Abstract

We proposed a novel strategy to design a deep subwavelength metasurface with full 2π transmission phase modulation and high transmission efficiency by applying resonators with interfering Fano resonance. Theoretical investigation demonstrates that the transmission efficiency of the resonators depends on the direct transmission coefficient, direct reflection coefficient, and Q factor. When an impedance layer is added in the resonators, the direct transmission and direct reflection coefficients can be facilely manipulated so that the span of the transmission phase around the resonance frequency can be extended to 2π. As a result, we can continuously adjust the transmission phase from 0 to 2π through changing the geometric parameters of the resonators and construct a deep subwavelength metasurface with the resonators to manipulate the transmission wave with high efficiency. We also find that a layer of grating can be used as the impedance layer to change direct transmission and direct reflection in the actual design of the metasurface. The proposed strategy may provide effective guidance to design a deep subwavelength metasurface for controlling a transmitted wave with high efficiency.

© 2017 Optical Society of America

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References

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  1. S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovski, Phys. Rep. 634, 1 (2016).
    [Crossref]
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    [Crossref]
  3. Z. Li, E. Palacios, S. Butun, and K. Aydin, Nano Lett. 15, 1615 (2015).
    [Crossref]
  4. J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, and M. Qiu, Appl. Phys. Lett. 96, 251104 (2010).
    [Crossref]
  5. S. J. Ma, S. Y. Xiao, and L. Zhou, Phys. Rev. B 93, 045305 (2016).
    [Crossref]
  6. X. Su, Z. Wei, C. Wu, Y. Long, and H. Li, Opt. Lett. 41, 348 (2016).
    [Crossref]
  7. Z. Su, X. Chen, J. Yin, and X. Zhao, Opt. Lett. 41, 3799 (2016).
    [Crossref]
  8. F. Monticone, N. M. Estakhri, and A. Alu, Phys. Rev. Lett. 110, 203903 (2013).
    [Crossref]
  9. A. Epstein and G. V. Eleftheriades, Phys. Rev. Lett. 117, 256103 (2016).
    [Crossref]
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    [Crossref]
  11. S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, APL Photon. 1, 030801 (2016).
    [Crossref]
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    [Crossref]
  13. Y. F. Yu, A. Y. Zhu, R. Paniagua-Domínguez, Y. H. Fu, B. Luk’yanchuk, and A. I. Kuznetsov, Laser Photon. Rev. 9, 412 (2015).
    [Crossref]
  14. D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, Nat. Photonics 4, 466 (2010).
    [Crossref]
  15. D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, Science 345, 298 (2014).
    [Crossref]
  16. A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, Nat. Nanotechnol. 10, 937 (2015).
    [Crossref]
  17. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  18. S. Fan, W. Suh, and J. D. Joannopoulos, J. Opt. Soc. Am. A 20, 569 (2003).
    [Crossref]
  19. S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
    [Crossref]
  20. P. Sheng, R. S. Stepleman, and P. N. Sanda, Phys. Rev. B 26, 2907 (1982).
    [Crossref]
  21. Z. Wei, H. Li, C. Wu, Y. Cao, J. Ren, Z. Hang, H. Chen, D. Zhang, and C. T. Chan, Opt. Express 18, 12119 (2010).
    [Crossref]
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  23. Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
    [Crossref]
  24. M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, Adv. Opt. Mater. 3, 813 (2015).
    [Crossref]

2016 (7)

S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovski, Phys. Rep. 634, 1 (2016).
[Crossref]

S. J. Ma, S. Y. Xiao, and L. Zhou, Phys. Rev. B 93, 045305 (2016).
[Crossref]

X. Su, Z. Wei, C. Wu, Y. Long, and H. Li, Opt. Lett. 41, 348 (2016).
[Crossref]

Z. Su, X. Chen, J. Yin, and X. Zhao, Opt. Lett. 41, 3799 (2016).
[Crossref]

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, APL Photon. 1, 030801 (2016).
[Crossref]

L. Wang, S. Kruk, H. Tang, T. Li, I. Kravchenko, D. N. Neshev, and Y. S. Kivshar, Optica 3, 1504 (2016).
[Crossref]

A. Epstein and G. V. Eleftheriades, Phys. Rev. Lett. 117, 256103 (2016).
[Crossref]

2015 (5)

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, Adv. Opt. Mater. 3, 813 (2015).
[Crossref]

Y. F. Yu, A. Y. Zhu, R. Paniagua-Domínguez, Y. H. Fu, B. Luk’yanchuk, and A. I. Kuznetsov, Laser Photon. Rev. 9, 412 (2015).
[Crossref]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, Nat. Nanotechnol. 10, 937 (2015).
[Crossref]

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, Phys. Rev. Lett. 115, 235503 (2015).
[Crossref]

Z. Li, E. Palacios, S. Butun, and K. Aydin, Nano Lett. 15, 1615 (2015).
[Crossref]

2014 (1)

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, Science 345, 298 (2014).
[Crossref]

2013 (3)

C. Pfeiffer and A. Grbic, Phys. Rev. Lett. 110, 197401 (2013).
[Crossref]

S. Xiao, Q. He, C. Qu, X. Li, S. Sun, and L. Zhou, Opt. Express 21, 27219 (2013).
[Crossref]

F. Monticone, N. M. Estakhri, and A. Alu, Phys. Rev. Lett. 110, 203903 (2013).
[Crossref]

2010 (3)

J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, and M. Qiu, Appl. Phys. Lett. 96, 251104 (2010).
[Crossref]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, Nat. Photonics 4, 466 (2010).
[Crossref]

Z. Wei, H. Li, C. Wu, Y. Cao, J. Ren, Z. Hang, H. Chen, D. Zhang, and C. T. Chan, Opt. Express 18, 12119 (2010).
[Crossref]

2003 (1)

2002 (1)

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[Crossref]

2000 (1)

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[Crossref]

1982 (1)

P. Sheng, R. S. Stepleman, and P. N. Sanda, Phys. Rev. B 26, 2907 (1982).
[Crossref]

Alu, A.

F. Monticone, N. M. Estakhri, and A. Alu, Phys. Rev. Lett. 110, 203903 (2013).
[Crossref]

Arbabi, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, Nat. Nanotechnol. 10, 937 (2015).
[Crossref]

Aydin, K.

Z. Li, E. Palacios, S. Butun, and K. Aydin, Nano Lett. 15, 1615 (2015).
[Crossref]

Bagheri, M.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, Nat. Nanotechnol. 10, 937 (2015).
[Crossref]

Beausoleil, R. G.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, Nat. Photonics 4, 466 (2010).
[Crossref]

Belov, P. A.

S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovski, Phys. Rep. 634, 1 (2016).
[Crossref]

Brener, I.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, Adv. Opt. Mater. 3, 813 (2015).
[Crossref]

Brongersma, M. L.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, Science 345, 298 (2014).
[Crossref]

Butun, S.

Z. Li, E. Palacios, S. Butun, and K. Aydin, Nano Lett. 15, 1615 (2015).
[Crossref]

Cao, Y.

Chan, C. T.

Chen, H.

Chen, X.

Dai, N.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, Phys. Rev. Lett. 115, 235503 (2015).
[Crossref]

Decker, M.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, Adv. Opt. Mater. 3, 813 (2015).
[Crossref]

Dominguez, J.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, Adv. Opt. Mater. 3, 813 (2015).
[Crossref]

Eleftheriades, G. V.

A. Epstein and G. V. Eleftheriades, Phys. Rev. Lett. 117, 256103 (2016).
[Crossref]

Epstein, A.

A. Epstein and G. V. Eleftheriades, Phys. Rev. Lett. 117, 256103 (2016).
[Crossref]

Estakhri, N. M.

F. Monticone, N. M. Estakhri, and A. Alu, Phys. Rev. Lett. 110, 203903 (2013).
[Crossref]

Falkner, M.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, Adv. Opt. Mater. 3, 813 (2015).
[Crossref]

Fan, P.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, Science 345, 298 (2014).
[Crossref]

Fan, S.

S. Fan, W. Suh, and J. D. Joannopoulos, J. Opt. Soc. Am. A 20, 569 (2003).
[Crossref]

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[Crossref]

Faraon, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, Nat. Nanotechnol. 10, 937 (2015).
[Crossref]

Fattal, D.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, Nat. Photonics 4, 466 (2010).
[Crossref]

Fiorentino, M.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, Nat. Photonics 4, 466 (2010).
[Crossref]

Fu, Y. H.

Y. F. Yu, A. Y. Zhu, R. Paniagua-Domínguez, Y. H. Fu, B. Luk’yanchuk, and A. I. Kuznetsov, Laser Photon. Rev. 9, 412 (2015).
[Crossref]

Glybovski, S. B.

S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovski, Phys. Rep. 634, 1 (2016).
[Crossref]

Grbic, A.

C. Pfeiffer and A. Grbic, Phys. Rev. Lett. 110, 197401 (2013).
[Crossref]

Hang, Z.

Hao, J.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, Phys. Rev. Lett. 115, 235503 (2015).
[Crossref]

J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, and M. Qiu, Appl. Phys. Lett. 96, 251104 (2010).
[Crossref]

Hasman, E.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, Science 345, 298 (2014).
[Crossref]

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

He, Q.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, Phys. Rev. Lett. 115, 235503 (2015).
[Crossref]

S. Xiao, Q. He, C. Qu, X. Li, S. Sun, and L. Zhou, Opt. Express 21, 27219 (2013).
[Crossref]

Hopkins, B.

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, APL Photon. 1, 030801 (2016).
[Crossref]

Horie, Y.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, Nat. Nanotechnol. 10, 937 (2015).
[Crossref]

Joannopoulos, J. D.

S. Fan, W. Suh, and J. D. Joannopoulos, J. Opt. Soc. Am. A 20, 569 (2003).
[Crossref]

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[Crossref]

Kivshar, Y. S.

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, APL Photon. 1, 030801 (2016).
[Crossref]

S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovski, Phys. Rep. 634, 1 (2016).
[Crossref]

L. Wang, S. Kruk, H. Tang, T. Li, I. Kravchenko, D. N. Neshev, and Y. S. Kivshar, Optica 3, 1504 (2016).
[Crossref]

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, Adv. Opt. Mater. 3, 813 (2015).
[Crossref]

Kravchenko, I.

Kravchenko, I. I.

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, APL Photon. 1, 030801 (2016).
[Crossref]

Kruk, S.

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, APL Photon. 1, 030801 (2016).
[Crossref]

L. Wang, S. Kruk, H. Tang, T. Li, I. Kravchenko, D. N. Neshev, and Y. S. Kivshar, Optica 3, 1504 (2016).
[Crossref]

Kuznetsov, A. I.

Y. F. Yu, A. Y. Zhu, R. Paniagua-Domínguez, Y. H. Fu, B. Luk’yanchuk, and A. I. Kuznetsov, Laser Photon. Rev. 9, 412 (2015).
[Crossref]

Lee, R. K.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[Crossref]

Li, H.

Li, J.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, Nat. Photonics 4, 466 (2010).
[Crossref]

Li, T.

Li, X.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, Phys. Rev. Lett. 115, 235503 (2015).
[Crossref]

S. Xiao, Q. He, C. Qu, X. Li, S. Sun, and L. Zhou, Opt. Express 21, 27219 (2013).
[Crossref]

Li, Y.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[Crossref]

Li, Z.

Z. Li, E. Palacios, S. Butun, and K. Aydin, Nano Lett. 15, 1615 (2015).
[Crossref]

Lin, D.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, Science 345, 298 (2014).
[Crossref]

Liu, X.

J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, and M. Qiu, Appl. Phys. Lett. 96, 251104 (2010).
[Crossref]

Long, Y.

Luk’yanchuk, B.

Y. F. Yu, A. Y. Zhu, R. Paniagua-Domínguez, Y. H. Fu, B. Luk’yanchuk, and A. I. Kuznetsov, Laser Photon. Rev. 9, 412 (2015).
[Crossref]

Ma, S.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, Phys. Rev. Lett. 115, 235503 (2015).
[Crossref]

Ma, S. J.

S. J. Ma, S. Y. Xiao, and L. Zhou, Phys. Rev. B 93, 045305 (2016).
[Crossref]

Miao, Z.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, Phys. Rev. Lett. 115, 235503 (2015).
[Crossref]

Miroshnichenko, A.

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, APL Photon. 1, 030801 (2016).
[Crossref]

Monticone, F.

F. Monticone, N. M. Estakhri, and A. Alu, Phys. Rev. Lett. 110, 203903 (2013).
[Crossref]

Neshev, D. N.

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, APL Photon. 1, 030801 (2016).
[Crossref]

L. Wang, S. Kruk, H. Tang, T. Li, I. Kravchenko, D. N. Neshev, and Y. S. Kivshar, Optica 3, 1504 (2016).
[Crossref]

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, Adv. Opt. Mater. 3, 813 (2015).
[Crossref]

Padilla, W. J.

J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, and M. Qiu, Appl. Phys. Lett. 96, 251104 (2010).
[Crossref]

Palacios, E.

Z. Li, E. Palacios, S. Butun, and K. Aydin, Nano Lett. 15, 1615 (2015).
[Crossref]

Paniagua-Domínguez, R.

Y. F. Yu, A. Y. Zhu, R. Paniagua-Domínguez, Y. H. Fu, B. Luk’yanchuk, and A. I. Kuznetsov, Laser Photon. Rev. 9, 412 (2015).
[Crossref]

Peng, Z.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, Nat. Photonics 4, 466 (2010).
[Crossref]

Pertsch, T.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, Adv. Opt. Mater. 3, 813 (2015).
[Crossref]

Pfeiffer, C.

C. Pfeiffer and A. Grbic, Phys. Rev. Lett. 110, 197401 (2013).
[Crossref]

Qiu, M.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, Phys. Rev. Lett. 115, 235503 (2015).
[Crossref]

J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, and M. Qiu, Appl. Phys. Lett. 96, 251104 (2010).
[Crossref]

Qu, C.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, Phys. Rev. Lett. 115, 235503 (2015).
[Crossref]

S. Xiao, Q. He, C. Qu, X. Li, S. Sun, and L. Zhou, Opt. Express 21, 27219 (2013).
[Crossref]

Ren, J.

Sanda, P. N.

P. Sheng, R. S. Stepleman, and P. N. Sanda, Phys. Rev. B 26, 2907 (1982).
[Crossref]

Sheng, P.

P. Sheng, R. S. Stepleman, and P. N. Sanda, Phys. Rev. B 26, 2907 (1982).
[Crossref]

Simovski, C. R.

S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovski, Phys. Rep. 634, 1 (2016).
[Crossref]

Staude, I.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, Adv. Opt. Mater. 3, 813 (2015).
[Crossref]

Stepleman, R. S.

P. Sheng, R. S. Stepleman, and P. N. Sanda, Phys. Rev. B 26, 2907 (1982).
[Crossref]

Su, X.

Su, Z.

Suh, W.

Sun, S.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, Phys. Rev. Lett. 115, 235503 (2015).
[Crossref]

S. Xiao, Q. He, C. Qu, X. Li, S. Sun, and L. Zhou, Opt. Express 21, 27219 (2013).
[Crossref]

Tang, H.

Tretyakov, S. A.

S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovski, Phys. Rep. 634, 1 (2016).
[Crossref]

Wang, J.

J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, and M. Qiu, Appl. Phys. Lett. 96, 251104 (2010).
[Crossref]

Wang, L.

Wei, Z.

Wu, C.

Xiao, S.

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, Phys. Rev. Lett. 115, 235503 (2015).
[Crossref]

S. Xiao, Q. He, C. Qu, X. Li, S. Sun, and L. Zhou, Opt. Express 21, 27219 (2013).
[Crossref]

Xiao, S. Y.

S. J. Ma, S. Y. Xiao, and L. Zhou, Phys. Rev. B 93, 045305 (2016).
[Crossref]

Xu, Y.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[Crossref]

Yariv, A.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, Phys. Rev. E 62, 7389 (2000).
[Crossref]

Yin, J.

Yu, Y. F.

Y. F. Yu, A. Y. Zhu, R. Paniagua-Domínguez, Y. H. Fu, B. Luk’yanchuk, and A. I. Kuznetsov, Laser Photon. Rev. 9, 412 (2015).
[Crossref]

Zhang, D.

Zhao, X.

Zhou, L.

S. J. Ma, S. Y. Xiao, and L. Zhou, Phys. Rev. B 93, 045305 (2016).
[Crossref]

C. Qu, S. Ma, J. Hao, M. Qiu, X. Li, S. Xiao, Z. Miao, N. Dai, Q. He, S. Sun, and L. Zhou, Phys. Rev. Lett. 115, 235503 (2015).
[Crossref]

S. Xiao, Q. He, C. Qu, X. Li, S. Sun, and L. Zhou, Opt. Express 21, 27219 (2013).
[Crossref]

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Figures (3)

Fig. 1.
Fig. 1.

(a) Two-port resonator model in CMT. (b) The span of transmission phase Δ φ dependent on Δ φ and Q around its resonance frequency when | r d | = 0.9 .

Fig. 2.
Fig. 2.

(a) and (d) Transmission amplitude and transmission phase when an electromagnetic wave with E | | x ^ is normal incident in the cavity without (a) and with (d) the surface impedance layer. The inset shows the schematic of the resonance cavity, and the geometrical parameters of the cavity are set as h m = 1 μm , h = 20 μm , a = 20 μm , p = 170 μm . (b) and (e) Calculated background spectrum without (b) and with (e) the surface impedance layer. (c) and (f) Transmission amplitude and transmission phase calculated from CMT through the background spectrum and Q factor without (c) and with (f) the surface impedance layer.

Fig. 3.
Fig. 3.

(a) Scheme of a unit cell of the metasurface constituted by three layers of grating. The periodicity of the unit cell is p = 170 μm . (b) Transmission phase and (c) transmission amplitude of the unit cell dependent on the width of slits of the gratings. The symbols in (b) and (c) represent the widths of the slits of the gratings that are chosen as the unit cells of the metasurface. (d) Electric field distribution ( E x ) when a TM polarized electromagnetic wave with f = 0.5 THz is incident at the metasurface. (e) Normalized far-field intensity for (d).

Equations (8)

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t = t d ( t d r d ) 2 / τ i ( ω ω 0 ) + 2 / τ .
t e i θ 1 = | t d | e i Δ φ ( | t d | e i Δ φ | r d | ) 2 / τ i ( ω ω 0 ) + 2 / τ .
E ( 1 ) = E 0 ( 1 ) , + n ρ n E n ( 1 ) , + E ( 2 ) = q ( a q + E q ( 2 ) , + + a q E q ( 2 ) , ) E ( 3 ) = n ( b n + E n ( 3 ) , + + b n E n ( 3 ) , ) E ( 4 ) = q ( a q + E q ( 4 ) , + + a q E q ( 4 ) , ) E ( 5 ) = n t n E n ( 5 ) , .
T 1 = [ 1 / t 1 * r 1 * / t 1 * r 1 / t 1 1 / t 1 ] .
[ t d 0 ] = T 1 T 1 [ 1 r d ] .
U = 1 4 Re [ d τ · ( ϵ ϵ 0 E x * · E x + ϵ ϵ 0 E z * · E z + μ 0 H z * · H z ) ] = 1 h n 4 ϵ 2 ϵ 0 k 0 2 ( ϵ k 0 2 ( 2 n π / p ) 2 ) 2 · sin 2 ( n π a / p ) ( n π a / p ) 2 .
P = | t 0 | 2 d S · 1 2 Re ( E 0 ( 5 ) , , * × H 0 ( 5 ) , ) = ω ϵ 0 2 k 0 , z I .
Q = 2 π f c U P = 1 h n 8 ϵ 2 k 0 3 ( ϵ k 0 2 ( 2 n π / p ) 2 ) 2 sin 2 ( n π a / p ) ( n π a / p ) 2 .