Abstract

Radar cross section reducing (RCSR) metasurfaces or coding metasurfaces were primarily designed for normally incident radiation in the past. It is evident that the performance of coding metasurfaces for RCSR can be significantly improved by additional backscattering reduction of obliquely incident radiation, which requires a valid analytic conception tool. Here, we derive an analytic current density distribution model for the calculation of the backscatter far-field of obliquely incident radiation on a coding metasurface for RCSR. For demonstration, we devise and fabricate a metasurface for a working frequency of $10.66 \, \textrm {GHz}$ and obtain good agreement between the measured, simulated, and analytically calculated backscatter far-fields. The metasurface significantly reduces backscattering for incidence angles between $-40^\circ$ and $40^\circ$ in a spectral working range of approximately $1\,$GHz.

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

Full Article  |  PDF Article
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References

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  1. D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
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    [Crossref]
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    [Crossref]
  4. T. J. Cui, S. Liu, and L. Zhang, “Information metamaterials and metasurfaces,” J. Mater. Chem. C 5(15), 3644–3668 (2017).
    [Crossref]
  5. T.-J. Cui, S. Liu, and L.-L. Li, “Information entropy of coding metasurface,” Light: Sci. Appl. 5(11), e16172 (2016).
    [Crossref]
  6. S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qing Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv. Sci. 3(10), 1600156 (2016).
    [Crossref]
  7. Y. Zhao, X. Cao, J. Gao, Y. Sun, H. Yang, X. Liu, Y. Zhou, T. Han, and W. Chen, “Broadband diffusion metasurface based on a single anisotropic element and optimized by the simulated annealing algorithm,” Sci. Rep. 6(1), 23896 (2016).
    [Crossref]
  8. S. J. Li, X. Y. Cao, L. M. Xu, L. J. Zhou, H. H. Yang, J. F. Han, Z. Zhang, D. Zhang, X. Liu, C. Zhang, Y. J. Zheng, and Y. Zhao, “Ultra-broadband reflective metamaterial with rcs reduction based on polarization convertor, information entropy theory and genetic optimization algorithm,” Sci. Rep. 6(1), 37409 (2016).
    [Crossref]
  9. H. Sun, C. Gu, X. Chen, Z. Li, L. Liu, B. Xu, and Z. Zhou, “Broadband and broad-angle polarization-independent metasurface for radar cross section reduction,” Sci. Rep. 7(1), 40782 (2017).
    [Crossref]
  10. Q. Zhang, X. Wan, S. Liu, J. Yuan Yin, L. Zhang, and T. Jun Cui, “Shaping electromagnetic waves using software-automatically-designed metasurfaces,” Sci. Rep. 7(1), 3588 (2017).
    [Crossref]
  11. M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: Scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017).
    [Crossref]
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  13. L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
    [Crossref]
  14. X. Yan, L. Liang, J. Yang, W. Liu, X. Ding, D. Xu, Y. Zhang, T. Cui, and J. Yao, “Broadband, wide-angle, low-scattering terahertz wave by a flexible 2-bit coding metasurface,” Opt. Express 23(22), 29128–29137 (2015).
    [Crossref]
  15. L. Liang, M. Wei, X. Yan, D. Wei, D. Liang, J. Han, X. Ding, G. Zhang, and J. Yao, “Broadband and wide-angle rcs reduction using a 2-bit coding ultrathin metasurface at terahertz frequencies,” Sci. Rep. 6(1), 39252 (2016).
    [Crossref]
  16. Y. Zhang, L. Liang, J. Yang, Y. Feng, B. Zhu, J. Zhao, T. Jiang, B. Jin, and W. Liu, “Broadband diffuse terahertz wave scattering by flexible metasurface with randomized phase distribution,” Sci. Rep. 6(1), 26875 (2016).
    [Crossref]
  17. Y. Zhou, X. y. Cao, J. Gao, S. Li, and X. Liu, “Rcs reduction for grazing incidence based on coding metasurface,” Electron. Lett. 53(20), 1381–1383 (2017).
    [Crossref]
  18. 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]
  19. X. Liu, J. Gao, L. Xu, X. Cao, Y. Zhao, and S. Li, “A coding diffuse metasurface for rcs reduction,” IEEE Antennas Wirel. Propag. Lett. 16, 724–727 (2017).
    [Crossref]
  20. S. Liu, T. Jun Cui, A. Noor, Z. Tao, H. Chi Zhang, G. Dong Bai, Y. Yang, and X. Yang Zhou, “Negative reflection and negative surface wave conversion from obliquely incident electromagnetic waves,” Light: Sci. Appl. 7(5), 18008 (2018).
    [Crossref]
  21. S. Liu and T. J. Cui, “Flexible controls of scattering clouds using coding metasurfaces,” Sci. Rep. 6(1), 37545 (2016).
    [Crossref]
  22. S. Liu and T. J. Cui, “Concepts, working principles, and applications of coding and programmable metamaterials,” Adv. Opt. Mater. 5(22), 1700624 (2017).
    [Crossref]

2018 (1)

S. Liu, T. Jun Cui, A. Noor, Z. Tao, H. Chi Zhang, G. Dong Bai, Y. Yang, and X. Yang Zhou, “Negative reflection and negative surface wave conversion from obliquely incident electromagnetic waves,” Light: Sci. Appl. 7(5), 18008 (2018).
[Crossref]

2017 (8)

Y. Zhou, X. y. Cao, J. Gao, S. Li, and X. Liu, “Rcs reduction for grazing incidence based on coding metasurface,” Electron. Lett. 53(20), 1381–1383 (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]

X. Liu, J. Gao, L. Xu, X. Cao, Y. Zhao, and S. Li, “A coding diffuse metasurface for rcs reduction,” IEEE Antennas Wirel. Propag. Lett. 16, 724–727 (2017).
[Crossref]

T. J. Cui, S. Liu, and L. Zhang, “Information metamaterials and metasurfaces,” J. Mater. Chem. C 5(15), 3644–3668 (2017).
[Crossref]

H. Sun, C. Gu, X. Chen, Z. Li, L. Liu, B. Xu, and Z. Zhou, “Broadband and broad-angle polarization-independent metasurface for radar cross section reduction,” Sci. Rep. 7(1), 40782 (2017).
[Crossref]

Q. Zhang, X. Wan, S. Liu, J. Yuan Yin, L. Zhang, and T. Jun Cui, “Shaping electromagnetic waves using software-automatically-designed metasurfaces,” Sci. Rep. 7(1), 3588 (2017).
[Crossref]

M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: Scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017).
[Crossref]

S. Liu and T. J. Cui, “Concepts, working principles, and applications of coding and programmable metamaterials,” Adv. Opt. Mater. 5(22), 1700624 (2017).
[Crossref]

2016 (7)

T.-J. Cui, S. Liu, and L.-L. Li, “Information entropy of coding metasurface,” Light: Sci. Appl. 5(11), e16172 (2016).
[Crossref]

S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qing Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv. Sci. 3(10), 1600156 (2016).
[Crossref]

Y. Zhao, X. Cao, J. Gao, Y. Sun, H. Yang, X. Liu, Y. Zhou, T. Han, and W. Chen, “Broadband diffusion metasurface based on a single anisotropic element and optimized by the simulated annealing algorithm,” Sci. Rep. 6(1), 23896 (2016).
[Crossref]

S. J. Li, X. Y. Cao, L. M. Xu, L. J. Zhou, H. H. Yang, J. F. Han, Z. Zhang, D. Zhang, X. Liu, C. Zhang, Y. J. Zheng, and Y. Zhao, “Ultra-broadband reflective metamaterial with rcs reduction based on polarization convertor, information entropy theory and genetic optimization algorithm,” Sci. Rep. 6(1), 37409 (2016).
[Crossref]

S. Liu and T. J. Cui, “Flexible controls of scattering clouds using coding metasurfaces,” Sci. Rep. 6(1), 37545 (2016).
[Crossref]

L. Liang, M. Wei, X. Yan, D. Wei, D. Liang, J. Han, X. Ding, G. Zhang, and J. Yao, “Broadband and wide-angle rcs reduction using a 2-bit coding ultrathin metasurface at terahertz frequencies,” Sci. Rep. 6(1), 39252 (2016).
[Crossref]

Y. Zhang, L. Liang, J. Yang, Y. Feng, B. Zhu, J. Zhao, T. Jiang, B. Jin, and W. Liu, “Broadband diffuse terahertz wave scattering by flexible metasurface with randomized phase distribution,” Sci. Rep. 6(1), 26875 (2016).
[Crossref]

2015 (2)

L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
[Crossref]

X. Yan, L. Liang, J. Yang, W. Liu, X. Ding, D. Xu, Y. Zhang, T. Cui, and J. Yao, “Broadband, wide-angle, low-scattering terahertz wave by a flexible 2-bit coding metasurface,” Opt. Express 23(22), 29128–29137 (2015).
[Crossref]

2014 (1)

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]

2007 (1)

M. Paquay, J. Iriarte, I. Ederra, R. Gonzalo, and P. de Maagt, “Thin amc structure for radar cross-section reduction,” IEEE Trans. Antennas Propag. 55(12), 3630–3638 (2007).
[Crossref]

2002 (1)

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[Crossref]

Andreone, A.

M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: Scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017).
[Crossref]

Bai, L.

L. Bai, X. G. Zhang, S. H. Bal, and W. X. Jiang, “Broadband coding metasurface for radar cross section reduction,” in 2018 Cross Strait Quad-Regional Radio Science and Wireless Technology Conference (CSQRWC), (2018), pp. 1–3.

Bal, S. H.

L. Bai, X. G. Zhang, S. H. Bal, and W. X. Jiang, “Broadband coding metasurface for radar cross section reduction,” in 2018 Cross Strait Quad-Regional Radio Science and Wireless Technology Conference (CSQRWC), (2018), pp. 1–3.

Cao, X.

X. Liu, J. Gao, L. Xu, X. Cao, Y. Zhao, and S. Li, “A coding diffuse metasurface for rcs reduction,” IEEE Antennas Wirel. Propag. Lett. 16, 724–727 (2017).
[Crossref]

Y. Zhao, X. Cao, J. Gao, Y. Sun, H. Yang, X. Liu, Y. Zhou, T. Han, and W. Chen, “Broadband diffusion metasurface based on a single anisotropic element and optimized by the simulated annealing algorithm,” Sci. Rep. 6(1), 23896 (2016).
[Crossref]

Cao, X. Y.

S. J. Li, X. Y. Cao, L. M. Xu, L. J. Zhou, H. H. Yang, J. F. Han, Z. Zhang, D. Zhang, X. Liu, C. Zhang, Y. J. Zheng, and Y. Zhao, “Ultra-broadband reflective metamaterial with rcs reduction based on polarization convertor, information entropy theory and genetic optimization algorithm,” Sci. Rep. 6(1), 37409 (2016).
[Crossref]

Castaldi, G.

M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: Scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017).
[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, H.-B.

L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
[Crossref]

Chen, W.

Y. Zhao, X. Cao, J. Gao, Y. Sun, H. Yang, X. Liu, Y. Zhou, T. Han, and W. Chen, “Broadband diffusion metasurface based on a single anisotropic element and optimized by the simulated annealing algorithm,” Sci. Rep. 6(1), 23896 (2016).
[Crossref]

Chen, X.

H. Sun, C. Gu, X. Chen, Z. Li, L. Liu, B. Xu, and Z. Zhou, “Broadband and broad-angle polarization-independent metasurface for radar cross section reduction,” Sci. Rep. 7(1), 40782 (2017).
[Crossref]

Cheng, Q.

S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qing Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv. Sci. 3(10), 1600156 (2016).
[Crossref]

L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
[Crossref]

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]

Chi Zhang, H.

S. Liu, T. Jun Cui, A. Noor, Z. Tao, H. Chi Zhang, G. Dong Bai, Y. Yang, and X. Yang Zhou, “Negative reflection and negative surface wave conversion from obliquely incident electromagnetic waves,” Light: Sci. Appl. 7(5), 18008 (2018).
[Crossref]

Cui, T.

Cui, T. J.

S. Liu and T. J. Cui, “Concepts, working principles, and applications of coding and programmable metamaterials,” Adv. Opt. Mater. 5(22), 1700624 (2017).
[Crossref]

T. J. Cui, S. Liu, and L. Zhang, “Information metamaterials and metasurfaces,” J. Mater. Chem. C 5(15), 3644–3668 (2017).
[Crossref]

M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: Scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017).
[Crossref]

S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qing Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv. Sci. 3(10), 1600156 (2016).
[Crossref]

S. Liu and T. J. Cui, “Flexible controls of scattering clouds using coding metasurfaces,” Sci. Rep. 6(1), 37545 (2016).
[Crossref]

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]

Cui, T.-J.

T.-J. Cui, S. Liu, and L.-L. Li, “Information entropy of coding metasurface,” Light: Sci. Appl. 5(11), e16172 (2016).
[Crossref]

L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
[Crossref]

de Maagt, P.

M. Paquay, J. Iriarte, I. Ederra, R. Gonzalo, and P. de Maagt, “Thin amc structure for radar cross-section reduction,” IEEE Trans. Antennas Propag. 55(12), 3630–3638 (2007).
[Crossref]

Ding, X.

L. Liang, M. Wei, X. Yan, D. Wei, D. Liang, J. Han, X. Ding, G. Zhang, and J. Yao, “Broadband and wide-angle rcs reduction using a 2-bit coding ultrathin metasurface at terahertz frequencies,” Sci. Rep. 6(1), 39252 (2016).
[Crossref]

X. Yan, L. Liang, J. Yang, W. Liu, X. Ding, D. Xu, Y. Zhang, T. Cui, and J. Yao, “Broadband, wide-angle, low-scattering terahertz wave by a flexible 2-bit coding metasurface,” Opt. Express 23(22), 29128–29137 (2015).
[Crossref]

Dong Bai, G.

S. Liu, T. Jun Cui, A. Noor, Z. Tao, H. Chi Zhang, G. Dong Bai, Y. Yang, and X. Yang Zhou, “Negative reflection and negative surface wave conversion from obliquely incident electromagnetic waves,” Light: Sci. Appl. 7(5), 18008 (2018).
[Crossref]

Ederra, I.

M. Paquay, J. Iriarte, I. Ederra, R. Gonzalo, and P. de Maagt, “Thin amc structure for radar cross-section reduction,” IEEE Trans. Antennas Propag. 55(12), 3630–3638 (2007).
[Crossref]

Feng, Y.

Y. Zhang, L. Liang, J. Yang, Y. Feng, B. Zhu, J. Zhao, T. Jiang, B. Jin, and W. Liu, “Broadband diffuse terahertz wave scattering by flexible metasurface with randomized phase distribution,” Sci. Rep. 6(1), 26875 (2016).
[Crossref]

Galdi, V.

M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: Scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017).
[Crossref]

Gao, J.

Y. Zhou, X. y. Cao, J. Gao, S. Li, and X. Liu, “Rcs reduction for grazing incidence based on coding metasurface,” Electron. Lett. 53(20), 1381–1383 (2017).
[Crossref]

X. Liu, J. Gao, L. Xu, X. Cao, Y. Zhao, and S. Li, “A coding diffuse metasurface for rcs reduction,” IEEE Antennas Wirel. Propag. Lett. 16, 724–727 (2017).
[Crossref]

Y. Zhao, X. Cao, J. Gao, Y. Sun, H. Yang, X. Liu, Y. Zhou, T. Han, and W. Chen, “Broadband diffusion metasurface based on a single anisotropic element and optimized by the simulated annealing algorithm,” Sci. Rep. 6(1), 23896 (2016).
[Crossref]

Gao, L.-H.

L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
[Crossref]

Gonzalo, R.

M. Paquay, J. Iriarte, I. Ederra, R. Gonzalo, and P. de Maagt, “Thin amc structure for radar cross-section reduction,” IEEE Trans. Antennas Propag. 55(12), 3630–3638 (2007).
[Crossref]

Gu, C.

H. Sun, C. Gu, X. Chen, Z. Li, L. Liu, B. Xu, and Z. Zhou, “Broadband and broad-angle polarization-independent metasurface for radar cross section reduction,” Sci. Rep. 7(1), 40782 (2017).
[Crossref]

Gu, J. Q.

S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qing Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv. Sci. 3(10), 1600156 (2016).
[Crossref]

Han, J.

L. Liang, M. Wei, X. Yan, D. Wei, D. Liang, J. Han, X. Ding, G. Zhang, and J. Yao, “Broadband and wide-angle rcs reduction using a 2-bit coding ultrathin metasurface at terahertz frequencies,” Sci. Rep. 6(1), 39252 (2016).
[Crossref]

Han, J. F.

S. J. Li, X. Y. Cao, L. M. Xu, L. J. Zhou, H. H. Yang, J. F. Han, Z. Zhang, D. Zhang, X. Liu, C. Zhang, Y. J. Zheng, and Y. Zhao, “Ultra-broadband reflective metamaterial with rcs reduction based on polarization convertor, information entropy theory and genetic optimization algorithm,” Sci. Rep. 6(1), 37409 (2016).
[Crossref]

Han, J. G.

S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qing Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv. Sci. 3(10), 1600156 (2016).
[Crossref]

Han, T.

Y. Zhao, X. Cao, J. Gao, Y. Sun, H. Yang, X. Liu, Y. Zhou, T. Han, and W. Chen, “Broadband diffusion metasurface based on a single anisotropic element and optimized by the simulated annealing algorithm,” Sci. Rep. 6(1), 23896 (2016).
[Crossref]

Han, Y.

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]

He, Q.

L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
[Crossref]

Iriarte, J.

M. Paquay, J. Iriarte, I. Ederra, R. Gonzalo, and P. de Maagt, “Thin amc structure for radar cross-section reduction,” IEEE Trans. Antennas Propag. 55(12), 3630–3638 (2007).
[Crossref]

Jiang, T.

Y. Zhang, L. Liang, J. Yang, Y. Feng, B. Zhu, J. Zhao, T. Jiang, B. Jin, and W. Liu, “Broadband diffuse terahertz wave scattering by flexible metasurface with randomized phase distribution,” Sci. Rep. 6(1), 26875 (2016).
[Crossref]

Jiang, W. X.

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L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
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Y. Zhang, L. Liang, J. Yang, Y. Feng, B. Zhu, J. Zhao, T. Jiang, B. Jin, and W. Liu, “Broadband diffuse terahertz wave scattering by flexible metasurface with randomized phase distribution,” Sci. Rep. 6(1), 26875 (2016).
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L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
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S. Liu, T. Jun Cui, A. Noor, Z. Tao, H. Chi Zhang, G. Dong Bai, Y. Yang, and X. Yang Zhou, “Negative reflection and negative surface wave conversion from obliquely incident electromagnetic waves,” Light: Sci. Appl. 7(5), 18008 (2018).
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Q. Zhang, X. Wan, S. Liu, J. Yuan Yin, L. Zhang, and T. Jun Cui, “Shaping electromagnetic waves using software-automatically-designed metasurfaces,” Sci. Rep. 7(1), 3588 (2017).
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T.-J. Cui, S. Liu, and L.-L. Li, “Information entropy of coding metasurface,” Light: Sci. Appl. 5(11), e16172 (2016).
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Y. Zhou, X. y. Cao, J. Gao, S. Li, and X. Liu, “Rcs reduction for grazing incidence based on coding metasurface,” Electron. Lett. 53(20), 1381–1383 (2017).
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X. Liu, J. Gao, L. Xu, X. Cao, Y. Zhao, and S. Li, “A coding diffuse metasurface for rcs reduction,” IEEE Antennas Wirel. Propag. Lett. 16, 724–727 (2017).
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Li, S. J.

S. J. Li, X. Y. Cao, L. M. Xu, L. J. Zhou, H. H. Yang, J. F. Han, Z. Zhang, D. Zhang, X. Liu, C. Zhang, Y. J. Zheng, and Y. Zhao, “Ultra-broadband reflective metamaterial with rcs reduction based on polarization convertor, information entropy theory and genetic optimization algorithm,” Sci. Rep. 6(1), 37409 (2016).
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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).
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H. Sun, C. Gu, X. Chen, Z. Li, L. Liu, B. Xu, and Z. Zhou, “Broadband and broad-angle polarization-independent metasurface for radar cross section reduction,” Sci. Rep. 7(1), 40782 (2017).
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L. Liang, M. Wei, X. Yan, D. Wei, D. Liang, J. Han, X. Ding, G. Zhang, and J. Yao, “Broadband and wide-angle rcs reduction using a 2-bit coding ultrathin metasurface at terahertz frequencies,” Sci. Rep. 6(1), 39252 (2016).
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L. Liang, M. Wei, X. Yan, D. Wei, D. Liang, J. Han, X. Ding, G. Zhang, and J. Yao, “Broadband and wide-angle rcs reduction using a 2-bit coding ultrathin metasurface at terahertz frequencies,” Sci. Rep. 6(1), 39252 (2016).
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Y. Zhang, L. Liang, J. Yang, Y. Feng, B. Zhu, J. Zhao, T. Jiang, B. Jin, and W. Liu, “Broadband diffuse terahertz wave scattering by flexible metasurface with randomized phase distribution,” Sci. Rep. 6(1), 26875 (2016).
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X. Yan, L. Liang, J. Yang, W. Liu, X. Ding, D. Xu, Y. Zhang, T. Cui, and J. Yao, “Broadband, wide-angle, low-scattering terahertz wave by a flexible 2-bit coding metasurface,” Opt. Express 23(22), 29128–29137 (2015).
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L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
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H. Sun, C. Gu, X. Chen, Z. Li, L. Liu, B. Xu, and Z. Zhou, “Broadband and broad-angle polarization-independent metasurface for radar cross section reduction,” Sci. Rep. 7(1), 40782 (2017).
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S. Liu, T. Jun Cui, A. Noor, Z. Tao, H. Chi Zhang, G. Dong Bai, Y. Yang, and X. Yang Zhou, “Negative reflection and negative surface wave conversion from obliquely incident electromagnetic waves,” Light: Sci. Appl. 7(5), 18008 (2018).
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M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: Scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017).
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Q. Zhang, X. Wan, S. Liu, J. Yuan Yin, L. Zhang, and T. Jun Cui, “Shaping electromagnetic waves using software-automatically-designed metasurfaces,” Sci. Rep. 7(1), 3588 (2017).
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T. J. Cui, S. Liu, and L. Zhang, “Information metamaterials and metasurfaces,” J. Mater. Chem. C 5(15), 3644–3668 (2017).
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S. Liu and T. J. Cui, “Concepts, working principles, and applications of coding and programmable metamaterials,” Adv. Opt. Mater. 5(22), 1700624 (2017).
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S. Liu and T. J. Cui, “Flexible controls of scattering clouds using coding metasurfaces,” Sci. Rep. 6(1), 37545 (2016).
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S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qing Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv. Sci. 3(10), 1600156 (2016).
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T.-J. Cui, S. Liu, and L.-L. Li, “Information entropy of coding metasurface,” Light: Sci. Appl. 5(11), e16172 (2016).
[Crossref]

L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
[Crossref]

Liu, W.

Y. Zhang, L. Liang, J. Yang, Y. Feng, B. Zhu, J. Zhao, T. Jiang, B. Jin, and W. Liu, “Broadband diffuse terahertz wave scattering by flexible metasurface with randomized phase distribution,” Sci. Rep. 6(1), 26875 (2016).
[Crossref]

X. Yan, L. Liang, J. Yang, W. Liu, X. Ding, D. Xu, Y. Zhang, T. Cui, and J. Yao, “Broadband, wide-angle, low-scattering terahertz wave by a flexible 2-bit coding metasurface,” Opt. Express 23(22), 29128–29137 (2015).
[Crossref]

Liu, W.-W.

L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
[Crossref]

Liu, X.

Y. Zhou, X. y. Cao, J. Gao, S. Li, and X. Liu, “Rcs reduction for grazing incidence based on coding metasurface,” Electron. Lett. 53(20), 1381–1383 (2017).
[Crossref]

X. Liu, J. Gao, L. Xu, X. Cao, Y. Zhao, and S. Li, “A coding diffuse metasurface for rcs reduction,” IEEE Antennas Wirel. Propag. Lett. 16, 724–727 (2017).
[Crossref]

S. J. Li, X. Y. Cao, L. M. Xu, L. J. Zhou, H. H. Yang, J. F. Han, Z. Zhang, D. Zhang, X. Liu, C. Zhang, Y. J. Zheng, and Y. Zhao, “Ultra-broadband reflective metamaterial with rcs reduction based on polarization convertor, information entropy theory and genetic optimization algorithm,” Sci. Rep. 6(1), 37409 (2016).
[Crossref]

Y. Zhao, X. Cao, J. Gao, Y. Sun, H. Yang, X. Liu, Y. Zhou, T. Han, and W. Chen, “Broadband diffusion metasurface based on a single anisotropic element and optimized by the simulated annealing algorithm,” Sci. Rep. 6(1), 23896 (2016).
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Ma, 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).
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Ma, H.-F.

L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
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L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
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D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
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Moccia, M.

M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: Scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017).
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Noor, A.

S. Liu, T. Jun Cui, A. Noor, Z. Tao, H. Chi Zhang, G. Dong Bai, Y. Yang, and X. Yang Zhou, “Negative reflection and negative surface wave conversion from obliquely incident electromagnetic waves,” Light: Sci. Appl. 7(5), 18008 (2018).
[Crossref]

Pang, Y.

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).
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M. Paquay, J. Iriarte, I. Ederra, R. Gonzalo, and P. de Maagt, “Thin amc structure for radar cross-section reduction,” IEEE Trans. Antennas Propag. 55(12), 3630–3638 (2007).
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Qi, M. Q.

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).
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Qing Qi, M.

S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qing Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv. Sci. 3(10), 1600156 (2016).
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Qu, S.

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).
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Schultz, S.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
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Shen, Y.

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).
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Smith, D. R.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[Crossref]

Soukoulis, C. M.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
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Sui, S.

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]

Sun, H.

H. Sun, C. Gu, X. Chen, Z. Li, L. Liu, B. Xu, and Z. Zhou, “Broadband and broad-angle polarization-independent metasurface for radar cross section reduction,” Sci. Rep. 7(1), 40782 (2017).
[Crossref]

Sun, Y.

Y. Zhao, X. Cao, J. Gao, Y. Sun, H. Yang, X. Liu, Y. Zhou, T. Han, and W. Chen, “Broadband diffusion metasurface based on a single anisotropic element and optimized by the simulated annealing algorithm,” Sci. Rep. 6(1), 23896 (2016).
[Crossref]

Tang, W. X.

S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qing Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv. Sci. 3(10), 1600156 (2016).
[Crossref]

Tao, Z.

S. Liu, T. Jun Cui, A. Noor, Z. Tao, H. Chi Zhang, G. Dong Bai, Y. Yang, and X. Yang Zhou, “Negative reflection and negative surface wave conversion from obliquely incident electromagnetic waves,” Light: Sci. Appl. 7(5), 18008 (2018).
[Crossref]

Wan, X.

Q. Zhang, X. Wan, S. Liu, J. Yuan Yin, L. Zhang, and T. Jun Cui, “Shaping electromagnetic waves using software-automatically-designed metasurfaces,” Sci. Rep. 7(1), 3588 (2017).
[Crossref]

S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qing Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv. Sci. 3(10), 1600156 (2016).
[Crossref]

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]

Wang, J.

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]

Wang, Q.

S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qing Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv. Sci. 3(10), 1600156 (2016).
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Wei, D.

L. Liang, M. Wei, X. Yan, D. Wei, D. Liang, J. Han, X. Ding, G. Zhang, and J. Yao, “Broadband and wide-angle rcs reduction using a 2-bit coding ultrathin metasurface at terahertz frequencies,” Sci. Rep. 6(1), 39252 (2016).
[Crossref]

Wei, M.

L. Liang, M. Wei, X. Yan, D. Wei, D. Liang, J. Han, X. Ding, G. Zhang, and J. Yao, “Broadband and wide-angle rcs reduction using a 2-bit coding ultrathin metasurface at terahertz frequencies,” Sci. Rep. 6(1), 39252 (2016).
[Crossref]

Wen, Q.-Y.

L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
[Crossref]

Wu, P.-H.

L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
[Crossref]

Wu, R. Y.

M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: Scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017).
[Crossref]

Xu, B.

H. Sun, C. Gu, X. Chen, Z. Li, L. Liu, B. Xu, and Z. Zhou, “Broadband and broad-angle polarization-independent metasurface for radar cross section reduction,” Sci. Rep. 7(1), 40782 (2017).
[Crossref]

Xu, D.

Xu, L.

X. Liu, J. Gao, L. Xu, X. Cao, Y. Zhao, and S. Li, “A coding diffuse metasurface for rcs reduction,” IEEE Antennas Wirel. Propag. Lett. 16, 724–727 (2017).
[Crossref]

Xu, L. M.

S. J. Li, X. Y. Cao, L. M. Xu, L. J. Zhou, H. H. Yang, J. F. Han, Z. Zhang, D. Zhang, X. Liu, C. Zhang, Y. J. Zheng, and Y. Zhao, “Ultra-broadband reflective metamaterial with rcs reduction based on polarization convertor, information entropy theory and genetic optimization algorithm,” Sci. Rep. 6(1), 37409 (2016).
[Crossref]

Xu, Q.

S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qing Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv. Sci. 3(10), 1600156 (2016).
[Crossref]

y. Cao, X.

Y. Zhou, X. y. Cao, J. Gao, S. Li, and X. Liu, “Rcs reduction for grazing incidence based on coding metasurface,” Electron. Lett. 53(20), 1381–1383 (2017).
[Crossref]

Yan, X.

L. Liang, M. Wei, X. Yan, D. Wei, D. Liang, J. Han, X. Ding, G. Zhang, and J. Yao, “Broadband and wide-angle rcs reduction using a 2-bit coding ultrathin metasurface at terahertz frequencies,” Sci. Rep. 6(1), 39252 (2016).
[Crossref]

X. Yan, L. Liang, J. Yang, W. Liu, X. Ding, D. Xu, Y. Zhang, T. Cui, and J. Yao, “Broadband, wide-angle, low-scattering terahertz wave by a flexible 2-bit coding metasurface,” Opt. Express 23(22), 29128–29137 (2015).
[Crossref]

Yang, H.

Y. Zhao, X. Cao, J. Gao, Y. Sun, H. Yang, X. Liu, Y. Zhou, T. Han, and W. Chen, “Broadband diffusion metasurface based on a single anisotropic element and optimized by the simulated annealing algorithm,” Sci. Rep. 6(1), 23896 (2016).
[Crossref]

Yang, H. H.

S. J. Li, X. Y. Cao, L. M. Xu, L. J. Zhou, H. H. Yang, J. F. Han, Z. Zhang, D. Zhang, X. Liu, C. Zhang, Y. J. Zheng, and Y. Zhao, “Ultra-broadband reflective metamaterial with rcs reduction based on polarization convertor, information entropy theory and genetic optimization algorithm,” Sci. Rep. 6(1), 37409 (2016).
[Crossref]

Yang, J.

Y. Zhang, L. Liang, J. Yang, Y. Feng, B. Zhu, J. Zhao, T. Jiang, B. Jin, and W. Liu, “Broadband diffuse terahertz wave scattering by flexible metasurface with randomized phase distribution,” Sci. Rep. 6(1), 26875 (2016).
[Crossref]

L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
[Crossref]

X. Yan, L. Liang, J. Yang, W. Liu, X. Ding, D. Xu, Y. Zhang, T. Cui, and J. Yao, “Broadband, wide-angle, low-scattering terahertz wave by a flexible 2-bit coding metasurface,” Opt. Express 23(22), 29128–29137 (2015).
[Crossref]

Yang, Y.

S. Liu, T. Jun Cui, A. Noor, Z. Tao, H. Chi Zhang, G. Dong Bai, Y. Yang, and X. Yang Zhou, “Negative reflection and negative surface wave conversion from obliquely incident electromagnetic waves,” Light: Sci. Appl. 7(5), 18008 (2018).
[Crossref]

Yang Zhou, X.

S. Liu, T. Jun Cui, A. Noor, Z. Tao, H. Chi Zhang, G. Dong Bai, Y. Yang, and X. Yang Zhou, “Negative reflection and negative surface wave conversion from obliquely incident electromagnetic waves,” Light: Sci. Appl. 7(5), 18008 (2018).
[Crossref]

Yao, J.

L. Liang, M. Wei, X. Yan, D. Wei, D. Liang, J. Han, X. Ding, G. Zhang, and J. Yao, “Broadband and wide-angle rcs reduction using a 2-bit coding ultrathin metasurface at terahertz frequencies,” Sci. Rep. 6(1), 39252 (2016).
[Crossref]

X. Yan, L. Liang, J. Yang, W. Liu, X. Ding, D. Xu, Y. Zhang, T. Cui, and J. Yao, “Broadband, wide-angle, low-scattering terahertz wave by a flexible 2-bit coding metasurface,” Opt. Express 23(22), 29128–29137 (2015).
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Yao, J.-Q.

L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
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Yuan Yin, J.

Q. Zhang, X. Wan, S. Liu, J. Yuan Yin, L. Zhang, and T. Jun Cui, “Shaping electromagnetic waves using software-automatically-designed metasurfaces,” Sci. Rep. 7(1), 3588 (2017).
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Zhang, C.

S. J. Li, X. Y. Cao, L. M. Xu, L. J. Zhou, H. H. Yang, J. F. Han, Z. Zhang, D. Zhang, X. Liu, C. Zhang, Y. J. Zheng, and Y. Zhao, “Ultra-broadband reflective metamaterial with rcs reduction based on polarization convertor, information entropy theory and genetic optimization algorithm,” Sci. Rep. 6(1), 37409 (2016).
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Zhang, D.

S. J. Li, X. Y. Cao, L. M. Xu, L. J. Zhou, H. H. Yang, J. F. Han, Z. Zhang, D. Zhang, X. Liu, C. Zhang, Y. J. Zheng, and Y. Zhao, “Ultra-broadband reflective metamaterial with rcs reduction based on polarization convertor, information entropy theory and genetic optimization algorithm,” Sci. Rep. 6(1), 37409 (2016).
[Crossref]

Zhang, G.

L. Liang, M. Wei, X. Yan, D. Wei, D. Liang, J. Han, X. Ding, G. Zhang, and J. Yao, “Broadband and wide-angle rcs reduction using a 2-bit coding ultrathin metasurface at terahertz frequencies,” Sci. Rep. 6(1), 39252 (2016).
[Crossref]

Zhang, J.

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]

Zhang, L.

Q. Zhang, X. Wan, S. Liu, J. Yuan Yin, L. Zhang, and T. Jun Cui, “Shaping electromagnetic waves using software-automatically-designed metasurfaces,” Sci. Rep. 7(1), 3588 (2017).
[Crossref]

T. J. Cui, S. Liu, and L. Zhang, “Information metamaterials and metasurfaces,” J. Mater. Chem. C 5(15), 3644–3668 (2017).
[Crossref]

S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qing Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv. Sci. 3(10), 1600156 (2016).
[Crossref]

Zhang, Q.

Q. Zhang, X. Wan, S. Liu, J. Yuan Yin, L. Zhang, and T. Jun Cui, “Shaping electromagnetic waves using software-automatically-designed metasurfaces,” Sci. Rep. 7(1), 3588 (2017).
[Crossref]

Zhang, W. L.

S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qing Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv. Sci. 3(10), 1600156 (2016).
[Crossref]

Zhang, X. G.

L. Bai, X. G. Zhang, S. H. Bal, and W. X. Jiang, “Broadband coding metasurface for radar cross section reduction,” in 2018 Cross Strait Quad-Regional Radio Science and Wireless Technology Conference (CSQRWC), (2018), pp. 1–3.

Zhang, Y.

Y. Zhang, L. Liang, J. Yang, Y. Feng, B. Zhu, J. Zhao, T. Jiang, B. Jin, and W. Liu, “Broadband diffuse terahertz wave scattering by flexible metasurface with randomized phase distribution,” Sci. Rep. 6(1), 26875 (2016).
[Crossref]

X. Yan, L. Liang, J. Yang, W. Liu, X. Ding, D. Xu, Y. Zhang, T. Cui, and J. Yao, “Broadband, wide-angle, low-scattering terahertz wave by a flexible 2-bit coding metasurface,” Opt. Express 23(22), 29128–29137 (2015).
[Crossref]

Zhang, Z.

S. J. Li, X. Y. Cao, L. M. Xu, L. J. Zhou, H. H. Yang, J. F. Han, Z. Zhang, D. Zhang, X. Liu, C. Zhang, Y. J. Zheng, and Y. Zhao, “Ultra-broadband reflective metamaterial with rcs reduction based on polarization convertor, information entropy theory and genetic optimization algorithm,” Sci. Rep. 6(1), 37409 (2016).
[Crossref]

Zhao, J.

Y. Zhang, L. Liang, J. Yang, Y. Feng, B. Zhu, J. Zhao, T. Jiang, B. Jin, and W. Liu, “Broadband diffuse terahertz wave scattering by flexible metasurface with randomized phase distribution,” Sci. Rep. 6(1), 26875 (2016).
[Crossref]

L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
[Crossref]

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]

Zhao, Y.

X. Liu, J. Gao, L. Xu, X. Cao, Y. Zhao, and S. Li, “A coding diffuse metasurface for rcs reduction,” IEEE Antennas Wirel. Propag. Lett. 16, 724–727 (2017).
[Crossref]

Y. Zhao, X. Cao, J. Gao, Y. Sun, H. Yang, X. Liu, Y. Zhou, T. Han, and W. Chen, “Broadband diffusion metasurface based on a single anisotropic element and optimized by the simulated annealing algorithm,” Sci. Rep. 6(1), 23896 (2016).
[Crossref]

S. J. Li, X. Y. Cao, L. M. Xu, L. J. Zhou, H. H. Yang, J. F. Han, Z. Zhang, D. Zhang, X. Liu, C. Zhang, Y. J. Zheng, and Y. Zhao, “Ultra-broadband reflective metamaterial with rcs reduction based on polarization convertor, information entropy theory and genetic optimization algorithm,” Sci. Rep. 6(1), 37409 (2016).
[Crossref]

Zheng, Q.

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]

Zheng, Y. J.

S. J. Li, X. Y. Cao, L. M. Xu, L. J. Zhou, H. H. Yang, J. F. Han, Z. Zhang, D. Zhang, X. Liu, C. Zhang, Y. J. Zheng, and Y. Zhao, “Ultra-broadband reflective metamaterial with rcs reduction based on polarization convertor, information entropy theory and genetic optimization algorithm,” Sci. Rep. 6(1), 37409 (2016).
[Crossref]

Zhou, L.

L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
[Crossref]

Zhou, L. J.

S. J. Li, X. Y. Cao, L. M. Xu, L. J. Zhou, H. H. Yang, J. F. Han, Z. Zhang, D. Zhang, X. Liu, C. Zhang, Y. J. Zheng, and Y. Zhao, “Ultra-broadband reflective metamaterial with rcs reduction based on polarization convertor, information entropy theory and genetic optimization algorithm,” Sci. Rep. 6(1), 37409 (2016).
[Crossref]

Zhou, X. Y.

S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qing Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv. Sci. 3(10), 1600156 (2016).
[Crossref]

Zhou, Y.

Y. Zhou, X. y. Cao, J. Gao, S. Li, and X. Liu, “Rcs reduction for grazing incidence based on coding metasurface,” Electron. Lett. 53(20), 1381–1383 (2017).
[Crossref]

Y. Zhao, X. Cao, J. Gao, Y. Sun, H. Yang, X. Liu, Y. Zhou, T. Han, and W. Chen, “Broadband diffusion metasurface based on a single anisotropic element and optimized by the simulated annealing algorithm,” Sci. Rep. 6(1), 23896 (2016).
[Crossref]

Zhou, Z.

H. Sun, C. Gu, X. Chen, Z. Li, L. Liu, B. Xu, and Z. Zhou, “Broadband and broad-angle polarization-independent metasurface for radar cross section reduction,” Sci. Rep. 7(1), 40782 (2017).
[Crossref]

Zhu, B.

Y. Zhang, L. Liang, J. Yang, Y. Feng, B. Zhu, J. Zhao, T. Jiang, B. Jin, and W. Liu, “Broadband diffuse terahertz wave scattering by flexible metasurface with randomized phase distribution,” Sci. Rep. 6(1), 26875 (2016).
[Crossref]

Adv. Opt. Mater. (2)

M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: Scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017).
[Crossref]

S. Liu and T. J. Cui, “Concepts, working principles, and applications of coding and programmable metamaterials,” Adv. Opt. Mater. 5(22), 1700624 (2017).
[Crossref]

Adv. Sci. (1)

S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qing Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv. Sci. 3(10), 1600156 (2016).
[Crossref]

Electron. Lett. (1)

Y. Zhou, X. y. Cao, J. Gao, S. Li, and X. Liu, “Rcs reduction for grazing incidence based on coding metasurface,” Electron. Lett. 53(20), 1381–1383 (2017).
[Crossref]

IEEE Antennas Wirel. Propag. Lett. (1)

X. Liu, J. Gao, L. Xu, X. Cao, Y. Zhao, and S. Li, “A coding diffuse metasurface for rcs reduction,” IEEE Antennas Wirel. Propag. Lett. 16, 724–727 (2017).
[Crossref]

IEEE Trans. Antennas Propag. (1)

M. Paquay, J. Iriarte, I. Ederra, R. Gonzalo, and P. de Maagt, “Thin amc structure for radar cross-section reduction,” IEEE Trans. Antennas Propag. 55(12), 3630–3638 (2007).
[Crossref]

J. Mater. Chem. C (1)

T. J. Cui, S. Liu, and L. Zhang, “Information metamaterials and metasurfaces,” J. Mater. Chem. C 5(15), 3644–3668 (2017).
[Crossref]

Light: Sci. Appl. (4)

T.-J. Cui, S. Liu, and L.-L. Li, “Information entropy of coding metasurface,” Light: Sci. Appl. 5(11), e16172 (2016).
[Crossref]

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]

L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
[Crossref]

S. Liu, T. Jun Cui, A. Noor, Z. Tao, H. Chi Zhang, G. Dong Bai, Y. Yang, and X. Yang Zhou, “Negative reflection and negative surface wave conversion from obliquely incident electromagnetic waves,” Light: Sci. Appl. 7(5), 18008 (2018).
[Crossref]

Opt. Express (1)

Phys. Rev. B (1)

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[Crossref]

Sci. Rep. (8)

S. Liu and T. J. Cui, “Flexible controls of scattering clouds using coding metasurfaces,” Sci. Rep. 6(1), 37545 (2016).
[Crossref]

L. Liang, M. Wei, X. Yan, D. Wei, D. Liang, J. Han, X. Ding, G. Zhang, and J. Yao, “Broadband and wide-angle rcs reduction using a 2-bit coding ultrathin metasurface at terahertz frequencies,” Sci. Rep. 6(1), 39252 (2016).
[Crossref]

Y. Zhang, L. Liang, J. Yang, Y. Feng, B. Zhu, J. Zhao, T. Jiang, B. Jin, and W. Liu, “Broadband diffuse terahertz wave scattering by flexible metasurface with randomized phase distribution,” Sci. Rep. 6(1), 26875 (2016).
[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]

Y. Zhao, X. Cao, J. Gao, Y. Sun, H. Yang, X. Liu, Y. Zhou, T. Han, and W. Chen, “Broadband diffusion metasurface based on a single anisotropic element and optimized by the simulated annealing algorithm,” Sci. Rep. 6(1), 23896 (2016).
[Crossref]

S. J. Li, X. Y. Cao, L. M. Xu, L. J. Zhou, H. H. Yang, J. F. Han, Z. Zhang, D. Zhang, X. Liu, C. Zhang, Y. J. Zheng, and Y. Zhao, “Ultra-broadband reflective metamaterial with rcs reduction based on polarization convertor, information entropy theory and genetic optimization algorithm,” Sci. Rep. 6(1), 37409 (2016).
[Crossref]

H. Sun, C. Gu, X. Chen, Z. Li, L. Liu, B. Xu, and Z. Zhou, “Broadband and broad-angle polarization-independent metasurface for radar cross section reduction,” Sci. Rep. 7(1), 40782 (2017).
[Crossref]

Q. Zhang, X. Wan, S. Liu, J. Yuan Yin, L. Zhang, and T. Jun Cui, “Shaping electromagnetic waves using software-automatically-designed metasurfaces,” Sci. Rep. 7(1), 3588 (2017).
[Crossref]

Other (1)

L. Bai, X. G. Zhang, S. H. Bal, and W. X. Jiang, “Broadband coding metasurface for radar cross section reduction,” in 2018 Cross Strait Quad-Regional Radio Science and Wireless Technology Conference (CSQRWC), (2018), pp. 1–3.

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Figures (5)

Fig. 1.
Fig. 1. Coordinate system and relevant variables for the calculation of the backscatter far-field of a coding metasurface for RCSR with $M\times N$ unit cells. Each unit cell has a length $D_x$ and a width $D_y$. $R_x$ and $R_z$ indicate rotation around the $x$- and $z$-axis, respectively. The signs of the incidence and reflection angles are indicated as used in the calculations. Variables attributed to incident waves are indexed by $i$, the quantities of backscattered waves are indexed by $r$. Spherical coordinates are described by a vector $(r,\theta ,\varphi )$.
Fig. 2.
Fig. 2. (a) Cut wire unit cell of the coding metasurface for RCSR with $p$: unit cell side length, $a$: cut wire length and distance, $w$: cut wire width, $t$: cut wire thickness, and $t_{\textrm {diel}}$: substrate thickness. $\left ( \textrm {b} \right )$ Alternating arrangement of the unit cells in regions A and B as rows of width $6p$. Each unit cell in region A pairs with a unit cell in region B. The four unit cell pairs, that are resonant at 4 neighboring frequencies, reflect incident waves with a phase difference of 180$^\circ$ in their individual frequency working range. (c) Frequency dependence of the relative phase shift $|\varphi _{a_{Ai}}-\varphi _{a_{Bi}}|_i$ of the $i^{\textrm {th}}$ unit cell pair calculated based on the numeric simulation results for the phase of the reflected electromagnetic waves of each unit cell. (d) Dependence of the spectral unit cell absorption on the cut wire length , where the solid and dashed lines of the same color correspond to a unit cell pair whose phase difference was plotted in (c).
Fig. 3.
Fig. 3. (a) Analytically and (b) numerically calculated electric backscatter far-field of the designed coding metasurface for oblique incidence at $40^\circ$. The incidence and reflection plane are highlighted for visual orientation.
Fig. 4.
Fig. 4. (a) Photograph of the fabricated metasurface. (b) Photograph of the microwave goniometer with the mounted metasurface.
Fig. 5.
Fig. 5. Comparison between the analytically calculated, numerically calculated and experimentally measured backscatter far-field of the coding metasurface for an incidence angle (a) $(\theta _i =+10^{\circ },\varphi =-90^{\circ })$, (b) $(\theta _{i} =+20^{\circ },\varphi =-90^{\circ })$, and (c) $(\theta _{i} =+40^{\circ },\varphi =-90^{\circ })$. The working frequency was $f=10.66$ GHz.

Equations (14)

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f ( r ) = V J ( r ) exp ( j k r | r | r ) d V A ( r ) , with  r = ( x , y , z ) T
J m , n ( r ) = I 0 exp ( j φ m , n + j k r r ) δ ( x ( m 1 2 ) D x ) δ ( y ( n 1 2 ) D y ) δ ( z )
f m , n ( r ) = V J m , n ( r ) exp ( j k r | r | r ) d V
= V I 0 exp ( j φ m , n + j k r r j k r | r | r ) δ ( x ( m 1 2 ) D x ) δ ( y ( n 1 2 ) D y ) δ ( z ) d V
f m , n ( r ) = V I 0 exp ( j φ m , n + j k ( z x x + y y + z z x 2 + y 2 + z 2 ) ) δ ( x ( m 1 2 ) D x ) δ ( y ( n 1 2 ) D y ) δ ( z ) d V
= I 0 exp ( j [ φ m , n k x x 2 + y 2 + z 2 ( m 1 2 ) D x k y x 2 + y 2 + z 2 ( n 1 2 ) D y ] )
f ( θ , φ ) = m = 1 M n = 1 N f m , n ( r )
= m = 1 M n = 1 N exp ( j [ φ m , n k | r | sin ( θ ) cos ( φ ) | r | ( m 1 2 ) D x k | r | sin ( θ ) sin ( φ ) | r | ( n 1 2 ) D y ] )
= m = 1 M n = 1 N exp ( j [ φ m , n k D x ( m 1 2 ) sin ( θ ) cos ( φ ) k D y ( n 1 2 ) sin ( θ ) sin ( φ ) ] ) ,
k i = R z ( φ i + 90 ) R x ( θ i ) k i , ( 0 , 0 , 1 ) T = k i , ( sin ( θ i ) cos ( φ i ) , sin ( θ i ) sin ( φ i ) , cos ( θ i ) ) T
k r = R z ( φ i 90 ) R x ( θ i ) k i , ( 0 , 0 , 1 ) T = k i , ( sin ( θ i ) cos ( φ i ) , sin ( θ i ) sin ( φ i ) , cos ( θ i ) ) T
f m , n ( r ) = V I 0 exp ( j φ m , n + j k ( x sin ( θ i ) cos ( φ i ) y sin ( θ i ) sin ( φ i ) + z cos ( θ i ) ) + j k ( z x x + y y + z z x 2 + y 2 + z 2 ) ) δ ( x ( m 1 2 ) D x ) δ ( y ( n 1 2 ) D y ) δ ( z ) d V
= I 0 exp ( j [ φ m , n k ( m 1 2 ) D x sin ( θ i ) cos ( φ i ) k ( n 1 2 ) D y sin ( θ i ) sin ( φ i ) k x x 2 + y 2 + z 2 ( m 1 2 ) D x k y x 2 + y 2 + z 2 ( n 1 2 ) D y ] )
f ( θ , φ ) = m = 1 M n = 1 N exp ( j ( φ m , n k D x ( m 1 2 ) [ sin ( θ ) cos ( φ ) + sin ( θ i ) cos ( φ i ) ] k D y ( n 1 2 ) [ sin ( θ ) sin ( φ ) + sin ( θ i ) sin ( φ i ) ] ) )

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