Abstract

We study polarization-dependent transmission of light through arrays of single-slit split-ring resonator (SSRR) based systems at normal incidence using finite integration time domain (FITD) and finite element methods (FEM). It is found that a conventional planar array of SSRRs acts as an effective optical wave plate at certain polarizations of incident light. The effect is attributed to the intrinsic linear birefringence of individual SSRRs. A comparison is made with other split-ring resonator-based systems exhibiting wave-plate-like properties due to inter-SSRR coupling.

© 2012 Optical Society of America

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  1. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Micro. Theory Tech. 47, 2075 (1999).
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    [CrossRef]
  4. N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 84, 2943 (2004).
    [CrossRef]
  5. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
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    [CrossRef]

2010 (2)

2009 (2)

N. Liu, H. Liu, S. Zhu, and H. Giessen, Nat. Photonics 3, 157 (2009).
[CrossRef]

M. Decker, S. Linden, and M. Wegener, Opt. Lett. 34, 1579 (2009).
[CrossRef]

2008 (1)

2007 (2)

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, Phys. Rev. B 76, 073101 (2007).
[CrossRef]

V. M. Shalaev, Nature Phot. 1, 41 (2007).
[CrossRef]

2006 (2)

2005 (1)

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

2004 (2)

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

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 84, 2943 (2004).
[CrossRef]

1999 (1)

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

1972 (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Burger, S.

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

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Corrigan, T. D.

Decker, M.

Drew, H. D.

Economou, E. N.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 84, 2943 (2004).
[CrossRef]

Enkrich, C.

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, Opt. Lett. 31, 1259 (2006).
[CrossRef]

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

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

Etrich, C.

Friberg, A. T.

Genov, D. A.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, Phys. Rev. B 76, 073101 (2007).
[CrossRef]

Giessen, H.

Holden, A. J.

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

Iyer, S.

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Kafesaki, M.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 84, 2943 (2004).
[CrossRef]

Katsarakis, N.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 84, 2943 (2004).
[CrossRef]

Klein, M. W.

Kolb, P. W.

Koschny, T.

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

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 84, 2943 (2004).
[CrossRef]

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

Kuhl, J.

Lederer, F.

Linden, S.

M. Decker, R. Zhao, C. M. Soukoulis, S. Linden, and M. Wegener, Opt. Lett. 35, 1593 (2010).
[CrossRef]

M. Decker, S. Linden, and M. Wegener, Opt. Lett. 34, 1579 (2009).
[CrossRef]

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, Opt. Lett. 31, 1259 (2006).
[CrossRef]

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

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

Liu, H.

N. Liu, H. Liu, S. Zhu, and H. Giessen, Nat. Photonics 3, 157 (2009).
[CrossRef]

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, Phys. Rev. B 76, 073101 (2007).
[CrossRef]

Liu, N.

N. Liu, H. Liu, S. Zhu, and H. Giessen, Nat. Photonics 3, 157 (2009).
[CrossRef]

Liu, Y. M.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, Phys. Rev. B 76, 073101 (2007).
[CrossRef]

Liu, Z. W.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, Phys. Rev. B 76, 073101 (2007).
[CrossRef]

Pendry, J. B.

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

Phaneuf, R. J.

Popov, S.

Robbins, D. J.

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

Rockstuhl, C.

Schmadel, D. C.

Schmidt, F.

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

Shalaev, V. M.

V. M. Shalaev, Nature Phot. 1, 41 (2007).
[CrossRef]

Soukoulis, C. M.

M. Decker, R. Zhao, C. M. Soukoulis, S. Linden, and M. Wegener, Opt. Lett. 35, 1593 (2010).
[CrossRef]

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, Opt. Lett. 31, 1259 (2006).
[CrossRef]

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

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

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 84, 2943 (2004).
[CrossRef]

Stewart, W. J.

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

Sun, C.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, Phys. Rev. B 76, 073101 (2007).
[CrossRef]

Sushkov, A. B.

Wegener, M.

M. Decker, R. Zhao, C. M. Soukoulis, S. Linden, and M. Wegener, Opt. Lett. 35, 1593 (2010).
[CrossRef]

M. Decker, S. Linden, and M. Wegener, Opt. Lett. 34, 1579 (2009).
[CrossRef]

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, Opt. Lett. 31, 1259 (2006).
[CrossRef]

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

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

Wu, D. M.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, Phys. Rev. B 76, 073101 (2007).
[CrossRef]

Zentgraf, T.

Zhang, X.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, Phys. Rev. B 76, 073101 (2007).
[CrossRef]

Zhao, R.

Zhou, J.

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

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

Zhu, S.

N. Liu, H. Liu, S. Zhu, and H. Giessen, Nat. Photonics 3, 157 (2009).
[CrossRef]

Zhu, S. N.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, Phys. Rev. B 76, 073101 (2007).
[CrossRef]

Zschiedrich, L.

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

Appl. Phys. Lett. (1)

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 84, 2943 (2004).
[CrossRef]

IEEE Trans. Micro. Theory Tech. (1)

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

Nat. Photonics (1)

N. Liu, H. Liu, S. Zhu, and H. Giessen, Nat. Photonics 3, 157 (2009).
[CrossRef]

Nature Phot. (1)

V. M. Shalaev, Nature Phot. 1, 41 (2007).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. B (2)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, Phys. Rev. B 76, 073101 (2007).
[CrossRef]

Phys. Rev. Lett. (1)

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

Science (1)

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

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Figures (4)

Fig. 1.
Fig. 1.

(a) Conventional square array of SSRRs with the corresponding unit cell. Geometrical parameters: lx=110nm, ly=95nm, wx=34nm, dr=45nm, unit cell periodicity a=240nm, and thickness of SSRRs 45 nm. (b) The transmission spectra for parallel [T] (solid) and perpendicular [T] (dotted) polarizations emerging out of the structure at normal incidence (k is along z). The color code represents polarizations of incident light along x (black), y (blue), and 45° (red), respectively. The dot-dash line marks the LC frequency of the SSRR, which corresponds to 338 THz.

Fig. 2.
Fig. 2.

Hz plots (with color scale) for polarizations of incident light along x and 45° at the LC resonance frequency (338 THz) of the SSRR. The white arrows represent the direction of current flow estimated from the projection of vector magnetic fields Hx, Hy, and Hz (arrow plots with emphasized direction) on the cross-sectional planes (1 and 2) of the SSRR arms.

Fig. 3.
Fig. 3.

Unit cells of inter-SSRR coupled systems A and B with coupling distance c, and their corresponding transmission spectra (T and T). The color code represents polarizations of incident light along x (black), y (blue), 45° (red solid), and 45° (red dots), respectively. The transmission spectrum for A is only calculated for x and 45° polarizations. Points 1, 2, and 3 are resonance positions for the y, ±45° and x polarizations for B.

Fig. 4.
Fig. 4.

Hz plots (red=positive, green=zero, blue=negative) for polarizations of incident light along y, 45°, and x direction at points 1, 2, and 3 (in Fig. 3), respectively.

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