Abstract

We investigate the propagating and evanescent field contributions in the scattering of an electromagnetic field from a collection of interacting electric point dipoles. Having applications of scanning near-field optical microscopy (SNOM) in mind, we study three different geometries of dipoles placed close to a bulk surface. One of them is chosen to allow a direct comparison with the results recently put forward in the literature [J. Mod. Opt. 44, 327 (1997)] and to point out the discrepancies in the near zone between the field decompositions applied in that paper and in our work. The other two geometries have been selected to illustrate SNOM action in the illumination and collection modes. Within the point-dipole model we investigate the effects of the probe-dipole polarization on the propagating and evanescent fields in the sample–probe system during the scanning of the probe at different heights above the sample.

© 2001 Optical Society of America

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  1. E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
    [CrossRef] [PubMed]
  2. D. Courjon, C. Bainier, “Near-field microscopy and near-field optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
    [CrossRef]
  3. M. Ohtsu, H. Hori, Near-Field Nano-Optics: From Basic Principles to Nano-Fabrication and Nano-Photonics (Kluwer Academic/Plenum, New York, 1999).
  4. C. Girard, A. Dereux, “Near-field optics theories,” Rep. Prog. Phys. 59, 657–699 (1996).
    [CrossRef]
  5. J.-J. Greffet, R. Carminati, “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237 (1997).
    [CrossRef]
  6. J. M. Vigoureux, C. Girard, D. Courjon, “General principles of scanning tunneling optical microscopy,” Opt. Lett. 14, 1039–1041 (1989).
    [CrossRef] [PubMed]
  7. C. Girard, C. Joachim, S. Gauthier, “The physics of the near-field,” Rep. Prog. Phys. 63, 893–938 (2000).
    [CrossRef]
  8. T. Setälä, A. T. Friberg, M. Kaivola, “Decomposition of the point-dipole field into homogeneous and evanescent parts,” Phys. Rev. E 59, 1200–1206 (1999).
    [CrossRef]
  9. M. Xiao, “A study of resolution in optical microscopy: near and far field,” Opt. Commun. 132, 403–409 (1996).
    [CrossRef]
  10. M. Xiao, “Evanescent field coupling of dipole to a surface: configurational resonance at long distances,” Chem. Phys. Lett. 258, 363–368 (1996).
    [CrossRef]
  11. M. Xiao, “On near-field scanning optical microscopy. Homogeneous and evanescent radiation,” J. Mod. Opt. 44, 327–344 (1997).
    [CrossRef]
  12. M. Xiao, “Polarization effects in reflection scanning near-field optical microscopy,” Opt. Commun. 136, 213–218 (1997).
    [CrossRef]
  13. M. Xiao, “Cutting off the diffraction: a numerical solution in scanning near-field optical microscopy,” Appl. Phys. Lett. 69, 3125–3127 (1996).
    [CrossRef]
  14. M. Xiao, A. Zayats, J. Siqueiros, “Scattering of surface-plasmon polaritons by dipoles near a surface: optical near-field localization,” Phys. Rev. B 55, 1824–1837 (1997).
    [CrossRef]
  15. M. Xiao, “Evanescent fields do contribute to the far field,” J. Mod. Opt. 46, 729–733 (1999).
    [CrossRef]
  16. E. Wolf, J. T. Foley, “Do evanescent waves contribute to the far field,” Opt. Lett. 23, 16–18 (1998).
    [CrossRef]
  17. O. Keller, “Attached and radiated electromagnetic fields of an electric point dipole,” J. Opt. Soc. Am. B 16, 835–847 (1999).
    [CrossRef]
  18. A. V. Shchegrov, P. S. Carney, “Far-field contribution of evanescent modes to the electromagnetic Green tensor,” J. Opt. Soc. Am. A 16, 2583–2584 (1999).
    [CrossRef]
  19. O. Keller, M. Xiao, S. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci. 280, 217–230 (1993).
    [CrossRef]
  20. B. Labani, C. Girard, D. Courjon, D. Van Labeke, “Optical interaction between a dielectric tip and a nanometric lattice: implications for near-field microscopy,” J. Opt. Soc. Am. B 7, 936–943 (1990).
    [CrossRef]
  21. C. Girard, A. Dereux, “Optical spectroscopy of a surface at the nanometer scale: a theoretical study in real space,” Phys. Rev. B 49, 11344–11351 (1994).
    [CrossRef]
  22. L. Novotny, B. Hecht, D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1798–1806 (1997).
    [CrossRef]
  23. L. Novotny, “Allowed and forbidden light in near-field optics. II. Interacting dipolar particles,” J. Opt. Soc. Am. A 14, 105–113 (1997).
    [CrossRef]
  24. B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
    [CrossRef]
  25. P. C. Chaumet, A. Rahmani, F. de Fornel, J.-P. Dufour, “Evanescent light scattering: the validity of the dipole approximation,” Phys. Rev. B 58, 2310–2315 (1998).
    [CrossRef]
  26. J. Michaelis, C. Hettich, J. Mlynek, V. Sandoghdar, “Optical microscopy using a single-molecule light source,” Nature 405, 325–328 (2000).
    [CrossRef] [PubMed]
  27. C.-T. Tai, Dyadic Green’s Functions in Electromagnetic Theory (Intext, Scranton, PA, 1971).
  28. P. de Vries, D. V. van Coevorden, A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys. 70, 447–466 (1998).
    [CrossRef]
  29. M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1980).
  30. N. W. Ashcroft, N. D. Mermin, Solid-State Physics (Saunders College Publishing, Philadelphia, Pa.1976).
  31. O. Keller, “Screened electromagnetic propagators in nonlocal metal optics,” Phys. Rev. B 34, 3883–3899 (1986).
    [CrossRef]
  32. O. Keller, “Tensor–product structure of a new electromagnetic propagator for nonlocal surface optics of metals,” Phys. Rev. B 37, 10588–10607 (1988).
    [CrossRef]
  33. J. E. Sipe, “New Green-function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481–489 (1987).
    [CrossRef]
  34. P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  35. C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Generation of optical standing waves around mesoscopic surface structures: scattering and light confinement,” Phys. Rev. B 52, 2889–2898 (1995).
    [CrossRef]
  36. J.-C. Weeber, E. Bourillot, A. Dereux, J.-P. Goudonnet, Y. Chen, C. Girard, “Observation of light confinement effects with a near-field optical microscope,” Phys. Rev. Lett. 77, 5332–5335 (1996).
    [CrossRef] [PubMed]

2000 (2)

C. Girard, C. Joachim, S. Gauthier, “The physics of the near-field,” Rep. Prog. Phys. 63, 893–938 (2000).
[CrossRef]

J. Michaelis, C. Hettich, J. Mlynek, V. Sandoghdar, “Optical microscopy using a single-molecule light source,” Nature 405, 325–328 (2000).
[CrossRef] [PubMed]

1999 (4)

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

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

A. V. Shchegrov, P. S. Carney, “Far-field contribution of evanescent modes to the electromagnetic Green tensor,” J. Opt. Soc. Am. A 16, 2583–2584 (1999).
[CrossRef]

O. Keller, “Attached and radiated electromagnetic fields of an electric point dipole,” J. Opt. Soc. Am. B 16, 835–847 (1999).
[CrossRef]

1998 (3)

E. Wolf, J. T. Foley, “Do evanescent waves contribute to the far field,” Opt. Lett. 23, 16–18 (1998).
[CrossRef]

P. de Vries, D. V. van Coevorden, A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys. 70, 447–466 (1998).
[CrossRef]

P. C. Chaumet, A. Rahmani, F. de Fornel, J.-P. Dufour, “Evanescent light scattering: the validity of the dipole approximation,” Phys. Rev. B 58, 2310–2315 (1998).
[CrossRef]

1997 (6)

M. Xiao, A. Zayats, J. Siqueiros, “Scattering of surface-plasmon polaritons by dipoles near a surface: optical near-field localization,” Phys. Rev. B 55, 1824–1837 (1997).
[CrossRef]

J.-J. Greffet, R. Carminati, “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237 (1997).
[CrossRef]

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

M. Xiao, “Polarization effects in reflection scanning near-field optical microscopy,” Opt. Commun. 136, 213–218 (1997).
[CrossRef]

L. Novotny, “Allowed and forbidden light in near-field optics. II. Interacting dipolar particles,” J. Opt. Soc. Am. A 14, 105–113 (1997).
[CrossRef]

L. Novotny, B. Hecht, D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1798–1806 (1997).
[CrossRef]

1996 (5)

J.-C. Weeber, E. Bourillot, A. Dereux, J.-P. Goudonnet, Y. Chen, C. Girard, “Observation of light confinement effects with a near-field optical microscope,” Phys. Rev. Lett. 77, 5332–5335 (1996).
[CrossRef] [PubMed]

M. Xiao, “Cutting off the diffraction: a numerical solution in scanning near-field optical microscopy,” Appl. Phys. Lett. 69, 3125–3127 (1996).
[CrossRef]

M. Xiao, “A study of resolution 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]

C. Girard, A. Dereux, “Near-field optics theories,” Rep. Prog. Phys. 59, 657–699 (1996).
[CrossRef]

1995 (1)

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Generation of optical standing waves around mesoscopic surface structures: scattering and light confinement,” Phys. Rev. B 52, 2889–2898 (1995).
[CrossRef]

1994 (3)

B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
[CrossRef]

C. Girard, A. Dereux, “Optical spectroscopy of a surface at the nanometer scale: a theoretical study in real space,” Phys. Rev. B 49, 11344–11351 (1994).
[CrossRef]

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

1993 (1)

O. Keller, M. Xiao, S. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci. 280, 217–230 (1993).
[CrossRef]

1992 (1)

E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
[CrossRef] [PubMed]

1990 (1)

1989 (1)

1988 (1)

O. Keller, “Tensor–product structure of a new electromagnetic propagator for nonlocal surface optics of metals,” Phys. Rev. B 37, 10588–10607 (1988).
[CrossRef]

1987 (1)

1986 (1)

O. Keller, “Screened electromagnetic propagators in nonlocal metal optics,” Phys. Rev. B 34, 3883–3899 (1986).
[CrossRef]

1972 (1)

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Ashcroft, N. W.

N. W. Ashcroft, N. D. Mermin, Solid-State Physics (Saunders College Publishing, Philadelphia, Pa.1976).

Bainier, C.

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

Betzig, E.

E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
[CrossRef] [PubMed]

Born, M.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1980).

Bourillot, E.

J.-C. Weeber, E. Bourillot, A. Dereux, J.-P. Goudonnet, Y. Chen, C. Girard, “Observation of light confinement effects with a near-field optical microscope,” Phys. Rev. Lett. 77, 5332–5335 (1996).
[CrossRef] [PubMed]

Bozhevolnyi, S.

O. Keller, M. Xiao, S. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci. 280, 217–230 (1993).
[CrossRef]

Carminati, R.

J.-J. Greffet, R. Carminati, “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237 (1997).
[CrossRef]

Carney, P. S.

Chaumet, P. C.

P. C. Chaumet, A. Rahmani, F. de Fornel, J.-P. Dufour, “Evanescent light scattering: the validity of the dipole approximation,” Phys. Rev. B 58, 2310–2315 (1998).
[CrossRef]

Chen, Y.

J.-C. Weeber, E. Bourillot, A. Dereux, J.-P. Goudonnet, Y. Chen, C. Girard, “Observation of light confinement effects with a near-field optical microscope,” Phys. Rev. Lett. 77, 5332–5335 (1996).
[CrossRef] [PubMed]

Christy, R. W.

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Courjon, D.

de Fornel, F.

P. C. Chaumet, A. Rahmani, F. de Fornel, J.-P. Dufour, “Evanescent light scattering: the validity of the dipole approximation,” Phys. Rev. B 58, 2310–2315 (1998).
[CrossRef]

de Vries, P.

P. de Vries, D. V. van Coevorden, A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys. 70, 447–466 (1998).
[CrossRef]

Dereux, A.

J.-C. Weeber, E. Bourillot, A. Dereux, J.-P. Goudonnet, Y. Chen, C. Girard, “Observation of light confinement effects with a near-field optical microscope,” Phys. Rev. Lett. 77, 5332–5335 (1996).
[CrossRef] [PubMed]

C. Girard, A. Dereux, “Near-field optics theories,” Rep. Prog. Phys. 59, 657–699 (1996).
[CrossRef]

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Generation of optical standing waves around mesoscopic surface structures: scattering and light confinement,” Phys. Rev. B 52, 2889–2898 (1995).
[CrossRef]

C. Girard, A. Dereux, “Optical spectroscopy of a surface at the nanometer scale: a theoretical study in real space,” Phys. Rev. B 49, 11344–11351 (1994).
[CrossRef]

Devel, M.

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Generation of optical standing waves around mesoscopic surface structures: scattering and light confinement,” Phys. Rev. B 52, 2889–2898 (1995).
[CrossRef]

Draine, B. T.

Dufour, J.-P.

P. C. Chaumet, A. Rahmani, F. de Fornel, J.-P. Dufour, “Evanescent light scattering: the validity of the dipole approximation,” Phys. Rev. B 58, 2310–2315 (1998).
[CrossRef]

Flatau, P. J.

Foley, J. T.

Friberg, A. T.

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

Gauthier, S.

C. Girard, C. Joachim, S. Gauthier, “The physics of the near-field,” Rep. Prog. Phys. 63, 893–938 (2000).
[CrossRef]

Girard, C.

C. Girard, C. Joachim, S. Gauthier, “The physics of the near-field,” Rep. Prog. Phys. 63, 893–938 (2000).
[CrossRef]

C. Girard, A. Dereux, “Near-field optics theories,” Rep. Prog. Phys. 59, 657–699 (1996).
[CrossRef]

J.-C. Weeber, E. Bourillot, A. Dereux, J.-P. Goudonnet, Y. Chen, C. Girard, “Observation of light confinement effects with a near-field optical microscope,” Phys. Rev. Lett. 77, 5332–5335 (1996).
[CrossRef] [PubMed]

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Generation of optical standing waves around mesoscopic surface structures: scattering and light confinement,” Phys. Rev. B 52, 2889–2898 (1995).
[CrossRef]

C. Girard, A. Dereux, “Optical spectroscopy of a surface at the nanometer scale: a theoretical study in real space,” Phys. Rev. B 49, 11344–11351 (1994).
[CrossRef]

B. Labani, C. Girard, D. Courjon, D. Van Labeke, “Optical interaction between a dielectric tip and a nanometric lattice: implications for near-field microscopy,” J. Opt. Soc. Am. B 7, 936–943 (1990).
[CrossRef]

J. M. Vigoureux, C. Girard, D. Courjon, “General principles of scanning tunneling optical microscopy,” Opt. Lett. 14, 1039–1041 (1989).
[CrossRef] [PubMed]

Goudonnet, J.-P.

J.-C. Weeber, E. Bourillot, A. Dereux, J.-P. Goudonnet, Y. Chen, C. Girard, “Observation of light confinement effects with a near-field optical microscope,” Phys. Rev. Lett. 77, 5332–5335 (1996).
[CrossRef] [PubMed]

Greffet, J.-J.

J.-J. Greffet, R. Carminati, “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237 (1997).
[CrossRef]

Hecht, B.

L. Novotny, B. Hecht, D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1798–1806 (1997).
[CrossRef]

Hettich, C.

J. Michaelis, C. Hettich, J. Mlynek, V. Sandoghdar, “Optical microscopy using a single-molecule light source,” Nature 405, 325–328 (2000).
[CrossRef] [PubMed]

Hori, H.

M. Ohtsu, H. Hori, Near-Field Nano-Optics: From Basic Principles to Nano-Fabrication and Nano-Photonics (Kluwer Academic/Plenum, New York, 1999).

Joachim, C.

C. Girard, C. Joachim, S. Gauthier, “The physics of the near-field,” Rep. Prog. Phys. 63, 893–938 (2000).
[CrossRef]

Johnson, P. B.

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Kaivola, M.

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

Keller, O.

O. Keller, “Attached and radiated electromagnetic fields of an electric point dipole,” J. Opt. Soc. Am. B 16, 835–847 (1999).
[CrossRef]

O. Keller, M. Xiao, S. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci. 280, 217–230 (1993).
[CrossRef]

O. Keller, “Tensor–product structure of a new electromagnetic propagator for nonlocal surface optics of metals,” Phys. Rev. B 37, 10588–10607 (1988).
[CrossRef]

O. Keller, “Screened electromagnetic propagators in nonlocal metal optics,” Phys. Rev. B 34, 3883–3899 (1986).
[CrossRef]

Labani, B.

Lagendijk, A.

P. de Vries, D. V. van Coevorden, A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys. 70, 447–466 (1998).
[CrossRef]

Martin, O. J. F.

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Generation of optical standing waves around mesoscopic surface structures: scattering and light confinement,” Phys. Rev. B 52, 2889–2898 (1995).
[CrossRef]

Mermin, N. D.

N. W. Ashcroft, N. D. Mermin, Solid-State Physics (Saunders College Publishing, Philadelphia, Pa.1976).

Michaelis, J.

J. Michaelis, C. Hettich, J. Mlynek, V. Sandoghdar, “Optical microscopy using a single-molecule light source,” Nature 405, 325–328 (2000).
[CrossRef] [PubMed]

Mlynek, J.

J. Michaelis, C. Hettich, J. Mlynek, V. Sandoghdar, “Optical microscopy using a single-molecule light source,” Nature 405, 325–328 (2000).
[CrossRef] [PubMed]

Novotny, L.

L. Novotny, “Allowed and forbidden light in near-field optics. II. Interacting dipolar particles,” J. Opt. Soc. Am. A 14, 105–113 (1997).
[CrossRef]

L. Novotny, B. Hecht, D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1798–1806 (1997).
[CrossRef]

Ohtsu, M.

M. Ohtsu, H. Hori, Near-Field Nano-Optics: From Basic Principles to Nano-Fabrication and Nano-Photonics (Kluwer Academic/Plenum, New York, 1999).

Pohl, D. W.

L. Novotny, B. Hecht, D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1798–1806 (1997).
[CrossRef]

Rahmani, A.

P. C. Chaumet, A. Rahmani, F. de Fornel, J.-P. Dufour, “Evanescent light scattering: the validity of the dipole approximation,” Phys. Rev. B 58, 2310–2315 (1998).
[CrossRef]

Sandoghdar, V.

J. Michaelis, C. Hettich, J. Mlynek, V. Sandoghdar, “Optical microscopy using a single-molecule light source,” Nature 405, 325–328 (2000).
[CrossRef] [PubMed]

Setälä, T.

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

Shchegrov, A. V.

Sipe, J. E.

Siqueiros, J.

M. Xiao, A. Zayats, J. Siqueiros, “Scattering of surface-plasmon polaritons by dipoles near a surface: optical near-field localization,” Phys. Rev. B 55, 1824–1837 (1997).
[CrossRef]

Tai, C.-T.

C.-T. Tai, Dyadic Green’s Functions in Electromagnetic Theory (Intext, Scranton, PA, 1971).

Trautman, J. K.

E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
[CrossRef] [PubMed]

van Coevorden, D. V.

P. de Vries, D. V. van Coevorden, A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys. 70, 447–466 (1998).
[CrossRef]

Van Labeke, D.

Vigoureux, J. M.

Weeber, J.-C.

J.-C. Weeber, E. Bourillot, A. Dereux, J.-P. Goudonnet, Y. Chen, C. Girard, “Observation of light confinement effects with a near-field optical microscope,” Phys. Rev. Lett. 77, 5332–5335 (1996).
[CrossRef] [PubMed]

Wolf, E.

E. Wolf, J. T. Foley, “Do evanescent waves contribute to the far field,” Opt. Lett. 23, 16–18 (1998).
[CrossRef]

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1980).

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, A. Zayats, J. Siqueiros, “Scattering of surface-plasmon polaritons by dipoles near a surface: optical near-field localization,” Phys. Rev. B 55, 1824–1837 (1997).
[CrossRef]

M. Xiao, “Polarization effects in reflection scanning near-field optical microscopy,” Opt. Commun. 136, 213–218 (1997).
[CrossRef]

M. Xiao, “A study of resolution 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]

M. Xiao, “Cutting off the diffraction: a numerical solution in scanning near-field optical microscopy,” Appl. Phys. Lett. 69, 3125–3127 (1996).
[CrossRef]

O. Keller, M. Xiao, S. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci. 280, 217–230 (1993).
[CrossRef]

Zayats, A.

M. Xiao, A. Zayats, J. Siqueiros, “Scattering of surface-plasmon polaritons by dipoles near a surface: optical near-field localization,” Phys. Rev. B 55, 1824–1837 (1997).
[CrossRef]

Appl. Phys. Lett. (1)

M. Xiao, “Cutting off the diffraction: a numerical solution in scanning near-field optical microscopy,” Appl. Phys. Lett. 69, 3125–3127 (1996).
[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. Appl. Phys. (1)

L. Novotny, B. Hecht, D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1798–1806 (1997).
[CrossRef]

J. Mod. Opt. (2)

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

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

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (3)

Nature (1)

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[CrossRef]

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Phys. Rev. B (7)

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

Phys. Rev. E (1)

T. Setälä, A. T. Friberg, M. Kaivola, “Decomposition of the point-dipole field into homogeneous and evanescent parts,” Phys. Rev. E 59, 1200–1206 (1999).
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Phys. Rev. Lett. (1)

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[CrossRef] [PubMed]

Prog. Surf. Sci. (1)

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Science (1)

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Figures (10)

Fig. 1
Fig. 1

Geometry I: Ten interacting point dipoles with the polarizability of a mesoscopic silver sphere of 20-nm radius are located at the height of z=20 nm above bulk silver, which fills the half-space z0. The dipoles lie in the range of x1=3000 nm to x10=4800 nm in the y=0 plane. The separation between the adjacent dipoles is 200 nm. The external polarizing field at the dipole sites is E0=(0, 0, 1). The wavelength of the light is λ=633 nm, and the refractive index34 used for silver is ηAg=0.06+i4.0.

Fig. 2
Fig. 2

Logarithmic intensity distributions of the evanescent field in geometry I, obtained with (a) our Green function,8 (b) Green function of Refs. 6-12. Solid curves, fields calculated at the height of z=40 nm; dotted curves, z=4λ. In both cases the calculations were performed for the y=0 plane.

Fig. 3
Fig. 3

Geometry II: SNOM action in the illumination mode. Nine interacting point dipoles are located symmetrically about the z axis 20 nm above the bulk silver, which fills the half-space z0. The distance between the nearest-neighbor dipoles is 60 nm. The probe dipole, which illuminates the nine sample dipoles, is scanned over the surface at different heights zp. The polarizabilities of the sample dipoles and the probe dipole correspond to those of mesoscopic silver and glass spheres, respectively, with a radius of 20 nm. In calculation of the case of no probe dipole present, the sample dipoles are excited with a p-polarized plane wave propagating at an angle of incidence of θ=45°. Both the incident and the reflected light contribute to the local field at the dipole sites. The wavelength of the light is λ=633 nm, and the refractive indices of silver34 and glass are nAg=0.06+i4.0 and nglass=1.5.

Fig. 4
Fig. 4

Logarithmic intensity distributions of the (a) homogeneous, (b) evanescent, and (c) total fields scattered from the sample dipoles in geometry II at the height of z=60 nm from the surface. The probe dipole is excluded and the incident field is a p-polarized plane wave with an angle of incidence of θ = 45°.

Fig. 5
Fig. 5

Logarithmic intensity distributions of the (a) homogeneous, (b) evanescent, and (c) total fields at the height of z=60 nm in geometry II when the probe dipole is included. The probe is swept in the plane zp=60 nm over the sample dipoles, and the intensity distributions represent the scattered field at the probe site. The probe is polarized in the z direction. The external field is zero in this case.

Fig. 6
Fig. 6

Logarithmic intensity distributions of the (a) homogeneous, (b) evanescent, and (c) total fields as in Fig. 5 but for a probe dipole polarized in the x direction.

Fig. 7
Fig. 7

Logarithmic intensity distributions of the (a) homogeneous, (b) evanescent, and (c) total fields as in Fig. 5 but for zp=80 nm.

Fig. 8
Fig. 8

Geometry III: SNOM action in the collection mode. Nine interacting point dipoles are located symmetrically around the z axis 20 nm above a bulk dielectric (glass, n=1.5), which fills the half-space z0. The distance between the nearest-neighbor dipoles is 60 nm. The polarizable probe dipole is scanned at the height of zp=60 nm over the surface. The field exciting the sample dipoles is the evanescent field created in total internal reflection of a plane wave propagating in the dielectric with an angle of incident of θ=60°. The polarizability of the sample dipoles and the probe dipole corresponds to that of mesoscopic silver (nAg=0.06+i4.0) and of glass spheres with a radius of 20 nm, respectively.

Fig. 9
Fig. 9

Logarithmic intensity distributions of the (a) homogeneous, (b) evanescent, and (c) total fields at the height of z=60 nm from the surface in geometry III. The incident light in the dielectric is s-polarized. The angle of incidence for the plane wave is θ=60°. The probe is swept in the plane zp=60 nm over the sample dipoles, and the intensity distributions represent the scattered field at the probe site.

Fig. 10
Fig. 10

Logarithmic intensity distributions of the (a) homogeneous, (b) evanescent, and (c) total fields at the height of z=60 nm above the surface in Geometry III. The sample dipoles are excited as in Fig. 9, but with a p-polarized plane wave incident at an angle of θ=60° from below the surface.

Equations (28)

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××E(r)-k2E(r)=k20P(r),
××G(r, r)-k2G(r, r)=4πδ(r-r)U,
G(r, r)=U+1k2 G(r, r),
G(r, r)=exp (ik|r-r|)|r-r|.
G(r, r)=1r+ikr2-1k2r3U+-1r-3ikr2+3k2r3r0r0exp (ikr),
EP(r)=k24π0G(r, r)P(r)dV,
E(r)=E0(r)+EP(r),
P(r)=i=1NPi(r)δ(r-ri).
Pi(ri)=αiE(ri),
E(r)=E0(r)+k24π0i=1NG(r, ri)[αiE(ri)].
E(rj)=E0(rj)+k24π0i=1NG(rj, ri)[αiE(ri)],
j=1, 2 ,, N.
G(r, ri)=GH(r, ri)+GE(r, ri),
EH,E(r)=k24π0i=1NGH,E(r, ri)[αiE(ri)],
αi(ω)=αi(ω)U,
αi(ω)=4π0αi3i(ω)-1i(ω)+2.
rp(ω)=s(ω)-1s(ω)+1,
M(ω)=rp(ω)-1000-10001.
αis(ω)=αi(ω)1/1-αi(ω)rp(ω)4π0(2h)30001/1-αi(ω)rp(ω)4π0(2h)30001/1-αi(ω)rp(ω)2π0(2h)3,
E(rj)=E0(rj)+k24π0i=1N[G(rj, ri)+G(rj, rim)M][αiE(ri)],
EE,H(r)=k24π0i=1N[GE,H(r, ri)+GE,H(r, rim)M][αiE(ri)].
GH(r)=ikI0H+k2(x2-y2)β3 L1H-k2x2β2 L2Hk2xyβ22β L1H-L2Hikxβ L3Hk2xyβ22β L1H-L2HI0H+k2(y2-x2)β3 L1H-k2y2β2 L2Hikyβ L3Hikxβ L3Hikyβ L3HL2H,
L1H(r)=iα [J1(β)-βI1H],L2H(r)=I0H-I2HL3H(r)=-1β [J0(β)+iαI0H-2I1H-iαI2H],
InH(r)=01vnexp[iα(z)v]J0[β(x, y)(1-v2)1/2]dv.
GE(r)=kI0E+k2(x2-y2)β3 L1E-k2x2β2 L2Ek2xyβ22β L1E-L2E±kxβ L3Ek2xyβ22β L1E-L2EI0E+k2(y2-x2)β3 L1E-k2y2β2 L2E±kyβ L3E±kxβ L3H±kyβ L3EL2E,
L1E(r)=1α [J1(β)+βI1E],L2E(r)=I0E+I2E,L3E(r)=1β [J0(β)-αI0E+2I1E-αI2E],
InE(r)=0vnexp [-α(z)v]J0[β(x, y)(v2+1)1/2]dv.
α(z)=k|z|,β(x, y)=k(x2+y2)1/2,

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