Abstract

In this paper, a 1-bit digital orbital angular momentum (OAM) vortex beam generator based on a coding reflective metasurface is proposed. Theoretical analyses are performed to demonstrate that the 1-bit digital metasurface with only 0 and π reflection phase response elements can generate different OAM vortex beams flexibly. The compensation phase distribution calculation formula and phase fuzzification method are concluded. To validate this concept, a 1-bit 12 × 12 digital OAM generator that is mounted with PIN diodes and driven by microcontroller unit is designed and measured in the radio frequency domain. The experiment of the prototype reveals that the 1-bit digital OAM generator is an efficient way to generate vortex beams. Also, this concept breaks through the constraint of phase continuity of elements when generating OAM beams using reflective metasurfaces.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (5)

S. Yu, L. Li, and N. Kou, “Generation, reception and separation of mixed-state orbital angular momentum vortex beams using metasurfaces,” Opt. Mater. Express 7(9), 3312–3321 (2017).
[Crossref]

Z. Tao, X. Wan, B. C. Pan, and T. J. Cui, “Reconfigurable conversions of reflection, transmission, and polarization states using active metasurface,” Appl. Phys. Lett. 110(12), 121901 (2017).
[Crossref]

Q. Zheng, Y. Li, J. Zhang, H. Ma, J. Wang, Y. Pang, Y. Han, S. Sui, Y. Shen, H. Chen, and S. Qu, “Wideband, wide-angle coding phase gradient metasurfaces based on Pancharatnam-Berry phase,” Sci. Rep. 7(1), 43543 (2017).
[Crossref]

L. Li, T. Jun Cui, W. Ji, S. Liu, J. Ding, X. Wan, Y. Bo Li, M. Jiang, C. W. Qiu, and S. Zhang, “Electromagnetic reprogrammable coding-metasurface holograms,” Nat. Commun. 8(1), 197 (2017).
[Crossref] [PubMed]

K. Chen, L. Cui, Y. Feng, J. Zhao, T. Jiang, and B. Zhu, “Coding metasurface for broadband microwave scattering reduction with optical transparency,” Opt. Express 25(5), 5571–5579 (2017).
[Crossref] [PubMed]

2016 (6)

X. Wan, M. Q. Qi, T. Y. Chen, and T. J. Cui, “Field-programmable beam reconfiguring based on digitally-controlled coding metasurface,” Sci. Rep. 6(1), 20663 (2016).
[Crossref] [PubMed]

Z. Shen, B. Jin, J. Zhao, Y. Feng, L. Kang, W. Xu, J. Chen, and P. Wu, “Design of transmission-type coding metasurface and its application of beam forming,” Appl. Phys. Lett. 109(12), 121103 (2016).
[Crossref]

S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light Sci. Appl. 5(5), e16076 (2016).
[Crossref] [PubMed]

S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurfaces 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, X. Zhou, 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]

B. Xu, C. Wu, Z. Wei, Y. Fan, and H. Li, “Generating an orbital-angular-momentum beam with a metasurface of gradient reflective phase,” Opt. Mater. Express 6(12), 3940–3945 (2016).
[Crossref]

2015 (1)

2014 (4)

S. Liu, H. X. Xu, H. C. Zhang, and T. J. Cui, “Tunable ultrathin mantle cloak via varactor-diode-loaded metasurface,” Opt. Express 22(11), 13403–13417 (2014).
[Crossref] [PubMed]

C. Della Giovampaola and N. Engheta, “Digital Metamaterials,” Nat. Mater. 13(12), 1115–1121 (2014).
[Crossref] [PubMed]

T. J. Cui, M. Q. Qi, X. Wan, J. Zhao, and Q. Cheng, “Coding metamaterials, digital metamaterials and programmable metamaterials,” Light Sci. Appl. 3(10), e218 (2014).
[Crossref]

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

2012 (1)

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 (3)

F. Tamburini, E. Mari, B. Thidé, C. Barbieri, and F. Romanato, “Experimental verification of photo angular momentum and vorticity with radio techniques,” Appl. Phys. Lett. 99, 204102 (2011).
[Crossref]

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

2010 (3)

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

B. Zhu, Y. Feng, J. Zhao, C. Huang, and T. Jiang, “Switchable metamaterial reflector/absorber for different polarized electromagnetic waves,” Appl. Phys. Lett. 97(5), 051906 (2010).
[Crossref]

S. M. Mohammadi, L. K. S. Daldorff, J. E. S. Bergman, R. L. Karlsson, B. Thidé, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital Angular Momentum in Radio—A System Study,” IEEE Trans. Antenn. Propag. 58(2), 565–572 (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 (1)

1997 (1)

D. M. Pozar, S. D. Targonski, and H. D. Syrigos, “Design of Millimeter Wave Microstrip Reflectarrays,” IEEE Trans. Antenn. Propag. 45(2), 287–296 (1997).
[Crossref]

1995 (1)

D. Chang and M. Huang, “Multiple-Polarization Microstrip Reflectarray Antenna with High Efficiency and Low Cross-Polarization,” IEEE Trans. Antenn. Propag. 43(8), 829–834 (1995).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. 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.

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.

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]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. 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]

Bao, D.

S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light Sci. Appl. 5(5), e16076 (2016).
[Crossref] [PubMed]

Barbieri, C.

F. Tamburini, E. Mari, B. Thidé, C. Barbieri, and F. Romanato, “Experimental verification of photo angular momentum and vorticity with radio techniques,” Appl. Phys. Lett. 99, 204102 (2011).
[Crossref]

Barnett, S.

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. 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]

Bergman, J.

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]

Bergman, J. E. S.

S. M. Mohammadi, L. K. S. Daldorff, J. E. S. Bergman, R. L. Karlsson, B. Thidé, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital Angular Momentum in Radio—A System Study,” IEEE Trans. Antenn. Propag. 58(2), 565–572 (2010).
[Crossref]

Bo Li, Y.

L. Li, T. Jun Cui, W. Ji, S. Liu, J. Ding, X. Wan, Y. Bo Li, M. Jiang, C. W. Qiu, and S. Zhang, “Electromagnetic reprogrammable coding-metasurface holograms,” Nat. Commun. 8(1), 197 (2017).
[Crossref] [PubMed]

Capasso, F.

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

Carozzi, T. D.

S. M. Mohammadi, L. K. S. Daldorff, J. E. S. Bergman, R. L. Karlsson, B. Thidé, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital Angular Momentum in Radio—A System Study,” IEEE Trans. Antenn. Propag. 58(2), 565–572 (2010).
[Crossref]

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]

Chang, D.

D. Chang and M. Huang, “Multiple-Polarization Microstrip Reflectarray Antenna with High Efficiency and Low Cross-Polarization,” IEEE Trans. Antenn. Propag. 43(8), 829–834 (1995).
[Crossref]

Chen, H.

Q. Zheng, Y. Li, J. Zhang, H. Ma, J. Wang, Y. Pang, Y. Han, S. Sui, Y. Shen, H. Chen, and S. Qu, “Wideband, wide-angle coding phase gradient metasurfaces based on Pancharatnam-Berry phase,” Sci. Rep. 7(1), 43543 (2017).
[Crossref]

Chen, J.

Z. Shen, B. Jin, J. Zhao, Y. Feng, L. Kang, W. Xu, J. Chen, and P. Wu, “Design of transmission-type coding metasurface and its application of beam forming,” Appl. Phys. Lett. 109(12), 121103 (2016).
[Crossref]

Chen, K.

Chen, T. Y.

X. Wan, M. Q. Qi, T. Y. Chen, and T. J. Cui, “Field-programmable beam reconfiguring based on digitally-controlled coding metasurface,” Sci. Rep. 6(1), 20663 (2016).
[Crossref] [PubMed]

Cheng, Q.

S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light Sci. Appl. 5(5), e16076 (2016).
[Crossref] [PubMed]

T. J. Cui, M. Q. Qi, X. Wan, J. Zhao, and Q. Cheng, “Coding metamaterials, digital metamaterials and programmable metamaterials,” Light Sci. Appl. 3(10), e218 (2014).
[Crossref]

Courtial, J.

Cui, L.

Cui, T.

Cui, T. J.

Z. Tao, X. Wan, B. C. Pan, and T. J. Cui, “Reconfigurable conversions of reflection, transmission, and polarization states using active metasurface,” Appl. Phys. Lett. 110(12), 121901 (2017).
[Crossref]

S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light Sci. Appl. 5(5), e16076 (2016).
[Crossref] [PubMed]

X. Wan, M. Q. Qi, T. Y. Chen, and T. J. Cui, “Field-programmable beam reconfiguring based on digitally-controlled coding metasurface,” Sci. Rep. 6(1), 20663 (2016).
[Crossref] [PubMed]

S. Liu, H. X. Xu, H. C. Zhang, and T. J. Cui, “Tunable ultrathin mantle cloak via varactor-diode-loaded metasurface,” Opt. Express 22(11), 13403–13417 (2014).
[Crossref] [PubMed]

T. J. Cui, M. Q. Qi, X. Wan, J. Zhao, and Q. Cheng, “Coding metamaterials, digital metamaterials and programmable metamaterials,” Light Sci. Appl. 3(10), e218 (2014).
[Crossref]

Daldorff, L. K. S.

S. M. Mohammadi, L. K. S. Daldorff, J. E. S. Bergman, R. L. Karlsson, B. Thidé, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital Angular Momentum in Radio—A System Study,” IEEE Trans. Antenn. Propag. 58(2), 565–572 (2010).
[Crossref]

Della Giovampaola, C.

C. Della Giovampaola and N. Engheta, “Digital Metamaterials,” Nat. Mater. 13(12), 1115–1121 (2014).
[Crossref] [PubMed]

Ding, J.

L. Li, T. Jun Cui, W. Ji, S. Liu, J. Ding, X. Wan, Y. Bo Li, M. Jiang, C. W. Qiu, and S. Zhang, “Electromagnetic reprogrammable coding-metasurface holograms,” Nat. Commun. 8(1), 197 (2017).
[Crossref] [PubMed]

Ding, X.

Dolinar, S.

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]

Du, L.

S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light Sci. Appl. 5(5), e16076 (2016).
[Crossref] [PubMed]

Engheta, N.

C. Della Giovampaola and N. Engheta, “Digital Metamaterials,” Nat. Mater. 13(12), 1115–1121 (2014).
[Crossref] [PubMed]

Fan, Y.

Fazal, I. M.

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]

Feng, Y.

K. Chen, L. Cui, Y. Feng, J. Zhao, T. Jiang, and B. Zhu, “Coding metasurface for broadband microwave scattering reduction with optical transparency,” Opt. Express 25(5), 5571–5579 (2017).
[Crossref] [PubMed]

Z. Shen, B. Jin, J. Zhao, Y. Feng, L. Kang, W. Xu, J. Chen, and P. Wu, “Design of transmission-type coding metasurface and its application of beam forming,” Appl. Phys. Lett. 109(12), 121103 (2016).
[Crossref]

B. Zhu, Y. Feng, J. Zhao, C. Huang, and T. Jiang, “Switchable metamaterial reflector/absorber for different polarized electromagnetic waves,” Appl. Phys. Lett. 97(5), 051906 (2010).
[Crossref]

Forozesh, K.

S. M. Mohammadi, L. K. S. Daldorff, J. E. S. Bergman, R. L. Karlsson, B. Thidé, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital Angular Momentum in Radio—A System Study,” IEEE Trans. Antenn. Propag. 58(2), 565–572 (2010).
[Crossref]

Franke-Arnold, S.

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]

Genevet, P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Gibson, G.

Han, J.

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X. Wan, M. Q. Qi, T. Y. Chen, and T. J. Cui, “Field-programmable beam reconfiguring based on digitally-controlled coding metasurface,” Sci. Rep. 6(1), 20663 (2016).
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Z. Shen, B. Jin, J. Zhao, Y. Feng, L. Kang, W. Xu, J. Chen, and P. Wu, “Design of transmission-type coding metasurface and its application of beam forming,” Appl. Phys. Lett. 109(12), 121103 (2016).
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S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, 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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S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurfaces for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).
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S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurfaces for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).
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Z. Shen, B. Jin, J. Zhao, Y. Feng, L. Kang, W. Xu, J. Chen, and P. Wu, “Design of transmission-type coding metasurface and its application of beam forming,” Appl. Phys. Lett. 109(12), 121103 (2016).
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S. Yu, L. Li, and N. Kou, “Generation, reception and separation of mixed-state orbital angular momentum vortex beams using metasurfaces,” Opt. Mater. Express 7(9), 3312–3321 (2017).
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S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light Sci. Appl. 5(5), e16076 (2016).
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K. Chen, L. Cui, Y. Feng, J. Zhao, T. Jiang, and B. Zhu, “Coding metasurface for broadband microwave scattering reduction with optical transparency,” Opt. Express 25(5), 5571–5579 (2017).
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B. Zhu, Y. Feng, J. Zhao, C. Huang, and T. Jiang, “Switchable metamaterial reflector/absorber for different polarized electromagnetic waves,” Appl. Phys. Lett. 97(5), 051906 (2010).
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S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurfaces for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).
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S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light Sci. Appl. 5(5), e16076 (2016).
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Figures (8)

Fig. 1
Fig. 1 Structure of 1-bit digital OAM generator.
Fig. 2
Fig. 2 Analog compensation phase distributions of different modes and corresponding binary compensation phase distributions, (a) l = 1, (b) l = 2, and (c) l = 3.
Fig. 3
Fig. 3 Theoretical analysis results of 1-bit digital OAM generator with (a) l = 1, (b) l = 2 and (c) l = 3.
Fig. 4
Fig. 4 (a) Layout of 1-bit digital element mounted with PIN diode, (b) reflection phase simulated in infinite boundary condition when PIN diode turns ON (red solid line) and OFF (blue dash line) states. Phase difference (yellow dash dot line) of 180° is at 4.75 GHz and 5.2 GHz.
Fig. 5
Fig. 5 (a) Top and bottom side of fabricated 12 × 12 1-bit digital OAM generator, (b) binary compensation phase distribution and corresponding control board PIN diodes working state for l = 1, (c) binary compensation phase distribution and corresponding control board PIN diodes working state for l = 2.
Fig. 6
Fig. 6 Measurement scene of 1-bit digital OAM generator using planar near field scanning technique.
Fig. 7
Fig. 7 Simulation and measurement results of (a) l = 1 and (b) l = 2 at 4.75 GHz.
Fig. 8
Fig. 8 OAM mode purity analysis results of measured (a) l = 1 and (b) l = 2.

Equations (3)

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E( u ^ )= i=1 I j=1 J F( r ij · r f )A( r ij · u ^ 0 )A( u ^ · u ^ 0 )exp[j k 0 (| r ij r f |+ r ij · u ^ )+j φ ij b ] ,
φ ij =l Φ 0 k 0 [ | r ij r f |+ r ij · u ^ 0 ], l=0,±1,±2,...
φ ij b ={ 0 ,0 φ ij <180° π ,180° φ ij <360° ,

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