Abstract

Exact calculations of the scattering of light and other electromagnetic waves by a dielectric tip in front of corrugated dielectric samples are carried out by means of surface integrals derived from the extinction theorem and related equations. The configuration tackled is two dimensional, and the active part of the probing tip is simulated by a cylinder. The surface under study is illuminated from its dielectric side with a Gaussian beam at different angles of incidence. The transmitted near-field distribution is calculated inside the tip when it scans the surface at a constant distance from its mean plane. Different calculations are performed both for extended corrugated profiles (surface-relief gratings) and for flat dielectric interfaces with topographic subwavelength defects. The results show that the near fields scattered from these two kinds of surface corrugation have a notably different behavior with respect to the profile. Also, the influence of the angle of incidence, the polarization, and the shape of the incident beam on the near-field distribution is studied. It is shown that tips with diameters not larger than 0.1λ and a dielectric permittivity similar to that of glass do not appreciably perturb the near field transmitted by the sample.

© 1997 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  17. R. Berndt, R. Gaisch, W. D. Schneider, J. K. Gimzewski, B. Reihl, R. R. Schlittler, M. Tschudy, “Atomic resolution in photon emission induced by a scanning tunneling microscope,” Phys. Rev. Lett. 74, 102–105 (1995); A. Madrazo, M. Nieto-Vesperinas, N. Garcı́a, “Exact calculations of Maxwell equations for a tip–metallic interface configuration: application to atomic resolution by photon emission,” Phys. Rev. B 53, 3654–3657 (1996).
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  19. P. Tran, V. Celli, A. A. Maradudin, “Electromagnetic scattering from a two-dimensional, randomly rough, perfectly conducting surface: iterative methods,” J. Opt. Soc. Am. A 11, 1686–1689 (1994).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  22. J. J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field date,” Opt. Commun. 116, 20–24 (1995); R. Carminati, J. J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope: concept of the transfer function,” Opt. Commun. 116, 316–321 (1995).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  25. J. J. Greffet, “Scattering of electromagnetics waves by rough dielectric surfaces,” Phys. Rev. B 37, 6436–6441 (1988); R. Carminati, J. J. Greffet, “Influence of dielectric contrast and topography on the near field scattered by an inhomogeneous surface,” J. Opt. Soc. Am. A 12, 2716–2725 (1995).
    [CrossRef]
  26. J. P. Goudonnet, E. Bourillot, P. M. Adam, F. de Fornel, L. Salomon, P. Vincent, M. Neviere, T. L. Ferrell, “Imaging of test quartz gratings with a photon scanning tunneling microscope: experiment and theory,” J. Opt. Soc. Am. A 12, 1749–1764 (1995).
    [CrossRef]
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    [CrossRef]
  29. N. Garcia, M. Nieto-Vesperinas, “Near-field optics inverse-scattering reconstruction of reflective surfaces,” Opt. Lett. 24, 2090–2092 (1993); N. Garcia, M. Nieto-Vesperinas, “A direct solution to the inverse scattering problem for surfaces from near field intensities without phase retrieval,” Opt. Lett. 20, 949–951 (1995); R. Carminati, J. J. Greffet, N. Garcia, M. Nieto-Vesperinas, “Direct reconstruction of surfaces from near-field intensity under spatially incoherent illumination,” Opt. Lett. 21, 501–503 (1996).
    [CrossRef] [PubMed]
  30. C. Girard, A. Dereux, O. J. F. Martin, “Theory of near field optics,” in Photons and Local Probes, Vol. 300 of NATO ASI Series (Kluwer, Dordrecht, 1995), Chap. 1.
  31. D. Van Labeke, D. Barchiesi, “Probes for scanning tunneling microscopy: a theoretical comparison,” J. Opt. Soc. Am. A 10, 2193–2201 (1993).
    [CrossRef]
  32. 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]
  33. C. Girard, A. Dereux, O. J. F. Martin, “Theoretical analysis of light-inductive forces in scanning probe microscopy,” Phys. Rev. B 49, 13872–13881 (1994).
    [CrossRef]
  34. O. J. F. Martin, A. Dereux, C. Girard, “Iterative scheme for computing exactly the total field propagating in dielectric structures of arbitrary shape,” J. Opt. Soc. Am. A 11, 1073–1080 (1994).
    [CrossRef]

1996 (2)

1995 (5)

A. Madrazo, M. Nieto-Vesperinas, “Detection of subwavelength Goos–Hänchen shifts from near-field intensities: a numerical simulation,” Opt. Lett. 20, 2445–2447 (1995).
[CrossRef]

R. Berndt, R. Gaisch, W. D. Schneider, J. K. Gimzewski, B. Reihl, R. R. Schlittler, M. Tschudy, “Atomic resolution in photon emission induced by a scanning tunneling microscope,” Phys. Rev. Lett. 74, 102–105 (1995); A. Madrazo, M. Nieto-Vesperinas, N. Garcı́a, “Exact calculations of Maxwell equations for a tip–metallic interface configuration: application to atomic resolution by photon emission,” Phys. Rev. B 53, 3654–3657 (1996).
[CrossRef] [PubMed]

A. Madrazo, M. Nieto-Vesperinas, “Scattering of electromagnetic waves from a cylinder in front of a conducting plane,” J. Opt. Soc. Am. A 12, 1298–1309 (1995).
[CrossRef]

J. J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field date,” Opt. Commun. 116, 20–24 (1995); R. Carminati, J. J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope: concept of the transfer function,” Opt. Commun. 116, 316–321 (1995).
[CrossRef]

J. P. Goudonnet, E. Bourillot, P. M. Adam, F. de Fornel, L. Salomon, P. Vincent, M. Neviere, T. L. Ferrell, “Imaging of test quartz gratings with a photon scanning tunneling microscope: experiment and theory,” J. Opt. Soc. Am. A 12, 1749–1764 (1995).
[CrossRef]

1994 (7)

R. Carminati, A. Madrazo, M. Nieto-Vesperinas, “Electromagnetic wave scattering from a cylinder in front of a perfectly conducting surface-relief grating,” Opt. Commun. 111, 26–33 (1994).
[CrossRef]

L. Tsang, Ch. H. Chan, K. Pak, “Backscattering enhancement of a two-dimensional random rough surface (three-dimensional scattering) based on Monte Carlo simulations,” J. Opt. Soc. Am. A 11, 711–715 (1994).
[CrossRef]

P. Tran, V. Celli, A. A. Maradudin, “Electromagnetic scattering from a two-dimensional, randomly rough, perfectly conducting surface: iterative methods,” J. Opt. Soc. Am. A 11, 1686–1689 (1994).
[CrossRef]

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

C. Girard, A. Dereux, O. J. F. Martin, “Theoretical analysis of light-inductive forces in scanning probe microscopy,” Phys. Rev. B 49, 13872–13881 (1994).
[CrossRef]

O. J. F. Martin, A. Dereux, C. Girard, “Iterative scheme for computing exactly the total field propagating in dielectric structures of arbitrary shape,” J. Opt. Soc. Am. A 11, 1073–1080 (1994).
[CrossRef]

1993 (2)

N. Garcia, M. Nieto-Vesperinas, “Near-field optics inverse-scattering reconstruction of reflective surfaces,” Opt. Lett. 24, 2090–2092 (1993); N. Garcia, M. Nieto-Vesperinas, “A direct solution to the inverse scattering problem for surfaces from near field intensities without phase retrieval,” Opt. Lett. 20, 949–951 (1995); R. Carminati, J. J. Greffet, N. Garcia, M. Nieto-Vesperinas, “Direct reconstruction of surfaces from near-field intensity under spatially incoherent illumination,” Opt. Lett. 21, 501–503 (1996).
[CrossRef] [PubMed]

D. Van Labeke, D. Barchiesi, “Probes for scanning tunneling microscopy: a theoretical comparison,” J. Opt. Soc. Am. A 10, 2193–2201 (1993).
[CrossRef]

1992 (1)

1991 (3)

L. Salomon, F. De Fornel, J. P. Goudonnet, “Sample–tip coupling efficiencies of the photon-scanning tunneling microscope,” J. Opt. Soc. Am. A 8, 2009–2015 (1991); P. Dawson, F. De Fornel, J. P. Goudonnet, “Imaging of surface plasmon propagation and edge interaction using a photon scanning tunneling microscope,” Phys. Rev. Lett. 72, 2927–2930 (1994); F. De Fornel, P. M. Adam, L. Salomon, J. P. Goudonnet, P. Guerin, “Effect of coherence of the source on the images obtained with a photon scanning tunneling microscope,” Opt. Lett. 19, 1082–1084 (1994).
[CrossRef] [PubMed]

G. Videen, “Light scattering from a sphere on or near a surface,” J. Opt. Soc. Am. A 8, 483–489 (1991); “Light scattering from a sphere behind a surface,” J. Opt. Soc. Am. A 10, 110–117 (1993); G. Videen, W. S. Bickel, V. J. Iafelice, D. Abromson, “Experimental light scattering Mueller matrix for a fiber on a reflecting optical surface as a function of incidence angle,” J. Opt. Soc. Am. A 9, 312–315 (1992); G. Videen, M. G. Turner, V. J. Iafelice, W. S. Bickel, W. L. Wolfe, “Scattering from a small sphere near a surface,” J. Opt. Soc. Am. A 10, 118–126 (1993).
[CrossRef]

I. V. Lindell, A. H. Sihvola, K. O. Muinonen, P. Barber, “Scattering by a small object close to an interface. I. Exact image theory formulation,” J. Opt. Soc. Am. A 8, 472–476 (1991); K. O. Muinonen, A. H. Sihvola, I. V. Lindell, K. A. Lumme, “Scattering by a small object close to an interface. II. Study of backscattering,” J. Opt. Soc. Am. A 8, 477–482 (1991); M. A. Taubenblatt, T. K. Tran, “Calculation of light scattering from particles and structures on a surface by the coupled-dipole method,” J. Opt. Soc. Am. A 10, 912–919 (1993).
[CrossRef]

1989 (2)

1988 (1)

J. J. Greffet, “Scattering of electromagnetics waves by rough dielectric surfaces,” Phys. Rev. B 37, 6436–6441 (1988); R. Carminati, J. J. Greffet, “Influence of dielectric contrast and topography on the near field scattered by an inhomogeneous surface,” J. Opt. Soc. Am. A 12, 2716–2725 (1995).
[CrossRef]

1986 (1)

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica (Utrecht) 137A, 209–242 (1986); K. Nahm, W. L. Wolfe, “Light scattering models for spheres on a conducting plane: comparison with experiment,” Appl. Opt. 26, 2995–2999 (1987).
[CrossRef] [PubMed]

1977 (1)

1975 (1)

V. Celli, A. Marvin, F. Toigo, “Light scattering from rough surfaces,” Phys. Rev. B 11, 1779–1786 (1975); A. A. Maradudin, D. L. Mills, “Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness,” Phys. Rev. B 11, 1392–1415 (1975).
[CrossRef]

Adam, P. M.

Bainier, C.

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

Ban^os, A.

A. Ban̂os, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, Oxford, 1966).

Barakat, R.

Barber, P.

Barchiesi, D.

Berndt, R.

R. Berndt, R. Gaisch, W. D. Schneider, J. K. Gimzewski, B. Reihl, R. R. Schlittler, M. Tschudy, “Atomic resolution in photon emission induced by a scanning tunneling microscope,” Phys. Rev. Lett. 74, 102–105 (1995); A. Madrazo, M. Nieto-Vesperinas, N. Garcı́a, “Exact calculations of Maxwell equations for a tip–metallic interface configuration: application to atomic resolution by photon emission,” Phys. Rev. B 53, 3654–3657 (1996).
[CrossRef] [PubMed]

Bobbert, P. A.

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica (Utrecht) 137A, 209–242 (1986); K. Nahm, W. L. Wolfe, “Light scattering models for spheres on a conducting plane: comparison with experiment,” Appl. Opt. 26, 2995–2999 (1987).
[CrossRef] [PubMed]

Bourillot, E.

Carminati, R.

F. De Fornel, P. M. Adam, L. Salomon, J. P. Goudonnet, A. Sentenac, R. Carminati, J. J. Greffet, “Analysis of the image formation with a photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 35–45 (1996).
[CrossRef]

J. J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field date,” Opt. Commun. 116, 20–24 (1995); R. Carminati, J. J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope: concept of the transfer function,” Opt. Commun. 116, 316–321 (1995).
[CrossRef]

R. Carminati, A. Madrazo, M. Nieto-Vesperinas, “Electromagnetic wave scattering from a cylinder in front of a perfectly conducting surface-relief grating,” Opt. Commun. 111, 26–33 (1994).
[CrossRef]

Carniglia, C. K.

Celli, V.

P. Tran, V. Celli, A. A. Maradudin, “Electromagnetic scattering from a two-dimensional, randomly rough, perfectly conducting surface: iterative methods,” J. Opt. Soc. Am. A 11, 1686–1689 (1994).
[CrossRef]

V. Celli, A. Marvin, F. Toigo, “Light scattering from rough surfaces,” Phys. Rev. B 11, 1779–1786 (1975); A. A. Maradudin, D. L. Mills, “Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness,” Phys. Rev. B 11, 1392–1415 (1975).
[CrossRef]

Chan, Ch. H.

Courjon, D.

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

D. Courjon, K. Sarayeddine, M. Spajer, “Scanning tunneling optical microscope,” Opt. Commun. 71, 23–29 (1989); R. C. Reddick, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
[CrossRef]

De Fornel, F.

Dereux, A.

O. J. F. Martin, A. Dereux, C. Girard, “Iterative scheme for computing exactly the total field propagating in dielectric structures of arbitrary shape,” J. Opt. Soc. Am. A 11, 1073–1080 (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]

C. Girard, A. Dereux, O. J. F. Martin, “Theoretical analysis of light-inductive forces in scanning probe microscopy,” Phys. Rev. B 49, 13872–13881 (1994).
[CrossRef]

C. Girard, A. Dereux, O. J. F. Martin, “Theory of near field optics,” in Photons and Local Probes, Vol. 300 of NATO ASI Series (Kluwer, Dordrecht, 1995), Chap. 1.

Ferrell, T. L.

Gaisch, R.

R. Berndt, R. Gaisch, W. D. Schneider, J. K. Gimzewski, B. Reihl, R. R. Schlittler, M. Tschudy, “Atomic resolution in photon emission induced by a scanning tunneling microscope,” Phys. Rev. Lett. 74, 102–105 (1995); A. Madrazo, M. Nieto-Vesperinas, N. Garcı́a, “Exact calculations of Maxwell equations for a tip–metallic interface configuration: application to atomic resolution by photon emission,” Phys. Rev. B 53, 3654–3657 (1996).
[CrossRef] [PubMed]

Garcia, N.

N. Garcia, M. Nieto-Vesperinas, “Near-field optics inverse-scattering reconstruction of reflective surfaces,” Opt. Lett. 24, 2090–2092 (1993); N. Garcia, M. Nieto-Vesperinas, “A direct solution to the inverse scattering problem for surfaces from near field intensities without phase retrieval,” Opt. Lett. 20, 949–951 (1995); R. Carminati, J. J. Greffet, N. Garcia, M. Nieto-Vesperinas, “Direct reconstruction of surfaces from near-field intensity under spatially incoherent illumination,” Opt. Lett. 21, 501–503 (1996).
[CrossRef] [PubMed]

Gimzewski, J. K.

R. Berndt, R. Gaisch, W. D. Schneider, J. K. Gimzewski, B. Reihl, R. R. Schlittler, M. Tschudy, “Atomic resolution in photon emission induced by a scanning tunneling microscope,” Phys. Rev. Lett. 74, 102–105 (1995); A. Madrazo, M. Nieto-Vesperinas, N. Garcı́a, “Exact calculations of Maxwell equations for a tip–metallic interface configuration: application to atomic resolution by photon emission,” Phys. Rev. B 53, 3654–3657 (1996).
[CrossRef] [PubMed]

Girard, C.

C. Girard, A. Dereux, O. J. F. Martin, “Theoretical analysis of light-inductive forces in scanning probe microscopy,” Phys. Rev. B 49, 13872–13881 (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]

O. J. F. Martin, A. Dereux, C. Girard, “Iterative scheme for computing exactly the total field propagating in dielectric structures of arbitrary shape,” J. Opt. Soc. Am. A 11, 1073–1080 (1994).
[CrossRef]

C. Girard, A. Dereux, O. J. F. Martin, “Theory of near field optics,” in Photons and Local Probes, Vol. 300 of NATO ASI Series (Kluwer, Dordrecht, 1995), Chap. 1.

Goudonnet, J. P.

Greffet, J. J.

F. De Fornel, P. M. Adam, L. Salomon, J. P. Goudonnet, A. Sentenac, R. Carminati, J. J. Greffet, “Analysis of the image formation with a photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 35–45 (1996).
[CrossRef]

J. J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field date,” Opt. Commun. 116, 20–24 (1995); R. Carminati, J. J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope: concept of the transfer function,” Opt. Commun. 116, 316–321 (1995).
[CrossRef]

J. J. Greffet, “Scattering of electromagnetics waves by rough dielectric surfaces,” Phys. Rev. B 37, 6436–6441 (1988); R. Carminati, J. J. Greffet, “Influence of dielectric contrast and topography on the near field scattered by an inhomogeneous surface,” J. Opt. Soc. Am. A 12, 2716–2725 (1995).
[CrossRef]

Lindell, I. V.

Madrazo, A.

Maradudin, A. A.

Martin, O. J. F.

O. J. F. Martin, A. Dereux, C. Girard, “Iterative scheme for computing exactly the total field propagating in dielectric structures of arbitrary shape,” J. Opt. Soc. Am. A 11, 1073–1080 (1994).
[CrossRef]

C. Girard, A. Dereux, O. J. F. Martin, “Theoretical analysis of light-inductive forces in scanning probe microscopy,” Phys. Rev. B 49, 13872–13881 (1994).
[CrossRef]

C. Girard, A. Dereux, O. J. F. Martin, “Theory of near field optics,” in Photons and Local Probes, Vol. 300 of NATO ASI Series (Kluwer, Dordrecht, 1995), Chap. 1.

Marvin, A.

V. Celli, A. Marvin, F. Toigo, “Light scattering from rough surfaces,” Phys. Rev. B 11, 1779–1786 (1975); A. A. Maradudin, D. L. Mills, “Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness,” Phys. Rev. B 11, 1392–1415 (1975).
[CrossRef]

McGuik, M.

Muinonen, K. O.

Neviere, M.

Nieto-Vesperinas, M.

A. Madrazo, M. Nieto-Vesperinas, “Surface structure and polariton interactions in the scattering of electromagnetic waves from a cylinder in front of a conducting grating: theory for the reflection photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 785–795 (1996).
[CrossRef]

A. Madrazo, M. Nieto-Vesperinas, “Scattering of electromagnetic waves from a cylinder in front of a conducting plane,” J. Opt. Soc. Am. A 12, 1298–1309 (1995).
[CrossRef]

A. Madrazo, M. Nieto-Vesperinas, “Detection of subwavelength Goos–Hänchen shifts from near-field intensities: a numerical simulation,” Opt. Lett. 20, 2445–2447 (1995).
[CrossRef]

R. Carminati, A. Madrazo, M. Nieto-Vesperinas, “Electromagnetic wave scattering from a cylinder in front of a perfectly conducting surface-relief grating,” Opt. Commun. 111, 26–33 (1994).
[CrossRef]

N. Garcia, M. Nieto-Vesperinas, “Near-field optics inverse-scattering reconstruction of reflective surfaces,” Opt. Lett. 24, 2090–2092 (1993); N. Garcia, M. Nieto-Vesperinas, “A direct solution to the inverse scattering problem for surfaces from near field intensities without phase retrieval,” Opt. Lett. 20, 949–951 (1995); R. Carminati, J. J. Greffet, N. Garcia, M. Nieto-Vesperinas, “Direct reconstruction of surfaces from near-field intensity under spatially incoherent illumination,” Opt. Lett. 21, 501–503 (1996).
[CrossRef] [PubMed]

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991), Chap. 2, p. 45.

Pak, K.

Pohl, D. W.

D. W. Pohl, “Scanning near field optical microscopy (SNOM),” in Advances in Optical and Electron Microscopy, J. R. Sheppard, T. Mulvey, eds. (Academic, New York, 1990), p. 243.

Rao, T. C.

Reihl, B.

R. Berndt, R. Gaisch, W. D. Schneider, J. K. Gimzewski, B. Reihl, R. R. Schlittler, M. Tschudy, “Atomic resolution in photon emission induced by a scanning tunneling microscope,” Phys. Rev. Lett. 74, 102–105 (1995); A. Madrazo, M. Nieto-Vesperinas, N. Garcı́a, “Exact calculations of Maxwell equations for a tip–metallic interface configuration: application to atomic resolution by photon emission,” Phys. Rev. B 53, 3654–3657 (1996).
[CrossRef] [PubMed]

Salomon, L.

Sarayeddine, K.

D. Courjon, K. Sarayeddine, M. Spajer, “Scanning tunneling optical microscope,” Opt. Commun. 71, 23–29 (1989); R. C. Reddick, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
[CrossRef]

Schlittler, R. R.

R. Berndt, R. Gaisch, W. D. Schneider, J. K. Gimzewski, B. Reihl, R. R. Schlittler, M. Tschudy, “Atomic resolution in photon emission induced by a scanning tunneling microscope,” Phys. Rev. Lett. 74, 102–105 (1995); A. Madrazo, M. Nieto-Vesperinas, N. Garcı́a, “Exact calculations of Maxwell equations for a tip–metallic interface configuration: application to atomic resolution by photon emission,” Phys. Rev. B 53, 3654–3657 (1996).
[CrossRef] [PubMed]

Schneider, W. D.

R. Berndt, R. Gaisch, W. D. Schneider, J. K. Gimzewski, B. Reihl, R. R. Schlittler, M. Tschudy, “Atomic resolution in photon emission induced by a scanning tunneling microscope,” Phys. Rev. Lett. 74, 102–105 (1995); A. Madrazo, M. Nieto-Vesperinas, N. Garcı́a, “Exact calculations of Maxwell equations for a tip–metallic interface configuration: application to atomic resolution by photon emission,” Phys. Rev. B 53, 3654–3657 (1996).
[CrossRef] [PubMed]

Sentenac, A.

F. De Fornel, P. M. Adam, L. Salomon, J. P. Goudonnet, A. Sentenac, R. Carminati, J. J. Greffet, “Analysis of the image formation with a photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 35–45 (1996).
[CrossRef]

J. J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field date,” Opt. Commun. 116, 20–24 (1995); R. Carminati, J. J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope: concept of the transfer function,” Opt. Commun. 116, 316–321 (1995).
[CrossRef]

Sihvola, A. H.

Sommerfeld, A.

A. Sommerfeld, Lectures on Theoretical Physics (Academic, New York, 1964), Vol. 6, Chap. 6; “Ueber die a usbreitung der wellen in der drahtlosen telegraphie,” Ann. Phys. (Leipzig) 28, 665–695 (1909); “Ueber die ausbreitung der wellen in der drahtlosen telegraphie,” Ann. Phys. (Leipzig) 81, 1135–1153 (1926).
[CrossRef]

Spajer, M.

D. Courjon, K. Sarayeddine, M. Spajer, “Scanning tunneling optical microscope,” Opt. Commun. 71, 23–29 (1989); R. C. Reddick, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
[CrossRef]

Toigo, F.

V. Celli, A. Marvin, F. Toigo, “Light scattering from rough surfaces,” Phys. Rev. B 11, 1779–1786 (1975); A. A. Maradudin, D. L. Mills, “Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness,” Phys. Rev. B 11, 1392–1415 (1975).
[CrossRef]

Tran, P.

Tsang, L.

Tschudy, M.

R. Berndt, R. Gaisch, W. D. Schneider, J. K. Gimzewski, B. Reihl, R. R. Schlittler, M. Tschudy, “Atomic resolution in photon emission induced by a scanning tunneling microscope,” Phys. Rev. Lett. 74, 102–105 (1995); A. Madrazo, M. Nieto-Vesperinas, N. Garcı́a, “Exact calculations of Maxwell equations for a tip–metallic interface configuration: application to atomic resolution by photon emission,” Phys. Rev. B 53, 3654–3657 (1996).
[CrossRef] [PubMed]

Van Labeke, D.

Videen, G.

Vincent, P.

Vlieger, J.

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica (Utrecht) 137A, 209–242 (1986); K. Nahm, W. L. Wolfe, “Light scattering models for spheres on a conducting plane: comparison with experiment,” Appl. Opt. 26, 2995–2999 (1987).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (13)

F. De Fornel, P. M. Adam, L. Salomon, J. P. Goudonnet, A. Sentenac, R. Carminati, J. J. Greffet, “Analysis of the image formation with a photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 35–45 (1996).
[CrossRef]

L. Salomon, F. De Fornel, J. P. Goudonnet, “Sample–tip coupling efficiencies of the photon-scanning tunneling microscope,” J. Opt. Soc. Am. A 8, 2009–2015 (1991); P. Dawson, F. De Fornel, J. P. Goudonnet, “Imaging of surface plasmon propagation and edge interaction using a photon scanning tunneling microscope,” Phys. Rev. Lett. 72, 2927–2930 (1994); F. De Fornel, P. M. Adam, L. Salomon, J. P. Goudonnet, P. Guerin, “Effect of coherence of the source on the images obtained with a photon scanning tunneling microscope,” Opt. Lett. 19, 1082–1084 (1994).
[CrossRef] [PubMed]

D. Van Labeke, D. Barchiesi, “Scanning-tunneling optical microscopy: a theoretical macroscopic approach,” J. Opt. Soc. Am. A 9, 732–739 (1992).
[CrossRef]

J. P. Goudonnet, E. Bourillot, P. M. Adam, F. de Fornel, L. Salomon, P. Vincent, M. Neviere, T. L. Ferrell, “Imaging of test quartz gratings with a photon scanning tunneling microscope: experiment and theory,” J. Opt. Soc. Am. A 12, 1749–1764 (1995).
[CrossRef]

D. Van Labeke, D. Barchiesi, “Probes for scanning tunneling microscopy: a theoretical comparison,” J. Opt. Soc. Am. A 10, 2193–2201 (1993).
[CrossRef]

O. J. F. Martin, A. Dereux, C. Girard, “Iterative scheme for computing exactly the total field propagating in dielectric structures of arbitrary shape,” J. Opt. Soc. Am. A 11, 1073–1080 (1994).
[CrossRef]

T. C. Rao, R. Barakat, “Plane wave scattering by a conducting cylinder partially buried in a ground plane. I: TM case,” J. Opt. Soc. Am. A 6, 1270–1280 (1989); “Plane wave scattering by a conducting cylinder partially buried in a ground plane. II: TE case,” J. Opt. Soc. Am. A 8, 1986–1990 (1991); P. J. Valle, F. Gonzalez, F. Moreno, “Electromagnetic wave scattering from conducting cylindrical structures on flat substrates,” Appl. Opt. 33, 512–523 (1994); P. J. Valle, F. Moreno, J. M. Saiz, F. Gonzalez, “Near-field scattering from subwavelength metallic protuberances on conducting flat substrates,” Phys. Rev. B 51, 13681–13690 (1995).
[CrossRef] [PubMed]

G. Videen, “Light scattering from a sphere on or near a surface,” J. Opt. Soc. Am. A 8, 483–489 (1991); “Light scattering from a sphere behind a surface,” J. Opt. Soc. Am. A 10, 110–117 (1993); G. Videen, W. S. Bickel, V. J. Iafelice, D. Abromson, “Experimental light scattering Mueller matrix for a fiber on a reflecting optical surface as a function of incidence angle,” J. Opt. Soc. Am. A 9, 312–315 (1992); G. Videen, M. G. Turner, V. J. Iafelice, W. S. Bickel, W. L. Wolfe, “Scattering from a small sphere near a surface,” J. Opt. Soc. Am. A 10, 118–126 (1993).
[CrossRef]

I. V. Lindell, A. H. Sihvola, K. O. Muinonen, P. Barber, “Scattering by a small object close to an interface. I. Exact image theory formulation,” J. Opt. Soc. Am. A 8, 472–476 (1991); K. O. Muinonen, A. H. Sihvola, I. V. Lindell, K. A. Lumme, “Scattering by a small object close to an interface. II. Study of backscattering,” J. Opt. Soc. Am. A 8, 477–482 (1991); M. A. Taubenblatt, T. K. Tran, “Calculation of light scattering from particles and structures on a surface by the coupled-dipole method,” J. Opt. Soc. Am. A 10, 912–919 (1993).
[CrossRef]

A. Madrazo, M. Nieto-Vesperinas, “Scattering of electromagnetic waves from a cylinder in front of a conducting plane,” J. Opt. Soc. Am. A 12, 1298–1309 (1995).
[CrossRef]

A. Madrazo, M. Nieto-Vesperinas, “Surface structure and polariton interactions in the scattering of electromagnetic waves from a cylinder in front of a conducting grating: theory for the reflection photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 785–795 (1996).
[CrossRef]

L. Tsang, Ch. H. Chan, K. Pak, “Backscattering enhancement of a two-dimensional random rough surface (three-dimensional scattering) based on Monte Carlo simulations,” J. Opt. Soc. Am. A 11, 711–715 (1994).
[CrossRef]

P. Tran, V. Celli, A. A. Maradudin, “Electromagnetic scattering from a two-dimensional, randomly rough, perfectly conducting surface: iterative methods,” J. Opt. Soc. Am. A 11, 1686–1689 (1994).
[CrossRef]

Opt. Commun. (3)

D. Courjon, K. Sarayeddine, M. Spajer, “Scanning tunneling optical microscope,” Opt. Commun. 71, 23–29 (1989); R. C. Reddick, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
[CrossRef]

R. Carminati, A. Madrazo, M. Nieto-Vesperinas, “Electromagnetic wave scattering from a cylinder in front of a perfectly conducting surface-relief grating,” Opt. Commun. 111, 26–33 (1994).
[CrossRef]

J. J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field date,” Opt. Commun. 116, 20–24 (1995); R. Carminati, J. J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope: concept of the transfer function,” Opt. Commun. 116, 316–321 (1995).
[CrossRef]

Opt. Lett. (2)

N. Garcia, M. Nieto-Vesperinas, “Near-field optics inverse-scattering reconstruction of reflective surfaces,” Opt. Lett. 24, 2090–2092 (1993); N. Garcia, M. Nieto-Vesperinas, “A direct solution to the inverse scattering problem for surfaces from near field intensities without phase retrieval,” Opt. Lett. 20, 949–951 (1995); R. Carminati, J. J. Greffet, N. Garcia, M. Nieto-Vesperinas, “Direct reconstruction of surfaces from near-field intensity under spatially incoherent illumination,” Opt. Lett. 21, 501–503 (1996).
[CrossRef] [PubMed]

A. Madrazo, M. Nieto-Vesperinas, “Detection of subwavelength Goos–Hänchen shifts from near-field intensities: a numerical simulation,” Opt. Lett. 20, 2445–2447 (1995).
[CrossRef]

Phys. Rev. B (4)

V. Celli, A. Marvin, F. Toigo, “Light scattering from rough surfaces,” Phys. Rev. B 11, 1779–1786 (1975); A. A. Maradudin, D. L. Mills, “Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness,” Phys. Rev. B 11, 1392–1415 (1975).
[CrossRef]

J. J. Greffet, “Scattering of electromagnetics waves by rough dielectric surfaces,” Phys. Rev. B 37, 6436–6441 (1988); R. Carminati, J. J. Greffet, “Influence of dielectric contrast and topography on the near field scattered by an inhomogeneous surface,” J. Opt. Soc. Am. A 12, 2716–2725 (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]

C. Girard, A. Dereux, O. J. F. Martin, “Theoretical analysis of light-inductive forces in scanning probe microscopy,” Phys. Rev. B 49, 13872–13881 (1994).
[CrossRef]

Phys. Rev. Lett. (1)

R. Berndt, R. Gaisch, W. D. Schneider, J. K. Gimzewski, B. Reihl, R. R. Schlittler, M. Tschudy, “Atomic resolution in photon emission induced by a scanning tunneling microscope,” Phys. Rev. Lett. 74, 102–105 (1995); A. Madrazo, M. Nieto-Vesperinas, N. Garcı́a, “Exact calculations of Maxwell equations for a tip–metallic interface configuration: application to atomic resolution by photon emission,” Phys. Rev. B 53, 3654–3657 (1996).
[CrossRef] [PubMed]

Physica (Utrecht) (1)

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica (Utrecht) 137A, 209–242 (1986); K. Nahm, W. L. Wolfe, “Light scattering models for spheres on a conducting plane: comparison with experiment,” Appl. Opt. 26, 2995–2999 (1987).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

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

Other (8)

O. Marti, R. Möller, eds., Photons and Local Probes, Vol. 300 of NATO ASI Series (Kluwer, Dordrecht, 1995).

M. Nieto-Vesperinas, N. Garcı́a, eds., Optics at the Nanometer Scale: Imaging and Storing with Photonic Near Fields, NATO ASI Series (Kluwer, Dordrecht, The Netherlands, 1996), Vol. 319.

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991), Chap. 2, p. 45.

A. Sommerfeld, Lectures on Theoretical Physics (Academic, New York, 1964), Vol. 6, Chap. 6; “Ueber die a usbreitung der wellen in der drahtlosen telegraphie,” Ann. Phys. (Leipzig) 28, 665–695 (1909); “Ueber die ausbreitung der wellen in der drahtlosen telegraphie,” Ann. Phys. (Leipzig) 81, 1135–1153 (1926).
[CrossRef]

A. Ban̂os, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, Oxford, 1966).

D. W. Pohl, “Scanning near field optical microscopy (SNOM),” in Advances in Optical and Electron Microscopy, J. R. Sheppard, T. Mulvey, eds. (Academic, New York, 1990), p. 243.

D. W. Pohl, D. Courjon, eds., Near Field Optics, Vol. 242 of NATO ASI Series (Kluwer, Dordrecht, 1993).

C. Girard, A. Dereux, O. J. F. Martin, “Theory of near field optics,” in Photons and Local Probes, Vol. 300 of NATO ASI Series (Kluwer, Dordrecht, 1995), Chap. 1.

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Figures (11)

Fig. 1
Fig. 1

Scattering geometry.

Fig. 2
Fig. 2

Near-field scattered intensity in arbitrary units at z=h+0.1λ for a grating with parameters p=1.25λ and 2=2.12. No cylinder is present. Solid curves: θi=0°; dotted curves: θi=50°. (a) s polarization, h=0.4λ; (b) s polarization, h=0.25λ; (c) s polarization, h=0.1λ; (d) p polarization, h=0.4λ; (e) p polarization, h=0.25λ; (f) p polarization, h=0.1λ.

Fig. 3
Fig. 3

Same as Fig. 2 but for p=0.5λ. (a) s polarization, h=0.1λ; (b) s polarization, h=0.04λ; (c) p polarization, h=0.1λ; (d) p polarization, h=0.04λ.

Fig. 4
Fig. 4

Same as Figs. 2(c) and 2(f). Also, the field intensity inside the cylinder (R=0.1λ, i=2.12) and integrated over its diameter is shown as the cylinder scans the surface with its center on z=d=0.25λ. Solid curves with circles: θi=0°; dotted curves with circles: θi=50°. (a) s polarization, (b) p polarization.

Fig. 5
Fig. 5

Near-field scattered intensity in arbitrary units z=0.15λ for the grating with parameters h=0.1λ, 2=2.12, and, from top to bottom, p=0.5λ, 0.75λ, 1λ, and 1.25λ. (a) s polarization, θi=0°; (b) s polarization, θi=50°; (c) p polarization, θi=0°; (d) p polarization, θi=50°.

Fig. 6
Fig. 6

Near-field scattered intensity in arbitrary units at z0=0.07λ for the grating D(x)=h[cos (2πx/p)+sin (6πx/p)] with parameters h=0.01λ, p=1.25λ, and 2=2.12. From the second highest plot to the bottom θi=0°, 25°, 45°, and 55°. The surface profile is shown on top. (a) s polarization, (b) p polarization.

Fig. 7
Fig. 7

Solid curves: near-field scattered intensity in arbitrary units at z0=0.07λ for the grating D(x)=h[cos (2πx/p)+sin (6πx/p)] with parameters h=0.01λ, p=1.25λ, and 2=2.12 and θi=50°; dashed curves: near-field intensity for a flat interface. The surface profile is shown on top. (a) s polarization, (b) p polarization.

Fig. 8
Fig. 8

Near-field scattered intensity in arbitrary units at z0=0.1λ for the surface D(x)=h{exp [-(x+x0)2/σ2]+exp[-(x-x0)2/σ2]} with parameters h=0.05λ, x0=0.1λ, and 2=2.12. In the bottom plots the solid curves with circles refer to p polarization and θi=0°, the solid curves without circles refer to p polarization and θi=50°, the dashed curves with circles refer to s polarization and θi=0°, and the dashed curves without circles refer to s polarization and θi=50°. (a) σ=0.03λ, (b) σ=0.06λ.

Fig. 9
Fig. 9

Same as Fig. 8 but for xo=0.15 and σ=0.06λ. Dotted curves: integrated intensities over the segment 2R, parallel to the surface mean plane, inside a cylinder with R=0.05λ and 1=2.12, as this cylinder moves with its center on z=d=0.1λ.

Fig. 10
Fig. 10

Near-field scattered intensity at different constant heights z0 and for θ0=0°. The surface parameters are h=0.05λ, x0=0.15λ, and σ=0.03λ. (1) z0=0.055λ, (2) z0=0.065λ, (3) z0=0.075λ, (4) z0=0.085λ, (5) z0 =0.095λ, (6) z0=0.1λ. (a) s polarization, (b) p polarization.

Fig. 11
Fig. 11

Same as Fig. 10 for θ0=50°. (a) s polarization, (b) p polarization.

Equations (25)

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E(i)(r, t)=(0, Φs(i)(r), 0)exp(-iωt),
H(i)(r, t)=(0, Φp(i)(r), 0)exp(-iωt),
Φα(i)(r)=exp[i2k(x sin θi+z cos θi)g(x, z)]×exp[-(x cos θi-z sin θi)2/W2],
g(x, z)=1+12k2W22W2[(xcos θi-zsin θi)2]-1,
Φα(0)(r)=i4D dsH0(1)(k|r-r|)nΦα(0)(r)-H0(1)(k|r-r|) Φα(0)(r)n+i4C dsH0(1)(k|r-r|)nΦα(0)(r)-H0(1)(k|r-r|) Φα(0)(r)n,
Φα(1)(r)=-i4C dsH0(1)(1k|r-r|)nΦα(1)(r)-H0(1)(1k|r-r|) Φα(1)(r)n,
Φα(2)(r)=Φα(i)(r)-i4D dsH0(1)(2k|r-r|)nΦα(2)×(r)-H0(1)(2k|r-r|) Φα(2)(r)n,
Φα(0)(r)=Φα,0(0)(r)+Φα,1(0)(r),
Φα,0(0)(r)=tα(Ki)Φα(i)(r),
Φα,1(0)(r)= dK2πMαˆ(K, Ki)Dˆ(K-Ki)×exp(i[Kx+q(K)z]),
Mαˆ(K, Ki)=q(K)-q2(K)2π×2k2q(K)q2(K)+K2,α=sq2(K)q(Ki)+KKi2k2,α=p,
Dˆ(K)=- dx D(x)exp(-iKx).
Iα(x, z0)=|Φα(0)(x, z0)|2=|Φα,0(0)(x, z0)|2+2 Re[Φα,1(0)(x, z0)Φα,0(0)*(x, z0)]+|Φα,1(0)(x, z0)|2.
Dˆ(K)=n=1 Dnδ(K-Λn).
|Φα,0(0)(x, z0)|2=|tα(Ki)|2×1,exp(-2γz0),KikKi>k,
2 Re[Φα,1(0)(x, z0)Φα,0(0)*(x, z0)]=Retα*(Ki)πexp(-iqi*z0)n=1 DnMαˆ(Ki+Λn, Ki)×exp(iΛnx)  exp(iqKi+Λnz0),
|Φα,1(0)(x, z0)|2=n=1 Dn2πMαˆ(Ki+Λn, Ki)×exp[i(Ki+Λn)x]×exp[iqKi+Λnz0]2.
Retα*(Ki)πexp(-iqi*z0) n=1 DnMαˆ(Ki+Λn, Ki)×exp(iΛnx)exp(iqKi+Λnz0)
const.×n=1 Dn exp(iΛnx).
2 Re[Φα,1(0)(x, z0)Φα,0(0)*(x, z0)]
=h Re(tα*(Ki)exp(-iqi*z0){Mαˆ(Ki-Λ, Ki)
×exp[i(-Λx+q-z0)]+Mαˆ(Ki+Λ, Ki)×exp[i(Λx+q+z0)]}),
|Φα,1(0)(x, z0)|2
=(h/2)2{|Mαˆ(Ki-Λ, Ki)exp(iq-z0)|2+|Mαˆ(Ki+Λ, Ki)exp(iq+z0)|2+2 Re(Mαˆ(Ki+Λ, Ki)Mα*ˆ(Ki-Λ, Ki)×exp[i(q+-q-*)z0]exp(i2Λx))}.
D(x)=h{exp[-(x-x0)2/σ2]+exp[-(x+x0)2/σ2]},

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