Abstract

In a recent paper, Zhao et al. [Opt. Express 19(12), 11605 (2011)], proposed the use of differential evolution technique to optimize figure of merit of a negative index metamaterial (NIM) for the visible spectrum. In this comment, we argue that certain ambiguities associated with the effective parameter retrieval should be also addressed in the paper for the accurate implementation of the technique for NIMs. Furthermore, the figure of merit reported in the paper is unrealistically large.

© 2014 Optical Society of America

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References

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  1. Y. Zhao, F. Chen, Q. Shen, Q. Liu, L. Zhang, “Optimizing low loss negative index metamaterial for visible spectrum using differential evolution,” Opt. Express 19(12), 11605–11614 (2011).
    [CrossRef] [PubMed]
  2. D. R. Smith, S. Schultz, P. Markos, C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
    [CrossRef]
  3. S. Arslanagic, T. V. Hansen, N. A. Mortensen, A. H. Gregersen, O. Sigmund, R. W. Ziolkowski, O. Breinbjerg, “A review of the scattering-parameter extraction method with clarification of ambiguity issues in relation to metamaterial homogenization,” IEEE Antenn. Propag. M. 55(2), 91–106 (2013).
    [CrossRef]
  4. J. Zhou, T. Koschny, M. Kafesaki, C. M. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B 80(3), 035109 (2009).
    [CrossRef]
  5. P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [CrossRef]
  6. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
    [CrossRef] [PubMed]

2013 (1)

S. Arslanagic, T. V. Hansen, N. A. Mortensen, A. H. Gregersen, O. Sigmund, R. W. Ziolkowski, O. Breinbjerg, “A review of the scattering-parameter extraction method with clarification of ambiguity issues in relation to metamaterial homogenization,” IEEE Antenn. Propag. M. 55(2), 91–106 (2013).
[CrossRef]

2011 (1)

2009 (1)

J. Zhou, T. Koschny, M. Kafesaki, C. M. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B 80(3), 035109 (2009).
[CrossRef]

2008 (1)

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

2002 (1)

D. R. Smith, S. Schultz, P. Markos, C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

1972 (1)

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Arslanagic, S.

S. Arslanagic, T. V. Hansen, N. A. Mortensen, A. H. Gregersen, O. Sigmund, R. W. Ziolkowski, O. Breinbjerg, “A review of the scattering-parameter extraction method with clarification of ambiguity issues in relation to metamaterial homogenization,” IEEE Antenn. Propag. M. 55(2), 91–106 (2013).
[CrossRef]

Bartal, G.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Breinbjerg, O.

S. Arslanagic, T. V. Hansen, N. A. Mortensen, A. H. Gregersen, O. Sigmund, R. W. Ziolkowski, O. Breinbjerg, “A review of the scattering-parameter extraction method with clarification of ambiguity issues in relation to metamaterial homogenization,” IEEE Antenn. Propag. M. 55(2), 91–106 (2013).
[CrossRef]

Chen, F.

Christy, R. W.

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Genov, D. A.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Gregersen, A. H.

S. Arslanagic, T. V. Hansen, N. A. Mortensen, A. H. Gregersen, O. Sigmund, R. W. Ziolkowski, O. Breinbjerg, “A review of the scattering-parameter extraction method with clarification of ambiguity issues in relation to metamaterial homogenization,” IEEE Antenn. Propag. M. 55(2), 91–106 (2013).
[CrossRef]

Hansen, T. V.

S. Arslanagic, T. V. Hansen, N. A. Mortensen, A. H. Gregersen, O. Sigmund, R. W. Ziolkowski, O. Breinbjerg, “A review of the scattering-parameter extraction method with clarification of ambiguity issues in relation to metamaterial homogenization,” IEEE Antenn. Propag. M. 55(2), 91–106 (2013).
[CrossRef]

Johnson, P. B.

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Kafesaki, M.

J. Zhou, T. Koschny, M. Kafesaki, C. M. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B 80(3), 035109 (2009).
[CrossRef]

Koschny, T.

J. Zhou, T. Koschny, M. Kafesaki, C. M. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B 80(3), 035109 (2009).
[CrossRef]

Liu, Q.

Markos, P.

D. R. Smith, S. Schultz, P. Markos, C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Mortensen, N. A.

S. Arslanagic, T. V. Hansen, N. A. Mortensen, A. H. Gregersen, O. Sigmund, R. W. Ziolkowski, O. Breinbjerg, “A review of the scattering-parameter extraction method with clarification of ambiguity issues in relation to metamaterial homogenization,” IEEE Antenn. Propag. M. 55(2), 91–106 (2013).
[CrossRef]

Schultz, S.

D. R. Smith, S. Schultz, P. Markos, C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Shen, Q.

Sigmund, O.

S. Arslanagic, T. V. Hansen, N. A. Mortensen, A. H. Gregersen, O. Sigmund, R. W. Ziolkowski, O. Breinbjerg, “A review of the scattering-parameter extraction method with clarification of ambiguity issues in relation to metamaterial homogenization,” IEEE Antenn. Propag. M. 55(2), 91–106 (2013).
[CrossRef]

Smith, D. R.

D. R. Smith, S. Schultz, P. Markos, C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Soukoulis, C. M.

J. Zhou, T. Koschny, M. Kafesaki, C. M. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B 80(3), 035109 (2009).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Ulin-Avila, E.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Valentine, J.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Zentgraf, T.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Zhang, L.

Zhang, S.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Zhang, X.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Zhao, Y.

Zhou, J.

J. Zhou, T. Koschny, M. Kafesaki, C. M. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B 80(3), 035109 (2009).
[CrossRef]

Ziolkowski, R. W.

S. Arslanagic, T. V. Hansen, N. A. Mortensen, A. H. Gregersen, O. Sigmund, R. W. Ziolkowski, O. Breinbjerg, “A review of the scattering-parameter extraction method with clarification of ambiguity issues in relation to metamaterial homogenization,” IEEE Antenn. Propag. M. 55(2), 91–106 (2013).
[CrossRef]

IEEE Antenn. Propag. M. (1)

S. Arslanagic, T. V. Hansen, N. A. Mortensen, A. H. Gregersen, O. Sigmund, R. W. Ziolkowski, O. Breinbjerg, “A review of the scattering-parameter extraction method with clarification of ambiguity issues in relation to metamaterial homogenization,” IEEE Antenn. Propag. M. 55(2), 91–106 (2013).
[CrossRef]

Nature (1)

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. B (3)

J. Zhou, T. Koschny, M. Kafesaki, C. M. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B 80(3), 035109 (2009).
[CrossRef]

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Retrieved effective index of optimized fishnet metamaterial using: (a) transient solver (b) frequency domain solver of CST MWS. In both cases, the discontinuity in n′ occurs at frequency close to possible negative index band, increasing the possibility of wrong interpretation of the DE-algorithm.

Fig. 2
Fig. 2

Simulated FOM (considering m = 0 branch only) for the optimized fishnet metamaterial using: (a) CST transient solver with fc = 13.5THz (b) CST frequency domain solver with fc = 13.5THz (c) CST frequency domain solver with fc = 85THz (d) COMSOL Multiphysics with fc = 13.5THz (e) CST with 2nd order fit of experimental values for permittivity of silver. All the FOMs are significantly smaller than what is reported in [1].

Equations (1)

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n = { Re ( cos 1 [ ( 1 s 11 2 + s 21 2 ) / ( 2 s 21 ) ] ) + 2 π m } / ( k d ) ; m = 0 , ± 1 , ± 2 , .

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