Abstract

Understanding the behavior of the evanescent part of the electromagnetic field has important implications in many branches of modern physics, such as near-field optics. Motivated by recent disagreement in the literature, we derive an expression for the far-field asymptotic behavior of the free-space electromagnetic Green tensor that is due to the evanescent modes.

© 1999 Optical Society of America

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References

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  1. M. Xiao, “A study of resolution limit in optical microscopy: near and far field,” Opt. Commun. 132, 403–409 (1996).
    [CrossRef]
  2. M. Xiao, “Evanescent field coupling of dipole to a surface: configurational resonance at long distances,” Chem. Phys. Lett. 258, 363–368 (1996).
    [CrossRef]
  3. M. Xiao, “On near-field scanning optical microscopy. Homogeneous and evanescent radiation,” J. Mod. Opt. 44, 327–344 (1997).
    [CrossRef]
  4. M. Xiao, “Two-point optical resolution with homogeneous, evanescent and self field: resolution criterion in near field imaging,” J. Mod. Opt. 44, 1609–1615 (1997).
    [CrossRef]
  5. M. Xiao, “Evanescent fields do contribute to the far field,” J. Mod. Opt. 46, 729–733 (1999).
    [CrossRef]
  6. E. Wolf, J. T. Foley, “Do evanescent waves contribute to the far field?” Opt. Lett. 23, 16–18 (1998).
    [CrossRef]
  7. T. Setälä, M. Kaivola, A. T. Friberg, “Decomposition of the point-dipole field into homogeneous and evanescent parts,” Phys. Rev. E 59, 1200–1206 (1999).
    [CrossRef]
  8. D. Courjon, C. Bannier, “Near field microscopy and near field optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
    [CrossRef]
  9. H. Weyl, “Ausbreitung elektromagnetischer Wellen über einem ebenen Leiter,” Ann. Phys. (Leipzig) 60, 481–500 (1919).See also A. Baños, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, New York, 1966), Eq. (2.19).
    [CrossRef]
  10. N. Bleistein, R. A. Handelsman, Asymptotic Expansions of Integrals (Holt, Rinehart & Winston, New York, 1975), Chap. 3.
  11. G. C. Sherman, J. J. Stamnes, A. J. Devaney, É Lalor, “Contribution of the inhomogeneous waves in angular-spectrum representations,” Opt. Commun. 8, 271–274 (1973).
    [CrossRef]

1999 (2)

M. Xiao, “Evanescent fields do contribute to the far field,” J. Mod. Opt. 46, 729–733 (1999).
[CrossRef]

T. Setälä, M. Kaivola, A. T. Friberg, “Decomposition of the point-dipole field into homogeneous and evanescent parts,” Phys. Rev. E 59, 1200–1206 (1999).
[CrossRef]

1998 (1)

1997 (2)

M. Xiao, “On near-field scanning optical microscopy. Homogeneous and evanescent radiation,” J. Mod. Opt. 44, 327–344 (1997).
[CrossRef]

M. Xiao, “Two-point optical resolution with homogeneous, evanescent and self field: resolution criterion in near field imaging,” J. Mod. Opt. 44, 1609–1615 (1997).
[CrossRef]

1996 (2)

M. Xiao, “A study of resolution limit in optical microscopy: near and far field,” Opt. Commun. 132, 403–409 (1996).
[CrossRef]

M. Xiao, “Evanescent field coupling of dipole to a surface: configurational resonance at long distances,” Chem. Phys. Lett. 258, 363–368 (1996).
[CrossRef]

1994 (1)

D. Courjon, C. Bannier, “Near field microscopy and near field optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
[CrossRef]

1973 (1)

G. C. Sherman, J. J. Stamnes, A. J. Devaney, É Lalor, “Contribution of the inhomogeneous waves in angular-spectrum representations,” Opt. Commun. 8, 271–274 (1973).
[CrossRef]

1919 (1)

H. Weyl, “Ausbreitung elektromagnetischer Wellen über einem ebenen Leiter,” Ann. Phys. (Leipzig) 60, 481–500 (1919).See also A. Baños, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, New York, 1966), Eq. (2.19).
[CrossRef]

Bannier, C.

D. Courjon, C. Bannier, “Near field microscopy and near field optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
[CrossRef]

Bleistein, N.

N. Bleistein, R. A. Handelsman, Asymptotic Expansions of Integrals (Holt, Rinehart & Winston, New York, 1975), Chap. 3.

Courjon, D.

D. Courjon, C. Bannier, “Near field microscopy and near field optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
[CrossRef]

Devaney, A. J.

G. C. Sherman, J. J. Stamnes, A. J. Devaney, É Lalor, “Contribution of the inhomogeneous waves in angular-spectrum representations,” Opt. Commun. 8, 271–274 (1973).
[CrossRef]

Foley, J. T.

Friberg, A. T.

T. Setälä, M. Kaivola, A. T. Friberg, “Decomposition of the point-dipole field into homogeneous and evanescent parts,” Phys. Rev. E 59, 1200–1206 (1999).
[CrossRef]

Handelsman, R. A.

N. Bleistein, R. A. Handelsman, Asymptotic Expansions of Integrals (Holt, Rinehart & Winston, New York, 1975), Chap. 3.

Kaivola, M.

T. Setälä, M. Kaivola, A. T. Friberg, “Decomposition of the point-dipole field into homogeneous and evanescent parts,” Phys. Rev. E 59, 1200–1206 (1999).
[CrossRef]

Lalor, É

G. C. Sherman, J. J. Stamnes, A. J. Devaney, É Lalor, “Contribution of the inhomogeneous waves in angular-spectrum representations,” Opt. Commun. 8, 271–274 (1973).
[CrossRef]

Setälä, T.

T. Setälä, M. Kaivola, A. T. Friberg, “Decomposition of the point-dipole field into homogeneous and evanescent parts,” Phys. Rev. E 59, 1200–1206 (1999).
[CrossRef]

Sherman, G. C.

G. C. Sherman, J. J. Stamnes, A. J. Devaney, É Lalor, “Contribution of the inhomogeneous waves in angular-spectrum representations,” Opt. Commun. 8, 271–274 (1973).
[CrossRef]

Stamnes, J. J.

G. C. Sherman, J. J. Stamnes, A. J. Devaney, É Lalor, “Contribution of the inhomogeneous waves in angular-spectrum representations,” Opt. Commun. 8, 271–274 (1973).
[CrossRef]

Weyl, H.

H. Weyl, “Ausbreitung elektromagnetischer Wellen über einem ebenen Leiter,” Ann. Phys. (Leipzig) 60, 481–500 (1919).See also A. Baños, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, New York, 1966), Eq. (2.19).
[CrossRef]

Wolf, E.

Xiao, M.

M. Xiao, “Evanescent fields do contribute to the far field,” J. Mod. Opt. 46, 729–733 (1999).
[CrossRef]

M. Xiao, “On near-field scanning optical microscopy. Homogeneous and evanescent radiation,” J. Mod. Opt. 44, 327–344 (1997).
[CrossRef]

M. Xiao, “Two-point optical resolution with homogeneous, evanescent and self field: resolution criterion in near field imaging,” J. Mod. Opt. 44, 1609–1615 (1997).
[CrossRef]

M. Xiao, “Evanescent field coupling of dipole to a surface: configurational resonance at long distances,” Chem. Phys. Lett. 258, 363–368 (1996).
[CrossRef]

M. Xiao, “A study of resolution limit in optical microscopy: near and far field,” Opt. Commun. 132, 403–409 (1996).
[CrossRef]

Ann. Phys. (Leipzig) (1)

H. Weyl, “Ausbreitung elektromagnetischer Wellen über einem ebenen Leiter,” Ann. Phys. (Leipzig) 60, 481–500 (1919).See also A. Baños, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, New York, 1966), Eq. (2.19).
[CrossRef]

Chem. Phys. Lett. (1)

M. Xiao, “Evanescent field coupling of dipole to a surface: configurational resonance at long distances,” Chem. Phys. Lett. 258, 363–368 (1996).
[CrossRef]

J. Mod. Opt. (3)

M. Xiao, “On near-field scanning optical microscopy. Homogeneous and evanescent radiation,” J. Mod. Opt. 44, 327–344 (1997).
[CrossRef]

M. Xiao, “Two-point optical resolution with homogeneous, evanescent and self field: resolution criterion in near field imaging,” J. Mod. Opt. 44, 1609–1615 (1997).
[CrossRef]

M. Xiao, “Evanescent fields do contribute to the far field,” J. Mod. Opt. 46, 729–733 (1999).
[CrossRef]

Opt. Commun. (2)

G. C. Sherman, J. J. Stamnes, A. J. Devaney, É Lalor, “Contribution of the inhomogeneous waves in angular-spectrum representations,” Opt. Commun. 8, 271–274 (1973).
[CrossRef]

M. Xiao, “A study of resolution limit in optical microscopy: near and far field,” Opt. Commun. 132, 403–409 (1996).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. E (1)

T. Setälä, M. Kaivola, A. T. Friberg, “Decomposition of the point-dipole field into homogeneous and evanescent parts,” Phys. Rev. E 59, 1200–1206 (1999).
[CrossRef]

Rep. Prog. Phys. (1)

D. Courjon, C. Bannier, “Near field microscopy and near field optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
[CrossRef]

Other (1)

N. Bleistein, R. A. Handelsman, Asymptotic Expansions of Integrals (Holt, Rinehart & Winston, New York, 1975), Chap. 3.

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Equations (10)

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Gαβ(x, ω)=δαβ+c2ω2 2xαxβG0(x, ω),
G0(x, ω)=12π d2k1β(k, ω)×exp[ikx-β(k, ω)|x3|],
β(k, ω)=k2-ω2/c2fork>ω/c-iω2/c2-k2fork<ω/c.
G0e(x, ω)=ω/cdk kβ(k, ω) J0(kr sin θ)×exp[-β(k, ω)r|cos θ|],
G0e(x, ω)=1r|cos θ| J0ωc r sin θ-|tan θ|ω/cdkJ1(kr sin θ)×exp[-β(k, ω)r|cos θ|].
G0e(x, ω)1r|cos θ| J0ωc r sin θ-sin θ(ω/c)r2|cos3 θ| J1ωc r sin θ+O(r-7/2),
(ω/c)r1.
G0e(x, ω)|θ=0,π=1/r,
Gαβe(x, ω)δαβ 1r|cos θ| J0ωc r sin θ+O(r-5/2),
(ω/c)r1.

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