Abstract

We show that properties attributed to planar metamaterials that support resonances due to an appropriately shaped unit cell can also be identified in a medium that exhibits a resonance evoked by its period only. By choosing a subwavelength period, the effective material parameters of such a medium can be retrieved from the complex reflected and transmitted amplitude. The parameters exhibit Lorentzian line shapes in the spectral vicinity of the resonances associated with the period. If this material is stacked to form a three-dimensional medium, a stop gap is observed in transmission in the frequency range where the real part of one effective material parameter becomes negative. The resonance at the origin of the response is related to the excitation of a higher-order Bloch mode. Because their negligible excitation is a prerequisite for deriving effective material parameters, the analyzed structure mimics only the response of a metamaterial but cannot be regarded as a metamaterial.

© 2007 Optical Society of America

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  1. D. R. Smith, W. J. Padila, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  4. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
    [CrossRef]
  5. F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B: Lasers Opt. 84, 139-148 (2006).
  6. C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B: Lasers Opt. 84, 219-227 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  17. T. Koschny, L. Zhang, and C. M. Soukoulis, "Isotropic three-dimensional left-handed metamaterials," Phys. Rev. B 71, 121103(R) (2005).
    [CrossRef]
  18. C. Rockstuhl and F. Lederer, "The effect of disorder on the local density of states in two-dimensional quasi-periodic photonic crystals," New J. Phys. 8, 206 (2006).
    [CrossRef]

2006 (6)

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B: Lasers Opt. 84, 139-148 (2006).

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B: Lasers Opt. 84, 219-227 (2006).
[CrossRef]

C. Rockstuhl, T. Zentgraf, C. Etrich, J. Kuhl, F. Lederer, and H. Giessen, "On the reinterpretation of resonances in split-ring-resonators at normal incidence," Opt. Express 14, 8827-8836 (2006).
[CrossRef]

M. S. Wheeler, J. S. Aitchinson, and M. Mojahedi, "Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies," Phys. Rev. B 73, 045105 (2006).
[CrossRef]

C. Rockstuhl, U. Peschel, and F. Lederer, "Correlation between single cylinder properties and band gap formation in photonic structures," Opt. Lett. 31, 1741-1743 (2006).
[CrossRef]

C. Rockstuhl and F. Lederer, "The effect of disorder on the local density of states in two-dimensional quasi-periodic photonic crystals," New J. Phys. 8, 206 (2006).
[CrossRef]

2005 (3)

T. Koschny, L. Zhang, and C. M. Soukoulis, "Isotropic three-dimensional left-handed metamaterials," Phys. Rev. B 71, 121103(R) (2005).
[CrossRef]

D. Seetharamdoo, R. Sauleau, K. Mahdjoubi, and A.-C. Tarot, "Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity," J. Appl. Phys. 98, 063505 (2005).
[CrossRef]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef]

2003 (1)

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602(R) (2003).
[CrossRef]

2002 (3)

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of the effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

D. K. Jacob, S. C. Dunn, and M. G. Moharam, "Flat-top narrow-band spectral response obtained from cascaded resonant grating reflection filters," Appl. Opt. 41, 1241-1245 (2002).

S. O'Brien and J. B. Pendry, "Photonic band-gap effects and magnetic activity in dielectric composites," J. Phys.: Condens. Matter 14, 4035-4044 (2002).
[CrossRef]

2000 (1)

D. R. Smith, W. J. Padila, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef]

1999 (1)

J. P. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors, and enhanced non-linear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1996 (1)

A. Sharon, D. Rosenblatt, and A. A. Friesem, "Narrow spectral bandwidths with grating waveguide structures," Appl. Phys. Lett. 69, 4154-4156 (1996).
[CrossRef]

1995 (1)

1962 (1)

W. Rotman, "Plasma simulation by artificial dielectrics and parallel-plate media," IRE Trans. Antennas Propag. 10, 82-95 (1962).
[CrossRef]

Aitchinson, J. S.

M. S. Wheeler, J. S. Aitchinson, and M. Mojahedi, "Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies," Phys. Rev. B 73, 045105 (2006).
[CrossRef]

Augustin, M.

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B: Lasers Opt. 84, 139-148 (2006).

Bauerschäfer, U.

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B: Lasers Opt. 84, 139-148 (2006).

Brueck, S. R. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef]

Dunn, S. C.

Etrich, C.

C. Rockstuhl, T. Zentgraf, C. Etrich, J. Kuhl, F. Lederer, and H. Giessen, "On the reinterpretation of resonances in split-ring-resonators at normal incidence," Opt. Express 14, 8827-8836 (2006).
[CrossRef]

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B: Lasers Opt. 84, 139-148 (2006).

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B: Lasers Opt. 84, 219-227 (2006).
[CrossRef]

Fan, W.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef]

Friesem, A. A.

A. Sharon, D. Rosenblatt, and A. A. Friesem, "Narrow spectral bandwidths with grating waveguide structures," Appl. Phys. Lett. 69, 4154-4156 (1996).
[CrossRef]

Garwe, F.

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B: Lasers Opt. 84, 139-148 (2006).

Gaylord, T. K.

Giessen, H.

C. Rockstuhl, T. Zentgraf, C. Etrich, J. Kuhl, F. Lederer, and H. Giessen, "On the reinterpretation of resonances in split-ring-resonators at normal incidence," Opt. Express 14, 8827-8836 (2006).
[CrossRef]

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B: Lasers Opt. 84, 219-227 (2006).
[CrossRef]

Grann, E. B.

Guo, H.

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B: Lasers Opt. 84, 219-227 (2006).
[CrossRef]

Holden, A. J.

J. P. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors, and enhanced non-linear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Hübner, U.

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B: Lasers Opt. 84, 139-148 (2006).

Jacob, D. K.

Koschny, T.

T. Koschny, L. Zhang, and C. M. Soukoulis, "Isotropic three-dimensional left-handed metamaterials," Phys. Rev. B 71, 121103(R) (2005).
[CrossRef]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602(R) (2003).
[CrossRef]

Kuhl, J.

C. Rockstuhl, T. Zentgraf, C. Etrich, J. Kuhl, F. Lederer, and H. Giessen, "On the reinterpretation of resonances in split-ring-resonators at normal incidence," Opt. Express 14, 8827-8836 (2006).
[CrossRef]

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B: Lasers Opt. 84, 219-227 (2006).
[CrossRef]

Lederer, F.

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B: Lasers Opt. 84, 219-227 (2006).
[CrossRef]

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B: Lasers Opt. 84, 139-148 (2006).

C. Rockstuhl, T. Zentgraf, C. Etrich, J. Kuhl, F. Lederer, and H. Giessen, "On the reinterpretation of resonances in split-ring-resonators at normal incidence," Opt. Express 14, 8827-8836 (2006).
[CrossRef]

C. Rockstuhl, U. Peschel, and F. Lederer, "Correlation between single cylinder properties and band gap formation in photonic structures," Opt. Lett. 31, 1741-1743 (2006).
[CrossRef]

C. Rockstuhl and F. Lederer, "The effect of disorder on the local density of states in two-dimensional quasi-periodic photonic crystals," New J. Phys. 8, 206 (2006).
[CrossRef]

Liu, N.

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B: Lasers Opt. 84, 219-227 (2006).
[CrossRef]

Loa, I.

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B: Lasers Opt. 84, 219-227 (2006).
[CrossRef]

Mahdjoubi, K.

D. Seetharamdoo, R. Sauleau, K. Mahdjoubi, and A.-C. Tarot, "Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity," J. Appl. Phys. 98, 063505 (2005).
[CrossRef]

Malloy, K. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef]

Markos, P.

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602(R) (2003).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of the effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Moharam, M. G.

Mojahedi, M.

M. S. Wheeler, J. S. Aitchinson, and M. Mojahedi, "Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies," Phys. Rev. B 73, 045105 (2006).
[CrossRef]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padila, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef]

O'Brien, S.

S. O'Brien and J. B. Pendry, "Photonic band-gap effects and magnetic activity in dielectric composites," J. Phys.: Condens. Matter 14, 4035-4044 (2002).
[CrossRef]

Osgood, R. M.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef]

Padila, W. J.

D. R. Smith, W. J. Padila, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef]

Panoiu, N. C.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef]

Pendry, J. B.

S. O'Brien and J. B. Pendry, "Photonic band-gap effects and magnetic activity in dielectric composites," J. Phys.: Condens. Matter 14, 4035-4044 (2002).
[CrossRef]

Pendry, J. P.

J. P. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors, and enhanced non-linear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Pertsch, T.

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B: Lasers Opt. 84, 139-148 (2006).

Peschel, U.

Pommet, D. A.

Robbins, D. J.

J. P. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors, and enhanced non-linear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Rockstuhl, C.

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B: Lasers Opt. 84, 139-148 (2006).

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B: Lasers Opt. 84, 219-227 (2006).
[CrossRef]

C. Rockstuhl, T. Zentgraf, C. Etrich, J. Kuhl, F. Lederer, and H. Giessen, "On the reinterpretation of resonances in split-ring-resonators at normal incidence," Opt. Express 14, 8827-8836 (2006).
[CrossRef]

C. Rockstuhl, U. Peschel, and F. Lederer, "Correlation between single cylinder properties and band gap formation in photonic structures," Opt. Lett. 31, 1741-1743 (2006).
[CrossRef]

C. Rockstuhl and F. Lederer, "The effect of disorder on the local density of states in two-dimensional quasi-periodic photonic crystals," New J. Phys. 8, 206 (2006).
[CrossRef]

Rosenblatt, D.

A. Sharon, D. Rosenblatt, and A. A. Friesem, "Narrow spectral bandwidths with grating waveguide structures," Appl. Phys. Lett. 69, 4154-4156 (1996).
[CrossRef]

Rotman, W.

W. Rotman, "Plasma simulation by artificial dielectrics and parallel-plate media," IRE Trans. Antennas Propag. 10, 82-95 (1962).
[CrossRef]

Sauleau, R.

D. Seetharamdoo, R. Sauleau, K. Mahdjoubi, and A.-C. Tarot, "Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity," J. Appl. Phys. 98, 063505 (2005).
[CrossRef]

Schultz, S.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of the effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

D. R. Smith, W. J. Padila, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef]

Seetharamdoo, D.

D. Seetharamdoo, R. Sauleau, K. Mahdjoubi, and A.-C. Tarot, "Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity," J. Appl. Phys. 98, 063505 (2005).
[CrossRef]

Setzpfandt, F.

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B: Lasers Opt. 84, 139-148 (2006).

Sharon, A.

A. Sharon, D. Rosenblatt, and A. A. Friesem, "Narrow spectral bandwidths with grating waveguide structures," Appl. Phys. Lett. 69, 4154-4156 (1996).
[CrossRef]

Smith, D. R.

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602(R) (2003).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of the effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

D. R. Smith, W. J. Padila, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef]

Soukoulis, C. M.

T. Koschny, L. Zhang, and C. M. Soukoulis, "Isotropic three-dimensional left-handed metamaterials," Phys. Rev. B 71, 121103(R) (2005).
[CrossRef]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602(R) (2003).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of the effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Stewart, W. J.

J. P. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors, and enhanced non-linear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Syassen, K.

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B: Lasers Opt. 84, 219-227 (2006).
[CrossRef]

Tarot, A.-C.

D. Seetharamdoo, R. Sauleau, K. Mahdjoubi, and A.-C. Tarot, "Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity," J. Appl. Phys. 98, 063505 (2005).
[CrossRef]

Tünnermann, A.

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B: Lasers Opt. 84, 139-148 (2006).

Vier, D. C.

D. R. Smith, W. J. Padila, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef]

Wheeler, M. S.

M. S. Wheeler, J. S. Aitchinson, and M. Mojahedi, "Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies," Phys. Rev. B 73, 045105 (2006).
[CrossRef]

Zentgraf, T.

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C. Rockstuhl, T. Zentgraf, C. Etrich, J. Kuhl, F. Lederer, and H. Giessen, "On the reinterpretation of resonances in split-ring-resonators at normal incidence," Opt. Express 14, 8827-8836 (2006).
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T. Koschny, L. Zhang, and C. M. Soukoulis, "Isotropic three-dimensional left-handed metamaterials," Phys. Rev. B 71, 121103(R) (2005).
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S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
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Appl. Opt. (1)

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C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B: Lasers Opt. 84, 219-227 (2006).
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C. Rockstuhl and F. Lederer, "The effect of disorder on the local density of states in two-dimensional quasi-periodic photonic crystals," New J. Phys. 8, 206 (2006).
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[CrossRef]

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[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Transmittance and reflectance for (a) a single periodically patterned film and (b) a stack of 60 such films (for an appropriate scaling the absorption A = 1 R T is shown). The period of the stack is a z = 3.7 a , and the illuminating field is TE-polarized (for other data see the text).

Fig. 2
Fig. 2

Transmittance of the film stack illuminated with TE-polarized light as a function of the longitudinal period a z . Two types of gaps can be observed. Bragg gaps depend strongly on the period, whereas the gap associated with the waveguide resonance is to a good approximation independent of the period. If the resonances coincide, the usual anticrossing is observed.

Fig. 3
Fig. 3

Results of the parameter retrieval algorithm for the structure shown in Fig. 1 for a TE-polarized illuminating field. The permittivity is shown in (a), the permeability in (b), the impedance in (c), and the refractive index in (d). The solid and dashed curves indicate an imaginary part of the refractive index of 10 10 and 10 3 , respectively.

Fig. 4
Fig. 4

(a) Amplitude of the electric field excited in the structure as described in the text using TE-polarized light for the illumination. The frequency is f = 0.7488 a λ 1 and corresponds to the resonance of the first guided mode of the structure. In (b) the corresponding vectorial magnetic field is shown at an arbitrary time.

Fig. 5
Fig. 5

Amplitudes of the zeroth and first diffracted transmission orders as a function of the frequency in the spectral vicinity of the resonance.

Fig. 6
Fig. 6

Results of the parameter retrieval algorithm for the structure shown in Fig. 1 for a TM-polarized illuminating field. The permittivity is shown in (a), the permeability in (b), the impedance in (c), and the refractive index in (d). The solid curve corresponds to a structure where the imaginary part of the refractive index was assumed to be 10 10 , and the dashed curve corresponds to a structure with an imaginary part of 10 3 .

Fig. 7
Fig. 7

(a) Transmission through a stack of 60 gratings if the longitudinal period of the structure a z varies statistically, as described in the text. The solid curve is the transmission of a single configuration. The dotted–dashed curve is the average of the transmittance over 100 different configurations. (b) Transmission through a stack of gratings where each layer is randomly displaced in the transversal direction. Again, the solid curve is the result of single realization, whereas the dotted–dashed curve is the average of the transmission of 100 different configurations. The structure in both cases is illuminated with a TE-polarized plane wave.

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