Abstract

Reflection and refraction of electromagnetic multipole radiation by an interface is studied. The multipole can be electric or magnetic and is of arbitrary order (dipole, quadrupole). From the angular spectrum representation of the radiation emitted by the multipole, I have obtained the angular spectrum representations of the reflected and transmitted fields, which involve the Fresnel reflection and transmission coefficients. The intensity distribution in the far field is evaluated with the method of stationary phase. The result is very simple in appearance and can be expressed in terms of two auxiliary functions of a complex variable. By exchanging the Fresnel coefficients for s and p polarization, the result for an electric multipole can be obtained from the result for a magnetic multipole.

© 2005 Optical Society of America

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  1. K. H. Drexhage, “Interaction of light with monomolecular dye layers,” Prog. Opt. 12, 163–232 (1974).
    [CrossRef]
  2. R. R. Chance, A. Prock, R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 39, 1–65 (1978).
  3. G. W. Ford, W. H. Weber, “Electromagnetic effects on a molecule at a metal surface,” Surf. Sci. 109, 451–481 (1981).
    [CrossRef]
  4. P. Goy, J. M. Raimond, M. Gross, S. Haroche, “Observation of cavity-enhanced single-atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983).
    [CrossRef]
  5. G. W. Ford, W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
    [CrossRef]
  6. R. G. Hulet, E. S. Hilfer, D. Kleppner, “Inhibited spontaneous emission by a Rydberg atom,” Phys. Rev. Lett. 55, 2137–2140 (1985).
    [CrossRef] [PubMed]
  7. W. Jhe, A. Anderson, E. A. Hinds, D. Meschede, L. Moi, S. Haroche, “Suppression of spontaneous decay at optical frequencies: test of vacuum-field anisotropy in confined space,” Phys. Rev. Lett. 58, 666–669 (1987).
    [CrossRef] [PubMed]
  8. D. J. Heinzen, J. J. Childs, J. E. Thomas, M. S. Feld, “Enhanced and inhibited visible spontaneous emissions by atoms in a confocal resonator,” Phys. Rev. Lett. 58, 1320–1323 (1987).
    [CrossRef] [PubMed]
  9. G. S. Agarwal, “Coherence in spontaneous emission in the presence of a dielectric,” Phys. Rev. Lett. 32, 703–706 (1974).
    [CrossRef]
  10. W. Lukosz, R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane interface. I. Total radiated power,” J. Opt. Soc. Am. 67, 1607–1615 (1977).
    [CrossRef]
  11. W. Lukosz, “Theory of optical-environment-dependent spontaneous-emission rates for emitters in thin layers,” Phys. Rev. B 22, 3030–3038 (1980).
    [CrossRef]
  12. W. Lukosz, R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane interface. II. Radiation patterns of perpendicular oriented dipoles,” J. Opt. Soc. Am. 67, 1615–1619 (1977).
    [CrossRef]
  13. H. F. Arnoldus, J. T. Foley, “Transmission of dipole ra- diation through interfaces and the phenomenon of anti-critical angles,” J. Opt. Soc. Am. A 21, 1109–1117 (2004).
    [CrossRef]
  14. B. Hecht, “Forbidden light scanning near-field optical microscopy,” Ph.D. thesis (University of Basel, Basel, Switzerland, 1996).
  15. L. Novotny, D. W. Pohl, P. Regli, “Light propagation through nanometer-sized structures: the two-dimensional-aperture scanning near-field optical microscope,” J. Opt. Soc. Am. A 11, 1768–1779 (1994).
    [CrossRef]
  16. H. Heinzelmann, B. Hecht, L. Novotny, D. W. Pohl, “Forbidden light scanning near-field optical microscopy,” J. Microsc. 177, 115–118 (1995).
    [CrossRef]
  17. D. Van Labeke, F. Baida, D. Barchiesi, D. Courjon, “A theoretical model for the inverse scanning tunneling optical microscope (ISTOM),” Opt. Commun. 114, 470–480 (1995).
    [CrossRef]
  18. G. A. Massey, “Microscopy and pattern generation with scanned evanescent waves,” Appl. Opt. 23, 658–660 (1984).
    [CrossRef] [PubMed]
  19. J. M. Vigoureux, F. Depasse, C. Girard, “Superresolution of near-field optical microscopy defined from properties of confined electromagnetic waves,” Appl. Opt. 31, 3036–3045 (1992).
    [CrossRef] [PubMed]
  20. D. Van Labeke, D. Barchiesi, F. Baida, “Optical characterization of nanosources used in scanning near-field optical microscopy,” J. Opt. Soc. Am. A 12, 695–703 (1995).
    [CrossRef]
  21. B. Hecht, D. W. Pohl, H. Heinzelmann, “Tunnel near-field optical microscopy: TNOM-2,” in Photons and Local Probes, O. Marti, R. Möller, eds. (Kluwer, Dordrecht, The Netherlands, 1995), pp. 93–107.
  22. B. Hecht, H. Bielefeldt, D. W. Pohl, “Influence of detection conditions on near-field optical imaging,” J. Appl. Phys. 84, 5873–5882 (1998).
    [CrossRef]
  23. H. F. Arnoldus, J. T. Foley, “Spatial separation of the traveling and evanescent parts of dipole radiation,” Opt. Lett. 28, 1299–1301 (2003).
    [CrossRef] [PubMed]
  24. M. E. Rose, Multipole Fields (Wiley, New York, 1955).
  25. J. M. Eisenberg, W. Greiner, Excitation Mechanisms of the Nucleus (North-Holland, Amsterdam, The Netherlands, 1970), Chap. 3.
  26. M. E. Rose, Elementary Theory of Angular Momentum (Dover, New York, 1995), Chap. 7.
  27. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999), p. 441.
  28. A. J. Devaney, E. Wolf, “Multipole expansion and plane wave representations of the electromagnetic field,” J. Math. Phys. 15, 234–244 (1974).
    [CrossRef]
  29. H. F. Arnoldus, “Angular spectrum representation of the electromagnetic multipole fields,” submitted to J. Math. Phys.
  30. A. Erdélyi, “Zur Theory der Kugelwellen,” Physica (Utrecht) 4, 107–120 (1937).
    [CrossRef]
  31. J. E. Sipe, “The dipole antenna problem in surface physics: a new approach,” Surf. Sci. 105, 489–504 (1981).
    [CrossRef]
  32. J. E. Sipe, “New Green function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481–489 (1987).
    [CrossRef]
  33. J. Gasper, G. C. Sherman, J. J. Stamnes, “Reflection and refraction of an arbitrary electromagnetic wave at a plane interface,” J. Opt. Soc. Am. 66, 955–961 (1976).
    [CrossRef]
  34. G. C. Sherman, J. J. Stamnes, É. Lalor, “Asymptotic approximations to angular-spectrum representations,” J. Math. Phys. 17, 760–776 (1976).
    [CrossRef]
  35. M. Born, E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge U. Press, Cambridge, UK, 1999), App. III, p. 890.

2004 (1)

2003 (1)

H. F. Arnoldus, J. T. Foley, “Spatial separation of the traveling and evanescent parts of dipole radiation,” Opt. Lett. 28, 1299–1301 (2003).
[CrossRef] [PubMed]

1998 (1)

B. Hecht, H. Bielefeldt, D. W. Pohl, “Influence of detection conditions on near-field optical imaging,” J. Appl. Phys. 84, 5873–5882 (1998).
[CrossRef]

1995 (3)

D. Van Labeke, D. Barchiesi, F. Baida, “Optical characterization of nanosources used in scanning near-field optical microscopy,” J. Opt. Soc. Am. A 12, 695–703 (1995).
[CrossRef]

H. Heinzelmann, B. Hecht, L. Novotny, D. W. Pohl, “Forbidden light scanning near-field optical microscopy,” J. Microsc. 177, 115–118 (1995).
[CrossRef]

D. Van Labeke, F. Baida, D. Barchiesi, D. Courjon, “A theoretical model for the inverse scanning tunneling optical microscope (ISTOM),” Opt. Commun. 114, 470–480 (1995).
[CrossRef]

1994 (1)

1992 (1)

1987 (3)

W. Jhe, A. Anderson, E. A. Hinds, D. Meschede, L. Moi, S. Haroche, “Suppression of spontaneous decay at optical frequencies: test of vacuum-field anisotropy in confined space,” Phys. Rev. Lett. 58, 666–669 (1987).
[CrossRef] [PubMed]

D. J. Heinzen, J. J. Childs, J. E. Thomas, M. S. Feld, “Enhanced and inhibited visible spontaneous emissions by atoms in a confocal resonator,” Phys. Rev. Lett. 58, 1320–1323 (1987).
[CrossRef] [PubMed]

J. E. Sipe, “New Green function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481–489 (1987).
[CrossRef]

1985 (1)

R. G. Hulet, E. S. Hilfer, D. Kleppner, “Inhibited spontaneous emission by a Rydberg atom,” Phys. Rev. Lett. 55, 2137–2140 (1985).
[CrossRef] [PubMed]

1984 (2)

G. W. Ford, W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

G. A. Massey, “Microscopy and pattern generation with scanned evanescent waves,” Appl. Opt. 23, 658–660 (1984).
[CrossRef] [PubMed]

1983 (1)

P. Goy, J. M. Raimond, M. Gross, S. Haroche, “Observation of cavity-enhanced single-atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983).
[CrossRef]

1981 (2)

G. W. Ford, W. H. Weber, “Electromagnetic effects on a molecule at a metal surface,” Surf. Sci. 109, 451–481 (1981).
[CrossRef]

J. E. Sipe, “The dipole antenna problem in surface physics: a new approach,” Surf. Sci. 105, 489–504 (1981).
[CrossRef]

1980 (1)

W. Lukosz, “Theory of optical-environment-dependent spontaneous-emission rates for emitters in thin layers,” Phys. Rev. B 22, 3030–3038 (1980).
[CrossRef]

1978 (1)

R. R. Chance, A. Prock, R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 39, 1–65 (1978).

1977 (2)

1976 (2)

J. Gasper, G. C. Sherman, J. J. Stamnes, “Reflection and refraction of an arbitrary electromagnetic wave at a plane interface,” J. Opt. Soc. Am. 66, 955–961 (1976).
[CrossRef]

G. C. Sherman, J. J. Stamnes, É. Lalor, “Asymptotic approximations to angular-spectrum representations,” J. Math. Phys. 17, 760–776 (1976).
[CrossRef]

1974 (3)

A. J. Devaney, E. Wolf, “Multipole expansion and plane wave representations of the electromagnetic field,” J. Math. Phys. 15, 234–244 (1974).
[CrossRef]

K. H. Drexhage, “Interaction of light with monomolecular dye layers,” Prog. Opt. 12, 163–232 (1974).
[CrossRef]

G. S. Agarwal, “Coherence in spontaneous emission in the presence of a dielectric,” Phys. Rev. Lett. 32, 703–706 (1974).
[CrossRef]

1937 (1)

A. Erdélyi, “Zur Theory der Kugelwellen,” Physica (Utrecht) 4, 107–120 (1937).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, “Coherence in spontaneous emission in the presence of a dielectric,” Phys. Rev. Lett. 32, 703–706 (1974).
[CrossRef]

Anderson, A.

W. Jhe, A. Anderson, E. A. Hinds, D. Meschede, L. Moi, S. Haroche, “Suppression of spontaneous decay at optical frequencies: test of vacuum-field anisotropy in confined space,” Phys. Rev. Lett. 58, 666–669 (1987).
[CrossRef] [PubMed]

Arnoldus, H. F.

H. F. Arnoldus, J. T. Foley, “Transmission of dipole ra- diation through interfaces and the phenomenon of anti-critical angles,” J. Opt. Soc. Am. A 21, 1109–1117 (2004).
[CrossRef]

H. F. Arnoldus, J. T. Foley, “Spatial separation of the traveling and evanescent parts of dipole radiation,” Opt. Lett. 28, 1299–1301 (2003).
[CrossRef] [PubMed]

H. F. Arnoldus, “Angular spectrum representation of the electromagnetic multipole fields,” submitted to J. Math. Phys.

Baida, F.

D. Van Labeke, F. Baida, D. Barchiesi, D. Courjon, “A theoretical model for the inverse scanning tunneling optical microscope (ISTOM),” Opt. Commun. 114, 470–480 (1995).
[CrossRef]

D. Van Labeke, D. Barchiesi, F. Baida, “Optical characterization of nanosources used in scanning near-field optical microscopy,” J. Opt. Soc. Am. A 12, 695–703 (1995).
[CrossRef]

Barchiesi, D.

D. Van Labeke, D. Barchiesi, F. Baida, “Optical characterization of nanosources used in scanning near-field optical microscopy,” J. Opt. Soc. Am. A 12, 695–703 (1995).
[CrossRef]

D. Van Labeke, F. Baida, D. Barchiesi, D. Courjon, “A theoretical model for the inverse scanning tunneling optical microscope (ISTOM),” Opt. Commun. 114, 470–480 (1995).
[CrossRef]

Bielefeldt, H.

B. Hecht, H. Bielefeldt, D. W. Pohl, “Influence of detection conditions on near-field optical imaging,” J. Appl. Phys. 84, 5873–5882 (1998).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge U. Press, Cambridge, UK, 1999), App. III, p. 890.

Chance, R. R.

R. R. Chance, A. Prock, R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 39, 1–65 (1978).

Childs, J. J.

D. J. Heinzen, J. J. Childs, J. E. Thomas, M. S. Feld, “Enhanced and inhibited visible spontaneous emissions by atoms in a confocal resonator,” Phys. Rev. Lett. 58, 1320–1323 (1987).
[CrossRef] [PubMed]

Courjon, D.

D. Van Labeke, F. Baida, D. Barchiesi, D. Courjon, “A theoretical model for the inverse scanning tunneling optical microscope (ISTOM),” Opt. Commun. 114, 470–480 (1995).
[CrossRef]

Depasse, F.

Devaney, A. J.

A. J. Devaney, E. Wolf, “Multipole expansion and plane wave representations of the electromagnetic field,” J. Math. Phys. 15, 234–244 (1974).
[CrossRef]

Drexhage, K. H.

K. H. Drexhage, “Interaction of light with monomolecular dye layers,” Prog. Opt. 12, 163–232 (1974).
[CrossRef]

Eisenberg, J. M.

J. M. Eisenberg, W. Greiner, Excitation Mechanisms of the Nucleus (North-Holland, Amsterdam, The Netherlands, 1970), Chap. 3.

Erdélyi, A.

A. Erdélyi, “Zur Theory der Kugelwellen,” Physica (Utrecht) 4, 107–120 (1937).
[CrossRef]

Feld, M. S.

D. J. Heinzen, J. J. Childs, J. E. Thomas, M. S. Feld, “Enhanced and inhibited visible spontaneous emissions by atoms in a confocal resonator,” Phys. Rev. Lett. 58, 1320–1323 (1987).
[CrossRef] [PubMed]

Foley, J. T.

H. F. Arnoldus, J. T. Foley, “Transmission of dipole ra- diation through interfaces and the phenomenon of anti-critical angles,” J. Opt. Soc. Am. A 21, 1109–1117 (2004).
[CrossRef]

H. F. Arnoldus, J. T. Foley, “Spatial separation of the traveling and evanescent parts of dipole radiation,” Opt. Lett. 28, 1299–1301 (2003).
[CrossRef] [PubMed]

Ford, G. W.

G. W. Ford, W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

G. W. Ford, W. H. Weber, “Electromagnetic effects on a molecule at a metal surface,” Surf. Sci. 109, 451–481 (1981).
[CrossRef]

Gasper, J.

J. Gasper, G. C. Sherman, J. J. Stamnes, “Reflection and refraction of an arbitrary electromagnetic wave at a plane interface,” J. Opt. Soc. Am. 66, 955–961 (1976).
[CrossRef]

Girard, C.

Goy, P.

P. Goy, J. M. Raimond, M. Gross, S. Haroche, “Observation of cavity-enhanced single-atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983).
[CrossRef]

Greiner, W.

J. M. Eisenberg, W. Greiner, Excitation Mechanisms of the Nucleus (North-Holland, Amsterdam, The Netherlands, 1970), Chap. 3.

Gross, M.

P. Goy, J. M. Raimond, M. Gross, S. Haroche, “Observation of cavity-enhanced single-atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983).
[CrossRef]

Haroche, S.

W. Jhe, A. Anderson, E. A. Hinds, D. Meschede, L. Moi, S. Haroche, “Suppression of spontaneous decay at optical frequencies: test of vacuum-field anisotropy in confined space,” Phys. Rev. Lett. 58, 666–669 (1987).
[CrossRef] [PubMed]

P. Goy, J. M. Raimond, M. Gross, S. Haroche, “Observation of cavity-enhanced single-atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983).
[CrossRef]

Hecht, B.

B. Hecht, H. Bielefeldt, D. W. Pohl, “Influence of detection conditions on near-field optical imaging,” J. Appl. Phys. 84, 5873–5882 (1998).
[CrossRef]

H. Heinzelmann, B. Hecht, L. Novotny, D. W. Pohl, “Forbidden light scanning near-field optical microscopy,” J. Microsc. 177, 115–118 (1995).
[CrossRef]

B. Hecht, D. W. Pohl, H. Heinzelmann, “Tunnel near-field optical microscopy: TNOM-2,” in Photons and Local Probes, O. Marti, R. Möller, eds. (Kluwer, Dordrecht, The Netherlands, 1995), pp. 93–107.

B. Hecht, “Forbidden light scanning near-field optical microscopy,” Ph.D. thesis (University of Basel, Basel, Switzerland, 1996).

Heinzelmann, H.

H. Heinzelmann, B. Hecht, L. Novotny, D. W. Pohl, “Forbidden light scanning near-field optical microscopy,” J. Microsc. 177, 115–118 (1995).
[CrossRef]

B. Hecht, D. W. Pohl, H. Heinzelmann, “Tunnel near-field optical microscopy: TNOM-2,” in Photons and Local Probes, O. Marti, R. Möller, eds. (Kluwer, Dordrecht, The Netherlands, 1995), pp. 93–107.

Heinzen, D. J.

D. J. Heinzen, J. J. Childs, J. E. Thomas, M. S. Feld, “Enhanced and inhibited visible spontaneous emissions by atoms in a confocal resonator,” Phys. Rev. Lett. 58, 1320–1323 (1987).
[CrossRef] [PubMed]

Hilfer, E. S.

R. G. Hulet, E. S. Hilfer, D. Kleppner, “Inhibited spontaneous emission by a Rydberg atom,” Phys. Rev. Lett. 55, 2137–2140 (1985).
[CrossRef] [PubMed]

Hinds, E. A.

W. Jhe, A. Anderson, E. A. Hinds, D. Meschede, L. Moi, S. Haroche, “Suppression of spontaneous decay at optical frequencies: test of vacuum-field anisotropy in confined space,” Phys. Rev. Lett. 58, 666–669 (1987).
[CrossRef] [PubMed]

Hulet, R. G.

R. G. Hulet, E. S. Hilfer, D. Kleppner, “Inhibited spontaneous emission by a Rydberg atom,” Phys. Rev. Lett. 55, 2137–2140 (1985).
[CrossRef] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999), p. 441.

Jhe, W.

W. Jhe, A. Anderson, E. A. Hinds, D. Meschede, L. Moi, S. Haroche, “Suppression of spontaneous decay at optical frequencies: test of vacuum-field anisotropy in confined space,” Phys. Rev. Lett. 58, 666–669 (1987).
[CrossRef] [PubMed]

Kleppner, D.

R. G. Hulet, E. S. Hilfer, D. Kleppner, “Inhibited spontaneous emission by a Rydberg atom,” Phys. Rev. Lett. 55, 2137–2140 (1985).
[CrossRef] [PubMed]

Kunz, R. E.

Lalor, É.

G. C. Sherman, J. J. Stamnes, É. Lalor, “Asymptotic approximations to angular-spectrum representations,” J. Math. Phys. 17, 760–776 (1976).
[CrossRef]

Lukosz, W.

Massey, G. A.

Meschede, D.

W. Jhe, A. Anderson, E. A. Hinds, D. Meschede, L. Moi, S. Haroche, “Suppression of spontaneous decay at optical frequencies: test of vacuum-field anisotropy in confined space,” Phys. Rev. Lett. 58, 666–669 (1987).
[CrossRef] [PubMed]

Moi, L.

W. Jhe, A. Anderson, E. A. Hinds, D. Meschede, L. Moi, S. Haroche, “Suppression of spontaneous decay at optical frequencies: test of vacuum-field anisotropy in confined space,” Phys. Rev. Lett. 58, 666–669 (1987).
[CrossRef] [PubMed]

Novotny, L.

Pohl, D. W.

B. Hecht, H. Bielefeldt, D. W. Pohl, “Influence of detection conditions on near-field optical imaging,” J. Appl. Phys. 84, 5873–5882 (1998).
[CrossRef]

H. Heinzelmann, B. Hecht, L. Novotny, D. W. Pohl, “Forbidden light scanning near-field optical microscopy,” J. Microsc. 177, 115–118 (1995).
[CrossRef]

L. Novotny, D. W. Pohl, P. Regli, “Light propagation through nanometer-sized structures: the two-dimensional-aperture scanning near-field optical microscope,” J. Opt. Soc. Am. A 11, 1768–1779 (1994).
[CrossRef]

B. Hecht, D. W. Pohl, H. Heinzelmann, “Tunnel near-field optical microscopy: TNOM-2,” in Photons and Local Probes, O. Marti, R. Möller, eds. (Kluwer, Dordrecht, The Netherlands, 1995), pp. 93–107.

Prock, A.

R. R. Chance, A. Prock, R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 39, 1–65 (1978).

Raimond, J. M.

P. Goy, J. M. Raimond, M. Gross, S. Haroche, “Observation of cavity-enhanced single-atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983).
[CrossRef]

Regli, P.

Rose, M. E.

M. E. Rose, Multipole Fields (Wiley, New York, 1955).

M. E. Rose, Elementary Theory of Angular Momentum (Dover, New York, 1995), Chap. 7.

Sherman, G. C.

J. Gasper, G. C. Sherman, J. J. Stamnes, “Reflection and refraction of an arbitrary electromagnetic wave at a plane interface,” J. Opt. Soc. Am. 66, 955–961 (1976).
[CrossRef]

G. C. Sherman, J. J. Stamnes, É. Lalor, “Asymptotic approximations to angular-spectrum representations,” J. Math. Phys. 17, 760–776 (1976).
[CrossRef]

Silbey, R.

R. R. Chance, A. Prock, R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 39, 1–65 (1978).

Sipe, J. E.

J. E. Sipe, “New Green function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481–489 (1987).
[CrossRef]

J. E. Sipe, “The dipole antenna problem in surface physics: a new approach,” Surf. Sci. 105, 489–504 (1981).
[CrossRef]

Stamnes, J. J.

G. C. Sherman, J. J. Stamnes, É. Lalor, “Asymptotic approximations to angular-spectrum representations,” J. Math. Phys. 17, 760–776 (1976).
[CrossRef]

J. Gasper, G. C. Sherman, J. J. Stamnes, “Reflection and refraction of an arbitrary electromagnetic wave at a plane interface,” J. Opt. Soc. Am. 66, 955–961 (1976).
[CrossRef]

Thomas, J. E.

D. J. Heinzen, J. J. Childs, J. E. Thomas, M. S. Feld, “Enhanced and inhibited visible spontaneous emissions by atoms in a confocal resonator,” Phys. Rev. Lett. 58, 1320–1323 (1987).
[CrossRef] [PubMed]

Van Labeke, D.

D. Van Labeke, D. Barchiesi, F. Baida, “Optical characterization of nanosources used in scanning near-field optical microscopy,” J. Opt. Soc. Am. A 12, 695–703 (1995).
[CrossRef]

D. Van Labeke, F. Baida, D. Barchiesi, D. Courjon, “A theoretical model for the inverse scanning tunneling optical microscope (ISTOM),” Opt. Commun. 114, 470–480 (1995).
[CrossRef]

Vigoureux, J. M.

Weber, W. H.

G. W. Ford, W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

G. W. Ford, W. H. Weber, “Electromagnetic effects on a molecule at a metal surface,” Surf. Sci. 109, 451–481 (1981).
[CrossRef]

Wolf, E.

A. J. Devaney, E. Wolf, “Multipole expansion and plane wave representations of the electromagnetic field,” J. Math. Phys. 15, 234–244 (1974).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge U. Press, Cambridge, UK, 1999), App. III, p. 890.

Adv. Chem. Phys. (1)

R. R. Chance, A. Prock, R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 39, 1–65 (1978).

Appl. Opt. (2)

J. Math. Phys. (1)

A. J. Devaney, E. Wolf, “Multipole expansion and plane wave representations of the electromagnetic field,” J. Math. Phys. 15, 234–244 (1974).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Gasper, G. C. Sherman, J. J. Stamnes, “Reflection and refraction of an arbitrary electromagnetic wave at a plane interface,” J. Opt. Soc. Am. 66, 955–961 (1976).
[CrossRef]

J. Opt. Soc. Am. A (1)

D. Van Labeke, D. Barchiesi, F. Baida, “Optical characterization of nanosources used in scanning near-field optical microscopy,” J. Opt. Soc. Am. A 12, 695–703 (1995).
[CrossRef]

J. Appl. Phys. (1)

B. Hecht, H. Bielefeldt, D. W. Pohl, “Influence of detection conditions on near-field optical imaging,” J. Appl. Phys. 84, 5873–5882 (1998).
[CrossRef]

J. Math. Phys. (1)

G. C. Sherman, J. J. Stamnes, É. Lalor, “Asymptotic approximations to angular-spectrum representations,” J. Math. Phys. 17, 760–776 (1976).
[CrossRef]

J. Microsc. (1)

H. Heinzelmann, B. Hecht, L. Novotny, D. W. Pohl, “Forbidden light scanning near-field optical microscopy,” J. Microsc. 177, 115–118 (1995).
[CrossRef]

J. Opt. Soc. Am. (2)

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

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

D. Van Labeke, F. Baida, D. Barchiesi, D. Courjon, “A theoretical model for the inverse scanning tunneling optical microscope (ISTOM),” Opt. Commun. 114, 470–480 (1995).
[CrossRef]

Opt. Lett. (1)

H. F. Arnoldus, J. T. Foley, “Spatial separation of the traveling and evanescent parts of dipole radiation,” Opt. Lett. 28, 1299–1301 (2003).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

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Figures (5)

Fig. 1
Fig. 1

Illustration of the multipole located on the z axis, a distance H above the x y plane, and embedded in a medium with dielectric constant ε 1 . The layer has a thickness L and a dielectric constant ε 2 . The substrate occupies the region z < - L and is made of a material with dielectric constant ε 3 . The circles around the multipole schematically indicate that the emitted radiation is a spherical wave. The arrows represent the wave vectors of the traveling partial waves of the angular spectrum, and the labels de, inc., r, and t indicate the directly emitted, incident, reflected, and transmitted waves, respectively.

Fig. 2
Fig. 2

Illustration of the intensity distribution N 11 ( r ˆ ;   α ) for α = e and α = m . The dimensionless distance between the dipole and the surface is h = 1.8 π (almost a wavelength) and l = 0 (single interface). The dielectric constants are ε 1 = 1.5 and ε 3 = 1 .

Fig. 3
Fig. 3

Intensity distribution for dipole radiation with m = 1 . The thin curve is for a magnetic dipole and the thick curve for an electric dipole. The parameters are h = l = 0 ,   ε 1 = 1 , and ε 3 = 4 . The anticritical angle is 30°.

Fig. 4
Fig. 4

Intensity distribution of electric quadrupole radiation with m = 2 for a free quadrupole (thin curve) and for a quadrupole near an interface (thick curve). For the free quadrupole the intensity distribution is independent of the dielectric constant ε 1 and the height h. For the quadrupole near the interface the parameters are h = π ,   l = 0 ,   ε 1 = 2 , and ε 3 = 1.7 .

Fig. 5
Fig. 5

Radiation pattern for an electric quadrupole with m = 2 near an interface. We took h = π and l = 0 , and the dielectric constants are ε 1 = 1.7 and ε 3 = 2 so that θ ac = 67 ° .

Equations (77)

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E ( r ) = ik 0 3 4 π ε 0   b lm ( α ) A lm ( r ;   α ) ,
A lm ( r ;   m ) = h l ( 1 ) ( n 1 k 0 r ) T llm ( θ ,   ϕ )
T jlm ( θ ,   ϕ ) = μ μ ( l μ 1 μ | jm ) Y l μ ( θ ,   ϕ ) e μ
A lm ( r ;   e ) = - i n 1 k 0   × A lm ( r ;   m ) .
B ( r ) = - i ω   × E ( r ) .
A lm ( r ,   m ) = ( - i ) l 2 π n 1 k 0   d 2 k   1 β × exp ( i K ± · r   ) V lm ( ± cos θ ¯ ,   ϕ ¯ ) .
β = ( n 1 2 k 0 2 - k 2 ) 1 / 2 , k < n 1 k 0 i ( k 2 - n 1 2 k 0 2 ) 1 / 2 , k > n 1 k 0 .
K ± = k ± β e z ,
cos   θ ¯ = β n 1 k 0 ,
k = n 1 k 0   sin   θ ¯ ,
K ± = n 1 k 0   sin   θ ¯ ( e x   cos   ϕ ¯ + e y   sin   ϕ ¯ ) + n 1 k 0 e z   cos   θ ¯ .
A lm ( r ,   e ) = ( - i ) l 2 π n 1 k 0   d 2 k   1 β × exp ( i K ± · r ) K ˆ ±   ×   V lm ( ± cos   θ ¯ ,   ϕ ¯ ) ,
E s ( r ) = - ( - i ) l + 1 k 0 2 8 π 2 ε 0 n 1   b lm ( m ) d 2 k   1 β exp ( i K ± · r in 1 h   cos   θ ¯ ) V lm ( ± cos   θ ¯ ,   ϕ ¯ ) ,
E s ( r ) = - ( - i ) l + 1 k 0 2 8 π 2 ε 0 n 1   b lm ( e ) × d 2 k   1 β exp ( i K ± · r in 1 h   cos   θ ¯ ) K ˆ ±   ×   V lm ( ± cos   θ ¯ ,   ϕ ¯ ) .
E ( r ) = E de ( r ) + E r ( r ) ,
e s ± = k ˆ   ×   e z ,
e p ± = K ˆ ±   ×   e s ,
e p ± = ± cos   θ ¯ K ˆ - sin   θ ¯ e z .
K ˆ ± · V lm ( ± cos   θ ¯ ,   ϕ ¯ ) = 0 ,
V lm ( ± cos   θ ¯ ,   ϕ ¯ ) = σ e σ ± [ e σ ± · V lm ( ± cos   θ ¯ ,   ϕ ¯ ) ] .
K ˆ ±   ×   V lm ( ± cos   θ ¯ ,   ϕ ¯ ) = σ e σ ± [ ( e σ ±   ×   K ˆ ± ) · V lm ( ± cos   θ ¯ ,   ϕ ¯ ) ] ,
E de ( r ) = - ( - i ) l + 1 k 0 2 8 π 2 ε 0 n 1   b lm ( m ) d 2 k   1 β × exp ( i K + · r - in 1 h   cos   θ ¯ ) × σ e σ + [ e σ + · V lm ( cos   θ ¯ ,   ϕ ¯ ) ] .
α = k / k 0 = n 1   sin   θ ¯ .
E r ( r ) = - ( - i ) l + 1 k 0 2 8 π 2 ε 0 n 1   b lm ( m ) d 2 k   1 β × exp ( i K + · r + in 1 h   cos   θ ¯ ) × σ R σ ( α ) e σ + [ e σ - · V lm ( - cos   θ ¯ ,   ϕ ¯ ) ] ,
k t = k - k 0 ν 3 e z ,
ν 3 = ( ε 3 - α 2 ) 1 / 2 .
e pt = - 1 n 3   ( ν 3 k ˆ + α e z ) .
E ( r ) = - ( - i ) l + 1 k 0 2 8 π 2 ε 0 n 1   b lm ( m ) d 2 k   1 β × exp ( i k t · r + in 1 h   cos   θ ¯ ) × σ T σ ( α ) e σ t [ e σ - · V lm ( - cos   θ ¯ ,   ϕ ¯ ) ] ,
d 2 k   1 β exp ( i K + · r ) g ( k ) - 2 π i r exp ( in 1 k 0 r ) g ( k , 1 )
k , 1 = n 1 k 0   sin   θ e ρ ,
( e p - ) 1 = - cos   θ e ρ - sin   θ e z .
E de ( r ) ( - i ) l k 0 2 4 π ε 0 n 1 r   b lm ( m ) exp [ in 1 ( k 0 r - h   cos   θ ) ] × { e θ [ e θ · V lm ( cos   θ ,   ϕ ) ] + e ϕ [ e ϕ · V lm ( cos   θ ,   ϕ ) ] } ,
E r ( r ) ( - i ) l k 0 2 4 π ε 0 n 1 r   b lm ( m ) exp [ in 1 ( k 0 r + h   cos   θ ) ] × { - R p ( α 1 ) e θ [ ( cos   θ e ρ + sin   θ e z ) · V lm ( - cos   θ ,   ϕ ) ] + R s ( α 1 ) e ϕ [ e ϕ · V lm ( - cos   θ ,   ϕ ) ] } .
e ρ · V lm ( - cos   θ ,   ϕ ) = ( - 1 ) l + m + 1 e ρ · V lm ( cos   θ ,   ϕ ) ,
e z · V lm ( - cos   θ ,   ϕ ) = ( - 1 ) l + m e z · V lm ( cos   θ ,   ϕ ) ,
e ϕ · V lm ( - cos   θ ,   ϕ ) = ( - 1 ) l + m + 1 e ϕ · V lm ( cos   θ ,   ϕ ) .
( cos   θ e ρ + sin   θ e z ) · V lm ( - cos   θ ,   ϕ ) = ( - 1 ) l + m + 1 e θ · V lm ( cos   θ ,   ϕ ) ,
E ( r ) ( - i ) l k 0 2 4 π ε 0 n 1 r   b lm ( m ) exp [ in 1 ( k 0 r - h   cos   θ ) ] × { [ 1 + ( - 1 ) l + m R p ( α 1 ) exp ( 2 in 1 h   cos   θ ) ] × e θ [ e θ · V lm ( cos   θ ,   ϕ ) ] + [ 1 - ( - 1 ) l + m R s ( α 1 ) exp ( 2 in 1 h   cos   θ ) ] × e ϕ [ e ϕ · V lm ( cos   θ ,   ϕ ) ] } .
B ( r ) n 1 c   r ˆ   ×   E ( r )
d 2 k   1 β exp ( i k t · r ) g ( k ) 2 π i r   n 3   cos   θ n 1 ( cos   θ ¯ ) 3 × exp ( in 3 k 0 r ) g ( k , 3 ) .
k , 3 = n 3 k 0   sin   θ e ρ .
sin   θ ˆ = n 3 n 1 sin   θ ,
( e p - ) 3 = cos   θ ˆ e ρ - sin   θ ˆ e z
T ˆ σ ( α ) = ν 3 ν 1   T σ ( α ) ,
E ( r ) ( - i ) l k 0 2 4 π ε 0 n 1 r   b lm ( m ) exp ( in 3 k 0 r - in 1 h   cos   θ ˆ ) × { T ˆ p ( α 3 ) e θ [ ( cos   θ ˆ e ρ - sin   θ ˆ e z ) · V lm ( cos   θ ˆ ,   ϕ ) ] + T ˆ s ( α 3 ) e ϕ [ e ϕ · V lm ( cos   θ ˆ ,   ϕ ) ] } .
B ( r ) n 3 c   r ˆ   ×   E ( r )
sin   θ ac = n 1 n 3 .
S ( r ) = 1 2 μ 0   Re   E ( r )   ×   B ( r ) * .
S ( r ) = n 2 μ 0 c   [ E ( r ) · E ( r ) * ] r ˆ ,
d P d Ω = n 2 μ 0 c   r 2 E ( r ) · E ( r ) * .
d P d Ω = P 1 N lm ( r ˆ ;   α ) ,
P 1 = 1 2 n 1 μ 0 c   k 0 2 4 π ε 0 2 | b lm ( α ) | 2 .
N lm ( r ˆ ;   m ) = | 1 + ( - 1 ) l + m R p ( α 1 ) × exp ( 2 in 1 h   cos   θ ) | 2 | e θ · V lm ( cos   θ ,   ϕ ) | 2 + | 1 - ( - 1 ) l + m R s ( α 1 ) × exp ( 2 in 1 h   cos   θ ) | 2 | e ϕ · V lm ( cos   θ ,   ϕ ) | 2 ;
N lm ( r ˆ ;   m ) = n 3 n 1 exp ( 2 n 1 h   Im   cos   θ ˆ ) [ | T ˆ p ( α 3 ) | 2 | ( cos   θ ˆ e ρ - sin   θ ˆ e z ) · V lm ( cos   θ ˆ ,   ϕ ) | 2 + | T ˆ s ( α 3 ) | 2 | e ϕ · V lm ( cos   θ ˆ ,   ϕ ) | 2 ] .
e ρ · V lm ( z ,   ϕ ) = exp ( im ϕ ) e x · V lm ( z ,   0 ) ,
e ϕ · V lm ( z ,   ϕ ) = exp ( im ϕ ) e y · V lm ( z ,   0 ) ,
e z · V lm ( z ,   ϕ ) = exp ( im ϕ ) e z · V lm ( z ,   0 ) ,
e x · V l , - m ( z ,   0 ) = ( - 1 ) m + 1 e x · V lm ( z ,   0 ) ,
e ν · V l , - m ( z ,   0 ) = ( - 1 ) m e x · V lm ( z ,   0 ) ,
e z · V l , - m ( z ,   0 ) = ( - 1 ) m + 1 e z · V lm ( z ,   0 ) ,
[ cos   β ( cos   ϕ e x + sin   ϕ e y ) - sin   β e z ] · V lm ( cos   β ,   ϕ ) = - 1 sin   β   e z · V lm ( cos   β ,   ϕ ) ,
f lm ( z ) = 1 | 1 - z 2 |   | e z · V lm ( z ,   0 ) | 2 ,
g lm ( z ) = | e y · V lm ( z ,   0 ) | 2 ,
N lm ( r ˆ ;   m ) = | 1 + ( - 1 ) l + m R p ( α 1 ) × exp ( 2 in 1 h   cos   θ ) | 2 f lm ( cos   θ ) + | 1 - ( - 1 ) l + m R s ( α 1 ) × exp ( 2 in 1 h   cos   θ ) | 2 g lm ( cos   θ ) ,
N lm ( r ˆ ;   m ) = n 3 n 1 exp ( 2 n 1 h   Im   cos   θ ˆ ) × [ | T ˆ p ( α 3 ) | 2 f lm ( cos   θ ˆ ) + | T ˆ s ( α 3 ) | 2 g lm ( cos   θ ˆ ) ]
N lm ( r ˆ ;   α ) = f lm ( cos   θ ) + g lm ( cos   θ )
N lm ( r ˆ ;   α ) = V lm ( cos   θ ,   0 ) · V lm ( cos   θ ,   0 ) * .
f 11 ( z ) = 3 16 π ,
g 11 ( z ) = 3 16 π   | z | 2 ,
f 10 ( z ) = 0 ,
g 10 ( z ) = 3 8 π   | 1 - z 2 | .
f 22 ( z ) = 5 16 π   | 1 - z 2 | ,
g 22 ( z ) = 5 16 π   | 1 - z 2 | | z | 2 ,
f 21 ( z ) = 5 16 π   | z | 2 ,
g 21 ( z ) = 5 16 π   | 2 z 2 - 1 | 2 ,
f 20 ( z ) = 0 ,
g 20 ( z ) = 15 8 π   | 1 - z 2 | | z | 2 .

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