Abstract

We investigate metamaterials based on arrays of rolled-up gold/(In)GaAs microrolls. By finite-integration-technique simulations we show that these arrays interact resonantly with the magnetic component of an electromagnetic field and exhibit a negative effective permeability at terahertz frequencies. We find a strong dependence of the resonance frequency on small variations in the winding number n. We show that this dependence can be removed, if desired, by applying an additional slit into the metal layer of the tube.

© 2011 Optical Society of America

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  1. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photon. 1, 224 (2007).
    [CrossRef]
  2. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, Science 328, 337 (2010).
    [CrossRef]
  3. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
    [CrossRef]
  4. X. Zhang and Z. Liu, Nat. Mater. 7, 435 (2008).
    [CrossRef]
  5. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theor. Tech. 47, 2075 (1999).
    [CrossRef]
  6. M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, Science 291, 849 (2001).
    [CrossRef]
  7. S. Linden, Ch. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
    [CrossRef]
  8. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
    [CrossRef]
  9. V. Y. Prinz, V. A. Seleznev, A. K. Gutakovsky, A. V. Chehovskiy, V. V. Preobrazhenskii, M. A. Putyato, and T. A. Gavrilova, Phys. E 6, 828 (2000).
    [CrossRef]
  10. O. Schumacher, S. Mendach, H. Welsch, A. Schramm, Ch. Heyn, and W. Hansen, Appl. Phys. Lett. 86, 143109 (2005).
    [CrossRef]
  11. S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, Ch. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
    [CrossRef]
  12. CST Microwave Studio, http://www.cst.com/ .
  13. D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, Phys. Rev. E 71, 036617 (2005).
    [CrossRef]
  14. J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
    [CrossRef]

2010 (1)

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, Science 328, 337 (2010).
[CrossRef]

2009 (1)

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, Ch. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

2008 (1)

X. Zhang and Z. Liu, Nat. Mater. 7, 435 (2008).
[CrossRef]

2007 (2)

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

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photon. 1, 224 (2007).
[CrossRef]

2005 (4)

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, Phys. Rev. E 71, 036617 (2005).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

O. Schumacher, S. Mendach, H. Welsch, A. Schramm, Ch. Heyn, and W. Hansen, Appl. Phys. Lett. 86, 143109 (2005).
[CrossRef]

2004 (1)

S. Linden, Ch. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef]

2001 (1)

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, Science 291, 849 (2001).
[CrossRef]

2000 (1)

V. Y. Prinz, V. A. Seleznev, A. K. Gutakovsky, A. V. Chehovskiy, V. V. Preobrazhenskii, M. A. Putyato, and T. A. Gavrilova, Phys. E 6, 828 (2000).
[CrossRef]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theor. Tech. 47, 2075 (1999).
[CrossRef]

Brenner, P.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, Science 328, 337 (2010).
[CrossRef]

Bröll, M.

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, Ch. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

Burger, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photon. 1, 224 (2007).
[CrossRef]

Chehovskiy, A. V.

V. Y. Prinz, V. A. Seleznev, A. K. Gutakovsky, A. V. Chehovskiy, V. V. Preobrazhenskii, M. A. Putyato, and T. A. Gavrilova, Phys. E 6, 828 (2000).
[CrossRef]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photon. 1, 224 (2007).
[CrossRef]

Economou, E. N.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

Enkrich, C.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

Enkrich, Ch.

S. Linden, Ch. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef]

Ergin, T.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, Science 328, 337 (2010).
[CrossRef]

Gavrilova, T. A.

V. Y. Prinz, V. A. Seleznev, A. K. Gutakovsky, A. V. Chehovskiy, V. V. Preobrazhenskii, M. A. Putyato, and T. A. Gavrilova, Phys. E 6, 828 (2000).
[CrossRef]

Gilderdale, D. J.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, Science 291, 849 (2001).
[CrossRef]

Gutakovsky, A. K.

V. Y. Prinz, V. A. Seleznev, A. K. Gutakovsky, A. V. Chehovskiy, V. V. Preobrazhenskii, M. A. Putyato, and T. A. Gavrilova, Phys. E 6, 828 (2000).
[CrossRef]

Hajnal, J. V.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, Science 291, 849 (2001).
[CrossRef]

Hansen, W.

O. Schumacher, S. Mendach, H. Welsch, A. Schramm, Ch. Heyn, and W. Hansen, Appl. Phys. Lett. 86, 143109 (2005).
[CrossRef]

Heitmann, D.

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, Ch. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

Heyn, Ch.

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, Ch. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

O. Schumacher, S. Mendach, H. Welsch, A. Schramm, Ch. Heyn, and W. Hansen, Appl. Phys. Lett. 86, 143109 (2005).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theor. Tech. 47, 2075 (1999).
[CrossRef]

Kafesaki, M.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

Kildishev, A. V.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photon. 1, 224 (2007).
[CrossRef]

Koschny, T.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, Phys. Rev. E 71, 036617 (2005).
[CrossRef]

S. Linden, Ch. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef]

Krohn, A.

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, Ch. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

Larkman, D. J.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, Science 291, 849 (2001).
[CrossRef]

Lee, H.

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

Linden, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

S. Linden, Ch. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef]

Liu, Z.

X. Zhang and Z. Liu, Nat. Mater. 7, 435 (2008).
[CrossRef]

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

Mendach, S.

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, Ch. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

O. Schumacher, S. Mendach, H. Welsch, A. Schramm, Ch. Heyn, and W. Hansen, Appl. Phys. Lett. 86, 143109 (2005).
[CrossRef]

Pendry, J. B.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, Science 328, 337 (2010).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, Science 291, 849 (2001).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theor. Tech. 47, 2075 (1999).
[CrossRef]

Preobrazhenskii, V. V.

V. Y. Prinz, V. A. Seleznev, A. K. Gutakovsky, A. V. Chehovskiy, V. V. Preobrazhenskii, M. A. Putyato, and T. A. Gavrilova, Phys. E 6, 828 (2000).
[CrossRef]

Prinz, V. Y.

V. Y. Prinz, V. A. Seleznev, A. K. Gutakovsky, A. V. Chehovskiy, V. V. Preobrazhenskii, M. A. Putyato, and T. A. Gavrilova, Phys. E 6, 828 (2000).
[CrossRef]

Putyato, M. A.

V. Y. Prinz, V. A. Seleznev, A. K. Gutakovsky, A. V. Chehovskiy, V. V. Preobrazhenskii, M. A. Putyato, and T. A. Gavrilova, Phys. E 6, 828 (2000).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theor. Tech. 47, 2075 (1999).
[CrossRef]

Schmidt, F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

Schramm, A.

O. Schumacher, S. Mendach, H. Welsch, A. Schramm, Ch. Heyn, and W. Hansen, Appl. Phys. Lett. 86, 143109 (2005).
[CrossRef]

Schumacher, O.

O. Schumacher, S. Mendach, H. Welsch, A. Schramm, Ch. Heyn, and W. Hansen, Appl. Phys. Lett. 86, 143109 (2005).
[CrossRef]

Schwaiger, S.

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, Ch. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

Seleznev, V. A.

V. Y. Prinz, V. A. Seleznev, A. K. Gutakovsky, A. V. Chehovskiy, V. V. Preobrazhenskii, M. A. Putyato, and T. A. Gavrilova, Phys. E 6, 828 (2000).
[CrossRef]

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photon. 1, 224 (2007).
[CrossRef]

Smith, D. R.

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, Phys. Rev. E 71, 036617 (2005).
[CrossRef]

Soukoulis, C. M.

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, Phys. Rev. E 71, 036617 (2005).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

S. Linden, Ch. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef]

Stark, Y.

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, Ch. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

Stemmann, A.

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, Ch. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

Stenger, N.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, Science 328, 337 (2010).
[CrossRef]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theor. Tech. 47, 2075 (1999).
[CrossRef]

Stickler, D.

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, Ch. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

Sun, C.

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

Vier, D. C.

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, Phys. Rev. E 71, 036617 (2005).
[CrossRef]

Wegener, M.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, Science 328, 337 (2010).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

S. Linden, Ch. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef]

Welsch, H.

O. Schumacher, S. Mendach, H. Welsch, A. Schramm, Ch. Heyn, and W. Hansen, Appl. Phys. Lett. 86, 143109 (2005).
[CrossRef]

Wiltshire, M. C. K.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, Science 291, 849 (2001).
[CrossRef]

Xiong, Y.

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

Young, I. R.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, Science 291, 849 (2001).
[CrossRef]

Zhang, X.

X. Zhang and Z. Liu, Nat. Mater. 7, 435 (2008).
[CrossRef]

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

Zhou, J.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

S. Linden, Ch. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef]

Zhou, J. F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

Zschiedrich, L.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

Appl. Phys. Lett. (1)

O. Schumacher, S. Mendach, H. Welsch, A. Schramm, Ch. Heyn, and W. Hansen, Appl. Phys. Lett. 86, 143109 (2005).
[CrossRef]

IEEE Trans. Microwave Theor. Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theor. Tech. 47, 2075 (1999).
[CrossRef]

Nat. Mater. (1)

X. Zhang and Z. Liu, Nat. Mater. 7, 435 (2008).
[CrossRef]

Nat. Photon. (1)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photon. 1, 224 (2007).
[CrossRef]

Phys. E (1)

V. Y. Prinz, V. A. Seleznev, A. K. Gutakovsky, A. V. Chehovskiy, V. V. Preobrazhenskii, M. A. Putyato, and T. A. Gavrilova, Phys. E 6, 828 (2000).
[CrossRef]

Phys. Rev. E (1)

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, Phys. Rev. E 71, 036617 (2005).
[CrossRef]

Phys. Rev. Lett. (3)

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef]

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, Ch. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef]

Science (4)

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, Science 328, 337 (2010).
[CrossRef]

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

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, Science 291, 849 (2001).
[CrossRef]

S. Linden, Ch. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef]

Other (1)

CST Microwave Studio, http://www.cst.com/ .

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Figures (3)

Fig. 1.
Fig. 1.

(a) Sketch of a microroll consisting of (In)GaAs and a metal layer. (b) Two-dimensional side view of microrolls with the overlap region forming a capacitance with and without an additional slit in the metal layer of width d. (c) Setup for the simulations performed in this Letter. The black lines indicate the simulation volume with periodic boundary conditions in the x and y directions and open boundaries in the z direction containing waveguide ports collecting the reflection and transmission data. The size of the simulation volume is determined by the lateral lattice constants ax and ay and the thickness az. The magnetic field vector of the incident plane wave points along the tube axis, i.e., in the y direction. The plane wave is incident in the z direction.

Fig. 2.
Fig. 2.

(a) Transmission spectra of microroll arrays with varying winding numbers and the resonance frequencies f0 calculated from the LO model. (b) Electric field distribution in the overlap region of the microroll at the resonance frequency of the array with winding number of n=1.05. (c) Induced magnetic field (red arrows) in the microroll at the resonance frequency of the array with winding number of n=1.05. The field is opposite to the external field (gray arrows), which leads to a negative permeability μ. (d) Retrieved and calculated permeabilities μeff and μLO of a microroll array with lattice constants ax=2μm, ay=1μm consisting of tubes with dimensions r=0.5μm, dAu=d(In)GaAs=10nm, and l=0.5μm for a winding number of n=1.05.

Fig. 3.
Fig. 3.

(a) Transmission spectra for an array of microrolls with an additional slit in the metal of width d=200nm for different winding numbers of n=1.1, 1.05, and 1.02. (b) Electric field distribution at the metal slit for a width of d=17.5nm.

Equations (1)

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μLO(ω)=1Fω2ω2+iRLωω02,

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