Abstract

We theoretically examine plasmonic resonance between two close metallic grains separated by a gap of width much less than the length of the incident electromagnetic wave. Resonance conditions are established and the electric field enhancement is found. Our general arguments are confirmed by analytic solution of the problem for simplest geometries. We discuss an extension of our results to more complex cases.

© 2010 Optical Society of America

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References

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2008

Z. Liu, A. Boltasseva, R. Pedersen, R. M. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, Metamaterials 2, 45 (2008).
[CrossRef]

V. P. Drachev, U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, and V. M. Shalaev, Opt. Express 16, 1186 (2008).
[CrossRef] [PubMed]

2007

P. K. Jain, W. Huang, and M. A. El-Sayed, Nano Lett. 7, 2080 (2007).
[CrossRef]

2006

D. A. Genov, K. Seal, A. K. Sarychev, H. Noh, V. M. Shalaev, Z. C. Ying, X. Zhang, and H. Cao, Appl. Phys. B 84, 205 (2006).
[CrossRef]

2003

K.-H. Su, Q.-H. Wei, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, Nano Lett. 3, 1087 (2003).
[CrossRef]

1977

A. D. Boardman and B. V. Paranjape, J. Phys. F: Met. Phys. 7, 1935 (1977).
[CrossRef]

1976

A. Goyette and A. Navon, Phys. Rev. B 13, 4320 (1976).
[CrossRef]

1974

Bakker, R. M.

Z. Liu, A. Boltasseva, R. Pedersen, R. M. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, Metamaterials 2, 45 (2008).
[CrossRef]

Boardman, A. D.

A. D. Boardman and B. V. Paranjape, J. Phys. F: Met. Phys. 7, 1935 (1977).
[CrossRef]

Boltasseva, A.

Z. Liu, A. Boltasseva, R. Pedersen, R. M. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, Metamaterials 2, 45 (2008).
[CrossRef]

Cai, W.

Cao, H.

D. A. Genov, K. Seal, A. K. Sarychev, H. Noh, V. M. Shalaev, Z. C. Ying, X. Zhang, and H. Cao, Appl. Phys. B 84, 205 (2006).
[CrossRef]

Chettiar, U. K.

Drachev, V. P.

V. P. Drachev, U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, and V. M. Shalaev, Opt. Express 16, 1186 (2008).
[CrossRef] [PubMed]

Z. Liu, A. Boltasseva, R. Pedersen, R. M. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, Metamaterials 2, 45 (2008).
[CrossRef]

El-Sayed, M. A.

P. K. Jain, W. Huang, and M. A. El-Sayed, Nano Lett. 7, 2080 (2007).
[CrossRef]

Genov, D. A.

D. A. Genov, K. Seal, A. K. Sarychev, H. Noh, V. M. Shalaev, Z. C. Ying, X. Zhang, and H. Cao, Appl. Phys. B 84, 205 (2006).
[CrossRef]

Goyette, A.

A. Goyette and A. Navon, Phys. Rev. B 13, 4320 (1976).
[CrossRef]

Huang, W.

P. K. Jain, W. Huang, and M. A. El-Sayed, Nano Lett. 7, 2080 (2007).
[CrossRef]

Jain, P. K.

P. K. Jain, W. Huang, and M. A. El-Sayed, Nano Lett. 7, 2080 (2007).
[CrossRef]

Kaminow, I. P.

Kildishev, A. V.

V. P. Drachev, U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, and V. M. Shalaev, Opt. Express 16, 1186 (2008).
[CrossRef] [PubMed]

Z. Liu, A. Boltasseva, R. Pedersen, R. M. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, Metamaterials 2, 45 (2008).
[CrossRef]

Liu, Z.

Z. Liu, A. Boltasseva, R. Pedersen, R. M. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, Metamaterials 2, 45 (2008).
[CrossRef]

Mammel, W. L.

Mock, J. J.

K.-H. Su, Q.-H. Wei, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, Nano Lett. 3, 1087 (2003).
[CrossRef]

Navon, A.

A. Goyette and A. Navon, Phys. Rev. B 13, 4320 (1976).
[CrossRef]

Noh, H.

D. A. Genov, K. Seal, A. K. Sarychev, H. Noh, V. M. Shalaev, Z. C. Ying, X. Zhang, and H. Cao, Appl. Phys. B 84, 205 (2006).
[CrossRef]

Paranjape, B. V.

A. D. Boardman and B. V. Paranjape, J. Phys. F: Met. Phys. 7, 1935 (1977).
[CrossRef]

Pedersen, R.

Z. Liu, A. Boltasseva, R. Pedersen, R. M. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, Metamaterials 2, 45 (2008).
[CrossRef]

Sarychev, A. K.

D. A. Genov, K. Seal, A. K. Sarychev, H. Noh, V. M. Shalaev, Z. C. Ying, X. Zhang, and H. Cao, Appl. Phys. B 84, 205 (2006).
[CrossRef]

A. K. Sarychev and V. M. Shalaev, Electrodynamics of Metamaterials (World Scientific, 2007).
[CrossRef]

Schultz, S.

K.-H. Su, Q.-H. Wei, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, Nano Lett. 3, 1087 (2003).
[CrossRef]

Seal, K.

D. A. Genov, K. Seal, A. K. Sarychev, H. Noh, V. M. Shalaev, Z. C. Ying, X. Zhang, and H. Cao, Appl. Phys. B 84, 205 (2006).
[CrossRef]

Shalaev, V. M.

V. P. Drachev, U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, and V. M. Shalaev, Opt. Express 16, 1186 (2008).
[CrossRef] [PubMed]

Z. Liu, A. Boltasseva, R. Pedersen, R. M. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, Metamaterials 2, 45 (2008).
[CrossRef]

D. A. Genov, K. Seal, A. K. Sarychev, H. Noh, V. M. Shalaev, Z. C. Ying, X. Zhang, and H. Cao, Appl. Phys. B 84, 205 (2006).
[CrossRef]

A. K. Sarychev and V. M. Shalaev, Electrodynamics of Metamaterials (World Scientific, 2007).
[CrossRef]

V. M. Shalaev, Nonlinear Optics of Random Media, Fractal Composites and Metal-Dielectric Films, Vol. 158 of Springer Tracts in Modern Physics (Springer, 2000).

Smith, D. R.

K.-H. Su, Q.-H. Wei, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, Nano Lett. 3, 1087 (2003).
[CrossRef]

Su, K. -H.

K.-H. Su, Q.-H. Wei, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, Nano Lett. 3, 1087 (2003).
[CrossRef]

Weber, H. P.

Wei, Q. -H.

K.-H. Su, Q.-H. Wei, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, Nano Lett. 3, 1087 (2003).
[CrossRef]

Ying, Z. C.

D. A. Genov, K. Seal, A. K. Sarychev, H. Noh, V. M. Shalaev, Z. C. Ying, X. Zhang, and H. Cao, Appl. Phys. B 84, 205 (2006).
[CrossRef]

Yuan, H. -K.

Zhang, X.

D. A. Genov, K. Seal, A. K. Sarychev, H. Noh, V. M. Shalaev, Z. C. Ying, X. Zhang, and H. Cao, Appl. Phys. B 84, 205 (2006).
[CrossRef]

K.-H. Su, Q.-H. Wei, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, Nano Lett. 3, 1087 (2003).
[CrossRef]

Appl. Opt.

Appl. Phys. B

D. A. Genov, K. Seal, A. K. Sarychev, H. Noh, V. M. Shalaev, Z. C. Ying, X. Zhang, and H. Cao, Appl. Phys. B 84, 205 (2006).
[CrossRef]

J. Phys. F: Met. Phys.

A. D. Boardman and B. V. Paranjape, J. Phys. F: Met. Phys. 7, 1935 (1977).
[CrossRef]

Metamaterials

Z. Liu, A. Boltasseva, R. Pedersen, R. M. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, Metamaterials 2, 45 (2008).
[CrossRef]

Nano Lett.

K.-H. Su, Q.-H. Wei, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, Nano Lett. 3, 1087 (2003).
[CrossRef]

P. K. Jain, W. Huang, and M. A. El-Sayed, Nano Lett. 7, 2080 (2007).
[CrossRef]

Opt. Express

Phys. Rev. B

A. Goyette and A. Navon, Phys. Rev. B 13, 4320 (1976).
[CrossRef]

Other

K.Kneipp, M.Moskovits, and H.Kneipp, eds., Surface-Enhances Raman Scattering, Vol. 103 of Topics in Applied Physics (Springer, 2006).
[CrossRef]

A. K. Sarychev and V. M. Shalaev, Electrodynamics of Metamaterials (World Scientific, 2007).
[CrossRef]

V. M. Shalaev, Nonlinear Optics of Random Media, Fractal Composites and Metal-Dielectric Films, Vol. 158 of Springer Tracts in Modern Physics (Springer, 2000).

V.M.Shalaev, ed., Optical Properties of Nanostructured Random Media (Springer, 2002).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Narrow gaps between (a) two metallic grains, (b) two parallel elongated grains, (c) two coaxial elongated grains.

Equations (7)

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

ε m ( ω p / ω ) 2 [ 1 i / ( ω τ ) ] ,
E c / E 0 = G / ( ε ε res ) + G bg ,
ε res a / δ / ( n + δ n ) ,
Q ω ε ( E c / ε ) 2 ( a δ ) 3 / 2 ,
I ω E c 2 δ 2 a 4 / λ 3 .
ε res = a / δ n 1 / 2 ,
G = 8 π 2 3 ( a / δ ) 3 / 2 ln ( a / δ ) ,     G bg = 2 a / δ .

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