Abstract

Reflection and transmission of electromagnetic waves at the boundaries of periodic composites (electromagnetic/optical metamaterials) depends in general on both bulk and surface waves. We investigate the interplay of these two contributions using three-dimensional full-wave numerical simulations and a recently developed non-asymptotic homogenization theory.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. D. Baena, L. Jelinek, R. Marques, and M. Silveirinha, “Unified homogenization theory for magnetoinductive and electromagnetic waves in split-ring metamaterials,” Phys. Rev. A78, 013842 (2008).
    [CrossRef]
  2. C. R. Simovski, “Material paremeters of metamaterials (a review),” Opt. Spectrosc.107, 766–793 (2009).
    [CrossRef]
  3. C. Fietz and G. Shvets, “Current-driven metamaterial homogenization,” Physica B405, 2930–2934 (2010).
    [CrossRef]
  4. C. R. Simovski, “On electromagnetic characterization and homogenization of nanostructured metamaterials,” J. Opt.13, 103001 (2011).
    [CrossRef]
  5. R. V. Craster, J. Kaplunov, E. Nolde, and S. Guenneau, “High-frequency homogenization for checkerboard structures: defect modes, ultrarefraction, and all-angle negative refraction,” J. Opt. Soc. Am. A28, 1032–1040 (2011).
    [CrossRef]
  6. S. Guenneau and F. Zolla, “Homogenization of three-dimensional finite photonic crystals,” Prog. Electromagnetic Res.27, 91–127 (2011).
    [CrossRef]
  7. Y. Liu, S. Guenneau, and B. Gralak, “A route to all frequency homogenization of periodic structures,” (2012). ArXiv:1210.6171v2.
  8. C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, “Validity of effective material parameters for optical fishnet metamaterials,” Phys. Rev. B81, 035320 (2010).
    [CrossRef]
  9. C. Menzel, C. Rockstuhl, R. Iliew, F. Lederer, A. Andryieuski, R. Malureanu, and A. V. Lavrinenko, “High symmetry versus optical isotropy of a negative-index metamaterial,” Phys. Rev. B81, 195123 (2010).
    [CrossRef]
  10. T. Paul, C. Menzel, W. Smigaj, C. Rockstuhl, P. Lalanne, and F. Lederer, “Reflection and transmission of light at periodic layered metamaterial films,” Phys. Rev. B84, 115142 (2011).
    [CrossRef]
  11. C. Rockstuhl, T. Paul, F. Lederer, T. Pertsch, T. Zentgraf, T. P. Meyrath, and H. Giessen, “Transition from thin-film to bulk properties of metamaterials,” Phys. Rev. B77, 035126 (2008).
    [CrossRef]
  12. D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65, 195104 (2002).
    [CrossRef]
  13. X. Chen, B. I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E71, 046610 (2005).
    [CrossRef]
  14. C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B77, 195328 (2008).
    [CrossRef]
  15. I. Tsukerman, “Effective parameters of metamaterials: a rigorous homogenization theory via Whitney interpolation,” J. Opt. Soc. Am. B28, 577–586 (2011).
    [CrossRef]
  16. A. Pors, I. Tsukerman, and S. I. Bozhevolnyi, “Effective constitutive parameters of plasmonic metamaterials: Homogenization by dual field interpolation,” Phys. Rev. E84, 016609 (2011).
    [CrossRef]
  17. I. Tsukerman, “Nonlocal homogenization of metamaterials by dual interpolation of fields,” J. Opt. Soc. Am. B28, 2956–2965 (2011).
    [CrossRef]
  18. V. A. Markel and J. C. Schotland, “On the sign of refraction in anisotropic non-magnetic media,” J. Opt.12, 015104 (2010).
    [CrossRef]
  19. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, New York, 1988).
  20. P. A. Belov and C. R. Simovski, “Boundary conditions for interfaces of electromagnetic crystals and the generalized Ewald-Oseen extinction principle,” Phys. Rev. B73, 045102 (2006).
    [CrossRef]
  21. V. A. Markel and J. C. Schotland, “Homogenization of Maxwell’s equations in periodic composites,” Phys. Rev. E85, 066603 (2012).
    [CrossRef]
  22. R. Hiptmair, “Discrete Hodge operators,” Num. Math.90, 265 (2001).
    [CrossRef]
  23. R. Hiptmair and I. Tsukerman, “Non-asymptotic homogenization of electromagnetic metamaterials via discrete Hodge operators with Trefftz calibration,” to appear in COMPUMAG – Proceedings of 19th International Conference on the Computation of Electromagnetic Fields (Budapest, 2013).
  24. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm.181, 687 (2010).
    [CrossRef]
  25. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt.37, 5271 (1998).
    [CrossRef]
  26. S. Ha, A. A. Sukhorukov, D. K. B., L. C. Botten, C. M. de Sterke, and Y. S. Kivshar, “Bloch-mode extraction from near-field data in periodic waveguides,” Opt. Lett.34, 3776 (2009).
    [CrossRef] [PubMed]
  27. L. Lewin, “The electrical constants of a material loaded with spherical particles,” Proc. Inst. Elec. Eng.94, 65–68 (1947).

2012 (1)

V. A. Markel and J. C. Schotland, “Homogenization of Maxwell’s equations in periodic composites,” Phys. Rev. E85, 066603 (2012).
[CrossRef]

2011 (7)

I. Tsukerman, “Effective parameters of metamaterials: a rigorous homogenization theory via Whitney interpolation,” J. Opt. Soc. Am. B28, 577–586 (2011).
[CrossRef]

A. Pors, I. Tsukerman, and S. I. Bozhevolnyi, “Effective constitutive parameters of plasmonic metamaterials: Homogenization by dual field interpolation,” Phys. Rev. E84, 016609 (2011).
[CrossRef]

I. Tsukerman, “Nonlocal homogenization of metamaterials by dual interpolation of fields,” J. Opt. Soc. Am. B28, 2956–2965 (2011).
[CrossRef]

C. R. Simovski, “On electromagnetic characterization and homogenization of nanostructured metamaterials,” J. Opt.13, 103001 (2011).
[CrossRef]

R. V. Craster, J. Kaplunov, E. Nolde, and S. Guenneau, “High-frequency homogenization for checkerboard structures: defect modes, ultrarefraction, and all-angle negative refraction,” J. Opt. Soc. Am. A28, 1032–1040 (2011).
[CrossRef]

S. Guenneau and F. Zolla, “Homogenization of three-dimensional finite photonic crystals,” Prog. Electromagnetic Res.27, 91–127 (2011).
[CrossRef]

T. Paul, C. Menzel, W. Smigaj, C. Rockstuhl, P. Lalanne, and F. Lederer, “Reflection and transmission of light at periodic layered metamaterial films,” Phys. Rev. B84, 115142 (2011).
[CrossRef]

2010 (5)

C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, “Validity of effective material parameters for optical fishnet metamaterials,” Phys. Rev. B81, 035320 (2010).
[CrossRef]

C. Menzel, C. Rockstuhl, R. Iliew, F. Lederer, A. Andryieuski, R. Malureanu, and A. V. Lavrinenko, “High symmetry versus optical isotropy of a negative-index metamaterial,” Phys. Rev. B81, 195123 (2010).
[CrossRef]

V. A. Markel and J. C. Schotland, “On the sign of refraction in anisotropic non-magnetic media,” J. Opt.12, 015104 (2010).
[CrossRef]

C. Fietz and G. Shvets, “Current-driven metamaterial homogenization,” Physica B405, 2930–2934 (2010).
[CrossRef]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm.181, 687 (2010).
[CrossRef]

2009 (2)

2008 (3)

J. D. Baena, L. Jelinek, R. Marques, and M. Silveirinha, “Unified homogenization theory for magnetoinductive and electromagnetic waves in split-ring metamaterials,” Phys. Rev. A78, 013842 (2008).
[CrossRef]

C. Rockstuhl, T. Paul, F. Lederer, T. Pertsch, T. Zentgraf, T. P. Meyrath, and H. Giessen, “Transition from thin-film to bulk properties of metamaterials,” Phys. Rev. B77, 035126 (2008).
[CrossRef]

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B77, 195328 (2008).
[CrossRef]

2006 (1)

P. A. Belov and C. R. Simovski, “Boundary conditions for interfaces of electromagnetic crystals and the generalized Ewald-Oseen extinction principle,” Phys. Rev. B73, 045102 (2006).
[CrossRef]

2005 (1)

X. Chen, B. I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E71, 046610 (2005).
[CrossRef]

2002 (1)

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65, 195104 (2002).
[CrossRef]

2001 (1)

R. Hiptmair, “Discrete Hodge operators,” Num. Math.90, 265 (2001).
[CrossRef]

1998 (1)

1947 (1)

L. Lewin, “The electrical constants of a material loaded with spherical particles,” Proc. Inst. Elec. Eng.94, 65–68 (1947).

Andryieuski, A.

C. Menzel, C. Rockstuhl, R. Iliew, F. Lederer, A. Andryieuski, R. Malureanu, and A. V. Lavrinenko, “High symmetry versus optical isotropy of a negative-index metamaterial,” Phys. Rev. B81, 195123 (2010).
[CrossRef]

B., D. K.

Baena, J. D.

J. D. Baena, L. Jelinek, R. Marques, and M. Silveirinha, “Unified homogenization theory for magnetoinductive and electromagnetic waves in split-ring metamaterials,” Phys. Rev. A78, 013842 (2008).
[CrossRef]

Belov, P. A.

P. A. Belov and C. R. Simovski, “Boundary conditions for interfaces of electromagnetic crystals and the generalized Ewald-Oseen extinction principle,” Phys. Rev. B73, 045102 (2006).
[CrossRef]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm.181, 687 (2010).
[CrossRef]

Botten, L. C.

Bozhevolnyi, S. I.

A. Pors, I. Tsukerman, and S. I. Bozhevolnyi, “Effective constitutive parameters of plasmonic metamaterials: Homogenization by dual field interpolation,” Phys. Rev. E84, 016609 (2011).
[CrossRef]

Chen, X.

X. Chen, B. I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E71, 046610 (2005).
[CrossRef]

Craster, R. V.

de Sterke, C. M.

Djurisic, A. B.

Elazar, J. M.

Fietz, C.

C. Fietz and G. Shvets, “Current-driven metamaterial homogenization,” Physica B405, 2930–2934 (2010).
[CrossRef]

Giessen, H.

C. Rockstuhl, T. Paul, F. Lederer, T. Pertsch, T. Zentgraf, T. P. Meyrath, and H. Giessen, “Transition from thin-film to bulk properties of metamaterials,” Phys. Rev. B77, 035126 (2008).
[CrossRef]

Gralak, B.

Y. Liu, S. Guenneau, and B. Gralak, “A route to all frequency homogenization of periodic structures,” (2012). ArXiv:1210.6171v2.

Grzegorczyk, T. M.

X. Chen, B. I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E71, 046610 (2005).
[CrossRef]

Guenneau, S.

S. Guenneau and F. Zolla, “Homogenization of three-dimensional finite photonic crystals,” Prog. Electromagnetic Res.27, 91–127 (2011).
[CrossRef]

R. V. Craster, J. Kaplunov, E. Nolde, and S. Guenneau, “High-frequency homogenization for checkerboard structures: defect modes, ultrarefraction, and all-angle negative refraction,” J. Opt. Soc. Am. A28, 1032–1040 (2011).
[CrossRef]

Y. Liu, S. Guenneau, and B. Gralak, “A route to all frequency homogenization of periodic structures,” (2012). ArXiv:1210.6171v2.

Ha, S.

Hiptmair, R.

R. Hiptmair, “Discrete Hodge operators,” Num. Math.90, 265 (2001).
[CrossRef]

R. Hiptmair and I. Tsukerman, “Non-asymptotic homogenization of electromagnetic metamaterials via discrete Hodge operators with Trefftz calibration,” to appear in COMPUMAG – Proceedings of 19th International Conference on the Computation of Electromagnetic Fields (Budapest, 2013).

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm.181, 687 (2010).
[CrossRef]

Iliew, R.

C. Menzel, C. Rockstuhl, R. Iliew, F. Lederer, A. Andryieuski, R. Malureanu, and A. V. Lavrinenko, “High symmetry versus optical isotropy of a negative-index metamaterial,” Phys. Rev. B81, 195123 (2010).
[CrossRef]

Jelinek, L.

J. D. Baena, L. Jelinek, R. Marques, and M. Silveirinha, “Unified homogenization theory for magnetoinductive and electromagnetic waves in split-ring metamaterials,” Phys. Rev. A78, 013842 (2008).
[CrossRef]

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm.181, 687 (2010).
[CrossRef]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm.181, 687 (2010).
[CrossRef]

Kaplunov, J.

Kivshar, Y. S.

Kong, J. A.

X. Chen, B. I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E71, 046610 (2005).
[CrossRef]

Lalanne, P.

T. Paul, C. Menzel, W. Smigaj, C. Rockstuhl, P. Lalanne, and F. Lederer, “Reflection and transmission of light at periodic layered metamaterial films,” Phys. Rev. B84, 115142 (2011).
[CrossRef]

Lavrinenko, A. V.

C. Menzel, C. Rockstuhl, R. Iliew, F. Lederer, A. Andryieuski, R. Malureanu, and A. V. Lavrinenko, “High symmetry versus optical isotropy of a negative-index metamaterial,” Phys. Rev. B81, 195123 (2010).
[CrossRef]

Lederer, F.

T. Paul, C. Menzel, W. Smigaj, C. Rockstuhl, P. Lalanne, and F. Lederer, “Reflection and transmission of light at periodic layered metamaterial films,” Phys. Rev. B84, 115142 (2011).
[CrossRef]

C. Menzel, C. Rockstuhl, R. Iliew, F. Lederer, A. Andryieuski, R. Malureanu, and A. V. Lavrinenko, “High symmetry versus optical isotropy of a negative-index metamaterial,” Phys. Rev. B81, 195123 (2010).
[CrossRef]

C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, “Validity of effective material parameters for optical fishnet metamaterials,” Phys. Rev. B81, 035320 (2010).
[CrossRef]

C. Rockstuhl, T. Paul, F. Lederer, T. Pertsch, T. Zentgraf, T. P. Meyrath, and H. Giessen, “Transition from thin-film to bulk properties of metamaterials,” Phys. Rev. B77, 035126 (2008).
[CrossRef]

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B77, 195328 (2008).
[CrossRef]

Lewin, L.

L. Lewin, “The electrical constants of a material loaded with spherical particles,” Proc. Inst. Elec. Eng.94, 65–68 (1947).

Liu, Y.

Y. Liu, S. Guenneau, and B. Gralak, “A route to all frequency homogenization of periodic structures,” (2012). ArXiv:1210.6171v2.

Majewski, M. L.

Malureanu, R.

C. Menzel, C. Rockstuhl, R. Iliew, F. Lederer, A. Andryieuski, R. Malureanu, and A. V. Lavrinenko, “High symmetry versus optical isotropy of a negative-index metamaterial,” Phys. Rev. B81, 195123 (2010).
[CrossRef]

Markel, V. A.

V. A. Markel and J. C. Schotland, “Homogenization of Maxwell’s equations in periodic composites,” Phys. Rev. E85, 066603 (2012).
[CrossRef]

V. A. Markel and J. C. Schotland, “On the sign of refraction in anisotropic non-magnetic media,” J. Opt.12, 015104 (2010).
[CrossRef]

Markoš, P.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65, 195104 (2002).
[CrossRef]

Marques, R.

J. D. Baena, L. Jelinek, R. Marques, and M. Silveirinha, “Unified homogenization theory for magnetoinductive and electromagnetic waves in split-ring metamaterials,” Phys. Rev. A78, 013842 (2008).
[CrossRef]

Menzel, C.

T. Paul, C. Menzel, W. Smigaj, C. Rockstuhl, P. Lalanne, and F. Lederer, “Reflection and transmission of light at periodic layered metamaterial films,” Phys. Rev. B84, 115142 (2011).
[CrossRef]

C. Menzel, C. Rockstuhl, R. Iliew, F. Lederer, A. Andryieuski, R. Malureanu, and A. V. Lavrinenko, “High symmetry versus optical isotropy of a negative-index metamaterial,” Phys. Rev. B81, 195123 (2010).
[CrossRef]

C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, “Validity of effective material parameters for optical fishnet metamaterials,” Phys. Rev. B81, 035320 (2010).
[CrossRef]

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B77, 195328 (2008).
[CrossRef]

Meyrath, T. P.

C. Rockstuhl, T. Paul, F. Lederer, T. Pertsch, T. Zentgraf, T. P. Meyrath, and H. Giessen, “Transition from thin-film to bulk properties of metamaterials,” Phys. Rev. B77, 035126 (2008).
[CrossRef]

Nolde, E.

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm.181, 687 (2010).
[CrossRef]

Paul, T.

T. Paul, C. Menzel, W. Smigaj, C. Rockstuhl, P. Lalanne, and F. Lederer, “Reflection and transmission of light at periodic layered metamaterial films,” Phys. Rev. B84, 115142 (2011).
[CrossRef]

C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, “Validity of effective material parameters for optical fishnet metamaterials,” Phys. Rev. B81, 035320 (2010).
[CrossRef]

C. Rockstuhl, T. Paul, F. Lederer, T. Pertsch, T. Zentgraf, T. P. Meyrath, and H. Giessen, “Transition from thin-film to bulk properties of metamaterials,” Phys. Rev. B77, 035126 (2008).
[CrossRef]

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B77, 195328 (2008).
[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. B81, 035320 (2010).
[CrossRef]

C. Rockstuhl, T. Paul, F. Lederer, T. Pertsch, T. Zentgraf, T. P. Meyrath, and H. Giessen, “Transition from thin-film to bulk properties of metamaterials,” Phys. Rev. B77, 035126 (2008).
[CrossRef]

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B77, 195328 (2008).
[CrossRef]

Pors, A.

A. Pors, I. Tsukerman, and S. I. Bozhevolnyi, “Effective constitutive parameters of plasmonic metamaterials: Homogenization by dual field interpolation,” Phys. Rev. E84, 016609 (2011).
[CrossRef]

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, New York, 1988).

Rakic, A. D.

Rockstuhl, C.

T. Paul, C. Menzel, W. Smigaj, C. Rockstuhl, P. Lalanne, and F. Lederer, “Reflection and transmission of light at periodic layered metamaterial films,” Phys. Rev. B84, 115142 (2011).
[CrossRef]

C. Menzel, C. Rockstuhl, R. Iliew, F. Lederer, A. Andryieuski, R. Malureanu, and A. V. Lavrinenko, “High symmetry versus optical isotropy of a negative-index metamaterial,” Phys. Rev. B81, 195123 (2010).
[CrossRef]

C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, “Validity of effective material parameters for optical fishnet metamaterials,” Phys. Rev. B81, 035320 (2010).
[CrossRef]

C. Rockstuhl, T. Paul, F. Lederer, T. Pertsch, T. Zentgraf, T. P. Meyrath, and H. Giessen, “Transition from thin-film to bulk properties of metamaterials,” Phys. Rev. B77, 035126 (2008).
[CrossRef]

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B77, 195328 (2008).
[CrossRef]

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm.181, 687 (2010).
[CrossRef]

Schotland, J. C.

V. A. Markel and J. C. Schotland, “Homogenization of Maxwell’s equations in periodic composites,” Phys. Rev. E85, 066603 (2012).
[CrossRef]

V. A. Markel and J. C. Schotland, “On the sign of refraction in anisotropic non-magnetic media,” J. Opt.12, 015104 (2010).
[CrossRef]

Schultz, S.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65, 195104 (2002).
[CrossRef]

Shvets, G.

C. Fietz and G. Shvets, “Current-driven metamaterial homogenization,” Physica B405, 2930–2934 (2010).
[CrossRef]

Silveirinha, M.

J. D. Baena, L. Jelinek, R. Marques, and M. Silveirinha, “Unified homogenization theory for magnetoinductive and electromagnetic waves in split-ring metamaterials,” Phys. Rev. A78, 013842 (2008).
[CrossRef]

Simovski, C. R.

C. R. Simovski, “On electromagnetic characterization and homogenization of nanostructured metamaterials,” J. Opt.13, 103001 (2011).
[CrossRef]

C. R. Simovski, “Material paremeters of metamaterials (a review),” Opt. Spectrosc.107, 766–793 (2009).
[CrossRef]

P. A. Belov and C. R. Simovski, “Boundary conditions for interfaces of electromagnetic crystals and the generalized Ewald-Oseen extinction principle,” Phys. Rev. B73, 045102 (2006).
[CrossRef]

Smigaj, W.

T. Paul, C. Menzel, W. Smigaj, C. Rockstuhl, P. Lalanne, and F. Lederer, “Reflection and transmission of light at periodic layered metamaterial films,” Phys. Rev. B84, 115142 (2011).
[CrossRef]

Smith, D. R.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65, 195104 (2002).
[CrossRef]

Soukoulis, C. M.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65, 195104 (2002).
[CrossRef]

Sukhorukov, A. A.

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. B81, 035320 (2010).
[CrossRef]

Tsukerman, I.

A. Pors, I. Tsukerman, and S. I. Bozhevolnyi, “Effective constitutive parameters of plasmonic metamaterials: Homogenization by dual field interpolation,” Phys. Rev. E84, 016609 (2011).
[CrossRef]

I. Tsukerman, “Effective parameters of metamaterials: a rigorous homogenization theory via Whitney interpolation,” J. Opt. Soc. Am. B28, 577–586 (2011).
[CrossRef]

I. Tsukerman, “Nonlocal homogenization of metamaterials by dual interpolation of fields,” J. Opt. Soc. Am. B28, 2956–2965 (2011).
[CrossRef]

R. Hiptmair and I. Tsukerman, “Non-asymptotic homogenization of electromagnetic metamaterials via discrete Hodge operators with Trefftz calibration,” to appear in COMPUMAG – Proceedings of 19th International Conference on the Computation of Electromagnetic Fields (Budapest, 2013).

Wu, B. I.

X. Chen, B. I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E71, 046610 (2005).
[CrossRef]

Zentgraf, T.

C. Rockstuhl, T. Paul, F. Lederer, T. Pertsch, T. Zentgraf, T. P. Meyrath, and H. Giessen, “Transition from thin-film to bulk properties of metamaterials,” Phys. Rev. B77, 035126 (2008).
[CrossRef]

Zolla, F.

S. Guenneau and F. Zolla, “Homogenization of three-dimensional finite photonic crystals,” Prog. Electromagnetic Res.27, 91–127 (2011).
[CrossRef]

Appl. Opt. (1)

Comp. Phys. Comm. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm.181, 687 (2010).
[CrossRef]

J. Opt. (2)

C. R. Simovski, “On electromagnetic characterization and homogenization of nanostructured metamaterials,” J. Opt.13, 103001 (2011).
[CrossRef]

V. A. Markel and J. C. Schotland, “On the sign of refraction in anisotropic non-magnetic media,” J. Opt.12, 015104 (2010).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (2)

Num. Math. (1)

R. Hiptmair, “Discrete Hodge operators,” Num. Math.90, 265 (2001).
[CrossRef]

Opt. Lett. (1)

Opt. Spectrosc. (1)

C. R. Simovski, “Material paremeters of metamaterials (a review),” Opt. Spectrosc.107, 766–793 (2009).
[CrossRef]

Phys. Rev. A (1)

J. D. Baena, L. Jelinek, R. Marques, and M. Silveirinha, “Unified homogenization theory for magnetoinductive and electromagnetic waves in split-ring metamaterials,” Phys. Rev. A78, 013842 (2008).
[CrossRef]

Phys. Rev. B (7)

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B77, 195328 (2008).
[CrossRef]

C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, “Validity of effective material parameters for optical fishnet metamaterials,” Phys. Rev. B81, 035320 (2010).
[CrossRef]

C. Menzel, C. Rockstuhl, R. Iliew, F. Lederer, A. Andryieuski, R. Malureanu, and A. V. Lavrinenko, “High symmetry versus optical isotropy of a negative-index metamaterial,” Phys. Rev. B81, 195123 (2010).
[CrossRef]

T. Paul, C. Menzel, W. Smigaj, C. Rockstuhl, P. Lalanne, and F. Lederer, “Reflection and transmission of light at periodic layered metamaterial films,” Phys. Rev. B84, 115142 (2011).
[CrossRef]

C. Rockstuhl, T. Paul, F. Lederer, T. Pertsch, T. Zentgraf, T. P. Meyrath, and H. Giessen, “Transition from thin-film to bulk properties of metamaterials,” Phys. Rev. B77, 035126 (2008).
[CrossRef]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65, 195104 (2002).
[CrossRef]

P. A. Belov and C. R. Simovski, “Boundary conditions for interfaces of electromagnetic crystals and the generalized Ewald-Oseen extinction principle,” Phys. Rev. B73, 045102 (2006).
[CrossRef]

Phys. Rev. E (3)

V. A. Markel and J. C. Schotland, “Homogenization of Maxwell’s equations in periodic composites,” Phys. Rev. E85, 066603 (2012).
[CrossRef]

X. Chen, B. I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E71, 046610 (2005).
[CrossRef]

A. Pors, I. Tsukerman, and S. I. Bozhevolnyi, “Effective constitutive parameters of plasmonic metamaterials: Homogenization by dual field interpolation,” Phys. Rev. E84, 016609 (2011).
[CrossRef]

Physica B (1)

C. Fietz and G. Shvets, “Current-driven metamaterial homogenization,” Physica B405, 2930–2934 (2010).
[CrossRef]

Proc. Inst. Elec. Eng. (1)

L. Lewin, “The electrical constants of a material loaded with spherical particles,” Proc. Inst. Elec. Eng.94, 65–68 (1947).

Prog. Electromagnetic Res. (1)

S. Guenneau and F. Zolla, “Homogenization of three-dimensional finite photonic crystals,” Prog. Electromagnetic Res.27, 91–127 (2011).
[CrossRef]

Other (3)

Y. Liu, S. Guenneau, and B. Gralak, “A route to all frequency homogenization of periodic structures,” (2012). ArXiv:1210.6171v2.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, New York, 1988).

R. Hiptmair and I. Tsukerman, “Non-asymptotic homogenization of electromagnetic metamaterials via discrete Hodge operators with Trefftz calibration,” to appear in COMPUMAG – Proceedings of 19th International Conference on the Computation of Electromagnetic Fields (Budapest, 2013).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(Left Panel) The simulation schematic. A metamaterial slab with a cubic lattice of gold spheres is modeled as a stack of lattice cells, with periodic boundary conditions (PBC, for normal incidence) or Bloch conditions (for oblique incidence) imposed on its boundaries as shown. The Perfectly Matched Layers (PML) are standard in FDTD simulations.

Fig. 2
Fig. 2

(Right Panel) Color plot of the electric field for λ = 20h/3; h = 80 nm. (a) Real part of the original field; (b) real part of the Bloch waves; (c) absolute value of the surface wave.

Fig. 3
Fig. 3

Effective parameters. Solid blue line: Lewin’s theory; red triangles: cubic cell located in the center of an L = 9 slab (l = 5); green diamonds: cubic cell located in the center of an L = 5 slab (l = 3); cyan circles: cubic cell at the surface of an L = 5 slab (l = 1).

Fig. 4
Fig. 4

The absolute values (top) and the phases (bottom) of the transmission and reflection coefficients for a five-layer slab of gold spheres. Triangles: parameters from Lewin’s theory; squares: parameters from our procedure; solid lines: FDTD. See text for the geometric and physical parameters of the material.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

P S ( r ) = χ [ F S ( r ) + Ω tot G ( r , r ) P S ( r ) d 3 r ] .
E i = A i exp [ i ( k i x x + k i z z ) ] ,
F S ( r ) = 2 π i h p 0 exp ( i k p r ) exp [ i ( Q p q z ) h ] 1 k 0 2 k p k p Q p P ˜ B ( k p ) ,
k p = x ^ k i x + p + z ^ Q p , Q p = k 0 2 ( x ^ k i x + p ) 2 .
P ˜ B ( k ) = 1 h 3 P cell ( R ) exp ( i k R ) d 3 R .
A i = 2 π i h k 0 2 k i k i exp [ i ( k i z q z ) h ] 1 P ˜ B ( k i ) .
F S ( r ) = 2 π i h p 0 k 0 2 ( p + i z ^ p ) ( p + i z ^ p ) p 2 exp [ ( i p z ^ p ) r ] P ˜ B ( p + z ^ p ) .
η W E H = l . s . W D B η = W D B W E H +
γ = W D B η W E H / W D B

Metrics