Abstract

We present a method to experimentally measure the complex reflection and transmission coefficients of optical waves at metamaterials under normal incidence. This allows us to determine their pertinent dispersion relation without resorting to numerical simulations. For this purpose we employ a spectrometer and a white light interferometer for amplitude and phase measurements, respectively. To demonstrate the reliability of the method, it is applied to two referential metamaterial geometries, namely, the fishnet and the double-element structure. Involved aspects of the phase measurements as well as the accuracy of the method are discussed.

© 2010 Optical Society of America

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  1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Physics-Uspekhi 10, 509 (1968).
    [CrossRef]
  2. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  3. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nature Mater. 7, 31-37 (2008).
    [CrossRef]
  4. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41-48 (2007).
    [CrossRef]
  5. C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47-49 (2007).
    [CrossRef] [PubMed]
  6. C. Rockstuhl, C. Menzel, T. Paul, T. Pertsch, and F. Lederer, “Light propagation in fishnet structure metamaterials,” Phys. Rev. B 78, 155101 (2008).
    [CrossRef]
  7. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788-792 (2004).
    [CrossRef] [PubMed]
  8. C. Rockstuhl, T. Zentgraf, E. Pshenay-Severin, J. Petschulat, A. Chipouline, J. Kuhl, T. Pertsch, H. Giessen, and F. Lederer, “The origin of magnetic polarizability in metamaterials at optical frequencies--an electrodynamic approach,” Opt. Express 15, 8871-8883 (2007).
    [CrossRef] [PubMed]
  9. 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. B 77, 035126 (2008).
    [CrossRef]
  10. C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77, 195328 (2008).
    [CrossRef]
  11. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758-2767 (1997).
    [CrossRef]
  12. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
  13. C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B 79, 233107 (2009).
    [CrossRef]
  14. W. J. Padilla, D. R. Smith, and D. N. Basov, “Spectroscopy of metamaterials from infrared to optical frequencies,”J. Opt. Soc. Am. B 23, 404-414 (2006).
    [CrossRef]
  15. V. Drachev, W. Cai, U. Chettiar, H. Yuan, A. Sarychev, A. Kildishev, G. Klimeck, and V. Shalaev, “Experimental verification of an optical negative-index material,” Laser Phys. Lett. 3, 49-55 (2006).
    [CrossRef]
  16. 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] [PubMed]
  17. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312, 892-894 (2006).
    [CrossRef] [PubMed]
  18. B. Kante, S. N. Burokur, F. Gadot, and A. de Lustrac, “Fully characterization of planar infrared metamaterials from far field diffraction pattern,” in Proceedings of SPIE Conference on Metamaterials III (International Society for Optical Engineering, 2008), Vol. 6987, paper 69870.
  19. L. Lepetit, G. Chériaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12, 2467-2474 (1995).
    [CrossRef]
  20. G. Genty, S. Coen, and J. M. Dudley, “Fiber supercontinuum sources (invited),” J. Opt. Soc. Am. B 24, 1771-1785 (2007).
    [CrossRef]
  21. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800-1802 (2006).
    [CrossRef] [PubMed]
  22. E. Pshenay-Severin, U. Hübner, C. Menzel, C. Helgert, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, “Double-element metamaterial with negative index at near-infrared wavelengths,” Opt. Lett. 34,1678-1680 (2009).
    [CrossRef] [PubMed]
  23. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  24. J. M. del Pozo and L. Díaz, “Method for the determination of optical constants of thin films: dependence on experimental uncertainties,” Appl. Opt. 31, 4474-4481 (1992).
    [CrossRef] [PubMed]
  25. A. V. Kildishev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and V. M. Shalaev, “Negative refractive index in optics of metal-dielectric composites,” J. Opt. Soc. Am. B 23, 423-433 (2006).
    [CrossRef]

2009 (2)

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B 79, 233107 (2009).
[CrossRef]

E. Pshenay-Severin, U. Hübner, C. Menzel, C. Helgert, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, “Double-element metamaterial with negative index at near-infrared wavelengths,” Opt. Lett. 34,1678-1680 (2009).
[CrossRef] [PubMed]

2008 (4)

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nature Mater. 7, 31-37 (2008).
[CrossRef]

C. Rockstuhl, C. Menzel, T. Paul, T. Pertsch, and F. Lederer, “Light propagation in fishnet structure metamaterials,” Phys. Rev. B 78, 155101 (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. B 77, 035126 (2008).
[CrossRef]

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77, 195328 (2008).
[CrossRef]

2007 (4)

2006 (5)

2005 (1)

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] [PubMed]

2004 (1)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788-792 (2004).
[CrossRef] [PubMed]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1997 (1)

1995 (1)

1992 (1)

1972 (1)

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

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Physics-Uspekhi 10, 509 (1968).
[CrossRef]

Basov, D. N.

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] [PubMed]

Burokur, S. N.

B. Kante, S. N. Burokur, F. Gadot, and A. de Lustrac, “Fully characterization of planar infrared metamaterials from far field diffraction pattern,” in Proceedings of SPIE Conference on Metamaterials III (International Society for Optical Engineering, 2008), Vol. 6987, paper 69870.

Cai, W.

V. Drachev, W. Cai, U. Chettiar, H. Yuan, A. Sarychev, A. Kildishev, G. Klimeck, and V. Shalaev, “Experimental verification of an optical negative-index material,” Laser Phys. Lett. 3, 49-55 (2006).
[CrossRef]

A. V. Kildishev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and V. M. Shalaev, “Negative refractive index in optics of metal-dielectric composites,” J. Opt. Soc. Am. B 23, 423-433 (2006).
[CrossRef]

Chériaux, G.

Chettiar, U.

V. Drachev, W. Cai, U. Chettiar, H. Yuan, A. Sarychev, A. Kildishev, G. Klimeck, and V. Shalaev, “Experimental verification of an optical negative-index material,” Laser Phys. Lett. 3, 49-55 (2006).
[CrossRef]

Chettiar, U. K.

Chipouline, A.

Christy, R. W.

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

Coen, S.

de Lustrac, A.

B. Kante, S. N. Burokur, F. Gadot, and A. de Lustrac, “Fully characterization of planar infrared metamaterials from far field diffraction pattern,” in Proceedings of SPIE Conference on Metamaterials III (International Society for Optical Engineering, 2008), Vol. 6987, paper 69870.

del Pozo, J. M.

Díaz, L.

Dolling, G.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312, 892-894 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800-1802 (2006).
[CrossRef] [PubMed]

Drachev, V.

V. Drachev, W. Cai, U. Chettiar, H. Yuan, A. Sarychev, A. Kildishev, G. Klimeck, and V. Shalaev, “Experimental verification of an optical negative-index material,” Laser Phys. Lett. 3, 49-55 (2006).
[CrossRef]

Drachev, V. P.

Dudley, J. M.

Enkrich, C.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800-1802 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Etrich, C.

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B 79, 233107 (2009).
[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] [PubMed]

Fu, L.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nature Mater. 7, 31-37 (2008).
[CrossRef]

Gadot, F.

B. Kante, S. N. Burokur, F. Gadot, and A. de Lustrac, “Fully characterization of planar infrared metamaterials from far field diffraction pattern,” in Proceedings of SPIE Conference on Metamaterials III (International Society for Optical Engineering, 2008), Vol. 6987, paper 69870.

Genty, G.

Giessen, H.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nature Mater. 7, 31-37 (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. B 77, 035126 (2008).
[CrossRef]

C. Rockstuhl, T. Zentgraf, E. Pshenay-Severin, J. Petschulat, A. Chipouline, J. Kuhl, T. Pertsch, H. Giessen, and F. Lederer, “The origin of magnetic polarizability in metamaterials at optical frequencies--an electrodynamic approach,” Opt. Express 15, 8871-8883 (2007).
[CrossRef] [PubMed]

Guo, H.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nature Mater. 7, 31-37 (2008).
[CrossRef]

Hagness, S.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Helgert, C.

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B 79, 233107 (2009).
[CrossRef]

E. Pshenay-Severin, U. Hübner, C. Menzel, C. Helgert, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, “Double-element metamaterial with negative index at near-infrared wavelengths,” Opt. Lett. 34,1678-1680 (2009).
[CrossRef] [PubMed]

Hübner, U.

Joffre, M.

Johnson, P. B.

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

Kaiser, S.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nature Mater. 7, 31-37 (2008).
[CrossRef]

Kante, B.

B. Kante, S. N. Burokur, F. Gadot, and A. de Lustrac, “Fully characterization of planar infrared metamaterials from far field diffraction pattern,” in Proceedings of SPIE Conference on Metamaterials III (International Society for Optical Engineering, 2008), Vol. 6987, paper 69870.

Kildishev, A.

V. Drachev, W. Cai, U. Chettiar, H. Yuan, A. Sarychev, A. Kildishev, G. Klimeck, and V. Shalaev, “Experimental verification of an optical negative-index material,” Laser Phys. Lett. 3, 49-55 (2006).
[CrossRef]

Kildishev, A. V.

Kley, E.-B.

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B 79, 233107 (2009).
[CrossRef]

Klimeck, G.

V. Drachev, W. Cai, U. Chettiar, H. Yuan, A. Sarychev, A. Kildishev, G. Klimeck, and V. Shalaev, “Experimental verification of an optical negative-index material,” Laser Phys. Lett. 3, 49-55 (2006).
[CrossRef]

Kuhl, J.

Lederer, F.

E. Pshenay-Severin, U. Hübner, C. Menzel, C. Helgert, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, “Double-element metamaterial with negative index at near-infrared wavelengths,” Opt. Lett. 34,1678-1680 (2009).
[CrossRef] [PubMed]

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B 79, 233107 (2009).
[CrossRef]

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77, 195328 (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. B 77, 035126 (2008).
[CrossRef]

C. Rockstuhl, C. Menzel, T. Paul, T. Pertsch, and F. Lederer, “Light propagation in fishnet structure metamaterials,” Phys. Rev. B 78, 155101 (2008).
[CrossRef]

C. Rockstuhl, T. Zentgraf, E. Pshenay-Severin, J. Petschulat, A. Chipouline, J. Kuhl, T. Pertsch, H. Giessen, and F. Lederer, “The origin of magnetic polarizability in metamaterials at optical frequencies--an electrodynamic approach,” Opt. Express 15, 8871-8883 (2007).
[CrossRef] [PubMed]

Lepetit, L.

Li, L.

Linden, S.

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47-49 (2007).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312, 892-894 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800-1802 (2006).
[CrossRef] [PubMed]

Liu, N.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nature Mater. 7, 31-37 (2008).
[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] [PubMed]

Menzel, C.

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B 79, 233107 (2009).
[CrossRef]

E. Pshenay-Severin, U. Hübner, C. Menzel, C. Helgert, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, “Double-element metamaterial with negative index at near-infrared wavelengths,” Opt. Lett. 34,1678-1680 (2009).
[CrossRef] [PubMed]

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77, 195328 (2008).
[CrossRef]

C. Rockstuhl, C. Menzel, T. Paul, T. Pertsch, and F. Lederer, “Light propagation in fishnet structure metamaterials,” Phys. Rev. B 78, 155101 (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. B 77, 035126 (2008).
[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] [PubMed]

Padilla, W. J.

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] [PubMed]

Paul, T.

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77, 195328 (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. B 77, 035126 (2008).
[CrossRef]

C. Rockstuhl, C. Menzel, T. Paul, T. Pertsch, and F. Lederer, “Light propagation in fishnet structure metamaterials,” Phys. Rev. B 78, 155101 (2008).
[CrossRef]

Pendry, J. B.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788-792 (2004).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Pertsch, T.

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B 79, 233107 (2009).
[CrossRef]

E. Pshenay-Severin, U. Hübner, C. Menzel, C. Helgert, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, “Double-element metamaterial with negative index at near-infrared wavelengths,” Opt. Lett. 34,1678-1680 (2009).
[CrossRef] [PubMed]

C. Rockstuhl, C. Menzel, T. Paul, T. Pertsch, and F. Lederer, “Light propagation in fishnet structure metamaterials,” Phys. Rev. B 78, 155101 (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. B 77, 035126 (2008).
[CrossRef]

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77, 195328 (2008).
[CrossRef]

C. Rockstuhl, T. Zentgraf, E. Pshenay-Severin, J. Petschulat, A. Chipouline, J. Kuhl, T. Pertsch, H. Giessen, and F. Lederer, “The origin of magnetic polarizability in metamaterials at optical frequencies--an electrodynamic approach,” Opt. Express 15, 8871-8883 (2007).
[CrossRef] [PubMed]

Petschulat, J.

Pshenay-Severin, E.

Rockstuhl, C.

E. Pshenay-Severin, U. Hübner, C. Menzel, C. Helgert, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, “Double-element metamaterial with negative index at near-infrared wavelengths,” Opt. Lett. 34,1678-1680 (2009).
[CrossRef] [PubMed]

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B 79, 233107 (2009).
[CrossRef]

C. Rockstuhl, C. Menzel, T. Paul, T. Pertsch, and F. Lederer, “Light propagation in fishnet structure metamaterials,” Phys. Rev. B 78, 155101 (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. B 77, 035126 (2008).
[CrossRef]

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77, 195328 (2008).
[CrossRef]

C. Rockstuhl, T. Zentgraf, E. Pshenay-Severin, J. Petschulat, A. Chipouline, J. Kuhl, T. Pertsch, H. Giessen, and F. Lederer, “The origin of magnetic polarizability in metamaterials at optical frequencies--an electrodynamic approach,” Opt. Express 15, 8871-8883 (2007).
[CrossRef] [PubMed]

Sarychev, A.

V. Drachev, W. Cai, U. Chettiar, H. Yuan, A. Sarychev, A. Kildishev, G. Klimeck, and V. Shalaev, “Experimental verification of an optical negative-index material,” Laser Phys. Lett. 3, 49-55 (2006).
[CrossRef]

Sarychev, A. K.

Schweizer, H.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nature Mater. 7, 31-37 (2008).
[CrossRef]

Shalaev, V.

V. Drachev, W. Cai, U. Chettiar, H. Yuan, A. Sarychev, A. Kildishev, G. Klimeck, and V. Shalaev, “Experimental verification of an optical negative-index material,” Laser Phys. Lett. 3, 49-55 (2006).
[CrossRef]

Shalaev, V. M.

Smith, D. R.

W. J. Padilla, D. R. Smith, and D. N. Basov, “Spectroscopy of metamaterials from infrared to optical frequencies,”J. Opt. Soc. Am. B 23, 404-414 (2006).
[CrossRef]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788-792 (2004).
[CrossRef] [PubMed]

Soukoulis, C. M.

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47-49 (2007).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312, 892-894 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800-1802 (2006).
[CrossRef] [PubMed]

Taflove, A.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Tünnermann, A.

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B 79, 233107 (2009).
[CrossRef]

E. Pshenay-Severin, U. Hübner, C. Menzel, C. Helgert, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, “Double-element metamaterial with negative index at near-infrared wavelengths,” Opt. Lett. 34,1678-1680 (2009).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Physics-Uspekhi 10, 509 (1968).
[CrossRef]

Wegener, M.

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47-49 (2007).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312, 892-894 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800-1802 (2006).
[CrossRef] [PubMed]

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788-792 (2004).
[CrossRef] [PubMed]

Yuan, H.

V. Drachev, W. Cai, U. Chettiar, H. Yuan, A. Sarychev, A. Kildishev, G. Klimeck, and V. Shalaev, “Experimental verification of an optical negative-index material,” Laser Phys. Lett. 3, 49-55 (2006).
[CrossRef]

Yuan, H.-K.

Zentgraf, T.

Zhang, S.

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] [PubMed]

Appl. Opt. (1)

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

J. Opt. Soc. Am. B (4)

Laser Phys. Lett. (1)

V. Drachev, W. Cai, U. Chettiar, H. Yuan, A. Sarychev, A. Kildishev, G. Klimeck, and V. Shalaev, “Experimental verification of an optical negative-index material,” Laser Phys. Lett. 3, 49-55 (2006).
[CrossRef]

Nat. Photonics (1)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41-48 (2007).
[CrossRef]

Nature Mater. (1)

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nature Mater. 7, 31-37 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (5)

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

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B 79, 233107 (2009).
[CrossRef]

C. Rockstuhl, C. Menzel, T. Paul, T. Pertsch, and F. Lederer, “Light propagation in fishnet structure metamaterials,” Phys. Rev. B 78, 155101 (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. B 77, 035126 (2008).
[CrossRef]

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77, 195328 (2008).
[CrossRef]

Phys. Rev. Lett. (2)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

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] [PubMed]

Physics-Uspekhi (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Physics-Uspekhi 10, 509 (1968).
[CrossRef]

Science (3)

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47-49 (2007).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788-792 (2004).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Other (2)

B. Kante, S. N. Burokur, F. Gadot, and A. de Lustrac, “Fully characterization of planar infrared metamaterials from far field diffraction pattern,” in Proceedings of SPIE Conference on Metamaterials III (International Society for Optical Engineering, 2008), Vol. 6987, paper 69870.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

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Figures (7)

Fig. 1
Fig. 1

(a) Measured interference pattern in the wavelength domain. (b) The signal as shown in (a) in the time domain after Fourier transformation; rectangle depicts the filter.

Fig. 2
Fig. 2

Interferometric setup. P1,P2, P3, polarizers; B1,B2,B3, beam displacers; L1,L2, half-wave plates; D, delay element. The insert shows the configuration of the experimental chip.

Fig. 3
Fig. 3

Investigated structures. (a) SEM image of the fishnet structure. (b) SEM image of the double-element structure.

Fig. 4
Fig. 4

Results for the fishnet structure. Solid curves correspond to measured data. Dotted curves correspond to simulated data. (a) Black curves (blue online) are transmittances; gray curves (red online) are reflectances. (b) Absorption. (c) Phase of the transmitted amplitude: solid curve is the normalized measured phase, dotted curve is the simulated data, crossed curve is the phase from the amplitude measurements. (d) Phase of the reflected amplitude: solid curve is the normalized measured phase, dotted is the simulated data, crossed line is the phase from the amplitude measurements.

Fig. 5
Fig. 5

Results for the double-element structure. Solid curves correspond to measured data. Dotted curves correspond to simulated data. (a) Black (blue online) curves are transmittances; gray (red online) curves are reflectances. (b) Absorption. (c) Phase of the transmitted amplitude: solid curve is the normalized measured phase, dotted curve is the simulated data, crossed curve is the phase from the amplitude measurements. (d) Phase of the reflected amplitude: solid curve is the normalized measured phase, dotted curve is the simulated data, crossed curve is the phase from the amplitude measurements.

Fig. 6
Fig. 6

Effective refractive index of (a) the fishnet structure and (b) the double-element structure. Real parts n are represented with dark curves, imaginary parts n are shown with gray (red) curves. Solid curves correspond to measured data; dashed curves correspond to simulated data.

Fig. 7
Fig. 7

Partial derivatives of n with respect to (a) | t | , (b) | r | , (c) arg t , and (d) arg r . Real part n is represented by black (blue online) curves, imaginary part n is shown by gray (red online) curves.

Tables (2)

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Table 1 Root Mean Square Errors

Tables Icon

Table 2 Partial Derivatives for the Fishnet Structure

Equations (14)

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k = k 0 n eff = 1 d [ arccos ( k s ( 1 r 2 ) + k c t 2 t ( k s ( 1 r ) + k c ( 1 + r ) ) + 2 m π ) ] .
T ref ( ω ) = A ref ( ω ) exp [ i φ ref ( ω ) ]
T sam ( ω ) = A sam ( ω ) exp [ i φ sam ( ω ) ] .
E ref ( ω ) = A ref ( ω ) exp [ i φ ref ( ω ) ] E in ( ω ) ,
E sam ( ω ) = A sam ( ω ) exp [ i ( φ sam ( ω ) + φ MM ( ω ) + ω τ ) ] E in ( ω ) .
I ( ω ) = | E sam ( ω ) + E ref ( ω ) | 2 = | E sam ( ω ) | 2 + | E ref ( ω ) | 2 + 2 | E sam ( ω ) | | E ref ( ω ) | cos ( φ sam ( ω ) + φ MM ( ω ) + ω τ φ ref ( ω ) ) .
S ( t ) = F T [ I ( ω ) ] = E sam ( t ) E sam * ( t ) + E ref ( t ) E ref * ( t ) + E sam ( t + τ ) E ref * ( t ) + E sam * ( τ t ) E ref ( t ) .
rect ( t , τ , δ τ ) = { 0 , t < τ δ τ 1 , τ δ τ t τ + δ τ 0 , t τ + δ τ } .
E int ( ω ) = F T 1 [ rect ( t , τ , δ τ ) S ( t ) ] .
Δ φ = φ sam ( ω ) + φ MM ( ω ) φ ref ( ω )
Δ φ ref . sam . = φ sam ( ω ) + φ ref . sam . ( ω ) φ ref ( ω ) .
φ MM ( ω ) = Δ φ Δ φ ref . sam . + φ ref . sam . ( ω ) .
σ = i = 1 n ( f ( x ) x i σ x i ) 2 ,
σ x = i = 1 n ( x ¯ x i ) 2 n ,

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