Luo, X. Zhang, H. Gao, X. Li, M. Pu, P. Gao, Z. Zhao, and X. Luo, “Generation and detection of orbital angular momentum via metasurface,” Sci. Rep. 6(1), 24286 (2016).
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J. Li, R. Jin, J. Geng, X. Liang, K. Wang, M. Premaratne, and W. Zhu, “Design of a Broadband Metasurface Luneburg Lens for Full-Angle Operation,” IEEE T. Antenn. Propag., doi: (2018).
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E. Karimi, S. A. Schulz, I. D. Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
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Kats, M. A.

P. Genevet, J. Lin, M. A. Kats, and F. Capasso, “Holographic detection of the orbital angular momentum of light with plasmonic photodiodes,” Nat. Commun. 3(1), 1278 (2012).
[Crossref] [PubMed]

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(12), 6328–6333 (2012).
[Crossref] [PubMed]

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

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]

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L. Liu, X. Zhang, M. Kenney, X. Su, N. Xu, C. Ouyang, Y. Shi, J. Han, W. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26(29), 5031–5036 (2014).
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Y. Ran, J. Liang, T. Cai, and H. Li, “High-performance broadband vortex beam generator using reflective Pancharatnam–Berry metasurface,” Opt. Commun. 427, 101–106 (2018).
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J. Jin, J. Luo, X. Zhang, H. Gao, X. Li, M. Pu, P. Gao, Z. Zhao, and X. Luo, “Generation and detection of orbital angular momentum via metasurface,” Sci. Rep. 6(1), 24286 (2016).
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T. Cai, G. Wang, X. Zhang, J. Liang, Y. Zhuang, D. Liu, and H. Xu, “Ultra-thin polarization beam splitter using 2-D transmissive phase gradient metasurface,” IEEE Trans. Antenn. Propag. 63(12), 5629–5636 (2015).
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Z. Wang, S. Dong, W. Luo, M. Jia, Z. Liang, Q. He, S. Sun, and L. Zhou, “High-efficiency generation of Bessel beams with transmissive metasurfaces,” Appl. Phys. Lett. 112(19), 191901 (2018).
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W. Luo, S. Sun, H. Xu, Q. He, and L. Zhou, “Transmissive ultrathin Pancharatnam-Berry metasurfaces with nearly 100% efficiency,” Phys. Rev. Appl. 7(4), 044033 (2017).
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H. X. Xu, S. Tang, S. Ma, W. Luo, T. Cai, S. Sun, Q. He, and L. Zhou, “Tunable microwave metasurfaces for high-performance operations: dispersion compensation and dynamical switch,” Sci. Rep. 6(1), 38255 (2016).
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J. Jin, J. Luo, X. Zhang, H. Gao, X. Li, M. Pu, P. Gao, Z. Zhao, and X. Luo, “Generation and detection of orbital angular momentum via metasurface,” Sci. Rep. 6(1), 24286 (2016).
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J. Wang, S. Qu, H. Ma, Z. Xu, A. Zhang, H. Zhou, H. Chen, and Y. Li, “High-efficiency spoof plasmon polariton coupler mediated by gradient metasurfaces,” Appl. Phys. Lett. 101(20), 201104 (2012).
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H. X. Xu, S. Tang, S. Ma, W. Luo, T. Cai, S. Sun, Q. He, and L. Zhou, “Tunable microwave metasurfaces for high-performance operations: dispersion compensation and dynamical switch,” Sci. Rep. 6(1), 38255 (2016).
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Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
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A. E. Willner, H Huang, Y Yan, Y. Ren, N Ahmed, G Xie, C Bao, L Li, Y Cao, Z Zhao, J. Wang, M. P. J. Lavery, M Tur, S Ramachandran, A. F Molisch, N Ashrafi, and S Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

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R. Niemiec, C. Brousseau, K. Mahdjoubi, O. Emile, and A. Ménard, “Characterization of an OAM Flat-Plate Antenna in the Millimeter Frequency Band,” IEEE Antenn. Wirel. Pr. 13(1), 1011–1014 (2014).
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Y. Guo, L. Yan, W. Pan, and B. Luo, “Generation and Manipulation of Orbital Angular Momentum by All-Dielectric Metasurfaces,” Plasmonics 11(1), 337–344 (2016).
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J. Jin, J. Luo, X. Zhang, H. Gao, X. Li, M. Pu, P. Gao, Z. Zhao, and X. Luo, “Generation and detection of orbital angular momentum via metasurface,” Sci. Rep. 6(1), 24286 (2016).
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E. Karimi, S. A. Schulz, I. D. Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
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M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C. W. Qiu, “Visible-Frequency Metasurface for Structuring and Spatially Multiplexing Optical Vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
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J. Wang, S. Qu, H. Ma, Z. Xu, A. Zhang, H. Zhou, H. Chen, and Y. Li, “High-efficiency spoof plasmon polariton coupler mediated by gradient metasurfaces,” Appl. Phys. Lett. 101(20), 201104 (2012).
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A. E. Willner, H Huang, Y Yan, Y. Ren, N Ahmed, G Xie, C Bao, L Li, Y Cao, Z Zhao, J. Wang, M. P. J. Lavery, M Tur, S Ramachandran, A. F Molisch, N Ashrafi, and S Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Ran, Y.

Y. Ran, J. Liang, T. Cai, and H. Li, “High-performance broadband vortex beam generator using reflective Pancharatnam–Berry metasurface,” Opt. Commun. 427, 101–106 (2018).
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Y. Ran, J. Liang, T. Cai, W. Ji, and G. Wang, “High-performance broadband vortex beam generator based on double-layered reflective metasurface,” AIP Adv. 8(9), 095201 (2018).
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A. E. Willner, H Huang, Y Yan, Y. Ren, N Ahmed, G Xie, C Bao, L Li, Y Cao, Z Zhao, J. Wang, M. P. J. Lavery, M Tur, S Ramachandran, A. F Molisch, N Ashrafi, and S Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

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C. Menzel, C. Rockstuhl, and F. Lederer, “Advanced Jones calculus for the classification of periodic metamaterials,” Phys. Rev. A 82(5), 053811 (2010).
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E. Karimi, S. A. Schulz, I. D. Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
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P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012).
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F. Ding, Z. Wang, S. He, V. M. Shalaev, and A. V. Kildishev, “Broadband high-efficiency half-wave plate: a supercell-based plasmonic metasurface approach,” ACS Nano 9(4), 4111–4119 (2015).
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S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurface for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).
[Crossref]

S. Yu, L. Li, G. Shi, C. Zhu, and Y. Shi, “Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain,” Appl. Phys. Lett. 108(24), 241901 (2016).
[Crossref]

Shi, Y.

S. Yu, L. Li, G. Shi, C. Zhu, and Y. Shi, “Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain,” Appl. Phys. Lett. 108(24), 241901 (2016).
[Crossref]

S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurface for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).
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L. Liu, X. Zhang, M. Kenney, X. Su, N. Xu, C. Ouyang, Y. Shi, J. Han, W. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26(29), 5031–5036 (2014).
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M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C. W. Qiu, “Visible-Frequency Metasurface for Structuring and Spatially Multiplexing Optical Vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
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B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
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L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
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Sun, S.

Z. Wang, S. Dong, W. Luo, M. Jia, Z. Liang, Q. He, S. Sun, and L. Zhou, “High-efficiency generation of Bessel beams with transmissive metasurfaces,” Appl. Phys. Lett. 112(19), 191901 (2018).
[Crossref]

W. Luo, S. Sun, H. Xu, Q. He, and L. Zhou, “Transmissive ultrathin Pancharatnam-Berry metasurfaces with nearly 100% efficiency,” Phys. Rev. Appl. 7(4), 044033 (2017).
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T. Cai, S. Tang, G. Wang, H. Xu, S. Sun, Q. He, and L. Zhou, “High‐performance bifunctional metasurfaces in transmission and reflection geometries,” Adv. Opt. Mater. 5(2), 1600506 (2017).
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S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012).
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H. X. Xu, H. Liu, X. Ling, Y. Sun, and F. Yuan, “Broadband Vortex Beam Generation Using Multimode Pancharatnam–Berry Metasurface,” IEEE Trans. Antenn. Propag. 65(12), 7378–7382 (2017).
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T. Cai, S. Tang, G. Wang, H. Xu, S. Sun, Q. He, and L. Zhou, “High‐performance bifunctional metasurfaces in transmission and reflection geometries,” Adv. Opt. Mater. 5(2), 1600506 (2017).
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H. X. Xu, S. Tang, S. Ma, W. Luo, T. Cai, S. Sun, Q. He, and L. Zhou, “Tunable microwave metasurfaces for high-performance operations: dispersion compensation and dynamical switch,” Sci. Rep. 6(1), 38255 (2016).
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N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
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M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C. W. Qiu, “Visible-Frequency Metasurface for Structuring and Spatially Multiplexing Optical Vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
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Xu, Z.

J. Wang, S. Qu, H. Ma, Z. Xu, A. Zhang, H. Zhou, H. Chen, and Y. Li, “High-efficiency spoof plasmon polariton coupler mediated by gradient metasurfaces,” Appl. Phys. Lett. 101(20), 201104 (2012).
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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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S. Yu, L. Li, G. Shi, C. Zhu, and Y. Shi, “Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain,” Appl. Phys. Lett. 108(24), 241901 (2016).
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H. X. Xu, H. Liu, X. Ling, Y. Sun, and F. Yuan, “Broadband Vortex Beam Generation Using Multimode Pancharatnam–Berry Metasurface,” IEEE Trans. Antenn. Propag. 65(12), 7378–7382 (2017).
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L. Liu, X. Zhang, M. Kenney, X. Su, N. Xu, C. Ouyang, Y. Shi, J. Han, W. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26(29), 5031–5036 (2014).
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A. E. Willner, H Huang, Y Yan, Y. Ren, N Ahmed, G Xie, C Bao, L Li, Y Cao, Z Zhao, J. Wang, M. P. J. Lavery, M Tur, S Ramachandran, A. F Molisch, N Ashrafi, and S Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Zhao, Z.

J. Jin, J. Luo, X. Zhang, H. Gao, X. Li, M. Pu, P. Gao, Z. Zhao, and X. Luo, “Generation and detection of orbital angular momentum via metasurface,” Sci. Rep. 6(1), 24286 (2016).
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Z. Zhao, J. Wang, S. Li, and A. E. Willner, “Metamaterials-based broadband generation of orbital angular momentum carrying vector beams,” Opt. Lett. 38(6), 932–934 (2013).
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J. Wang, S. Qu, H. Ma, Z. Xu, A. Zhang, H. Zhou, H. Chen, and Y. Li, “High-efficiency spoof plasmon polariton coupler mediated by gradient metasurfaces,” Appl. Phys. Lett. 101(20), 201104 (2012).
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Z. Wang, S. Dong, W. Luo, M. Jia, Z. Liang, Q. He, S. Sun, and L. Zhou, “High-efficiency generation of Bessel beams with transmissive metasurfaces,” Appl. Phys. Lett. 112(19), 191901 (2018).
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W. Luo, S. Sun, H. Xu, Q. He, and L. Zhou, “Transmissive ultrathin Pancharatnam-Berry metasurfaces with nearly 100% efficiency,” Phys. Rev. Appl. 7(4), 044033 (2017).
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T. Cai, G. M. Wang, S. W. Tang, H. X. Xu, J. W. Duan, H. J. Guo, F. X. Guan, S. L. Sun, Q. He, and L. Zhou, “High-Efficiency and Full-Space Manipulation of Electromagnetic Wave Fronts with Metasurfaces,” Phys. Rev. Appl. 8(3), 034033 (2017).
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T. Cai, S. Tang, G. Wang, H. Xu, S. Sun, Q. He, and L. Zhou, “High‐performance bifunctional metasurfaces in transmission and reflection geometries,” Adv. Opt. Mater. 5(2), 1600506 (2017).
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H. X. Xu, S. Tang, S. Ma, W. Luo, T. Cai, S. Sun, Q. He, and L. Zhou, “Tunable microwave metasurfaces for high-performance operations: dispersion compensation and dynamical switch,” Sci. Rep. 6(1), 38255 (2016).
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S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012).
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Zhou, X.

S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurface for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).
[Crossref]

Zhu, C.

S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurface for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).
[Crossref]

S. Yu, L. Li, G. Shi, C. Zhu, and Y. Shi, “Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain,” Appl. Phys. Lett. 108(24), 241901 (2016).
[Crossref]

Zhu, W.

J. Li, R. Jin, J. Geng, X. Liang, K. Wang, M. Premaratne, and W. Zhu, “Design of a Broadband Metasurface Luneburg Lens for Full-Angle Operation,” IEEE T. Antenn. Propag., doi: (2018).
[Crossref]

Zhuang, Y.

T. Cai, G. Wang, X. Zhang, J. Liang, Y. Zhuang, D. Liu, and H. Xu, “Ultra-thin polarization beam splitter using 2-D transmissive phase gradient metasurface,” IEEE Trans. Antenn. Propag. 63(12), 5629–5636 (2015).
[Crossref]

Zong, B. F.

Y. W. Wang, G. M. Wang, and B. F. Zong, “Directivity Improvement of Vivaldi Antenna Using Double-Slot Structure,” IEEE Antenn. Wirel. Pr. 12(3), 1380–1383 (2013).
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ACS Nano (1)

F. Ding, Z. Wang, S. He, V. M. Shalaev, and A. V. Kildishev, “Broadband high-efficiency half-wave plate: a supercell-based plasmonic metasurface approach,” ACS Nano 9(4), 4111–4119 (2015).
[Crossref] [PubMed]

Adv. Mater. (2)

L. Liu, X. Zhang, M. Kenney, X. Su, N. Xu, C. Ouyang, Y. Shi, J. Han, W. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26(29), 5031–5036 (2014).
[Crossref] [PubMed]

M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C. W. Qiu, “Visible-Frequency Metasurface for Structuring and Spatially Multiplexing Optical Vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
[Crossref] [PubMed]

Adv. Opt. Mater. (1)

T. Cai, S. Tang, G. Wang, H. Xu, S. Sun, Q. He, and L. Zhou, “High‐performance bifunctional metasurfaces in transmission and reflection geometries,” Adv. Opt. Mater. 5(2), 1600506 (2017).
[Crossref]

Adv. Opt. Photonics (2)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

A. E. Willner, H Huang, Y Yan, Y. Ren, N Ahmed, G Xie, C Bao, L Li, Y Cao, Z Zhao, J. Wang, M. P. J. Lavery, M Tur, S Ramachandran, A. F Molisch, N Ashrafi, and S Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

AIP Adv. (1)

Y. Ran, J. Liang, T. Cai, W. Ji, and G. Wang, “High-performance broadband vortex beam generator based on double-layered reflective metasurface,” AIP Adv. 8(9), 095201 (2018).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (7)

S. Yu, L. Li, G. Shi, C. Zhu, and Y. Shi, “Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain,” Appl. Phys. Lett. 108(24), 241901 (2016).
[Crossref]

S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurface for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).
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Figures (6)

Fig. 1
Fig. 1 The topology of the building block and simulated transmission spectra. (a) The perspective view of the meta-atom. (b) Middle layer of the meta-atom. The geometrical parameters are: p = 11 mm, r = 4.25 mm, w = 1.5 mm. α represents the open angle of the symmetric split ring and β is the rotation angle of the unit cell. (c) FDTD simulated spectra of transmission coefficient t xy , t yy , t xx and t yx . (d) FDTD simulated spectra of phase.
Fig. 2
Fig. 2 The cross-polarized transmission coefficients and phase for different ɑ and β value. (a) magnitude. (b) the phase of cross-polarized for different ɑ and β value for normal y-polarized incidence.
Fig. 3
Fig. 3 Design of transmissive vortex beam generator. The phase distribution of (a) focusing metasurface; (b) spiral phase plate; and (c) the vortex beam generator. (d) The middle metallic layer of our designed meta-device.
Fig. 4
Fig. 4 The calculated Re( E x ) and the phase distributions from 8 to 13 GHz in steps of 1 GHz under normal y-polarized incidence.
Fig. 5
Fig. 5 Numerically calculated far-field patterns of the metasurface with l=1from 8 to 13 GHz in steps of 1 GHz under normal y-polarized incidence.
Fig. 6
Fig. 6 Simulated 2D far-field radiation patterns characterization of the broadband metasurface with l=1 under normal y-polarized incidence. (a) 8 GHz, (b) 9 GHz, (c) 10 GHz, (d) 11 GHz, (e) 12 GHz, (b) 13 GHz.

Equations (8)

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φ( x,y ) f 1 φ( x,y ) f i φ( x,y ) f 2
E i (r,t)=( i x i y ) e i(kzωt) ,
E t (r,t)=( t x t y ) e i(kzωt) .
( t x t y )=( T xx T xy T yx T yy )( i x i y )=( A B C D )( i x i y )=T( i x i y ).
T 45° =( 0 AD 0 0 ), T 135° =( 0 (AD) 0 0 ),
φ 1 ( mp, np )= k 0 ( F 0 2 + ( mp ) 2 + ( np ) 2 F 0 )+ φ 0
φ 2 ( mp, np )=l tan 1 ( n m )
φ total ( mp, np )= φ 1 ( mp, np )+ φ 2 ( mp, np )

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