Abstract

We develop an electrostatic theory for designing bulk composites with effective lossless negative permittivities. The theory and associated design procedure are validated by comparing their predictions with those of rigorous full-wave simulations. It is demonstrated that the excitation of the Fröhlich mode (the first-order surface mode) of the constitutive nanoparticles plays a key role in achieving negative permittivities with compensated losses.

© 2010 Optical Society of America

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2010 (2)

Z. Y. Li and Y. Xia, Nano Lett. 10, 243 (2010).
[CrossRef]

M. I. Stockman, J. Opt. 12, 024004 (2010).
[CrossRef]

2009 (6)

J. M. McMahon, S. K. Gray, and G. C. Schatz, Phys. Rev. Lett. 103, 097403 (2009).
[CrossRef] [PubMed]

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef] [PubMed]

A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, Phys. Rev. B 79, 241104(R) (2009).
[CrossRef]

E. Ponizovskaya, L. Thylén, A. Bratkovsky, and Y. Fu, Appl. Phys. A 95, 1029 (2009).
[CrossRef]

C. R. Simovski, Opt. Spektrosk. 107, 726 (2009).
[CrossRef]

2008 (5)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

D.-H. Kwon and D. H. Werner, New J. Phys. 10, 115023 (2008).
[CrossRef]

Y. Fu, L. Thylén and H. Ågren, Nano Lett. 8, 1551 (2008).
[CrossRef] [PubMed]

A. Bratkovsky, E. Ponizovskaya, S. Y. Wang, P. Holmström, L. Thylén, Y. Fu, and H. Ågren, Appl. Phys. Lett. 93, 193106 (2008).
[CrossRef]

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, Nat. Photonics 2, 351 (2008).
[CrossRef]

2007 (1)

2006 (5)

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, Opt. Lett. 31, 3022 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, Phys. Rev. B 73, 045105 (2006).
[CrossRef]

2005 (2)

A. Vial, A. S. Grimault, D. Macías, D. Barchiesi, and M. L. de la Chapelle, Phys. Rev. B 71, 085416 (2005).
[CrossRef]

V. Yannopapas and A. Moroz, J. Phys.: Condens. Matter 17, 3717 (2005).
[CrossRef]

2004 (1)

N. M. Lawandya, Appl. Phys. Lett. 85, 5040 (2004).
[CrossRef]

2003 (1)

D. J. Bergman and M. I. Stockman, Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

2002 (1)

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

2000 (2)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

1951 (1)

A. L. Aden and M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

Adegoke, J.

Aden, A. L.

A. L. Aden and M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

Ågren, H.

A. Bratkovsky, E. Ponizovskaya, S. Y. Wang, P. Holmström, L. Thylén, Y. Fu, and H. Ågren, Appl. Phys. Lett. 93, 193106 (2008).
[CrossRef]

Y. Fu, L. Thylén and H. Ågren, Nano Lett. 8, 1551 (2008).
[CrossRef] [PubMed]

Aitchison, J. S.

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, Phys. Rev. B 73, 045105 (2006).
[CrossRef]

Bahoura, M.

Bakker, R.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

Barchiesi, D.

A. Vial, A. S. Grimault, D. Macías, D. Barchiesi, and M. L. de la Chapelle, Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Bartal, G.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef] [PubMed]

Belgrave, A. M.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

Bergman, D. J.

D. J. Bergman and M. I. Stockman, Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

Bratkovsky, A.

E. Ponizovskaya, L. Thylén, A. Bratkovsky, and Y. Fu, Appl. Phys. A 95, 1029 (2009).
[CrossRef]

A. Bratkovsky, E. Ponizovskaya, S. Y. Wang, P. Holmström, L. Thylén, Y. Fu, and H. Ågren, Appl. Phys. Lett. 93, 193106 (2008).
[CrossRef]

Cummer, S. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

Dai, L.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef] [PubMed]

de la Chapelle, M. L.

A. Vial, A. S. Grimault, D. Macías, D. Barchiesi, and M. L. de la Chapelle, Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Drachev, V. P.

Fang, A.

A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, Phys. Rev. B 79, 241104(R) (2009).
[CrossRef]

Fedotov, V. A.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, Nat. Photonics 2, 351 (2008).
[CrossRef]

Fröhlich, H.

H. Fröhlich, Theory of Dielectrics (Oxford Univ. Press, 1949).

Fu, Y.

E. Ponizovskaya, L. Thylén, A. Bratkovsky, and Y. Fu, Appl. Phys. A 95, 1029 (2009).
[CrossRef]

Y. Fu, L. Thylén and H. Ågren, Nano Lett. 8, 1551 (2008).
[CrossRef] [PubMed]

A. Bratkovsky, E. Ponizovskaya, S. Y. Wang, P. Holmström, L. Thylén, Y. Fu, and H. Ågren, Appl. Phys. Lett. 93, 193106 (2008).
[CrossRef]

Gladden, C.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef] [PubMed]

Gordon, J. A.

Gray, S. K.

J. M. McMahon, S. K. Gray, and G. C. Schatz, Phys. Rev. Lett. 103, 097403 (2009).
[CrossRef] [PubMed]

Grimault, A. S.

A. Vial, A. S. Grimault, D. Macías, D. Barchiesi, and M. L. de la Chapelle, Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Herz, E.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

Holmström, P.

A. Bratkovsky, E. Ponizovskaya, S. Y. Wang, P. Holmström, L. Thylén, Y. Fu, and H. Ågren, Appl. Phys. Lett. 93, 193106 (2008).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 2001).

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

Kerker, M.

A. L. Aden and M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

Koschny, Th.

A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, Phys. Rev. B 79, 241104(R) (2009).
[CrossRef]

Kwon, D.-H.

D.-H. Kwon and D. H. Werner, New J. Phys. 10, 115023 (2008).
[CrossRef]

Lawandya, N. M.

N. M. Lawandya, Appl. Phys. Lett. 85, 5040 (2004).
[CrossRef]

Leonhardt, U.

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

Li, Z. Y.

Z. Y. Li and Y. Xia, Nano Lett. 10, 243 (2010).
[CrossRef]

Ma, R. M.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef] [PubMed]

Macías, D.

A. Vial, A. S. Grimault, D. Macías, D. Barchiesi, and M. L. de la Chapelle, Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Markoš, P.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Marqués, R.

R. Marqués, F. Martín, and M. Sorolla, Metamaterials with Negative Parameters (Wiley, 2008).

Martín, F.

R. Marqués, F. Martín, and M. Sorolla, Metamaterials with Negative Parameters (Wiley, 2008).

McMahon, J. M.

J. M. McMahon, S. K. Gray, and G. C. Schatz, Phys. Rev. Lett. 103, 097403 (2009).
[CrossRef] [PubMed]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

Mojahedi, M.

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, Phys. Rev. B 73, 045105 (2006).
[CrossRef]

Moroz, A.

V. Yannopapas and A. Moroz, J. Phys.: Condens. Matter 17, 3717 (2005).
[CrossRef]

Narimanov, E. E.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

Noginov, M. A.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, Opt. Lett. 31, 3022 (2006).
[CrossRef] [PubMed]

Oulton, R. F.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef] [PubMed]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

Papasimakis, N.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, Nat. Photonics 2, 351 (2008).
[CrossRef]

Pendry, J. B.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Ponizovskaya, E.

E. Ponizovskaya, L. Thylén, A. Bratkovsky, and Y. Fu, Appl. Phys. A 95, 1029 (2009).
[CrossRef]

A. Bratkovsky, E. Ponizovskaya, S. Y. Wang, P. Holmström, L. Thylén, Y. Fu, and H. Ågren, Appl. Phys. Lett. 93, 193106 (2008).
[CrossRef]

Prosvirnin, S. L.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, Nat. Photonics 2, 351 (2008).
[CrossRef]

Rahm, M.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

Ritzo, B. A.

Roberts, D. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

Schatz, G. C.

J. M. McMahon, S. K. Gray, and G. C. Schatz, Phys. Rev. Lett. 103, 097403 (2009).
[CrossRef] [PubMed]

Schultz, S.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

Schurig, D.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, Opt. Lett. 31, 3022 (2006).
[CrossRef] [PubMed]

Shamonina, E.

L. Solymar and E. Shamonina, Waves in Metamaterials (Oxford Univ. Press, 2009).

Simovski, C. R.

C. R. Simovski, Opt. Spektrosk. 107, 726 (2009).
[CrossRef]

Small, C. E.

Smith, D. R.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

Solymar, L.

L. Solymar and E. Shamonina, Waves in Metamaterials (Oxford Univ. Press, 2009).

Sorger, V. J.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef] [PubMed]

Sorolla, M.

R. Marqués, F. Martín, and M. Sorolla, Metamaterials with Negative Parameters (Wiley, 2008).

Soukoulis, C. M.

A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, Phys. Rev. B 79, 241104(R) (2009).
[CrossRef]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

Stockman, M. I.

M. I. Stockman, J. Opt. 12, 024004 (2010).
[CrossRef]

D. J. Bergman and M. I. Stockman, Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

Stout, S.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, Nature 460, 1110 (2009).
[CrossRef] [PubMed]

Suteewong, T.

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Figures (2)

Fig. 1
Fig. 1

Spherical semiconductor quantum dots coated with a silver film. (a) Effective permittivity ϵ c of the individual particle and (b) effective permittivity ϵ b of the bulk composite. The dotted curves are obtained by full-wave simulations (see text). (c) First-order surface mode of the individual particle. The field magnitude is color coded. The blue color (darkest in print) corresponds to the minimum, while the red color (medium gray in print) represents the maximum. The polarization of the incident light is along the horizontal direction.

Fig. 2
Fig. 2

Same as Fig. 1, except that the example is a gold-coated gain medium whose refractive index is 1.33 0.1437 i .

Equations (8)

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α = 4 π r 2 3 ( ϵ 2 ϵ m ) ( ϵ 1 + 2 ϵ 2 ) + ρ ( ϵ 1 ϵ 2 ) ( ϵ m + 2 ϵ 2 ) ( ϵ 2 + 2 ϵ m ) ( ϵ 1 + 2 ϵ 2 ) + 2 ρ ( ϵ 2 ϵ m ) ( ϵ 1 ϵ 2 ) ,
α = 4 π r 3 ϵ ϵ m ϵ + 2 ϵ m ,
ϵ c = ϵ 2 ϵ 1 ( 1 + 2 ρ ) + 2 ϵ 2 ( 1 ρ ) ϵ 1 ( 1 ρ ) + ϵ 2 ( 2 + ρ ) ,
ϵ b = ϵ m 4 π r 2 3 + 2 f α 4 π r 2 3 f α ,
ϵ b = ϵ m ϵ c ( 1 + 2 f ) + 2 ϵ m ( 1 f ) ϵ c ( 1 f ) + ϵ m ( 2 + f ) .
Im ( ϵ c ) = 0 ,
ϵ m 2 + f f 1 < Re ( ϵ c ) < ϵ m 2 f 2 1 + 2 f .
ϵ β ω 0 ω i γ ,

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