Abstract

We describe how the finite-difference time-domain (FDTD) technique can be used to compute the quasi-normal mode (QNM) for metallic nano-resonators, which is important for describing and understanding light–matter interactions in nanoplasmonics. We use the QNM to model the enhanced spontaneous emission rate for dipole emitters near a gold nanorod dimer structure using a newly developed QNM expansion technique. Enhanced single photon emission factors of around 1500 and output β-factors of around 60% are found near the localized plasmon resonance.

© 2014 Optical Society of America

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  1. R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific, 1996).
  2. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  3. K. A. Willets and R. P. Van Duyne, Annu. Rev. Phys. Chem. 58, 267 (2007).
    [CrossRef]
  4. K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
    [CrossRef]
  5. R. Zhang, Y. Zhang, Z.-C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J.-L. Yang, and J.-G. Hou, Nature 498, 82 (2013).
    [CrossRef]
  6. P. Bharadwaj, B. Deutsch, and L. Novotny, Adv. Opt. Photon. 1, 438 (2009).
    [CrossRef]
  7. C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, Nano Lett. 13, 1516 (2013).
  8. P. T. Leung, S. Y. Liu, and K. Young, Phys. Rev. A 49, 3982 (1994).
    [CrossRef]
  9. K. M. Lee, P. T. Leung, and K. M. Pang, J. Opt. Soc. Am. B 16, 1409 (1999).
    [CrossRef]
  10. P. T. Kristensen, C. Van Vlack, and S. Hughes, Opt. Lett. 37, 1649 (2012).
    [CrossRef]
  11. E. M. Purcell, Phys. Rev. 69, 37 (1946).
    [CrossRef]
  12. P. T. Kristensen and S. Hughes, ACS Photonics 1, 2 (2014).
    [CrossRef]
  13. C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, Phys. Rev. Lett. 110, 237401 (2013).
    [CrossRef]
  14. R.-C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasi-normal mode approach to modeling light emission and propagation in nanoplasmonics,” arXiv:1312.2939 (2014).
  15. A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech, 2005).
  16. e.g., see K. Stannigel, M. König, J. Niegemann, and K. Busch, Opt. Express 17, 14934 (2009).
    [CrossRef]
  17. K. C. Y. Huang, Y.-C. Jun, M.-K. Seo, and M. L. Brongersma, Opt. Express 19, 19084 (2011).
    [CrossRef]
  18. Q. Bai, M. Perrin, C. Sauvan, J.-P. Hugonin, and P. Lalanne, Opt. Express 21, 27371 (2013).
    [CrossRef]
  19. J. R. de Lasson, J. Mørk, and P. T. Kristensen, J. Opt. Soc. Am. B 30, 1996 (2013).
    [CrossRef]
  20. A. Dhawan, S. J. Norton, M. D. Gerhold, and T. Vo-Dinh, Opt. Express 17, 9688 (2009).
    [CrossRef]
  21. C. Van Vlack and S. Hughes, Opt. Lett. 37, 2880 (2012).
    [CrossRef]
  22. P. Yao, V. S. C. Manga Rao, and S. Hughes, Laser Photon. Rev. 4, 499 (2010).
    [CrossRef]
  23. V. S. C. Manga Rao and S. Hughes, Phys. Rev. Lett. 99, 193901 (2007).
    [CrossRef]
  24. We use FDTD Solutions: www.lumerical.com .
  25. G. Sun and J. B. Khurgin, Appl. Phys. Lett. 98, 113116 (2011).
    [CrossRef]
  26. L. Novotny and B. Hecht, Principles of Nano Optics (Cambridge University, 2006).
  27. C. Van Vlack, P. T. Kristensen, and S. Hughes, Phys. Rev. B 85, 075303 (2012).
    [CrossRef]

2014 (1)

P. T. Kristensen and S. Hughes, ACS Photonics 1, 2 (2014).
[CrossRef]

2013 (5)

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, Phys. Rev. Lett. 110, 237401 (2013).
[CrossRef]

R. Zhang, Y. Zhang, Z.-C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J.-L. Yang, and J.-G. Hou, Nature 498, 82 (2013).
[CrossRef]

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, Nano Lett. 13, 1516 (2013).

J. R. de Lasson, J. Mørk, and P. T. Kristensen, J. Opt. Soc. Am. B 30, 1996 (2013).
[CrossRef]

Q. Bai, M. Perrin, C. Sauvan, J.-P. Hugonin, and P. Lalanne, Opt. Express 21, 27371 (2013).
[CrossRef]

2012 (3)

2011 (2)

2010 (1)

P. Yao, V. S. C. Manga Rao, and S. Hughes, Laser Photon. Rev. 4, 499 (2010).
[CrossRef]

2009 (3)

2007 (2)

K. A. Willets and R. P. Van Duyne, Annu. Rev. Phys. Chem. 58, 267 (2007).
[CrossRef]

V. S. C. Manga Rao and S. Hughes, Phys. Rev. Lett. 99, 193901 (2007).
[CrossRef]

1999 (1)

1997 (1)

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

1994 (1)

P. T. Leung, S. Y. Liu, and K. Young, Phys. Rev. A 49, 3982 (1994).
[CrossRef]

1946 (1)

E. M. Purcell, Phys. Rev. 69, 37 (1946).
[CrossRef]

Aizpurua, J.

R. Zhang, Y. Zhang, Z.-C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J.-L. Yang, and J.-G. Hou, Nature 498, 82 (2013).
[CrossRef]

Bai, Q.

Belacel, C.

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, Nano Lett. 13, 1516 (2013).

Bharadwaj, P.

Bigourdan, F.

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, Nano Lett. 13, 1516 (2013).

Brongersma, M. L.

Busch, K.

Campillo, A. J.

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific, 1996).

Chang, R. K.

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific, 1996).

Chen, L. G.

R. Zhang, Y. Zhang, Z.-C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J.-L. Yang, and J.-G. Hou, Nature 498, 82 (2013).
[CrossRef]

Coolen, L.

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, Nano Lett. 13, 1516 (2013).

Dasari, R. R.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

de Lasson, J. R.

de Vasconcellos, S. M.

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, Nano Lett. 13, 1516 (2013).

Deutsch, B.

Dhawan, A.

Dong, Z.-C.

R. Zhang, Y. Zhang, Z.-C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J.-L. Yang, and J.-G. Hou, Nature 498, 82 (2013).
[CrossRef]

Dubertret, B.

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, Nano Lett. 13, 1516 (2013).

Feld, M. S.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Ge, R.-C.

R.-C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasi-normal mode approach to modeling light emission and propagation in nanoplasmonics,” arXiv:1312.2939 (2014).

Gerhold, M. D.

Greffet, J.-J.

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, Nano Lett. 13, 1516 (2013).

Habert, B.

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, Nano Lett. 13, 1516 (2013).

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech, 2005).

Hecht, B.

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

Hou, J.-G.

R. Zhang, Y. Zhang, Z.-C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J.-L. Yang, and J.-G. Hou, Nature 498, 82 (2013).
[CrossRef]

Huang, K. C. Y.

Hughes, S.

P. T. Kristensen and S. Hughes, ACS Photonics 1, 2 (2014).
[CrossRef]

P. T. Kristensen, C. Van Vlack, and S. Hughes, Opt. Lett. 37, 1649 (2012).
[CrossRef]

C. Van Vlack and S. Hughes, Opt. Lett. 37, 2880 (2012).
[CrossRef]

C. Van Vlack, P. T. Kristensen, and S. Hughes, Phys. Rev. B 85, 075303 (2012).
[CrossRef]

P. Yao, V. S. C. Manga Rao, and S. Hughes, Laser Photon. Rev. 4, 499 (2010).
[CrossRef]

V. S. C. Manga Rao and S. Hughes, Phys. Rev. Lett. 99, 193901 (2007).
[CrossRef]

R.-C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasi-normal mode approach to modeling light emission and propagation in nanoplasmonics,” arXiv:1312.2939 (2014).

Hugonin, J. P.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, Phys. Rev. Lett. 110, 237401 (2013).
[CrossRef]

Hugonin, J.-P.

Q. Bai, M. Perrin, C. Sauvan, J.-P. Hugonin, and P. Lalanne, Opt. Express 21, 27371 (2013).
[CrossRef]

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, Nano Lett. 13, 1516 (2013).

Itzkan, I.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Javaux, C.

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, Nano Lett. 13, 1516 (2013).

Jiang, S.

R. Zhang, Y. Zhang, Z.-C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J.-L. Yang, and J.-G. Hou, Nature 498, 82 (2013).
[CrossRef]

Jun, Y.-C.

Khurgin, J. B.

G. Sun and J. B. Khurgin, Appl. Phys. Lett. 98, 113116 (2011).
[CrossRef]

Kneipp, H.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Kneipp, K.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

König, M.

Kristensen, P. T.

P. T. Kristensen and S. Hughes, ACS Photonics 1, 2 (2014).
[CrossRef]

J. R. de Lasson, J. Mørk, and P. T. Kristensen, J. Opt. Soc. Am. B 30, 1996 (2013).
[CrossRef]

C. Van Vlack, P. T. Kristensen, and S. Hughes, Phys. Rev. B 85, 075303 (2012).
[CrossRef]

P. T. Kristensen, C. Van Vlack, and S. Hughes, Opt. Lett. 37, 1649 (2012).
[CrossRef]

R.-C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasi-normal mode approach to modeling light emission and propagation in nanoplasmonics,” arXiv:1312.2939 (2014).

Lafosse, X.

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, Nano Lett. 13, 1516 (2013).

Lalanne, P.

Q. Bai, M. Perrin, C. Sauvan, J.-P. Hugonin, and P. Lalanne, Opt. Express 21, 27371 (2013).
[CrossRef]

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, Phys. Rev. Lett. 110, 237401 (2013).
[CrossRef]

Lee, K. M.

Leung, P. T.

K. M. Lee, P. T. Leung, and K. M. Pang, J. Opt. Soc. Am. B 16, 1409 (1999).
[CrossRef]

P. T. Leung, S. Y. Liu, and K. Young, Phys. Rev. A 49, 3982 (1994).
[CrossRef]

Liao, Y.

R. Zhang, Y. Zhang, Z.-C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J.-L. Yang, and J.-G. Hou, Nature 498, 82 (2013).
[CrossRef]

Liu, S. Y.

P. T. Leung, S. Y. Liu, and K. Young, Phys. Rev. A 49, 3982 (1994).
[CrossRef]

Luo, Y.

R. Zhang, Y. Zhang, Z.-C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J.-L. Yang, and J.-G. Hou, Nature 498, 82 (2013).
[CrossRef]

Maier, S. A.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

Maitre, A.

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, Nano Lett. 13, 1516 (2013).

Maksymov, I. S.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, Phys. Rev. Lett. 110, 237401 (2013).
[CrossRef]

Manga Rao, V. S. C.

P. Yao, V. S. C. Manga Rao, and S. Hughes, Laser Photon. Rev. 4, 499 (2010).
[CrossRef]

V. S. C. Manga Rao and S. Hughes, Phys. Rev. Lett. 99, 193901 (2007).
[CrossRef]

Marquier, F.

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, Nano Lett. 13, 1516 (2013).

Mørk, J.

Niegemann, J.

Norton, S. J.

Novotny, L.

P. Bharadwaj, B. Deutsch, and L. Novotny, Adv. Opt. Photon. 1, 438 (2009).
[CrossRef]

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

Pang, K. M.

Perelman, L. T.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Perrin, M.

Purcell, E. M.

E. M. Purcell, Phys. Rev. 69, 37 (1946).
[CrossRef]

Sauvan, C.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, Phys. Rev. Lett. 110, 237401 (2013).
[CrossRef]

Q. Bai, M. Perrin, C. Sauvan, J.-P. Hugonin, and P. Lalanne, Opt. Express 21, 27371 (2013).
[CrossRef]

Schwob, C.

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, Nano Lett. 13, 1516 (2013).

Senellart, P.

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, Nano Lett. 13, 1516 (2013).

Seo, M.-K.

Stannigel, K.

Sun, G.

G. Sun and J. B. Khurgin, Appl. Phys. Lett. 98, 113116 (2011).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech, 2005).

Van Duyne, R. P.

K. A. Willets and R. P. Van Duyne, Annu. Rev. Phys. Chem. 58, 267 (2007).
[CrossRef]

Van Vlack, C.

Vo-Dinh, T.

Wang, Y.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Willets, K. A.

K. A. Willets and R. P. Van Duyne, Annu. Rev. Phys. Chem. 58, 267 (2007).
[CrossRef]

Yang, J.-L.

R. Zhang, Y. Zhang, Z.-C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J.-L. Yang, and J.-G. Hou, Nature 498, 82 (2013).
[CrossRef]

Yao, P.

P. Yao, V. S. C. Manga Rao, and S. Hughes, Laser Photon. Rev. 4, 499 (2010).
[CrossRef]

Young, J. F.

R.-C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasi-normal mode approach to modeling light emission and propagation in nanoplasmonics,” arXiv:1312.2939 (2014).

Young, K.

P. T. Leung, S. Y. Liu, and K. Young, Phys. Rev. A 49, 3982 (1994).
[CrossRef]

Zhang, C.

R. Zhang, Y. Zhang, Z.-C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J.-L. Yang, and J.-G. Hou, Nature 498, 82 (2013).
[CrossRef]

Zhang, L.

R. Zhang, Y. Zhang, Z.-C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J.-L. Yang, and J.-G. Hou, Nature 498, 82 (2013).
[CrossRef]

Zhang, R.

R. Zhang, Y. Zhang, Z.-C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J.-L. Yang, and J.-G. Hou, Nature 498, 82 (2013).
[CrossRef]

Zhang, Y.

R. Zhang, Y. Zhang, Z.-C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J.-L. Yang, and J.-G. Hou, Nature 498, 82 (2013).
[CrossRef]

ACS Photonics (1)

P. T. Kristensen and S. Hughes, ACS Photonics 1, 2 (2014).
[CrossRef]

Adv. Opt. Photon. (1)

Annu. Rev. Phys. Chem. (1)

K. A. Willets and R. P. Van Duyne, Annu. Rev. Phys. Chem. 58, 267 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

G. Sun and J. B. Khurgin, Appl. Phys. Lett. 98, 113116 (2011).
[CrossRef]

J. Opt. Soc. Am. B (2)

Laser Photon. Rev. (1)

P. Yao, V. S. C. Manga Rao, and S. Hughes, Laser Photon. Rev. 4, 499 (2010).
[CrossRef]

Nano Lett. (1)

C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. M. de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, Nano Lett. 13, 1516 (2013).

Nature (1)

R. Zhang, Y. Zhang, Z.-C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, J.-L. Yang, and J.-G. Hou, Nature 498, 82 (2013).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. (1)

E. M. Purcell, Phys. Rev. 69, 37 (1946).
[CrossRef]

Phys. Rev. A (1)

P. T. Leung, S. Y. Liu, and K. Young, Phys. Rev. A 49, 3982 (1994).
[CrossRef]

Phys. Rev. B (1)

C. Van Vlack, P. T. Kristensen, and S. Hughes, Phys. Rev. B 85, 075303 (2012).
[CrossRef]

Phys. Rev. Lett. (3)

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

V. S. C. Manga Rao and S. Hughes, Phys. Rev. Lett. 99, 193901 (2007).
[CrossRef]

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, Phys. Rev. Lett. 110, 237401 (2013).
[CrossRef]

Other (6)

R.-C. Ge, P. T. Kristensen, J. F. Young, and S. Hughes, “Quasi-normal mode approach to modeling light emission and propagation in nanoplasmonics,” arXiv:1312.2939 (2014).

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech, 2005).

We use FDTD Solutions: www.lumerical.com .

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

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific, 1996).

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

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Figures (3)

Fig. 1.
Fig. 1.

Spatial profile of the dipole mode of a gold nanorod dimer, showing both the scattered field and QNM. Left: |ES(x,y,0;ωc)| and right: |f˜(x,y,0;ωc)| at ωc=291.06THz. The excitation source is a y-polarized plane wave incident in the x direction.

Fig. 2.
Fig. 2.

Close-up view of the QNM profile of the gold dimer. Left: |f˜(x,y,0;ωc)|, middle: |f˜y(x,y,0;ωc)|, and right: |f˜x(x,y,0;ωc)| at ωc=291.06THz. A y-polarized dipole at the center of the gap is shown by the white dot and double arrow in the left panel.

Fig. 3.
Fig. 3.

Enhanced SE factor for the gold nanorod dimer structure, with the blue (dashed) curve given by direct FDTD calculation [Eq. (4)] and the orange (solid) curve given by the mode expansion technique [Eq. (3)]. The emission dipole is y-polarized at the center of the gap of the dimer (see left panel of Fig. 2).

Equations (5)

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f˜μ|f˜ν=limVV(12ω(ε(r,ω)ω2)ω)ω=ω˜μf˜μ(r)·f˜ν(r)dr+ic2ω˜μVϵ(r)f˜μ(r)·f˜ν(r)dr=δμν.
1Veff=Re{1vQ},vQ=f˜c|f˜cεBf˜c2(r0),
Fa(ra,ω)=FPη(ra,na;ω)+1,
FaFDTD(ra,ω)=Im{na·GFDTD(ra,ra;ω)·na}Im{na·GB(ra,ra;ω)·na},
f˜c(r;ωμ)=0tendES(r,t)eiωcte(ttoff)22(τwin)2dt,

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