Abstract

We study optical properties of optomagnetic metamaterials produced by regular arrays of double gold dots (nanopillars). Using combined data of spectroscopic ellipsometry, transmission and reflection measurements, we identify localized plasmon resonances of a nanopillar pair and measure their dependences on dot sizes. We formulate the necessary condition at which an effective field theory can be applied to describe optical properties of a composite medium and employ interferometry to measure phase shifts for our samples. A negative phase shift for transmitted green light coupled to an antisymmetric magnetic mode of a double-dot array is observed.

© 2010 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
  46. A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics 2(6), 365–370 (2008).
    [CrossRef]
  47. V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Plasmonic blackbody: almost complete absorption of light in nanostructured metallic coatings,” Phys. Rev. B 78(20), 205405 (2008).
    [CrossRef]
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    [CrossRef]
  49. V. A. Markel, “Divergence of dipole sums and the nature of non-Lorentzian exponentially narrow resonances in one-dimensional periodic arrays of nanospheres,” J. Phys. At. Mol. Opt. Phys. 38(7), L115–L121 (2005).
    [CrossRef]

2009 (2)

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quantum Electron . (2009).

A. L. Koh, K. Bao, I. Khan, W. E. Smith, G. Kothleitner, P. Nordlander, S. A. Maier, and D. W. McComb, “Electron energy-loss spectroscopy (EELS) of surface plasmons in single silver nanoparticles and dimers: influence of beam damage and mapping of dark modes,” ACS Nano 3(10), 3015–3022 (2009).
[CrossRef] [PubMed]

2008 (6)

A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics 2(6), 365–370 (2008).
[CrossRef]

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Plasmonic blackbody: almost complete absorption of light in nanostructured metallic coatings,” Phys. Rev. B 78(20), 205405 (2008).
[CrossRef]

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[CrossRef] [PubMed]

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008).
[CrossRef] [PubMed]

X. Zhang, M. Davanço, Y. Urzhumov, G. Shvets, and S. R. Forrest, “From scattering parameters to Snell’s law: a subwavelength near-infrared negative-index metamaterial,” Phys. Rev. Lett. 101(26), 267401 (2008).
[CrossRef] [PubMed]

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 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

2007 (2)

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[CrossRef] [PubMed]

A. N. Grigorenko, “Reply to comment on “Negative refractive index in artificial metamaterials”,” Opt. Lett. 32(11), 1512–1514 (2007).
[CrossRef] [PubMed]

2006 (4)

V. M. Agranovich and Yu. N. Gartstein, “Spatial dispersion and negative refraction of light,” Usp. Fiz. Nauk. 176(10), 1051–1068 (2006).
[CrossRef]

W. J. Padilla, D. R. Smith, and D. Basov, “Spectroscopy of metamaterials from infrared to optical frequencies,” J. Opt. Soc. Am. B 23(3), 404–414 (2006).
[CrossRef]

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(5775), 892–894 (2006).
[CrossRef] [PubMed]

A. N. Grigorenko, “Negative refractive index in artificial metamaterials,” Opt. Lett. 31(16), 2483–2485 (2006).
[CrossRef] [PubMed]

2005 (4)

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Near-infrared double negative metamaterials,” Opt. Express 13(13), 4922–4930 (2005).
[CrossRef] [PubMed]

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Th. Koschny, P. Markoš, E. Economou, D. Smith, D. Vier, and C. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71(24), 245105 (2005).
[CrossRef]

V. A. Markel, “Divergence of dipole sums and the nature of non-Lorentzian exponentially narrow resonances in one-dimensional periodic arrays of nanospheres,” J. Phys. At. Mol. Opt. Phys. 38(7), L115–L121 (2005).
[CrossRef]

2004 (2)

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

2003 (2)

J. Pendry, “Optics: Positively negative,” Nature 423(6935), 22–23 (2003).
[CrossRef] [PubMed]

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

2002 (3)

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, “Optomagnetic composite medium with conducting nanoelements,” Phys. Rev. B 66(15), 155411 (2002).
[CrossRef]

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, “Plasmon modes in metal nanowires,” J. Nonlinear Opt. Phys. Mater. 11(1), 65–74 (2002).
[CrossRef]

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

2001 (2)

M. C. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, “Microstructured magnetic materials for RF flux guides in magnetic resonance imaging,” Science 291(5505), 849–851 (2001).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

2000 (2)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

1998 (1)

C. M. Herzinger, D. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83(6), 3323–3336 (1998).
[CrossRef]

1982 (1)

O. S. Heavens, “Optical properties of thin films,” Rep. Prog. Phys. 23(1), 249–262 (1982).

1974 (2)

J. E. Sipe and J. Van Kranendonk, “Macroscopic electromagnetic theory of resonant dielectrics,” Phys. Rev. A 9(5), 1806–1822 (1974).
[CrossRef]

T. Yamaguchi, S. Yoshida, and A. Kinbara, “Optical effect of the substrate on the anomalous absorption of aggregated silver films,” Thin Solid Films 21(1), 173–187 (1974).
[CrossRef]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

1956 (2)

F. Abelès, “Remarques sur les proprietes des lames minces inhomogenes,” J. Phys. Radium 17(3), 190–193 (1956).
[CrossRef]

D. V. Sivukhin, “Theory of elliptical polarization of light reflected from isotropic media,” Sov. Phys. JETP 3, 269–274 (1956).

1952 (2)

H. Schopper, “Die bestimmung der optischen konstanten und der schichtdicke beliebig dicker schichten mit hilfe der absoluten phase,” Z. Phys. 131(2), 215–224 (1952).
[CrossRef]

H. Schopper, “Zur optik diinner doppelbrechender und dichroitischer schichten,” Z. Phys. 132(2), 146–170 (1952).
[CrossRef]

1951 (1)

H. Schopper, “Die untersuchung diinner absorbierender schichten mit hilfe der absoluten phase,” Z. Phys. 130(5), 565–584 (1951).
[CrossRef]

Abelès, F.

F. Abelès, “Remarques sur les proprietes des lames minces inhomogenes,” J. Phys. Radium 17(3), 190–193 (1956).
[CrossRef]

Agranovich, V. M.

V. M. Agranovich and Yu. N. Gartstein, “Spatial dispersion and negative refraction of light,” Usp. Fiz. Nauk. 176(10), 1051–1068 (2006).
[CrossRef]

Aussenegg, F. R.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

Bao, K.

A. L. Koh, K. Bao, I. Khan, W. E. Smith, G. Kothleitner, P. Nordlander, S. A. Maier, and D. W. McComb, “Electron energy-loss spectroscopy (EELS) of surface plasmons in single silver nanoparticles and dimers: influence of beam damage and mapping of dark modes,” ACS Nano 3(10), 3015–3022 (2009).
[CrossRef] [PubMed]

Bartal, G.

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 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Basov, D.

Basov, D. N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Blake, P.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[CrossRef] [PubMed]

Boardman, A. D.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[CrossRef] [PubMed]

Booth, T. J.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[CrossRef] [PubMed]

Brueck, S. R. J.

Davanço, M.

X. Zhang, M. Davanço, Y. Urzhumov, G. Shvets, and S. R. Forrest, “From scattering parameters to Snell’s law: a subwavelength near-infrared negative-index metamaterial,” Phys. Rev. Lett. 101(26), 267401 (2008).
[CrossRef] [PubMed]

Dickinson, M. R.

A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics 2(6), 365–370 (2008).
[CrossRef]

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(5775), 892–894 (2006).
[CrossRef] [PubMed]

Economou, E.

Th. Koschny, P. Markoš, E. Economou, D. Smith, D. Vier, and C. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71(24), 245105 (2005).
[CrossRef]

Enkrich, C.

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(5775), 892–894 (2006).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Fan, W.

Fang, N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Firsov, A. A.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Forrest, S. R.

X. Zhang, M. Davanço, Y. Urzhumov, G. Shvets, and S. R. Forrest, “From scattering parameters to Snell’s law: a subwavelength near-infrared negative-index metamaterial,” Phys. Rev. Lett. 101(26), 267401 (2008).
[CrossRef] [PubMed]

Gartstein, Yu. N.

V. M. Agranovich and Yu. N. Gartstein, “Spatial dispersion and negative refraction of light,” Usp. Fiz. Nauk. 176(10), 1051–1068 (2006).
[CrossRef]

Geim, A. K.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[CrossRef] [PubMed]

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Genov, D. A.

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 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Gilderdale, D. J.

M. C. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, “Microstructured magnetic materials for RF flux guides in magnetic resonance imaging,” Science 291(5505), 849–851 (2001).
[CrossRef] [PubMed]

Gleeson, H. F.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Grigorenko, A. N.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[CrossRef] [PubMed]

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Localized plasmon resonances of gold nanodots evaluated with Mie theory. (a) Main LPR modes in single and double dots (the arrows show currents in the dots, the dotted arrows show image currents in the substrate). Insets show the axes and an example of incident electromagnetic wave for the x-resonance. Dependence of LPR on the dot diameter D for (b) single dots and (c) double dots. The dot height is h = 90nm, the dot separation in the pair s = 140nm.

Fig. 2
Fig. 2

Optical transmission through the nanodot samples. (a), (c), (e) - single dots and (b), (d), (f) - double dots. Dot sizes are 90nm (black squares), 110nm (red circles) and 130nm (blue triangles). The insets show the unit cell of the arrays. Resonant features are marked by the dotted arrows.

Fig. 3
Fig. 3

Optical properties of the arrays. (a) Normal reflection from a single dot array (black squares), and a double dot array – TM light (red circles) and TE light (blue triangles). Dot sizes are D = 110nm. Insets show the unit cell of arrays. (b) Ellipsometry data for the double-dot array of (a): Ψ (green circles) and Δ (blue triangles). The solid line show the best fit to the combined ellipsometry data (including data for the sample rotated onto 90° in the plane) with teff = 35nm. The dotted line show the best fit with fixed teff = 90nm. Experimental values of LPR wavelengths for (c) single dots and (d) dot pairs ( λza – green triangles, λys – olive hexagons).

Fig. 4
Fig. 4

Interferometry of optomagnetic structures produced by double-dot arrays. (a) Schematics of the installation. Insets show typical interferograms of our samples for TM light and TE light at λ = 543nm. Phase shift as a function of the dot diameter for (b) TM light and (c) TE light. Red circles corresponds to light of λ = 650nm, green squares to λ = 543nm.

Equations (2)

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M(t)=(cos(k0ntcos(θ))ipsin(k0ntcos(θ))ipsin(k0ntcos(θ))cos(k0ntcos(θ))),
m11=m22.

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