Abstract

We investigate the radiation rate of a dipole in close proximity to a hyperbolic metamaterial and confirm that both the radiation rate and its fraction directed into the metamaterial are greatly increased compared to bulk dielectric or metal. However, we find that the homogenized effective-medium approach greatly overestimates the Purcell factor compared to metal–dielectric subwavelength multilayers with previously reported layer thicknesses.

© 2011 Optical Society of America

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  1. M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, Appl. Phys. Lett. 94, 151105 (2009).
    [CrossRef]
  2. D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, Appl. Phys. Lett. 84, 2244 (2004).
    [CrossRef]
  3. M. A. Noginov, H. Li, Yu. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, and E. E. Narimanov, Opt. Lett. 35, 1863 (2010).
    [CrossRef] [PubMed]
  4. Z. Jacob, I. Smolyaninov, and E. Narimanov, http://arxiv.org/abs/0910.3981.
  5. Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, Appl. Phys. B 100, 215(2010).
    [CrossRef]
  6. I. I. Smolyaninov and E. E. Narimanov, Phys. Rev. Lett. 105, 067402 (2010).
    [CrossRef] [PubMed]
  7. E. Narimanov, M. A. Noginov, H. Li, and Y. Barnakov, in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper QPDA6.
  8. M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, Appl. Phys. Lett. 94, 151105 (2009).
    [CrossRef]
  9. J. Kanungo and J. Schilling, Appl. Phys. Lett. 97, 021903(2010).
    [CrossRef]
  10. A. Fang, T. Koschny, and C. M. Soukoulis, Phys. Rev. B 79, 245127 (2009).
    [CrossRef]
  11. J. E. Sipe, Surf. Sci. 105, 489 (1981).
    [CrossRef]
  12. J. J. Saarinen and J. E. Sipe, J. Mod. Opt. 55, 13 (2008).
    [CrossRef]
  13. J. M. Wylie and J. E. Sipe, Phys. Rev. A 32, 2030 (1985).
    [CrossRef] [PubMed]
  14. A. Yariv and P. Yeh, Optical Waves in Crystals(Wiley, 1983).
  15. P. G. Etchegoin, E. C. Le Ru, and M. Meyer, J. Chem. Phys. 125, 164705 (2006).
    [CrossRef] [PubMed]

2010 (5)

M. A. Noginov, H. Li, Yu. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, and E. E. Narimanov, Opt. Lett. 35, 1863 (2010).
[CrossRef] [PubMed]

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, Appl. Phys. B 100, 215(2010).
[CrossRef]

I. I. Smolyaninov and E. E. Narimanov, Phys. Rev. Lett. 105, 067402 (2010).
[CrossRef] [PubMed]

E. Narimanov, M. A. Noginov, H. Li, and Y. Barnakov, in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper QPDA6.

J. Kanungo and J. Schilling, Appl. Phys. Lett. 97, 021903(2010).
[CrossRef]

2009 (3)

A. Fang, T. Koschny, and C. M. Soukoulis, Phys. Rev. B 79, 245127 (2009).
[CrossRef]

M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, Appl. Phys. Lett. 94, 151105 (2009).
[CrossRef]

M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, Appl. Phys. Lett. 94, 151105 (2009).
[CrossRef]

2008 (1)

J. J. Saarinen and J. E. Sipe, J. Mod. Opt. 55, 13 (2008).
[CrossRef]

2006 (1)

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, J. Chem. Phys. 125, 164705 (2006).
[CrossRef] [PubMed]

2004 (1)

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, Appl. Phys. Lett. 84, 2244 (2004).
[CrossRef]

1985 (1)

J. M. Wylie and J. E. Sipe, Phys. Rev. A 32, 2030 (1985).
[CrossRef] [PubMed]

1983 (1)

A. Yariv and P. Yeh, Optical Waves in Crystals(Wiley, 1983).

1981 (1)

J. E. Sipe, Surf. Sci. 105, 489 (1981).
[CrossRef]

Barnakov, Y.

E. Narimanov, M. A. Noginov, H. Li, and Y. Barnakov, in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper QPDA6.

Barnakov, Yu. A.

M. A. Noginov, H. Li, Yu. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, and E. E. Narimanov, Opt. Lett. 35, 1863 (2010).
[CrossRef] [PubMed]

M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, Appl. Phys. Lett. 94, 151105 (2009).
[CrossRef]

M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, Appl. Phys. Lett. 94, 151105 (2009).
[CrossRef]

Boltasseva, A.

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, Appl. Phys. B 100, 215(2010).
[CrossRef]

Bonner, C. E.

Dryden, D.

Etchegoin, P. G.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, J. Chem. Phys. 125, 164705 (2006).
[CrossRef] [PubMed]

Fang, A.

A. Fang, T. Koschny, and C. M. Soukoulis, Phys. Rev. B 79, 245127 (2009).
[CrossRef]

Jacob, Z.

M. A. Noginov, H. Li, Yu. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, and E. E. Narimanov, Opt. Lett. 35, 1863 (2010).
[CrossRef] [PubMed]

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, Appl. Phys. B 100, 215(2010).
[CrossRef]

Z. Jacob, I. Smolyaninov, and E. Narimanov, http://arxiv.org/abs/0910.3981.

Kanungo, J.

J. Kanungo and J. Schilling, Appl. Phys. Lett. 97, 021903(2010).
[CrossRef]

Kim, J.-Y.

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, Appl. Phys. B 100, 215(2010).
[CrossRef]

Kolinko, P.

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, Appl. Phys. Lett. 84, 2244 (2004).
[CrossRef]

Koschny, T.

A. Fang, T. Koschny, and C. M. Soukoulis, Phys. Rev. B 79, 245127 (2009).
[CrossRef]

Le Ru, E. C.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, J. Chem. Phys. 125, 164705 (2006).
[CrossRef] [PubMed]

Li, H.

E. Narimanov, M. A. Noginov, H. Li, and Y. Barnakov, in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper QPDA6.

M. A. Noginov, H. Li, Yu. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, and E. E. Narimanov, Opt. Lett. 35, 1863 (2010).
[CrossRef] [PubMed]

M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, Appl. Phys. Lett. 94, 151105 (2009).
[CrossRef]

M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, Appl. Phys. Lett. 94, 151105 (2009).
[CrossRef]

Mayy, M.

Meyer, M.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, J. Chem. Phys. 125, 164705 (2006).
[CrossRef] [PubMed]

Mock, J. J.

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, Appl. Phys. Lett. 84, 2244 (2004).
[CrossRef]

Naik, G. V.

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, Appl. Phys. B 100, 215(2010).
[CrossRef]

Narimanov, E.

E. Narimanov, M. A. Noginov, H. Li, and Y. Barnakov, in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper QPDA6.

Z. Jacob, I. Smolyaninov, and E. Narimanov, http://arxiv.org/abs/0910.3981.

Narimanov, E. E.

I. I. Smolyaninov and E. E. Narimanov, Phys. Rev. Lett. 105, 067402 (2010).
[CrossRef] [PubMed]

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, Appl. Phys. B 100, 215(2010).
[CrossRef]

M. A. Noginov, H. Li, Yu. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, and E. E. Narimanov, Opt. Lett. 35, 1863 (2010).
[CrossRef] [PubMed]

M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, Appl. Phys. Lett. 94, 151105 (2009).
[CrossRef]

M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, Appl. Phys. Lett. 94, 151105 (2009).
[CrossRef]

Nataraj, G.

Noginov, M. A.

M. A. Noginov, H. Li, Yu. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, and E. E. Narimanov, Opt. Lett. 35, 1863 (2010).
[CrossRef] [PubMed]

E. Narimanov, M. A. Noginov, H. Li, and Y. Barnakov, in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper QPDA6.

M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, Appl. Phys. Lett. 94, 151105 (2009).
[CrossRef]

M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, Appl. Phys. Lett. 94, 151105 (2009).
[CrossRef]

Rye, P.

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, Appl. Phys. Lett. 84, 2244 (2004).
[CrossRef]

Saarinen, J. J.

J. J. Saarinen and J. E. Sipe, J. Mod. Opt. 55, 13 (2008).
[CrossRef]

Schilling, J.

J. Kanungo and J. Schilling, Appl. Phys. Lett. 97, 021903(2010).
[CrossRef]

Schurig, D.

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, Appl. Phys. Lett. 84, 2244 (2004).
[CrossRef]

Shalaev, V. M.

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, Appl. Phys. B 100, 215(2010).
[CrossRef]

Sipe, J. E.

J. J. Saarinen and J. E. Sipe, J. Mod. Opt. 55, 13 (2008).
[CrossRef]

J. M. Wylie and J. E. Sipe, Phys. Rev. A 32, 2030 (1985).
[CrossRef] [PubMed]

J. E. Sipe, Surf. Sci. 105, 489 (1981).
[CrossRef]

Smith, D. R.

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, Appl. Phys. Lett. 84, 2244 (2004).
[CrossRef]

Smolyaninov, I.

Z. Jacob, I. Smolyaninov, and E. Narimanov, http://arxiv.org/abs/0910.3981.

Smolyaninov, I. I.

I. I. Smolyaninov and E. E. Narimanov, Phys. Rev. Lett. 105, 067402 (2010).
[CrossRef] [PubMed]

Soukoulis, C. M.

A. Fang, T. Koschny, and C. M. Soukoulis, Phys. Rev. B 79, 245127 (2009).
[CrossRef]

Tumkur, T.

M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, Appl. Phys. Lett. 94, 151105 (2009).
[CrossRef]

M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, Appl. Phys. Lett. 94, 151105 (2009).
[CrossRef]

Wylie, J. M.

J. M. Wylie and J. E. Sipe, Phys. Rev. A 32, 2030 (1985).
[CrossRef] [PubMed]

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals(Wiley, 1983).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals(Wiley, 1983).

Zhu, G.

M. A. Noginov, H. Li, Yu. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, and E. E. Narimanov, Opt. Lett. 35, 1863 (2010).
[CrossRef] [PubMed]

M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, Appl. Phys. Lett. 94, 151105 (2009).
[CrossRef]

M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, Appl. Phys. Lett. 94, 151105 (2009).
[CrossRef]

Appl. Phys. B (1)

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, Appl. Phys. B 100, 215(2010).
[CrossRef]

Appl. Phys. Lett. (4)

M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, Appl. Phys. Lett. 94, 151105 (2009).
[CrossRef]

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, Appl. Phys. Lett. 84, 2244 (2004).
[CrossRef]

M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, Appl. Phys. Lett. 94, 151105 (2009).
[CrossRef]

J. Kanungo and J. Schilling, Appl. Phys. Lett. 97, 021903(2010).
[CrossRef]

J. Chem. Phys. (1)

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, J. Chem. Phys. 125, 164705 (2006).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

J. J. Saarinen and J. E. Sipe, J. Mod. Opt. 55, 13 (2008).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

J. M. Wylie and J. E. Sipe, Phys. Rev. A 32, 2030 (1985).
[CrossRef] [PubMed]

Phys. Rev. B (1)

A. Fang, T. Koschny, and C. M. Soukoulis, Phys. Rev. B 79, 245127 (2009).
[CrossRef]

Phys. Rev. Lett. (1)

I. I. Smolyaninov and E. E. Narimanov, Phys. Rev. Lett. 105, 067402 (2010).
[CrossRef] [PubMed]

Surf. Sci. (1)

J. E. Sipe, Surf. Sci. 105, 489 (1981).
[CrossRef]

Other (3)

Z. Jacob, I. Smolyaninov, and E. Narimanov, http://arxiv.org/abs/0910.3981.

E. Narimanov, M. A. Noginov, H. Li, and Y. Barnakov, in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper QPDA6.

A. Yariv and P. Yeh, Optical Waves in Crystals(Wiley, 1983).

Supplementary Material (1)

» Media 1: PDF (244 KB)     

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Figures (3)

Fig. 1
Fig. 1

(a) HMM composition and the dependence of (b) the total radiation rate b and (c) its fraction f directed into the cladding for an isotropically averaged dipole at a distance h above a real HMM, a homogenized effective medium given by Eq. (5), and a bulk metal.

Fig. 2
Fig. 2

(a) Total radiation rate b and (b) fraction of radiation reflected away from semi-infinite HMM f with varying d for a dipole placed at h = 100 nm from the HMM surface.

Fig. 3
Fig. 3

Same as Fig. 2 but for h = 10 nm . (inset) Dependence R s , p ( κ ) (Media 1).

Equations (5)

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

b c = 0 π / 2 β c sin θ d θ = 1 ω ˜ n c 0 ω ˜ n c β c κ d κ w c .
β c ( θ ) = 3 4 ( f 2 κ 2 ω ˜ 2 n c 2 | 1 + e i ζ R N p | 2 + f 2 2 [ | 1 + e i ζ R N s | 2 + | w c | 2 ω ˜ 2 n c 2 | 1 e i ζ R N p | 2 ] ) ,
b = 1 + 3 2 ω ˜ n c Re ( κ d κ w c [ f 2 κ 2 ω ˜ 2 n c 2 R N p + 1 2 f 2 ( R N s w c 2 ω ˜ 2 n c 2 R N p ) ] e i ζ ) .
( R s , p 1 ) = M ( a up s , p a down s , p ) .
ϵ x = ϵ y = 1 2 ( ϵ m + ϵ d ) ; ϵ z = [ 1 2 ( ϵ m 1 + ϵ d 1 ) ] 1 .

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