Abstract

We show that a flat metasurface with a parabolic reflection-phase distribution can focus an impinging plane wave to a point image in reflection geometry. Our system is much thinner than conventional geometric-optics devices and does not suffer the energy-loss issues encountered by many metamaterial devices working in transmission geometry. We designed realistic microwave samples and performed near-field scanning experiments to verify the focusing effect. Experimental results are in good agreement with full wave simulations, model calculations, and theoretical analyses.

© 2012 Optical Society of America

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  1. R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
    [CrossRef]
  2. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef]
  3. N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
    [CrossRef]
  4. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
    [CrossRef]
  5. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
    [CrossRef]
  6. Q. Lin, T. J. Cui, J. Y. Chin, X. M. Yang, Q. Cheng, and R. Liu, Appl. Phys. Lett. 92, 131904 (2008).
    [CrossRef]
  7. R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, Appl. Phys. Lett. 94, 073506 (2009).
    [CrossRef]
  8. N. Kundtz and D. R. Smith, Nat. Mater. 9, 129 (2009).
    [CrossRef]
  9. O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, Appl. Phys. Lett. 96, 241110 (2010).
    [CrossRef]
  10. J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, Opt. Express 18, 27748 (2010).
    [CrossRef]
  11. L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
    [CrossRef]
  12. L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, Nano Lett. 10, 1936 (2010).
    [CrossRef]
  13. C. Ma and Z. Liu, Appl. Phys. Lett. 96, 183103 (2010).
    [CrossRef]
  14. C. Ma, M. A. Escobar, and Z. Liu, Phys. Rev. B 84, 195142 (2011).
    [CrossRef]
  15. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  16. S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, Nat. Mater. 11, 426 (2012).
    [CrossRef]
  17. We neglected the amplitude differences of waves radiated from the SC at different local positions. We expect that it may not significantly influence the focusing effect since field radiated from a point (line) source varies slowly versus r(E(r)∝r−1,ln(r)).
  18. L. Zhou, X. Q. Huang, and C. T. Chan, Photonics Nanostruct. Fundam. Appl. 3, 100 (2005).
    [CrossRef]
  19. Some of calculated/measured field patterns are for Re(Ey) (with phase included) so that wave propagations can be easily identified.
  20. D. Sievenpiper, L. Zhang, R. Broas, N. G. Alexopolous, and E. Yablonovitch, IEEE Trans. Microw. Theory Technol. 47, 2059 (1999).
    [CrossRef]
  21. J. M. Hao, L. Zhou, and C. T. Chan, Appl. Phys. A 87, 281 (2007).
    [CrossRef]
  22. Simulations were performed using the EastFDTD v2.0 Beta, DONGJUN Science and Technology Co., China.
  23. B. J. Justice, J. J. Mock, L. Guo, A. Degiron, D. Schurig, and D. R. Smith, Opt. Express 14, 8694 (2006).
    [CrossRef]
  24. The magnetic slab represents the region occupied by the spacer and the upper metal sheet, with a total thickness of 1.65 mm.

2012 (1)

S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, Nat. Mater. 11, 426 (2012).
[CrossRef]

2011 (2)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

C. Ma, M. A. Escobar, and Z. Liu, Phys. Rev. B 84, 195142 (2011).
[CrossRef]

2010 (4)

J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, Opt. Express 18, 27748 (2010).
[CrossRef]

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, Appl. Phys. Lett. 96, 241110 (2010).
[CrossRef]

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, Nano Lett. 10, 1936 (2010).
[CrossRef]

C. Ma and Z. Liu, Appl. Phys. Lett. 96, 183103 (2010).
[CrossRef]

2009 (3)

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, Appl. Phys. Lett. 94, 073506 (2009).
[CrossRef]

N. Kundtz and D. R. Smith, Nat. Mater. 9, 129 (2009).
[CrossRef]

2008 (1)

Q. Lin, T. J. Cui, J. Y. Chin, X. M. Yang, Q. Cheng, and R. Liu, Appl. Phys. Lett. 92, 131904 (2008).
[CrossRef]

2007 (2)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

J. M. Hao, L. Zhou, and C. T. Chan, Appl. Phys. A 87, 281 (2007).
[CrossRef]

2006 (1)

2005 (2)

L. Zhou, X. Q. Huang, and C. T. Chan, Photonics Nanostruct. Fundam. Appl. 3, 100 (2005).
[CrossRef]

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef]

2000 (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

1999 (1)

D. Sievenpiper, L. Zhang, R. Broas, N. G. Alexopolous, and E. Yablonovitch, IEEE Trans. Microw. Theory Technol. 47, 2059 (1999).
[CrossRef]

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Alexopolous, N. G.

D. Sievenpiper, L. Zhang, R. Broas, N. G. Alexopolous, and E. Yablonovitch, IEEE Trans. Microw. Theory Technol. 47, 2059 (1999).
[CrossRef]

Barnard, E. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

Beigang, R.

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, Appl. Phys. Lett. 96, 241110 (2010).
[CrossRef]

J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, Opt. Express 18, 27748 (2010).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Broas, R.

D. Sievenpiper, L. Zhang, R. Broas, N. G. Alexopolous, and E. Yablonovitch, IEEE Trans. Microw. Theory Technol. 47, 2059 (1999).
[CrossRef]

Brongersma, M. L.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

Capasso, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

Chan, C. T.

J. M. Hao, L. Zhou, and C. T. Chan, Appl. Phys. A 87, 281 (2007).
[CrossRef]

L. Zhou, X. Q. Huang, and C. T. Chan, Photonics Nanostruct. Fundam. Appl. 3, 100 (2005).
[CrossRef]

Cheng, Q.

Q. Lin, T. J. Cui, J. Y. Chin, X. M. Yang, Q. Cheng, and R. Liu, Appl. Phys. Lett. 92, 131904 (2008).
[CrossRef]

Chin, J. Y.

Q. Lin, T. J. Cui, J. Y. Chin, X. M. Yang, Q. Cheng, and R. Liu, Appl. Phys. Lett. 92, 131904 (2008).
[CrossRef]

Cui, T. J.

R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, Appl. Phys. Lett. 94, 073506 (2009).
[CrossRef]

Q. Lin, T. J. Cui, J. Y. Chin, X. M. Yang, Q. Cheng, and R. Liu, Appl. Phys. Lett. 92, 131904 (2008).
[CrossRef]

Degiron, A.

Escobar, M. A.

C. Ma, M. A. Escobar, and Z. Liu, Phys. Rev. B 84, 195142 (2011).
[CrossRef]

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Gaburro, Z.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Genevet, P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Goh, X. M.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, Nano Lett. 10, 1936 (2010).
[CrossRef]

Gollub, J. G.

R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, Appl. Phys. Lett. 94, 073506 (2009).
[CrossRef]

Guo, L.

Hao, J. M.

J. M. Hao, L. Zhou, and C. T. Chan, Appl. Phys. A 87, 281 (2007).
[CrossRef]

He, Q.

S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, Nat. Mater. 11, 426 (2012).
[CrossRef]

Huang, X. Q.

L. Zhou, X. Q. Huang, and C. T. Chan, Photonics Nanostruct. Fundam. Appl. 3, 100 (2005).
[CrossRef]

Justice, B. J.

Kats, M. A.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Krolla, B.

J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, Opt. Express 18, 27748 (2010).
[CrossRef]

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, Appl. Phys. Lett. 96, 241110 (2010).
[CrossRef]

Kundtz, N.

N. Kundtz and D. R. Smith, Nat. Mater. 9, 129 (2009).
[CrossRef]

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Li, X.

S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, Nat. Mater. 11, 426 (2012).
[CrossRef]

Lin, L.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, Nano Lett. 10, 1936 (2010).
[CrossRef]

Lin, Q.

Q. Lin, T. J. Cui, J. Y. Chin, X. M. Yang, Q. Cheng, and R. Liu, Appl. Phys. Lett. 92, 131904 (2008).
[CrossRef]

Liu, R.

R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, Appl. Phys. Lett. 94, 073506 (2009).
[CrossRef]

Q. Lin, T. J. Cui, J. Y. Chin, X. M. Yang, Q. Cheng, and R. Liu, Appl. Phys. Lett. 92, 131904 (2008).
[CrossRef]

Liu, Z.

C. Ma, M. A. Escobar, and Z. Liu, Phys. Rev. B 84, 195142 (2011).
[CrossRef]

C. Ma and Z. Liu, Appl. Phys. Lett. 96, 183103 (2010).
[CrossRef]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Ma, C.

C. Ma, M. A. Escobar, and Z. Liu, Phys. Rev. B 84, 195142 (2011).
[CrossRef]

C. Ma and Z. Liu, Appl. Phys. Lett. 96, 183103 (2010).
[CrossRef]

McGuinness, L. P.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, Nano Lett. 10, 1936 (2010).
[CrossRef]

Mock, J. J.

R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, Appl. Phys. Lett. 94, 073506 (2009).
[CrossRef]

B. J. Justice, J. J. Mock, L. Guo, A. Degiron, D. Schurig, and D. R. Smith, Opt. Express 14, 8694 (2006).
[CrossRef]

Neu, J.

Paul, O.

J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, Opt. Express 18, 27748 (2010).
[CrossRef]

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, Appl. Phys. Lett. 96, 241110 (2010).
[CrossRef]

Pendry, J. B.

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

Rahm, M.

J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, Opt. Express 18, 27748 (2010).
[CrossRef]

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, Appl. Phys. Lett. 96, 241110 (2010).
[CrossRef]

Reinhard, B.

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, Appl. Phys. Lett. 96, 241110 (2010).
[CrossRef]

J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, Opt. Express 18, 27748 (2010).
[CrossRef]

Roberts, A.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, Nano Lett. 10, 1936 (2010).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef]

Schurig, D.

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef]

Sievenpiper, D.

D. Sievenpiper, L. Zhang, R. Broas, N. G. Alexopolous, and E. Yablonovitch, IEEE Trans. Microw. Theory Technol. 47, 2059 (1999).
[CrossRef]

Smith, D. R.

R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, Appl. Phys. Lett. 94, 073506 (2009).
[CrossRef]

N. Kundtz and D. R. Smith, Nat. Mater. 9, 129 (2009).
[CrossRef]

B. J. Justice, J. J. Mock, L. Guo, A. Degiron, D. Schurig, and D. R. Smith, Opt. Express 14, 8694 (2006).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef]

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Sun, S.

S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, Nat. Mater. 11, 426 (2012).
[CrossRef]

Tetienne, J. P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

White, J. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Xiao, S.

S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, Nat. Mater. 11, 426 (2012).
[CrossRef]

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Xu, Q.

S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, Nat. Mater. 11, 426 (2012).
[CrossRef]

Yablonovitch, E.

D. Sievenpiper, L. Zhang, R. Broas, N. G. Alexopolous, and E. Yablonovitch, IEEE Trans. Microw. Theory Technol. 47, 2059 (1999).
[CrossRef]

Yang, X. M.

R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, Appl. Phys. Lett. 94, 073506 (2009).
[CrossRef]

Q. Lin, T. J. Cui, J. Y. Chin, X. M. Yang, Q. Cheng, and R. Liu, Appl. Phys. Lett. 92, 131904 (2008).
[CrossRef]

Yu, N.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

Zhang, L.

D. Sievenpiper, L. Zhang, R. Broas, N. G. Alexopolous, and E. Yablonovitch, IEEE Trans. Microw. Theory Technol. 47, 2059 (1999).
[CrossRef]

Zhang, X.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Zhou, L.

S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, Nat. Mater. 11, 426 (2012).
[CrossRef]

J. M. Hao, L. Zhou, and C. T. Chan, Appl. Phys. A 87, 281 (2007).
[CrossRef]

L. Zhou, X. Q. Huang, and C. T. Chan, Photonics Nanostruct. Fundam. Appl. 3, 100 (2005).
[CrossRef]

Appl. Phys. A (1)

J. M. Hao, L. Zhou, and C. T. Chan, Appl. Phys. A 87, 281 (2007).
[CrossRef]

Appl. Phys. Lett. (4)

Q. Lin, T. J. Cui, J. Y. Chin, X. M. Yang, Q. Cheng, and R. Liu, Appl. Phys. Lett. 92, 131904 (2008).
[CrossRef]

R. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, Appl. Phys. Lett. 94, 073506 (2009).
[CrossRef]

O. Paul, B. Reinhard, B. Krolla, R. Beigang, and M. Rahm, Appl. Phys. Lett. 96, 241110 (2010).
[CrossRef]

C. Ma and Z. Liu, Appl. Phys. Lett. 96, 183103 (2010).
[CrossRef]

IEEE Trans. Microw. Theory Technol. (1)

D. Sievenpiper, L. Zhang, R. Broas, N. G. Alexopolous, and E. Yablonovitch, IEEE Trans. Microw. Theory Technol. 47, 2059 (1999).
[CrossRef]

Nano Lett. (2)

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, Nano Lett. 9, 235 (2009).
[CrossRef]

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, Nano Lett. 10, 1936 (2010).
[CrossRef]

Nat. Mater. (2)

N. Kundtz and D. R. Smith, Nat. Mater. 9, 129 (2009).
[CrossRef]

S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, Nat. Mater. 11, 426 (2012).
[CrossRef]

Opt. Express (2)

Photonics Nanostruct. Fundam. Appl. (1)

L. Zhou, X. Q. Huang, and C. T. Chan, Photonics Nanostruct. Fundam. Appl. 3, 100 (2005).
[CrossRef]

Phys. Rev. B (1)

C. Ma, M. A. Escobar, and Z. Liu, Phys. Rev. B 84, 195142 (2011).
[CrossRef]

Phys. Rev. Lett. (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

Science (4)

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef]

Other (5)

Some of calculated/measured field patterns are for Re(Ey) (with phase included) so that wave propagations can be easily identified.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

We neglected the amplitude differences of waves radiated from the SC at different local positions. We expect that it may not significantly influence the focusing effect since field radiated from a point (line) source varies slowly versus r(E(r)∝r−1,ln(r)).

Simulations were performed using the EastFDTD v2.0 Beta, DONGJUN Science and Technology Co., China.

The magnetic slab represents the region occupied by the spacer and the upper metal sheet, with a total thickness of 1.65 mm.

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Figures (4)

Fig. 1.
Fig. 1.

(a) Calculated E field pattern on the xy plane with z=f for an SC described by Eq. (1); insets show the Re(Ey) patterns on two symmetry planes. (b) For an SC described by Eq. (2) with L=8λ and f=5λ, calculated Re(Ey) pattern on the xz plane. For two SCs described by Eq. (2) with f=5λ and different L, calculated E distributions on the focal line with z=f (c) and along the center symmetry line (d). All fields are normalized against the field E0 of a uniform SC, J⃗=J0eiωtδ(z)e⃗y.

Fig. 2.
Fig. 2.

(a) Reflection phase (Φ) versus Ly for HISs with unit cell shown in the inset, obtained by FDTD simulations and experiments. Other parameters are a=6mm, h=1.6mm, w=0.5mm, and Lx=5mm. (b) Ly versus position x for the designed metasurface; inset shows a picture of real sample. (c) FDTD-calculated Φ(x) profile. (d) Retrieved μeff(x) profile of the designed metasurface.

Fig. 3.
Fig. 3.

(a) Sketch for the experimental setup. (b) E field distributions along the focal line, obtained by experiment and FDTD simulations on realistic samples and on the model system. (c) Re(Ey) on the xz plane, obtained by experiment, FDTD simulations (d) on realistic sample and (e) on the model system. The dashed line denotes the designed focal line (f=100mm). All fields are normalized against the input field strength, and the metasurface is placed at the z=0 plane.

Fig. 4.
Fig. 4.

Re(Ey) patterns obtained by FDTD simulations and experiments as the metasurface is illuminated by TE-polarized microwaves at incident angles (a), (b) θi=10° and (c), (d) θi=30°. All fields are normalized against the input field strength.

Equations (3)

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

J⃗=J0eik0(x2+y2+f2f)eiωtδ(z)e⃗y
J⃗=J0eik0(x2+f2f)eiωtδ(z)e⃗y.
Φ(x)=Φ0+k0x2+f2k0f

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