Abstract

Spontaneous emission in the presence of complex nanostructures is discussed by use of a calculational scheme that permits us to deal with interfaces of arbitrary shape. Control over the field associated with the emission is shown to be attainable. In particular, decay rates are offered for geometries that lead to focusing and collimation of near- and far-field distributions. Emission from axially symmetric gratings is shown to lead to narrow angular distributions of emission, and focusing at the foci of dielectric ellipsoids is achieved for dimensions comparable with the wavelength. In the latter case the total emission rate for two atoms in an ellipsoidal cavity is shown to be enhanced in a way that deviates from the predictions of the Dicke effect by means of intermediate- and far-field contributions.

© 2004 Optical Society of America

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  1. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, Phys. Rev. Lett. 78, 3294 (1997).
    [CrossRef]
  2. S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
    [CrossRef]
  3. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef] [PubMed]
  4. S. John and T. Quang, Phys. Rev. A 50, 1764 (1994).
    [CrossRef] [PubMed]
  5. S. Y. Lin, J. Moreno, and J. G. Fleming, Appl. Phys. Lett. 83, 380 (2003).
    [CrossRef]
  6. V. A. Shubin, W. Kim, V. P. Safonov, A. K. Sarychev, R. L. Armstrong, and V. M. Shalaev, J. Lightwave Technol. 17, 2183 (1999).
    [CrossRef]
  7. H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, Phys. Rev. Lett. 83, 4357 (1999).
    [CrossRef]
  8. V. V. Klimov, M. Ducloy, and V. S. Letokhov, Eur. Phys. J. D 20, 133 (2002).
    [CrossRef]
  9. H. P. Urbach and G. L. J. A. Rikken, Phys. Rev. A 57, 3913 (1998).
    [CrossRef]
  10. See M. Al-Amri and M. Babiker, Phys. Rev. A 67, 043820 (2003), and references therein.
    [CrossRef]
  11. G. L. James, Electron. Lett. 13, 293 (1977).
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    [CrossRef] [PubMed]
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    [CrossRef]
  14. F. J. García de Abajo and A. Howie, Phys. Rev. B 65, 115418 (2002).
    [CrossRef]
  15. L. A. Blanco and F. J. García de Abajo, Phys. Rev. B (to be published).
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    [CrossRef]
  17. R. H. Dicke, Phys. Rev. 93, 99 (1954).
    [CrossRef]
  18. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions. Basic Processes and Applications (Wiley, New York, 1992).
  19. E. V. Goldstein and P. Meystre, Phys. Rev. A 56, 5135 (1997).
    [CrossRef]

2003 (3)

See M. Al-Amri and M. Babiker, Phys. Rev. A 67, 043820 (2003), and references therein.
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef]

S. Y. Lin, J. Moreno, and J. G. Fleming, Appl. Phys. Lett. 83, 380 (2003).
[CrossRef]

2002 (4)

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

F. J. García de Abajo and A. Howie, Phys. Rev. B 65, 115418 (2002).
[CrossRef]

V. V. Klimov, M. Ducloy, and V. S. Letokhov, Eur. Phys. J. D 20, 133 (2002).
[CrossRef]

1999 (2)

1998 (1)

H. P. Urbach and G. L. J. A. Rikken, Phys. Rev. A 57, 3913 (1998).
[CrossRef]

1997 (3)

J. U. Nöckel and A. D. Stone, Nature 385, 45 (1997).
[CrossRef]

E. V. Goldstein and P. Meystre, Phys. Rev. A 56, 5135 (1997).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, Phys. Rev. Lett. 78, 3294 (1997).
[CrossRef]

1994 (1)

S. John and T. Quang, Phys. Rev. A 50, 1764 (1994).
[CrossRef] [PubMed]

1987 (1)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

1977 (1)

G. L. James, Electron. Lett. 13, 293 (1977).
[CrossRef]

1954 (1)

R. H. Dicke, Phys. Rev. 93, 99 (1954).
[CrossRef]

Al-Amri, M.

See M. Al-Amri and M. Babiker, Phys. Rev. A 67, 043820 (2003), and references therein.
[CrossRef]

Armstrong, R. L.

Babiker, M.

See M. Al-Amri and M. Babiker, Phys. Rev. A 67, 043820 (2003), and references therein.
[CrossRef]

Bjerneld, E. J.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, Phys. Rev. Lett. 83, 4357 (1999).
[CrossRef]

Blanco, L. A.

L. A. Blanco and F. J. García de Abajo, Phys. Rev. B (to be published).

Börjesson, L.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, Phys. Rev. Lett. 83, 4357 (1999).
[CrossRef]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions. Basic Processes and Applications (Wiley, New York, 1992).

Degiron, A.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

Devaux, E.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

Dicke, R. H.

R. H. Dicke, Phys. Rev. 93, 99 (1954).
[CrossRef]

Ducloy, M.

V. V. Klimov, M. Ducloy, and V. S. Letokhov, Eur. Phys. J. D 20, 133 (2002).
[CrossRef]

Dupont-Roc, J.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions. Basic Processes and Applications (Wiley, New York, 1992).

Ebbesen, T. W.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

Enoch, S.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Fan, S.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, Phys. Rev. Lett. 78, 3294 (1997).
[CrossRef]

Fleming, J. G.

S. Y. Lin, J. Moreno, and J. G. Fleming, Appl. Phys. Lett. 83, 380 (2003).
[CrossRef]

García de Abajo, F. J.

F. J. García de Abajo and A. Howie, Phys. Rev. B 65, 115418 (2002).
[CrossRef]

L. A. Blanco and F. J. García de Abajo, Phys. Rev. B (to be published).

García-Vidal, F. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

Goldstein, E. V.

E. V. Goldstein and P. Meystre, Phys. Rev. A 56, 5135 (1997).
[CrossRef]

Grynberg, G.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions. Basic Processes and Applications (Wiley, New York, 1992).

Guérin, N.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Howie, A.

F. J. García de Abajo and A. Howie, Phys. Rev. B 65, 115418 (2002).
[CrossRef]

James, G. L.

G. L. James, Electron. Lett. 13, 293 (1977).
[CrossRef]

Joannopoulos, J. D.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, Phys. Rev. Lett. 78, 3294 (1997).
[CrossRef]

John, S.

S. John and T. Quang, Phys. Rev. A 50, 1764 (1994).
[CrossRef] [PubMed]

Käll, M.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, Phys. Rev. Lett. 83, 4357 (1999).
[CrossRef]

Kim, W.

Klimov, V. V.

V. V. Klimov, M. Ducloy, and V. S. Letokhov, Eur. Phys. J. D 20, 133 (2002).
[CrossRef]

Letokhov, V. S.

V. V. Klimov, M. Ducloy, and V. S. Letokhov, Eur. Phys. J. D 20, 133 (2002).
[CrossRef]

Lezec, H. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

Lin, S. Y.

S. Y. Lin, J. Moreno, and J. G. Fleming, Appl. Phys. Lett. 83, 380 (2003).
[CrossRef]

Linke, R. A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

Martín-Moreno, L.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

Meystre, P.

E. V. Goldstein and P. Meystre, Phys. Rev. A 56, 5135 (1997).
[CrossRef]

Moreno, J.

S. Y. Lin, J. Moreno, and J. G. Fleming, Appl. Phys. Lett. 83, 380 (2003).
[CrossRef]

Nöckel, J. U.

J. U. Nöckel and A. D. Stone, Nature 385, 45 (1997).
[CrossRef]

Quang, T.

S. John and T. Quang, Phys. Rev. A 50, 1764 (1994).
[CrossRef] [PubMed]

Rikken, G. L. J. A.

H. P. Urbach and G. L. J. A. Rikken, Phys. Rev. A 57, 3913 (1998).
[CrossRef]

Sabouroux, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Safonov, V. P.

Sarychev, A. K.

Schubert, E. F.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, Phys. Rev. Lett. 78, 3294 (1997).
[CrossRef]

Shalaev, V. M.

Shubin, V. A.

Stone, A. D.

J. U. Nöckel and A. D. Stone, Nature 385, 45 (1997).
[CrossRef]

Tayeb, G.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Urbach, H. P.

H. P. Urbach and G. L. J. A. Rikken, Phys. Rev. A 57, 3913 (1998).
[CrossRef]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, Phys. Rev. Lett. 78, 3294 (1997).
[CrossRef]

Vincent, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Xu, H.

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, Phys. Rev. Lett. 83, 4357 (1999).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

S. Y. Lin, J. Moreno, and J. G. Fleming, Appl. Phys. Lett. 83, 380 (2003).
[CrossRef]

Electron. Lett. (1)

G. L. James, Electron. Lett. 13, 293 (1977).
[CrossRef]

Eur. Phys. J. D (1)

V. V. Klimov, M. Ducloy, and V. S. Letokhov, Eur. Phys. J. D 20, 133 (2002).
[CrossRef]

J. Lightwave Technol. (1)

Nature (1)

J. U. Nöckel and A. D. Stone, Nature 385, 45 (1997).
[CrossRef]

Phys. Rev. (1)

R. H. Dicke, Phys. Rev. 93, 99 (1954).
[CrossRef]

Phys. Rev. A (4)

E. V. Goldstein and P. Meystre, Phys. Rev. A 56, 5135 (1997).
[CrossRef]

H. P. Urbach and G. L. J. A. Rikken, Phys. Rev. A 57, 3913 (1998).
[CrossRef]

See M. Al-Amri and M. Babiker, Phys. Rev. A 67, 043820 (2003), and references therein.
[CrossRef]

S. John and T. Quang, Phys. Rev. A 50, 1764 (1994).
[CrossRef] [PubMed]

Phys. Rev. B (1)

F. J. García de Abajo and A. Howie, Phys. Rev. B 65, 115418 (2002).
[CrossRef]

Phys. Rev. Lett. (5)

H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, Phys. Rev. Lett. 83, 4357 (1999).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, Phys. Rev. Lett. 78, 3294 (1997).
[CrossRef]

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Science (1)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

Other (2)

L. A. Blanco and F. J. García de Abajo, Phys. Rev. B (to be published).

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions. Basic Processes and Applications (Wiley, New York, 1992).

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Figures (3)

Fig. 1
Fig. 1

(a) Square of the electric field strength near a five-groove axially symmetric silver grating illuminated by circularly polarized 600-nm light under normal incidence conditions. The field strength E is normalized to the incident field strength E0. (b), (c) Same as (a) for light coming at 5° and 30° off normal, respectively (see arrows). The geometric parameters are s=0.91λ, h=0.2s, and b=0.6s.

Fig. 2
Fig. 2

(a), (b) Square of the total electric field strength in the proximities of two five-groove axially symmetric silver gratings when a spontaneous-emitter atom is placed near and above the lower grating, with its transition electric dipole oriented toward the second grating [s=0.99λ, h=0.2s, b=0.6s; see Fig. 1(a)]. (c) Same as (b) for s=0.91λ. (d), (e) Same as (a) and (b) but with the electric dipole oriented perpendicularly to the symmetry axis of the system and s=0.91λ.

Fig. 3
Fig. 3

(a) Reflected near-field distribution produced by spontaneous emission from an atom located at the upper focus of an axially symmetric ellipsoid filled with a dielectric (=3), with aspect ratio 1:2 and short-axis radius a=0.68λ. Transition dipole d is oriented along the symmetry axis. (b) Emission rate for the system of (a) with (solid curve) and without (dashed curve) another atom identical to the first one and placed at the lower focus of the ellipsoid.

Equations (3)

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

Er=ikcdrjr+1k2jr·rrGr-r,
Edirr=expikrr3k2r2+ikr-1d-k2r2+3ikr-3d·rˆ·rˆ,
Hdirr=-ikexpikrr2ikr-1rˆ×d,

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