Abstract

The perfectly conducting stacked fishnet metamaterial is studied in this paper. The analysis is based on a combination of the mode matching method together with the generalized eigenvalue problem, and takes into account wave propagation along all three Cartesian axes. The analysis has been developed for a fishnet of square lateral periodicity and for two particular polarizations, namely TE and TM, corresponding to the two most common excitations. The 1D and 2D dispersion characteristics are calculated for both polarizations, showing that the TM waves undergo negative refraction in a narrow frequency band just below Wood's anomaly, whereas TE polarized waves exhibit ordinary positive refraction. Finally, possible homogenization of the fishnet metamaterial is considered, showing that only for small angles of incidence and in the immediate vicinity of Wood's anomaly can the fishnet be seen as homogenizable uniaxial medium.

© 2010 Optical Society of America

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  1. S. Zhang,W. Fan, K. J. Malloy, and S. R. J. Brueck, "Near-infrared double negative metamaterials," Opt. Express 13, 4922-4929 (2005).
    [CrossRef]
  2. 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]
  3. G. Dolling, Ch. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Low-loss negative-index metamaterial at telecommunication wavelengths," Opt. Lett. 31, 1800-1802 (2005).
    [CrossRef]
  4. M. Beruete, M. Sorolla, and I. Campillo, "Left-handed extraordinary optical transmission through a photonic crystal of subwavelength hole arrays," Opt. Express 14, 5445-5455 (2006).
    [CrossRef]
  5. G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780 nm wavelength," Opt. Lett. 32, 53-55 (2007).
    [CrossRef]
  6. M. Beruete, I. Campillo, M. Navarro-Cia, F. Falcone, and M. S. Ayza, "Molding left- or right-handed metamaterials by stacked cutoff metallic hole arrays," IEEE Trans. Antennas Propag. 55, 1514-1521 (2007).
    [CrossRef]
  7. M. Navarro-Cia, M. Beruete, M. Sorolla, and I. Campillo, "Negative refraction in a prism made of stacked subwavelength hole arrays," Opt. Express 16, 560-566 (2008).
    [CrossRef]
  8. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature (London) 455, 376-379 (2008).
    [CrossRef]
  9. A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, "Theory of negative-refractive-index response of double-fishnet structures," Phys. Rev. Lett. 101, 103902 (2008).
    [CrossRef]
  10. M. Beruete, M. Navarro-Cia, M. Sorolla, and I. Campillo, "Negative refraction through an extraordinary transmission left-handed metamaterial slab," Phys. Rev. B 79, 195107 (2009).
    [CrossRef]
  11. R. Marques, L. Jelinek, F. Mesa, and F. Medina, "Analytical theory of wave propagation through stacked Fishnet metamaterials," Opt. Express 17, 11582-11593 (2009).
    [CrossRef]
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    [CrossRef]
  13. C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, "Validity of effective material parameters for optical fishnet metamaterials," Phys. Rev. B 81, 035320 (2010).
    [CrossRef]
  14. M. Beruete, M. Navarro-Cia and M. Sorolla, "Strong lateral displacement in polarization anisotropic extraordinary transmission metamaterial," New J. Phys. 12, 063037 (2010).
    [CrossRef]
  15. C. Garcia-Meca, R. Ortuno, F. J. Rodriguez-Fortuno, J. Marti, and A. Martinez, "Negative refractive index metamaterials aided by extraordinary optical transmission," Opt. Express 17, 6026-6031 (2009).
    [CrossRef]
  16. L. D. Landau, E. M. Lifshitz and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon Press, New York, 1984).

2010 (2)

C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, "Validity of effective material parameters for optical fishnet metamaterials," Phys. Rev. B 81, 035320 (2010).
[CrossRef]

M. Beruete, M. Navarro-Cia and M. Sorolla, "Strong lateral displacement in polarization anisotropic extraordinary transmission metamaterial," New J. Phys. 12, 063037 (2010).
[CrossRef]

2009 (4)

2008 (3)

M. Navarro-Cia, M. Beruete, M. Sorolla, and I. Campillo, "Negative refraction in a prism made of stacked subwavelength hole arrays," Opt. Express 16, 560-566 (2008).
[CrossRef]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature (London) 455, 376-379 (2008).
[CrossRef]

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, "Theory of negative-refractive-index response of double-fishnet structures," Phys. Rev. Lett. 101, 103902 (2008).
[CrossRef]

2007 (2)

M. Beruete, I. Campillo, M. Navarro-Cia, F. Falcone, and M. S. Ayza, "Molding left- or right-handed metamaterials by stacked cutoff metallic hole arrays," IEEE Trans. Antennas Propag. 55, 1514-1521 (2007).
[CrossRef]

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780 nm wavelength," Opt. Lett. 32, 53-55 (2007).
[CrossRef]

2006 (1)

2005 (3)

Ayza, M. S.

M. Beruete, I. Campillo, M. Navarro-Cia, F. Falcone, and M. S. Ayza, "Molding left- or right-handed metamaterials by stacked cutoff metallic hole arrays," IEEE Trans. Antennas Propag. 55, 1514-1521 (2007).
[CrossRef]

Beruete, M.

M. Beruete, M. Navarro-Cia and M. Sorolla, "Strong lateral displacement in polarization anisotropic extraordinary transmission metamaterial," New J. Phys. 12, 063037 (2010).
[CrossRef]

M. Beruete, M. Navarro-Cia, M. Sorolla, and I. Campillo, "Negative refraction through an extraordinary transmission left-handed metamaterial slab," Phys. Rev. B 79, 195107 (2009).
[CrossRef]

M. Navarro-Cia, M. Beruete, M. Sorolla, and I. Campillo, "Negative refraction in a prism made of stacked subwavelength hole arrays," Opt. Express 16, 560-566 (2008).
[CrossRef]

M. Beruete, I. Campillo, M. Navarro-Cia, F. Falcone, and M. S. Ayza, "Molding left- or right-handed metamaterials by stacked cutoff metallic hole arrays," IEEE Trans. Antennas Propag. 55, 1514-1521 (2007).
[CrossRef]

M. Beruete, M. Sorolla, and I. Campillo, "Left-handed extraordinary optical transmission through a photonic crystal of subwavelength hole arrays," Opt. Express 14, 5445-5455 (2006).
[CrossRef]

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]

S. Zhang,W. Fan, K. J. Malloy, and S. R. J. Brueck, "Near-infrared double negative metamaterials," Opt. Express 13, 4922-4929 (2005).
[CrossRef]

Campillo, I.

M. Beruete, M. Navarro-Cia, M. Sorolla, and I. Campillo, "Negative refraction through an extraordinary transmission left-handed metamaterial slab," Phys. Rev. B 79, 195107 (2009).
[CrossRef]

M. Navarro-Cia, M. Beruete, M. Sorolla, and I. Campillo, "Negative refraction in a prism made of stacked subwavelength hole arrays," Opt. Express 16, 560-566 (2008).
[CrossRef]

M. Beruete, I. Campillo, M. Navarro-Cia, F. Falcone, and M. S. Ayza, "Molding left- or right-handed metamaterials by stacked cutoff metallic hole arrays," IEEE Trans. Antennas Propag. 55, 1514-1521 (2007).
[CrossRef]

M. Beruete, M. Sorolla, and I. Campillo, "Left-handed extraordinary optical transmission through a photonic crystal of subwavelength hole arrays," Opt. Express 14, 5445-5455 (2006).
[CrossRef]

Dolling, G.

Enkrich, Ch.

Falcone, F.

M. Beruete, I. Campillo, M. Navarro-Cia, F. Falcone, and M. S. Ayza, "Molding left- or right-handed metamaterials by stacked cutoff metallic hole arrays," IEEE Trans. Antennas Propag. 55, 1514-1521 (2007).
[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]

S. Zhang,W. Fan, K. J. Malloy, and S. R. J. Brueck, "Near-infrared double negative metamaterials," Opt. Express 13, 4922-4929 (2005).
[CrossRef]

Garcia-Meca, C.

Garcia-Vidal, F. J.

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, "Theory of negative-refractive-index response of double-fishnet structures," Phys. Rev. Lett. 101, 103902 (2008).
[CrossRef]

Jelinek, L.

Lederer, F.

C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, "Validity of effective material parameters for optical fishnet metamaterials," Phys. Rev. B 81, 035320 (2010).
[CrossRef]

Linden, S.

Malloy, K. J.

S. Zhang,W. Fan, K. J. Malloy, and S. R. J. Brueck, "Near-infrared double negative metamaterials," Opt. Express 13, 4922-4929 (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]

Marques, R.

Marti, J.

Martinez, A.

Martin-Moreno, L.

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, "Theory of negative-refractive-index response of double-fishnet structures," Phys. Rev. Lett. 101, 103902 (2008).
[CrossRef]

Mary, A.

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, "Theory of negative-refractive-index response of double-fishnet structures," Phys. Rev. Lett. 101, 103902 (2008).
[CrossRef]

Medina, F.

Menzel, C.

C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, "Validity of effective material parameters for optical fishnet metamaterials," Phys. Rev. B 81, 035320 (2010).
[CrossRef]

Mesa, F.

Navarro-Cia, M.

M. Beruete, M. Navarro-Cia and M. Sorolla, "Strong lateral displacement in polarization anisotropic extraordinary transmission metamaterial," New J. Phys. 12, 063037 (2010).
[CrossRef]

M. Beruete, M. Navarro-Cia, M. Sorolla, and I. Campillo, "Negative refraction through an extraordinary transmission left-handed metamaterial slab," Phys. Rev. B 79, 195107 (2009).
[CrossRef]

M. Navarro-Cia, M. Beruete, M. Sorolla, and I. Campillo, "Negative refraction in a prism made of stacked subwavelength hole arrays," Opt. Express 16, 560-566 (2008).
[CrossRef]

M. Beruete, I. Campillo, M. Navarro-Cia, F. Falcone, and M. S. Ayza, "Molding left- or right-handed metamaterials by stacked cutoff metallic hole arrays," IEEE Trans. Antennas Propag. 55, 1514-1521 (2007).
[CrossRef]

Ortuno, R.

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]

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]

Paul, T.

C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, "Validity of effective material parameters for optical fishnet metamaterials," Phys. Rev. B 81, 035320 (2010).
[CrossRef]

Pertsch, T.

C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, "Validity of effective material parameters for optical fishnet metamaterials," Phys. Rev. B 81, 035320 (2010).
[CrossRef]

Rockstuhl, C.

C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, "Validity of effective material parameters for optical fishnet metamaterials," Phys. Rev. B 81, 035320 (2010).
[CrossRef]

Rodrigo, S. G.

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, "Theory of negative-refractive-index response of double-fishnet structures," Phys. Rev. Lett. 101, 103902 (2008).
[CrossRef]

Rodriguez-Fortuno, F. J.

Sorolla, M.

M. Beruete, M. Navarro-Cia and M. Sorolla, "Strong lateral displacement in polarization anisotropic extraordinary transmission metamaterial," New J. Phys. 12, 063037 (2010).
[CrossRef]

M. Beruete, M. Navarro-Cia, M. Sorolla, and I. Campillo, "Negative refraction through an extraordinary transmission left-handed metamaterial slab," Phys. Rev. B 79, 195107 (2009).
[CrossRef]

M. Navarro-Cia, M. Beruete, M. Sorolla, and I. Campillo, "Negative refraction in a prism made of stacked subwavelength hole arrays," Opt. Express 16, 560-566 (2008).
[CrossRef]

M. Beruete, M. Sorolla, and I. Campillo, "Left-handed extraordinary optical transmission through a photonic crystal of subwavelength hole arrays," Opt. Express 14, 5445-5455 (2006).
[CrossRef]

Soukoulis, C. M.

Tretyakov, S.

C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, "Validity of effective material parameters for optical fishnet metamaterials," Phys. Rev. B 81, 035320 (2010).
[CrossRef]

Ulin-Avila, E.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature (London) 455, 376-379 (2008).
[CrossRef]

Valentine, J.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature (London) 455, 376-379 (2008).
[CrossRef]

Wegener, M.

Zentgraf, T.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature (London) 455, 376-379 (2008).
[CrossRef]

Zhang, S.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature (London) 455, 376-379 (2008).
[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]

S. Zhang,W. Fan, K. J. Malloy, and S. R. J. Brueck, "Near-infrared double negative metamaterials," Opt. Express 13, 4922-4929 (2005).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

M. Beruete, I. Campillo, M. Navarro-Cia, F. Falcone, and M. S. Ayza, "Molding left- or right-handed metamaterials by stacked cutoff metallic hole arrays," IEEE Trans. Antennas Propag. 55, 1514-1521 (2007).
[CrossRef]

Nature (London) (1)

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, "Three-dimensional optical metamaterial with a negative refractive index," Nature (London) 455, 376-379 (2008).
[CrossRef]

New J. Phys. (1)

M. Beruete, M. Navarro-Cia and M. Sorolla, "Strong lateral displacement in polarization anisotropic extraordinary transmission metamaterial," New J. Phys. 12, 063037 (2010).
[CrossRef]

Opt. Express (6)

Opt. Lett. (2)

Phys. Rev. B (2)

C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, "Validity of effective material parameters for optical fishnet metamaterials," Phys. Rev. B 81, 035320 (2010).
[CrossRef]

M. Beruete, M. Navarro-Cia, M. Sorolla, and I. Campillo, "Negative refraction through an extraordinary transmission left-handed metamaterial slab," Phys. Rev. B 79, 195107 (2009).
[CrossRef]

Phys. Rev. Lett. (2)

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]

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, "Theory of negative-refractive-index response of double-fishnet structures," Phys. Rev. Lett. 101, 103902 (2008).
[CrossRef]

Other (1)

L. D. Landau, E. M. Lifshitz and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon Press, New York, 1984).

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