Abstract

We report on theoretical studies of the inhibition of the spontaneous emission process in subwavelength dielectric media. We discuss the modification of the spontaneous emission rate as a function of the size and shape of the medium as well as the position of the emitter in it.

© 2003 Optical Society of America

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  1. E. M. Purcell, Phys. Rev. 69, 681 (1946).
    [CrossRef]
  2. K. H. Drexhage, J. Lumin. 1–2, 693 (1970).
    [CrossRef]
  3. P. R. Berman, ed., Cavity Quantum Electrodynamics (Academic, San Diego, Calif., 1994).
  4. R. K. Chang A. J. Campillo, eds., Optical Processes in Microcavities (World Scientific, Singapore, 1996).
  5. J. Gersten and A. Nitzan, J. Chem. Phys. 75, 1139 (1981).
  6. C. Girard, O. Martin, and A. Dereux, Phys. Rev. Lett. 75, 3098 (1995).
    [CrossRef] [PubMed]
  7. H. Chew, Phys. Rev. A 38, 3410 (1988).
    [CrossRef] [PubMed]
  8. V. V. Klimov, M. Ducloy, and V. S. Letokhov, J. Mod. Opt. 43, 549 (1996).
    [CrossRef]
  9. L. Novotny, Appl. Phys. Lett. 69, 3806 (1996).
    [CrossRef]
  10. C. Henkel and V. Sandoghdar, Opt. Commun. 158, 250 (1998).
    [CrossRef]
  11. G. Parent, D. van Labeke, and D. Barchiesi, J. Opt. Soc. Am. A 16, 896 (1999).
    [CrossRef]
  12. A. Rahmani, P. C. Chaumet, and F. de Fornel, Phys. Rev. A 63, 023819 (2001).
    [CrossRef]
  13. H. Schniepp and V. Sandoghdar, Phys. Rev. Lett. 89, 257403 (2002).
    [CrossRef]
  14. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).
  15. A perpendicular dipole in two dimensions is in fact equivalent to an oscillating point charge. At short scales its electric field is qualitatively different from a dipole field. Since this orientation is not a good representation of the physical (three-dimensional) situation in the laboratory, we do not consider it in this work.
  16. R. F. Harrington, Field Computation by Moment Methods (Institute for Electrical and Electronics Engineers, Piscataway, N.J., 1993).
    [CrossRef]
  17. A. Lagendijk, B. Nienhuis, B. A. van Tiggelen, and P. de Vries, Phys. Rev. Lett. 79, 657 (1997).
    [CrossRef]
  18. F. J. P. Schuurmans, P. de Vries, and A. Lagendijk, Phys. Lett. A 264, 472 (2000).
    [CrossRef]
  19. A. Rahmani, Opt. Lett. 27, 430 (2002).
    [CrossRef]
  20. L. Rogobete, V. Sandoghdar, and C. Henkel, “Modification of spontaneous emission in nanoscopic environments,” submitted to J. Opt. B.
  21. W. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
  22. M. Kreiter, M. Prummer, B. Hecht, and U. P. Wild, J. Chem. Phys. 117, 9430 (2002).
  23. R. Loudon, The Quantum Theory of Light (Oxford U. Press, London, 1983).
  24. G. Nienhuis and C. Th. J. Alkemade, Physica (Amsterdam) 81C, 181 (1976).
  25. In a two-dimensional problem, as a result of the functional form of the mode density r, the factor 1/n becomes 1.
  26. V. V. Batygin and I. N. Toptygin, Problems in Electrodynamics (Academic, London, 1978), problems 193–200.
  27. J. van Kranendonk and J. Sipe, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1977), Vol. 15, p. 245.
    [CrossRef]

2002

H. Schniepp and V. Sandoghdar, Phys. Rev. Lett. 89, 257403 (2002).
[CrossRef]

M. Kreiter, M. Prummer, B. Hecht, and U. P. Wild, J. Chem. Phys. 117, 9430 (2002).

A. Rahmani, Opt. Lett. 27, 430 (2002).
[CrossRef]

2001

A. Rahmani, P. C. Chaumet, and F. de Fornel, Phys. Rev. A 63, 023819 (2001).
[CrossRef]

2000

F. J. P. Schuurmans, P. de Vries, and A. Lagendijk, Phys. Lett. A 264, 472 (2000).
[CrossRef]

1999

G. Parent, D. van Labeke, and D. Barchiesi, J. Opt. Soc. Am. A 16, 896 (1999).
[CrossRef]

1998

C. Henkel and V. Sandoghdar, Opt. Commun. 158, 250 (1998).
[CrossRef]

1997

A. Lagendijk, B. Nienhuis, B. A. van Tiggelen, and P. de Vries, Phys. Rev. Lett. 79, 657 (1997).
[CrossRef]

1996

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

V. V. Klimov, M. Ducloy, and V. S. Letokhov, J. Mod. Opt. 43, 549 (1996).
[CrossRef]

L. Novotny, Appl. Phys. Lett. 69, 3806 (1996).
[CrossRef]

1995

C. Girard, O. Martin, and A. Dereux, Phys. Rev. Lett. 75, 3098 (1995).
[CrossRef] [PubMed]

1994

P. R. Berman, ed., Cavity Quantum Electrodynamics (Academic, San Diego, Calif., 1994).

1993

R. F. Harrington, Field Computation by Moment Methods (Institute for Electrical and Electronics Engineers, Piscataway, N.J., 1993).
[CrossRef]

1991

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).

1988

H. Chew, Phys. Rev. A 38, 3410 (1988).
[CrossRef] [PubMed]

1983

R. Loudon, The Quantum Theory of Light (Oxford U. Press, London, 1983).

1981

J. Gersten and A. Nitzan, J. Chem. Phys. 75, 1139 (1981).

1978

V. V. Batygin and I. N. Toptygin, Problems in Electrodynamics (Academic, London, 1978), problems 193–200.

1977

J. van Kranendonk and J. Sipe, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1977), Vol. 15, p. 245.
[CrossRef]

1976

G. Nienhuis and C. Th. J. Alkemade, Physica (Amsterdam) 81C, 181 (1976).

1975

W. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

1970

K. H. Drexhage, J. Lumin. 1–2, 693 (1970).
[CrossRef]

1946

E. M. Purcell, Phys. Rev. 69, 681 (1946).
[CrossRef]

Alkemade, C. Th. J.

G. Nienhuis and C. Th. J. Alkemade, Physica (Amsterdam) 81C, 181 (1976).

Barchiesi, D.

G. Parent, D. van Labeke, and D. Barchiesi, J. Opt. Soc. Am. A 16, 896 (1999).
[CrossRef]

Batygin, V. V.

V. V. Batygin and I. N. Toptygin, Problems in Electrodynamics (Academic, London, 1978), problems 193–200.

Chaumet, P. C.

A. Rahmani, P. C. Chaumet, and F. de Fornel, Phys. Rev. A 63, 023819 (2001).
[CrossRef]

Chew, H.

H. Chew, Phys. Rev. A 38, 3410 (1988).
[CrossRef] [PubMed]

de Fornel, F.

A. Rahmani, P. C. Chaumet, and F. de Fornel, Phys. Rev. A 63, 023819 (2001).
[CrossRef]

de Vries, P.

F. J. P. Schuurmans, P. de Vries, and A. Lagendijk, Phys. Lett. A 264, 472 (2000).
[CrossRef]

A. Lagendijk, B. Nienhuis, B. A. van Tiggelen, and P. de Vries, Phys. Rev. Lett. 79, 657 (1997).
[CrossRef]

Dereux, A.

C. Girard, O. Martin, and A. Dereux, Phys. Rev. Lett. 75, 3098 (1995).
[CrossRef] [PubMed]

Drexhage, K. H.

K. H. Drexhage, J. Lumin. 1–2, 693 (1970).
[CrossRef]

Ducloy, M.

V. V. Klimov, M. Ducloy, and V. S. Letokhov, J. Mod. Opt. 43, 549 (1996).
[CrossRef]

Gersten, J.

J. Gersten and A. Nitzan, J. Chem. Phys. 75, 1139 (1981).

Girard, C.

C. Girard, O. Martin, and A. Dereux, Phys. Rev. Lett. 75, 3098 (1995).
[CrossRef] [PubMed]

Harrington, R. F.

R. F. Harrington, Field Computation by Moment Methods (Institute for Electrical and Electronics Engineers, Piscataway, N.J., 1993).
[CrossRef]

Hecht, B.

M. Kreiter, M. Prummer, B. Hecht, and U. P. Wild, J. Chem. Phys. 117, 9430 (2002).

Henkel, C.

C. Henkel and V. Sandoghdar, Opt. Commun. 158, 250 (1998).
[CrossRef]

L. Rogobete, V. Sandoghdar, and C. Henkel, “Modification of spontaneous emission in nanoscopic environments,” submitted to J. Opt. B.

Jackson, W. D.

W. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

Klimov, V. V.

V. V. Klimov, M. Ducloy, and V. S. Letokhov, J. Mod. Opt. 43, 549 (1996).
[CrossRef]

Kreiter, M.

M. Kreiter, M. Prummer, B. Hecht, and U. P. Wild, J. Chem. Phys. 117, 9430 (2002).

Lagendijk, A.

F. J. P. Schuurmans, P. de Vries, and A. Lagendijk, Phys. Lett. A 264, 472 (2000).
[CrossRef]

A. Lagendijk, B. Nienhuis, B. A. van Tiggelen, and P. de Vries, Phys. Rev. Lett. 79, 657 (1997).
[CrossRef]

Letokhov, V. S.

V. V. Klimov, M. Ducloy, and V. S. Letokhov, J. Mod. Opt. 43, 549 (1996).
[CrossRef]

Loudon, R.

R. Loudon, The Quantum Theory of Light (Oxford U. Press, London, 1983).

Martin, O.

C. Girard, O. Martin, and A. Dereux, Phys. Rev. Lett. 75, 3098 (1995).
[CrossRef] [PubMed]

Nienhuis, B.

A. Lagendijk, B. Nienhuis, B. A. van Tiggelen, and P. de Vries, Phys. Rev. Lett. 79, 657 (1997).
[CrossRef]

Nienhuis, G.

G. Nienhuis and C. Th. J. Alkemade, Physica (Amsterdam) 81C, 181 (1976).

Nieto-Vesperinas, M.

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).

Nitzan, A.

J. Gersten and A. Nitzan, J. Chem. Phys. 75, 1139 (1981).

Novotny, L.

L. Novotny, Appl. Phys. Lett. 69, 3806 (1996).
[CrossRef]

Parent, G.

G. Parent, D. van Labeke, and D. Barchiesi, J. Opt. Soc. Am. A 16, 896 (1999).
[CrossRef]

Prummer, M.

M. Kreiter, M. Prummer, B. Hecht, and U. P. Wild, J. Chem. Phys. 117, 9430 (2002).

Purcell, E. M.

E. M. Purcell, Phys. Rev. 69, 681 (1946).
[CrossRef]

Rahmani, A.

A. Rahmani, Opt. Lett. 27, 430 (2002).
[CrossRef]

A. Rahmani, P. C. Chaumet, and F. de Fornel, Phys. Rev. A 63, 023819 (2001).
[CrossRef]

Rogobete, L.

L. Rogobete, V. Sandoghdar, and C. Henkel, “Modification of spontaneous emission in nanoscopic environments,” submitted to J. Opt. B.

Sandoghdar, V.

H. Schniepp and V. Sandoghdar, Phys. Rev. Lett. 89, 257403 (2002).
[CrossRef]

C. Henkel and V. Sandoghdar, Opt. Commun. 158, 250 (1998).
[CrossRef]

L. Rogobete, V. Sandoghdar, and C. Henkel, “Modification of spontaneous emission in nanoscopic environments,” submitted to J. Opt. B.

Schniepp, H.

H. Schniepp and V. Sandoghdar, Phys. Rev. Lett. 89, 257403 (2002).
[CrossRef]

Schuurmans, F. J. P.

F. J. P. Schuurmans, P. de Vries, and A. Lagendijk, Phys. Lett. A 264, 472 (2000).
[CrossRef]

Sipe, J.

J. van Kranendonk and J. Sipe, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1977), Vol. 15, p. 245.
[CrossRef]

Toptygin, I. N.

V. V. Batygin and I. N. Toptygin, Problems in Electrodynamics (Academic, London, 1978), problems 193–200.

van Kranendonk, J.

J. van Kranendonk and J. Sipe, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1977), Vol. 15, p. 245.
[CrossRef]

van Labeke, D.

G. Parent, D. van Labeke, and D. Barchiesi, J. Opt. Soc. Am. A 16, 896 (1999).
[CrossRef]

van Tiggelen, B. A.

A. Lagendijk, B. Nienhuis, B. A. van Tiggelen, and P. de Vries, Phys. Rev. Lett. 79, 657 (1997).
[CrossRef]

Wild, U. P.

M. Kreiter, M. Prummer, B. Hecht, and U. P. Wild, J. Chem. Phys. 117, 9430 (2002).

Appl. Phys. Lett.

L. Novotny, Appl. Phys. Lett. 69, 3806 (1996).
[CrossRef]

J. Chem. Phys.

J. Gersten and A. Nitzan, J. Chem. Phys. 75, 1139 (1981).

M. Kreiter, M. Prummer, B. Hecht, and U. P. Wild, J. Chem. Phys. 117, 9430 (2002).

J. Lumin.

K. H. Drexhage, J. Lumin. 1–2, 693 (1970).
[CrossRef]

J. Mod. Opt.

V. V. Klimov, M. Ducloy, and V. S. Letokhov, J. Mod. Opt. 43, 549 (1996).
[CrossRef]

J. Opt. B

L. Rogobete, V. Sandoghdar, and C. Henkel, “Modification of spontaneous emission in nanoscopic environments,” submitted to J. Opt. B.

J. Opt. Soc. Am. A

G. Parent, D. van Labeke, and D. Barchiesi, J. Opt. Soc. Am. A 16, 896 (1999).
[CrossRef]

Opt. Commun.

C. Henkel and V. Sandoghdar, Opt. Commun. 158, 250 (1998).
[CrossRef]

Opt. Lett.

Phys. Lett. A

F. J. P. Schuurmans, P. de Vries, and A. Lagendijk, Phys. Lett. A 264, 472 (2000).
[CrossRef]

Phys. Rev.

E. M. Purcell, Phys. Rev. 69, 681 (1946).
[CrossRef]

Phys. Rev. A

H. Chew, Phys. Rev. A 38, 3410 (1988).
[CrossRef] [PubMed]

A. Rahmani, P. C. Chaumet, and F. de Fornel, Phys. Rev. A 63, 023819 (2001).
[CrossRef]

Phys. Rev. Lett.

H. Schniepp and V. Sandoghdar, Phys. Rev. Lett. 89, 257403 (2002).
[CrossRef]

A. Lagendijk, B. Nienhuis, B. A. van Tiggelen, and P. de Vries, Phys. Rev. Lett. 79, 657 (1997).
[CrossRef]

C. Girard, O. Martin, and A. Dereux, Phys. Rev. Lett. 75, 3098 (1995).
[CrossRef] [PubMed]

Physica (Amsterdam)

G. Nienhuis and C. Th. J. Alkemade, Physica (Amsterdam) 81C, 181 (1976).

Other

In a two-dimensional problem, as a result of the functional form of the mode density r, the factor 1/n becomes 1.

V. V. Batygin and I. N. Toptygin, Problems in Electrodynamics (Academic, London, 1978), problems 193–200.

J. van Kranendonk and J. Sipe, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1977), Vol. 15, p. 245.
[CrossRef]

R. Loudon, The Quantum Theory of Light (Oxford U. Press, London, 1983).

P. R. Berman, ed., Cavity Quantum Electrodynamics (Academic, San Diego, Calif., 1994).

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

W. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).

A perpendicular dipole in two dimensions is in fact equivalent to an oscillating point charge. At short scales its electric field is qualitatively different from a dipole field. Since this orientation is not a good representation of the physical (three-dimensional) situation in the laboratory, we do not consider it in this work.

R. F. Harrington, Field Computation by Moment Methods (Institute for Electrical and Electronics Engineers, Piscataway, N.J., 1993).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Normalized radiative decay rate versus host particle size. Symbols, numerical calculation for triangles, square, pentagons, and circles. Solid curve, analytical result for a circular object.

Fig. 2
Fig. 2

Normalized radiative decay rate versus source position as it approaches a corner of the particle. The same particle geometries were considered as in Fig. 1, but the particle size was chosen to have a surface area of 56 nm2.

Fig. 3
Fig. 3

Normalized decay rate for rectangular particles with different aspect ratios a:b=1:20, 1:5, 1:1, 5:1, 20:1, as indicated by the boxes at the left. The molecular dipole points upward along the b edge. The horizontal lines signify the limiting values 1 and 1/n4 obtained from Eq. (1) for elliptical particles. Insets, relative orientations and strengths of the relevant vacuum electric fields and their depolarization fields inside the particles.

Equations (1)

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γ2Dγbulkf2=γbulka+b2n2a+b2,

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