Abstract

Evanescent modes of the electromagnetic field are seldom invoked in conventional far-field optics, as their contribution far from the source (a few wavelengths) is negligible. Contradicting this fact, in recent theoretical works, based on a particular decomposition of the free-space Green tensor, it has been asserted that evanescent waves do indeed contribute to the far field, where they appear as an additional 1/r component of the field. We provide an explicit demonstration that evanescent modes do not contribute to the power radiated to the far field by any dipolar source. First we derive an expression for the free-space field susceptibility in which contributions from evanescent and homogeneous modes are separated, and then we use linear response theory to compute the decay rate for an atomic dipole in vacuum.

© 2000 Optical Society of America

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References

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  1. J.-J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133 (1997).
  2. M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, Cambridge, 1980).
  3. P. Dawson, B. A. F. Puygranier, W. Cao, and F. de Fornel, J. Microsc. 194, 578 (1999), and references therein.
    [CrossRef]
  4. M. Xiao, Opt. Commun. 132, 403 (1996); Chem. Phys. Lett. 258, 363 (1996); J. Mod. Opt. 44, 327, 1609 (1997); Opt. Commun. 136, 213 (1997); J. Mod. Opt. 46, 729 (1999).
    [CrossRef]
  5. E. Wolf and J. T. Foley, Opt. Lett. 23, 16 (1998).
    [CrossRef]
  6. T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. E 59, 1200 (1999).
    [CrossRef]
  7. G. C. Sherman, J. J. Stamnes, A. D. Devaney, and É Lalor, Opt. Commun. 8, 271 (1973); G. C. Sherman, J. J. Stamnes, and É. Lalor, J. Math. Phys. 17, 760 (1976).
    [CrossRef]
  8. A. V. Shchegrov and P. S. Carney, J. Opt. Soc. Am. A 16, 2583 (1999).
    [CrossRef]
  9. A. Banõs, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, New York, 1966).
  10. P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields (Pergamon, New York, 1966).
  11. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
    [CrossRef]
  12. G. S. Agarwal, Phys. Rev. A 11, 230 (1975).
    [CrossRef]
  13. A. Rahmani, P. C. Chaumet, F. de Fornel, and C. Girard, Phys. Rev. A 56, 3245 (1997).
    [CrossRef]
  14. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, corrected and enlarged ed. (Academic, New York, 1980).
  15. O. Keller, J. Opt. Soc. Am. B 16, 835 (1999).
    [CrossRef]
  16. J. Dalibard, J. Dupont-Roc, and C. Cohen-Tannoudji, J. Phys. (Paris) 43, 1617 (1982).
    [CrossRef]
  17. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley-Interscience, New York, 1992).
  18. J. M. Wylie and J. E. Sipe, Phys. Rev. A 30, 1185 (1984); Phys. Rev. A 32, 2030 (1985).
    [CrossRef]
  19. S. M. Barnett, B. Huttner, R. Loudon, and R. Matloob, J. Phys. B 29, 3763 (1996).
    [CrossRef]
  20. L. Mandel, J. Opt. Soc. Am. 72, 1011 (1972).

1999

P. Dawson, B. A. F. Puygranier, W. Cao, and F. de Fornel, J. Microsc. 194, 578 (1999), and references therein.
[CrossRef]

T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. E 59, 1200 (1999).
[CrossRef]

A. V. Shchegrov and P. S. Carney, J. Opt. Soc. Am. A 16, 2583 (1999).
[CrossRef]

O. Keller, J. Opt. Soc. Am. B 16, 835 (1999).
[CrossRef]

1998

1997

J.-J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133 (1997).

A. Rahmani, P. C. Chaumet, F. de Fornel, and C. Girard, Phys. Rev. A 56, 3245 (1997).
[CrossRef]

1996

M. Xiao, Opt. Commun. 132, 403 (1996); Chem. Phys. Lett. 258, 363 (1996); J. Mod. Opt. 44, 327, 1609 (1997); Opt. Commun. 136, 213 (1997); J. Mod. Opt. 46, 729 (1999).
[CrossRef]

S. M. Barnett, B. Huttner, R. Loudon, and R. Matloob, J. Phys. B 29, 3763 (1996).
[CrossRef]

1984

J. M. Wylie and J. E. Sipe, Phys. Rev. A 30, 1185 (1984); Phys. Rev. A 32, 2030 (1985).
[CrossRef]

1982

J. Dalibard, J. Dupont-Roc, and C. Cohen-Tannoudji, J. Phys. (Paris) 43, 1617 (1982).
[CrossRef]

1975

G. S. Agarwal, Phys. Rev. A 11, 230 (1975).
[CrossRef]

1973

G. C. Sherman, J. J. Stamnes, A. D. Devaney, and É Lalor, Opt. Commun. 8, 271 (1973); G. C. Sherman, J. J. Stamnes, and É. Lalor, J. Math. Phys. 17, 760 (1976).
[CrossRef]

1972

L. Mandel, J. Opt. Soc. Am. 72, 1011 (1972).

Agarwal, G. S.

G. S. Agarwal, Phys. Rev. A 11, 230 (1975).
[CrossRef]

Banõs, A.

A. Banõs, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, New York, 1966).

Barnett, S. M.

S. M. Barnett, B. Huttner, R. Loudon, and R. Matloob, J. Phys. B 29, 3763 (1996).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, Cambridge, 1980).

Cao, W.

P. Dawson, B. A. F. Puygranier, W. Cao, and F. de Fornel, J. Microsc. 194, 578 (1999), and references therein.
[CrossRef]

Carminati, R.

J.-J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133 (1997).

Carney, P. S.

Chaumet, P. C.

A. Rahmani, P. C. Chaumet, F. de Fornel, and C. Girard, Phys. Rev. A 56, 3245 (1997).
[CrossRef]

Clemmow, P. C.

P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields (Pergamon, New York, 1966).

Cohen-Tannoudji, C.

J. Dalibard, J. Dupont-Roc, and C. Cohen-Tannoudji, J. Phys. (Paris) 43, 1617 (1982).
[CrossRef]

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

Dalibard, J.

J. Dalibard, J. Dupont-Roc, and C. Cohen-Tannoudji, J. Phys. (Paris) 43, 1617 (1982).
[CrossRef]

Dawson, P.

P. Dawson, B. A. F. Puygranier, W. Cao, and F. de Fornel, J. Microsc. 194, 578 (1999), and references therein.
[CrossRef]

de Fornel, F.

P. Dawson, B. A. F. Puygranier, W. Cao, and F. de Fornel, J. Microsc. 194, 578 (1999), and references therein.
[CrossRef]

A. Rahmani, P. C. Chaumet, F. de Fornel, and C. Girard, Phys. Rev. A 56, 3245 (1997).
[CrossRef]

Devaney, A. D.

G. C. Sherman, J. J. Stamnes, A. D. Devaney, and É Lalor, Opt. Commun. 8, 271 (1973); G. C. Sherman, J. J. Stamnes, and É. Lalor, J. Math. Phys. 17, 760 (1976).
[CrossRef]

Dupont-Roc, J.

J. Dalibard, J. Dupont-Roc, and C. Cohen-Tannoudji, J. Phys. (Paris) 43, 1617 (1982).
[CrossRef]

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

Foley, J. T.

Friberg, A. T.

T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. E 59, 1200 (1999).
[CrossRef]

Girard, C.

A. Rahmani, P. C. Chaumet, F. de Fornel, and C. Girard, Phys. Rev. A 56, 3245 (1997).
[CrossRef]

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, corrected and enlarged ed. (Academic, New York, 1980).

Greffet, J.-J.

J.-J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133 (1997).

Grynberg, G.

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

Huttner, B.

S. M. Barnett, B. Huttner, R. Loudon, and R. Matloob, J. Phys. B 29, 3763 (1996).
[CrossRef]

Kaivola, M.

T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. E 59, 1200 (1999).
[CrossRef]

Keller, O.

Lalor, É

G. C. Sherman, J. J. Stamnes, A. D. Devaney, and É Lalor, Opt. Commun. 8, 271 (1973); G. C. Sherman, J. J. Stamnes, and É. Lalor, J. Math. Phys. 17, 760 (1976).
[CrossRef]

Loudon, R.

S. M. Barnett, B. Huttner, R. Loudon, and R. Matloob, J. Phys. B 29, 3763 (1996).
[CrossRef]

Mandel, L.

L. Mandel, J. Opt. Soc. Am. 72, 1011 (1972).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

Matloob, R.

S. M. Barnett, B. Huttner, R. Loudon, and R. Matloob, J. Phys. B 29, 3763 (1996).
[CrossRef]

Puygranier, B. A. F.

P. Dawson, B. A. F. Puygranier, W. Cao, and F. de Fornel, J. Microsc. 194, 578 (1999), and references therein.
[CrossRef]

Rahmani, A.

A. Rahmani, P. C. Chaumet, F. de Fornel, and C. Girard, Phys. Rev. A 56, 3245 (1997).
[CrossRef]

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, corrected and enlarged ed. (Academic, New York, 1980).

Setälä, T.

T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. E 59, 1200 (1999).
[CrossRef]

Shchegrov, A. V.

Sherman, G. C.

G. C. Sherman, J. J. Stamnes, A. D. Devaney, and É Lalor, Opt. Commun. 8, 271 (1973); G. C. Sherman, J. J. Stamnes, and É. Lalor, J. Math. Phys. 17, 760 (1976).
[CrossRef]

Sipe, J. E.

J. M. Wylie and J. E. Sipe, Phys. Rev. A 30, 1185 (1984); Phys. Rev. A 32, 2030 (1985).
[CrossRef]

Stamnes, J. J.

G. C. Sherman, J. J. Stamnes, A. D. Devaney, and É Lalor, Opt. Commun. 8, 271 (1973); G. C. Sherman, J. J. Stamnes, and É. Lalor, J. Math. Phys. 17, 760 (1976).
[CrossRef]

Wolf, E.

E. Wolf and J. T. Foley, Opt. Lett. 23, 16 (1998).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, Cambridge, 1980).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

Wylie, J. M.

J. M. Wylie and J. E. Sipe, Phys. Rev. A 30, 1185 (1984); Phys. Rev. A 32, 2030 (1985).
[CrossRef]

Xiao, M.

M. Xiao, Opt. Commun. 132, 403 (1996); Chem. Phys. Lett. 258, 363 (1996); J. Mod. Opt. 44, 327, 1609 (1997); Opt. Commun. 136, 213 (1997); J. Mod. Opt. 46, 729 (1999).
[CrossRef]

J. Microsc.

P. Dawson, B. A. F. Puygranier, W. Cao, and F. de Fornel, J. Microsc. 194, 578 (1999), and references therein.
[CrossRef]

J. Opt. Soc. Am.

L. Mandel, J. Opt. Soc. Am. 72, 1011 (1972).

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Phys. (Paris)

J. Dalibard, J. Dupont-Roc, and C. Cohen-Tannoudji, J. Phys. (Paris) 43, 1617 (1982).
[CrossRef]

J. Phys. B

S. M. Barnett, B. Huttner, R. Loudon, and R. Matloob, J. Phys. B 29, 3763 (1996).
[CrossRef]

Opt. Commun.

M. Xiao, Opt. Commun. 132, 403 (1996); Chem. Phys. Lett. 258, 363 (1996); J. Mod. Opt. 44, 327, 1609 (1997); Opt. Commun. 136, 213 (1997); J. Mod. Opt. 46, 729 (1999).
[CrossRef]

G. C. Sherman, J. J. Stamnes, A. D. Devaney, and É Lalor, Opt. Commun. 8, 271 (1973); G. C. Sherman, J. J. Stamnes, and É. Lalor, J. Math. Phys. 17, 760 (1976).
[CrossRef]

Opt. Lett.

Phys. Rev. A

J. M. Wylie and J. E. Sipe, Phys. Rev. A 30, 1185 (1984); Phys. Rev. A 32, 2030 (1985).
[CrossRef]

G. S. Agarwal, Phys. Rev. A 11, 230 (1975).
[CrossRef]

A. Rahmani, P. C. Chaumet, F. de Fornel, and C. Girard, Phys. Rev. A 56, 3245 (1997).
[CrossRef]

Phys. Rev. E

T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. E 59, 1200 (1999).
[CrossRef]

Prog. Surf. Sci.

J.-J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133 (1997).

Other

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, Cambridge, 1980).

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, corrected and enlarged ed. (Academic, New York, 1980).

A. Banõs, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, New York, 1966).

P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields (Pergamon, New York, 1966).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

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

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Equations (15)

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Edipr;ω=i2πdkxdkyw0k02μ+μ·×expikxx+ikyy+iw0z,
Edipαr;ω=βFαβμβ,
Fxx=i20k0-0idw0k02+w02×J0k02-w021/2R+k02-w02×cos 2ϕJ2k02-w021/2Rexpiw0z,
Fxy=i20k0-0idw0k02-w02×sin 2ϕJ2k02-w021/2Rexpiw0z,
Fxz=0k0-0idw0w0k02-w021/2×cos ϕJ1k02-w021/2R×expiw0zsgnz,
Fyy=i20k0-0idw0k02+w02×J0k02-w021/2R-k02-w02×cos 2ϕJ2k02-w021/2R×expiw0z,
Fyz=0k0-0idw0w0k02-w021/2×sin ϕJ1k02-w021/2R×expiw0zsgnz,
Fzz=i0k0-0idw0k02-w02×J0k02-w021/2Rexpiw0z,
Γba=2α,βμαμβ ImFαβR=0,z=0;ω,
Fαβr;ω=δαβ-3rαrβr21r3+k031k0r+ik02r2-1k03r3δαβ-1k0r+3ik03r2-3k03r3rαrβr2expik0r,
limr0 ImFαβr;ω=k03δαβ,
Γba=4k03μ23,
I1=120k0dw0k02+w02
I2=0k0dw0k02-w02
limR,z0 ImFαβR,z;ω=k03δαβ;

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