Abstract

The Purcell factor is the standard figure of merit for spontaneous emission enhancement in microcavities and has also been proposed to describe emission enhancements for plasmonic resonances. A comparison of quality factor, mode volume, and Purcell factor for single and coupled plasmon spheres to exact calculations of emission rates shows that a Purcell factor derived from quality factor and mode volume does not describe emission changes due to plasmon antennas.

© 2010 Optical Society of America

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  1. L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2006).
  2. K.J.Vahala, Optical Microcavities (World Scientific, 2004).
    [CrossRef]
  3. J.-M. Gérard and B. Gayral, J. Lightwave Technol. 17, 2089 (1999).
    [CrossRef]
  4. J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Yun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
    [CrossRef] [PubMed]
  5. P. Anger, P. Bharadwaj, and L. Novotny, Phys. Rev. Lett. 96, 113002 (2006).
    [CrossRef] [PubMed]
  6. S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, Phys. Rev. Lett. 97, 017402 (2006).
    [CrossRef] [PubMed]
  7. O. L. Muskens, V. Giannini, J. A. Sánchez Gil, and J. Gómez Rivas, Nano Lett. 7, 2871 (2007).
    [CrossRef] [PubMed]
  8. H. Mertens, A. F. Koenderink, and A. Polman, Phys. Rev. B 76, 115123 (2007).
    [CrossRef]
  9. G. W. Ford and W. H. Weber, Phys. Rep. 113, 195 (1984).
    [CrossRef]
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    [CrossRef]
  11. A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlavesich, K. Müllen, and W. E. Moerner, Nat. Photon. 3, 654 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. S. A. Maier, Opt. Express 14, 1957 (2006).
    [CrossRef] [PubMed]
  15. R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008).
    [CrossRef]
  16. C.-T. Tai, Dyadic Green Functions in Electromagnetic Theory, 2nd ed. (IEEE, 1993).
  17. R. Ruppin, Phys. Lett. A 299, 309 (2002).
    [CrossRef]
  18. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1960).
  19. P. de Vries, A. F. Koenderink, and A. Lagendijk are preparing a manuscript to be entitled “Spontaneous emission and quantum cavity physics: making the Purcell factor exact”.
  20. B. J. Dalton, S. M. Barnett, and P. L. Knight, J. Mod. Opt. 46, 1315 (1999).
  21. S. M. Dutra and G. Nienhuis, Phys. Rev. A , 62, 063805(2000).
    [CrossRef]
  22. F. J. García de Abajo, Phys. Rev. B 60, 6086 (1999).
    [CrossRef]
  23. E. Castanié, M. Boffety, and R. Carminati, Opt. Lett. 35, 291 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  25. P. de Vries, D. V. van Coevorden, and A. Lagendijk, Rev. Mod. Phys. 70, 447 (1998).
    [CrossRef]

2010

J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Yun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef] [PubMed]

M. Kuttge, F. J. García de Abajo, and A. Polman, Nano Lett. 10, 1537 (2010).
[CrossRef]

E. Castanié, M. Boffety, and R. Carminati, Opt. Lett. 35, 291 (2010).
[CrossRef] [PubMed]

2009

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlavesich, K. Müllen, and W. E. Moerner, Nat. Photon. 3, 654 (2009).
[CrossRef]

2008

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, Nat. Photon. 2, 234 (2008).
[CrossRef]

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008).
[CrossRef]

2007

O. L. Muskens, V. Giannini, J. A. Sánchez Gil, and J. Gómez Rivas, Nano Lett. 7, 2871 (2007).
[CrossRef] [PubMed]

H. Mertens, A. F. Koenderink, and A. Polman, Phys. Rev. B 76, 115123 (2007).
[CrossRef]

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, Nature Phys. 3, 807 (2007).
[CrossRef]

2006

P. Anger, P. Bharadwaj, and L. Novotny, Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef] [PubMed]

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, Phys. Rev. Lett. 97, 017402 (2006).
[CrossRef] [PubMed]

S. A. Maier, Opt. Express 14, 1957 (2006).
[CrossRef] [PubMed]

2002

R. Ruppin, Phys. Lett. A 299, 309 (2002).
[CrossRef]

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Möller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef] [PubMed]

2000

S. M. Dutra and G. Nienhuis, Phys. Rev. A , 62, 063805(2000).
[CrossRef]

1999

F. J. García de Abajo, Phys. Rev. B 60, 6086 (1999).
[CrossRef]

J.-M. Gérard and B. Gayral, J. Lightwave Technol. 17, 2089 (1999).
[CrossRef]

B. J. Dalton, S. M. Barnett, and P. L. Knight, J. Mod. Opt. 46, 1315 (1999).

1998

P. de Vries, D. V. van Coevorden, and A. Lagendijk, Rev. Mod. Phys. 70, 447 (1998).
[CrossRef]

1984

G. W. Ford and W. H. Weber, Phys. Rep. 113, 195 (1984).
[CrossRef]

Anger, P.

P. Anger, P. Bharadwaj, and L. Novotny, Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef] [PubMed]

Avlavesich, Y.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlavesich, K. Müllen, and W. E. Moerner, Nat. Photon. 3, 654 (2009).
[CrossRef]

Barnard, E. S.

J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Yun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef] [PubMed]

Barnett, S. M.

B. J. Dalton, S. M. Barnett, and P. L. Knight, J. Mod. Opt. 46, 1315 (1999).

Bartal, G.

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008).
[CrossRef]

Bharadwaj, P.

P. Anger, P. Bharadwaj, and L. Novotny, Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef] [PubMed]

Boffety, M.

Brongersma, M. L.

J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Yun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef] [PubMed]

Cai, W. S.

J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Yun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef] [PubMed]

Carminati, R.

Castanié, E.

Chang, D. E.

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, Nature Phys. 3, 807 (2007).
[CrossRef]

Dalton, B. J.

B. J. Dalton, S. M. Barnett, and P. L. Knight, J. Mod. Opt. 46, 1315 (1999).

de Abajo, F. J. García

M. Kuttge, F. J. García de Abajo, and A. Polman, Nano Lett. 10, 1537 (2010).
[CrossRef]

de Vries, P.

P. de Vries, D. V. van Coevorden, and A. Lagendijk, Rev. Mod. Phys. 70, 447 (1998).
[CrossRef]

P. de Vries, A. F. Koenderink, and A. Lagendijk are preparing a manuscript to be entitled “Spontaneous emission and quantum cavity physics: making the Purcell factor exact”.

Demler, E. A.

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, Nature Phys. 3, 807 (2007).
[CrossRef]

Dulkeith, E.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Möller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef] [PubMed]

Dutra, S. M.

S. M. Dutra and G. Nienhuis, Phys. Rev. A , 62, 063805(2000).
[CrossRef]

Fan, S.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlavesich, K. Müllen, and W. E. Moerner, Nat. Photon. 3, 654 (2009).
[CrossRef]

Feldmann, J.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Möller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef] [PubMed]

Ford, G. W.

G. W. Ford and W. H. Weber, Phys. Rep. 113, 195 (1984).
[CrossRef]

García de Abajo, F. J.

F. J. García de Abajo, Phys. Rev. B 60, 6086 (1999).
[CrossRef]

Gayral, B.

Gérard, J.-M.

Giannini, V.

O. L. Muskens, V. Giannini, J. A. Sánchez Gil, and J. Gómez Rivas, Nano Lett. 7, 2871 (2007).
[CrossRef] [PubMed]

Gittins, D. I.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Möller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef] [PubMed]

Gómez Rivas, J.

O. L. Muskens, V. Giannini, J. A. Sánchez Gil, and J. Gómez Rivas, Nano Lett. 7, 2871 (2007).
[CrossRef] [PubMed]

Håkanson, U.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, Phys. Rev. Lett. 97, 017402 (2006).
[CrossRef] [PubMed]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2006).

Kinkhabwala, A.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlavesich, K. Müllen, and W. E. Moerner, Nat. Photon. 3, 654 (2009).
[CrossRef]

Klar, T. A.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Möller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef] [PubMed]

Knight, P. L.

B. J. Dalton, S. M. Barnett, and P. L. Knight, J. Mod. Opt. 46, 1315 (1999).

Koenderink, A. F.

H. Mertens, A. F. Koenderink, and A. Polman, Phys. Rev. B 76, 115123 (2007).
[CrossRef]

P. de Vries, A. F. Koenderink, and A. Lagendijk are preparing a manuscript to be entitled “Spontaneous emission and quantum cavity physics: making the Purcell factor exact”.

Kühn, S.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, Phys. Rev. Lett. 97, 017402 (2006).
[CrossRef] [PubMed]

Kuttge, M.

M. Kuttge, F. J. García de Abajo, and A. Polman, Nano Lett. 10, 1537 (2010).
[CrossRef]

Lagendijk, A.

P. de Vries, D. V. van Coevorden, and A. Lagendijk, Rev. Mod. Phys. 70, 447 (1998).
[CrossRef]

P. de Vries, A. F. Koenderink, and A. Lagendijk are preparing a manuscript to be entitled “Spontaneous emission and quantum cavity physics: making the Purcell factor exact”.

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1960).

Levi, S. A.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Möller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef] [PubMed]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1960).

Lukin, M. D.

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, Nature Phys. 3, 807 (2007).
[CrossRef]

Maier, S. A.

Mertens, H.

H. Mertens, A. F. Koenderink, and A. Polman, Phys. Rev. B 76, 115123 (2007).
[CrossRef]

Moerner, W. E.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlavesich, K. Müllen, and W. E. Moerner, Nat. Photon. 3, 654 (2009).
[CrossRef]

Möller, M.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Möller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef] [PubMed]

Morteani, A. C.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Möller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef] [PubMed]

Müllen, K.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlavesich, K. Müllen, and W. E. Moerner, Nat. Photon. 3, 654 (2009).
[CrossRef]

Muskens, O. L.

O. L. Muskens, V. Giannini, J. A. Sánchez Gil, and J. Gómez Rivas, Nano Lett. 7, 2871 (2007).
[CrossRef] [PubMed]

Niedereichholz, T.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Möller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef] [PubMed]

Nienhuis, G.

S. M. Dutra and G. Nienhuis, Phys. Rev. A , 62, 063805(2000).
[CrossRef]

Novotny, L.

P. Anger, P. Bharadwaj, and L. Novotny, Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef] [PubMed]

L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2006).

Oulton, R. F.

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008).
[CrossRef]

Pile, D. F. P.

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008).
[CrossRef]

Polman, A.

M. Kuttge, F. J. García de Abajo, and A. Polman, Nano Lett. 10, 1537 (2010).
[CrossRef]

H. Mertens, A. F. Koenderink, and A. Polman, Phys. Rev. B 76, 115123 (2007).
[CrossRef]

Reinhoudt, D. N.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Möller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef] [PubMed]

Rogobete, L.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, Phys. Rev. Lett. 97, 017402 (2006).
[CrossRef] [PubMed]

Ruppin, R.

R. Ruppin, Phys. Lett. A 299, 309 (2002).
[CrossRef]

Sánchez Gil, J. A.

O. L. Muskens, V. Giannini, J. A. Sánchez Gil, and J. Gómez Rivas, Nano Lett. 7, 2871 (2007).
[CrossRef] [PubMed]

Sandoghdar, V.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, Phys. Rev. Lett. 97, 017402 (2006).
[CrossRef] [PubMed]

Schuller, J. A.

J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Yun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef] [PubMed]

Segerink, F. B.

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, Nat. Photon. 2, 234 (2008).
[CrossRef]

Sørensen, A. S.

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, Nature Phys. 3, 807 (2007).
[CrossRef]

Stefani, F. D.

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, Nat. Photon. 2, 234 (2008).
[CrossRef]

Tai, C.-T.

C.-T. Tai, Dyadic Green Functions in Electromagnetic Theory, 2nd ed. (IEEE, 1993).

Taminiau, T. H.

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, Nat. Photon. 2, 234 (2008).
[CrossRef]

van Coevorden, D. V.

P. de Vries, D. V. van Coevorden, and A. Lagendijk, Rev. Mod. Phys. 70, 447 (1998).
[CrossRef]

van Hulst, N. F.

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, Nat. Photon. 2, 234 (2008).
[CrossRef]

van Veggel, F. C. J. M.

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Möller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef] [PubMed]

Weber, W. H.

G. W. Ford and W. H. Weber, Phys. Rep. 113, 195 (1984).
[CrossRef]

White, J. S.

J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Yun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef] [PubMed]

Yu, Z.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlavesich, K. Müllen, and W. E. Moerner, Nat. Photon. 3, 654 (2009).
[CrossRef]

Yun, Y. C.

J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Yun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef] [PubMed]

Zhang, X.

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008).
[CrossRef]

J. Lightwave Technol.

J. Mod. Opt.

B. J. Dalton, S. M. Barnett, and P. L. Knight, J. Mod. Opt. 46, 1315 (1999).

Nano Lett.

O. L. Muskens, V. Giannini, J. A. Sánchez Gil, and J. Gómez Rivas, Nano Lett. 7, 2871 (2007).
[CrossRef] [PubMed]

M. Kuttge, F. J. García de Abajo, and A. Polman, Nano Lett. 10, 1537 (2010).
[CrossRef]

Nat. Mater.

J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Yun, J. S. White, and M. L. Brongersma, Nat. Mater. 9, 193 (2010).
[CrossRef] [PubMed]

Nat. Photon.

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, Nat. Photon. 2, 234 (2008).
[CrossRef]

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlavesich, K. Müllen, and W. E. Moerner, Nat. Photon. 3, 654 (2009).
[CrossRef]

Nature Phys.

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, Nature Phys. 3, 807 (2007).
[CrossRef]

New J. Phys.

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, New J. Phys. 10, 105018 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

R. Ruppin, Phys. Lett. A 299, 309 (2002).
[CrossRef]

Phys. Rep.

G. W. Ford and W. H. Weber, Phys. Rep. 113, 195 (1984).
[CrossRef]

Phys. Rev. A

S. M. Dutra and G. Nienhuis, Phys. Rev. A , 62, 063805(2000).
[CrossRef]

Phys. Rev. B

F. J. García de Abajo, Phys. Rev. B 60, 6086 (1999).
[CrossRef]

H. Mertens, A. F. Koenderink, and A. Polman, Phys. Rev. B 76, 115123 (2007).
[CrossRef]

Phys. Rev. Lett.

P. Anger, P. Bharadwaj, and L. Novotny, Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef] [PubMed]

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, Phys. Rev. Lett. 97, 017402 (2006).
[CrossRef] [PubMed]

E. Dulkeith, A. C. Morteani, T. Niedereichholz, T. A. Klar, J. Feldmann, S. A. Levi, F. C. J. M. van Veggel, D. N. Reinhoudt, M. Möller, and D. I. Gittins, Phys. Rev. Lett. 89, 203002 (2002).
[CrossRef] [PubMed]

Rev. Mod. Phys.

P. de Vries, D. V. van Coevorden, and A. Lagendijk, Rev. Mod. Phys. 70, 447 (1998).
[CrossRef]

Other

L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2006).

K.J.Vahala, Optical Microcavities (World Scientific, 2004).
[CrossRef]

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1960).

P. de Vries, A. F. Koenderink, and A. Lagendijk are preparing a manuscript to be entitled “Spontaneous emission and quantum cavity physics: making the Purcell factor exact”.

C.-T. Tai, Dyadic Green Functions in Electromagnetic Theory, 2nd ed. (IEEE, 1993).

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Figures (2)

Fig. 1
Fig. 1

Contour plots of | E | 2 and energy density W for a 35 nm radius Ag sphere in vacuum. The color bar ranges from 0 to 107 (respectively, 0 to 118) in units of | E | 2 (respectively, W) of the incident plane wave (from below, horizontal polarization). (b) Mode volume W d r / max ( W ) evaluated over a spherical integration domain truncated at R, plotted versus R. Vertical line, particle radius. Dashed line, linear divergence due to radiation loss. Red dashed horizontal line, mode volume. (c) Mode volume (red solid curve) and physical volume (dashed curve) versus sphere (Ag in vacuum) radius. Green curve with symbols, quality factor Q (right-hand axis). (d) Dashed curve, F from Q and V. Solid curves, total decay rate at 1 and 0.1 nm from the sphere.

Fig. 2
Fig. 2

Radiative decay rate (dashed curve) and total decay rate (joined symbols) along the centerline joining two 25 nm silver spheres with a 10 nm gap. Rates are relative to the rate in the n = 1.5 host medium. Red solid line, prediction from Purcell theory. The dipole is oriented along the centerline. Right, contour plot of | E | 2 (scale from 0 to 1890 in units of incident | E | 2 ) upon illumination by a vertically polarized plane wave).

Equations (3)

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N ( ω , r , e d ) = 6 ω π c 2 ( e d T · Im ( G ( r , r , ω ) ) · e d ) .
N ( ω 0 , r , e d ) = 3 λ , ω | e d T · E λ ( r , ω ) | 2 δ ( ω ω 0 ) .
F = 3 Q 4 π 2 V ( λ n ) 3 with V = ϵ | E | 2 d r max ( ϵ | E | 2 ) .

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