Abstract

The influence of topography and variations of optical properties on the near field scattered by an inhomogeneous sample is analyzed. A perturbative expression of the near field is derived and its range of validity is investigated. This expression shows quantitatively how dielectric contrast and topography modulate the near-field distribution close to a surface. It is shown that the near-field images, produced by conventional near-field optical devices, are sensitive to the integral of the dielectric contrast along the vertical direction across the sample. This point is illustrated by a numerical simulation of the near field scattered by surfaces exhibiting submicronic asperities and subsurface structures.

© 1995 Optical Society of America

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  3. E. Bourillot, F. de Fornel, L. Salomon, P. M. Adam, J.-P. Goudonnet, “Observation de structures guidantes en microscopie à effet tunnel photonique,” J. Opt. (Paris) 23, 57–62 (1992).
    [CrossRef]
  4. D. Courjon, C. Bainier, M. Spajer, “Imaging of submicron index variations by scanning optical tunneling,” J. Vac. Sci. Technol. B 10, 2436–2439 (1992).
    [CrossRef]
  5. E. Betzig, P. L. Finn, J. S. Weiner, “Combined shear force and near-field scanning optical microscopy,” Appl. Phys. Lett. 60, 2484–2486 (1992).
    [CrossRef]
  6. R. Toledo-Crow, P. C. Yang, Y. Chen, M. Vaez-Iravani, “Near-field differential scanning optical microscope with atomic force regulation,” Appl. Phys. Lett. 60, 2957–2959 (1992).
    [CrossRef]
  7. D. Van Labeke, D. Barchiesi, “Scanning tunneling optical microscopy: a theoretical macroscopic approach,” J. Opt. Soc. Am. A 9, 732–739 (1992).
    [CrossRef]
  8. M. Nevière, P. Vincent, “Diffraction gratings as components for photon scanning tunneling microscope image interpretation,” in Near Field Optics, D. W. Pohl, D. Courjon, eds. (Kluwer, Dordrecht, The Netherlands, 1993), pp. 377–378.
    [CrossRef]
  9. N. Garcia, M. Nieto-Vesperinas, “Near-field optics inverse-scattering reconstruction of reflective surfaces,” Opt. Lett. 18, 2090–2092 (1993).
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  10. J.-J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near field data,” Opt. Commun. 11620–24 (1995).
    [CrossRef]
  11. N. Joachimowicz, C. Pichot, J.-P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag. 29, 1742–1752 (1991).
    [CrossRef]
  12. E. Bourillot, F. de Fornel, J.-P. Goudonnet, D. Persegol, A. Kevorkian, D. Delacourt, “Analysis of photonscanning tunneling microscope images of inhomogeneous samples: determination of the local refractive index of channel waveguides,” J. Opt. Soc. Am. A 12, 95–106 (1995).
    [CrossRef]
  13. M. H. P. Moers, R. G. Tack, O. F. J. Noordman, F. B. Segerink, N. F. Van-Hulst, B. Bolger, “Combined photon scanning tunneling microscope and atomic force microscope using silicon nitride probes,” in Near Field Optics, D. W. Pohl, D. Courjon, eds. (Kluwer, Dordrecht, The Netherlands, 1993), pp. 79–86.
    [CrossRef]
  14. 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]
  15. D. Barchiesi, D. Van Labeke, “PSTM: an alternative to measure local variation of optical index,” Microsc. Microanal. Microstruct. 5, 435–446 (1994).
    [CrossRef]
  16. C. Girard, A. Dereux, “Optical spectroscopy of a surface at a nanometer scale: a theoretical study in real space,” Phys. Rev. B 49, 11,334–11,351 (1994).
    [CrossRef]
  17. J. Cites, M. F. M. Sanghadasa, C. S. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrel, “Analysis of photon scanning tunneling microscope images,” J. Appl. Phys. 71, 7–10 (1992).
    [CrossRef]
  18. A. Sentenac, J.-J. Greffet, “Study of the features of the PSTM images by means of a perturbative approach,” Ultramicroscopy 57, 246–250 (1995).
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  19. U. Schollwock, H. Wagner, “A perturbation theory approach to scanning near field optical microscopy,” in Near Field Optics, D. W. Pohl, D. Courjon, eds. (Kluwer, Dordrecht, The Netherlands, 1993), pp. 247–254.
    [CrossRef]
  20. D. Van Labeke, D. Barchiesi, “Probes for scanning tunneling optical microscopy: a theoretical comparison,” J. Opt. Soc. Am. A 10, 2193–2201 (1993).
    [CrossRef]
  21. R. Carminati, J.-J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope: concept of transfer function,” Opt. Commun. 116, 316–321 (1995).
    [CrossRef]
  22. F. de Fornel, P. M. Adam, L. Salomon, J.-P. Goudonnet, A. Sentenac, J.-J. Greffet, R. Carminati, “Analysis of image formation with a photon scanning tunneling microscope,” J. Opt. Soc. Am. A (to be published).
  23. D. Van Labeke, F. Baida, D. Barchiesi, D. Courjon, “A theoretical model for the inverse scanning tunneling microscope (ISTOM),” Opt. Commun. 114, 470–480 (1995).
    [CrossRef]
  24. 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]
  25. G. S. Agarwal, “Integral equation treatment of scattering from rough surfaces,” Phys. Rev. B 14, 846–848 (1976).
    [CrossRef]
  26. J.-J. Greffet, “Scattering of s-polarized electromagnetic waves by a 2D obstacle near an interface,” Opt. Commun. 72, 274–278 (1989).
    [CrossRef]
  27. F. Pincemin, A. Sentenac, J.-J. Greffet, “Near field scattered by a dielectric rod below a metallic surface,” J. Opt. Soc. Am. A 11, 1117–1127 (1994).
    [CrossRef]
  28. R. F. Wallis, M. Balkanski, Many-Body Aspects of Solid State Spectroscopy (North-Holland, Amsterdam, 1986).
  29. D. M. Wood, N. W. Ashcroft, “Quantum size effect in the optical properties of small metallic particles,” Phys. Rev. B 25, 6255–6274 (1982).
    [CrossRef]
  30. D. W. Oxtoby, F. Novak, S. A. Rice, “The Ewald–Oseen theorem in the x-ray frequency region: a microscopic analysis,” J. Chem. Phys. 76, 5278–5282 (1982).
    [CrossRef]
  31. A. Sammar, J.-M. Andre, B. Pardo, “Diffraction and scattering by lamellar amplitude multilayer gratings in the X-UV region,” Opt. Commun. 86, 245–254 (1991).
    [CrossRef]
  32. C. S. West, K. A. O’Donnell, “Observations of backscattering enhancement from polaritons on a rough metal surface,” J. Opt. Soc. Am. A 12, 390–397 (1995).
    [CrossRef]
  33. A. A Maradudin, A. R. McGurn, E. R. Méndez, “Surface-plasmon polariton mechanism for the enhanced backscattering of light from one-dimensional randomly rough metal surfaces,” J. Opt. Soc. Am. A 12, 2500–2506 (1995).
    [CrossRef]
  34. K. Gottfried, Quantum Mechanics (Benjamin, New York, 1966).
  35. C. Girard, A. Dereux, O. Martin, M. Devel, “Importance of confined field in near-field optical imaging of subwavelength objects,” Phys. Rev. B 50, 14,467–14,473 (1994).
    [CrossRef]
  36. O. J. F. Martin, C. Girard, A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
    [CrossRef] [PubMed]
  37. M. Garcia-Parajo, J. Rosiu, Y. Chen, “On the way to a multi-task near field optical microscope: simultaneous STM/SNOM and PSTM imaging,” Microsc. Microanal. Microstruct. 5, 399–407 (1994).
    [CrossRef]
  38. G. S. Agarwal, “Scattering from rough surfaces,” Opt. Commun. 14, 161–166 (1975).
    [CrossRef]
  39. J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
    [CrossRef]

1995 (8)

E. Bourillot, F. de Fornel, J.-P. Goudonnet, D. Persegol, A. Kevorkian, D. Delacourt, “Analysis of photonscanning tunneling microscope images of inhomogeneous samples: determination of the local refractive index of channel waveguides,” J. Opt. Soc. Am. A 12, 95–106 (1995).
[CrossRef]

J.-J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near field data,” Opt. Commun. 11620–24 (1995).
[CrossRef]

A. Sentenac, J.-J. Greffet, “Study of the features of the PSTM images by means of a perturbative approach,” Ultramicroscopy 57, 246–250 (1995).
[CrossRef]

R. Carminati, J.-J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope: concept of transfer function,” Opt. Commun. 116, 316–321 (1995).
[CrossRef]

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

C. S. West, K. A. O’Donnell, “Observations of backscattering enhancement from polaritons on a rough metal surface,” J. Opt. Soc. Am. A 12, 390–397 (1995).
[CrossRef]

A. A Maradudin, A. R. McGurn, E. R. Méndez, “Surface-plasmon polariton mechanism for the enhanced backscattering of light from one-dimensional randomly rough metal surfaces,” J. Opt. Soc. Am. A 12, 2500–2506 (1995).
[CrossRef]

O. J. F. Martin, C. Girard, A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
[CrossRef] [PubMed]

1994 (7)

M. Garcia-Parajo, J. Rosiu, Y. Chen, “On the way to a multi-task near field optical microscope: simultaneous STM/SNOM and PSTM imaging,” Microsc. Microanal. Microstruct. 5, 399–407 (1994).
[CrossRef]

C. Girard, A. Dereux, O. Martin, M. Devel, “Importance of confined field in near-field optical imaging of subwavelength objects,” Phys. Rev. B 50, 14,467–14,473 (1994).
[CrossRef]

F. Pincemin, A. Sentenac, J.-J. Greffet, “Near field scattered by a dielectric rod below a metallic surface,” J. Opt. Soc. Am. A 11, 1117–1127 (1994).
[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]

D. Barchiesi, D. Van Labeke, “PSTM: an alternative to measure local variation of optical index,” Microsc. Microanal. Microstruct. 5, 435–446 (1994).
[CrossRef]

C. Girard, A. Dereux, “Optical spectroscopy of a surface at a nanometer scale: a theoretical study in real space,” Phys. Rev. B 49, 11,334–11,351 (1994).
[CrossRef]

H. Heinzelmann, D. W. Pohl, “Scanning near-field optical microscopy,” Appl. Phys. A 59, 89–101 (1994).
[CrossRef]

1993 (2)

1992 (6)

E. Bourillot, F. de Fornel, L. Salomon, P. M. Adam, J.-P. Goudonnet, “Observation de structures guidantes en microscopie à effet tunnel photonique,” J. Opt. (Paris) 23, 57–62 (1992).
[CrossRef]

D. Courjon, C. Bainier, M. Spajer, “Imaging of submicron index variations by scanning optical tunneling,” J. Vac. Sci. Technol. B 10, 2436–2439 (1992).
[CrossRef]

E. Betzig, P. L. Finn, J. S. Weiner, “Combined shear force and near-field scanning optical microscopy,” Appl. Phys. Lett. 60, 2484–2486 (1992).
[CrossRef]

R. Toledo-Crow, P. C. Yang, Y. Chen, M. Vaez-Iravani, “Near-field differential scanning optical microscope with atomic force regulation,” Appl. Phys. Lett. 60, 2957–2959 (1992).
[CrossRef]

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

J. Cites, M. F. M. Sanghadasa, C. S. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrel, “Analysis of photon scanning tunneling microscope images,” J. Appl. Phys. 71, 7–10 (1992).
[CrossRef]

1991 (2)

N. Joachimowicz, C. Pichot, J.-P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag. 29, 1742–1752 (1991).
[CrossRef]

A. Sammar, J.-M. Andre, B. Pardo, “Diffraction and scattering by lamellar amplitude multilayer gratings in the X-UV region,” Opt. Commun. 86, 245–254 (1991).
[CrossRef]

1989 (1)

J.-J. Greffet, “Scattering of s-polarized electromagnetic waves by a 2D obstacle near an interface,” Opt. Commun. 72, 274–278 (1989).
[CrossRef]

1984 (1)

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
[CrossRef]

1982 (2)

D. M. Wood, N. W. Ashcroft, “Quantum size effect in the optical properties of small metallic particles,” Phys. Rev. B 25, 6255–6274 (1982).
[CrossRef]

D. W. Oxtoby, F. Novak, S. A. Rice, “The Ewald–Oseen theorem in the x-ray frequency region: a microscopic analysis,” J. Chem. Phys. 76, 5278–5282 (1982).
[CrossRef]

1976 (1)

G. S. Agarwal, “Integral equation treatment of scattering from rough surfaces,” Phys. Rev. B 14, 846–848 (1976).
[CrossRef]

1975 (2)

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]

G. S. Agarwal, “Scattering from rough surfaces,” Opt. Commun. 14, 161–166 (1975).
[CrossRef]

Adam, P. M.

E. Bourillot, F. de Fornel, L. Salomon, P. M. Adam, J.-P. Goudonnet, “Observation de structures guidantes en microscopie à effet tunnel photonique,” J. Opt. (Paris) 23, 57–62 (1992).
[CrossRef]

F. de Fornel, P. M. Adam, L. Salomon, J.-P. Goudonnet, A. Sentenac, J.-J. Greffet, R. Carminati, “Analysis of image formation with a photon scanning tunneling microscope,” J. Opt. Soc. Am. A (to be published).

Agarwal, G. S.

G. S. Agarwal, “Integral equation treatment of scattering from rough surfaces,” Phys. Rev. B 14, 846–848 (1976).
[CrossRef]

G. S. Agarwal, “Scattering from rough surfaces,” Opt. Commun. 14, 161–166 (1975).
[CrossRef]

Andre, J.-M.

A. Sammar, J.-M. Andre, B. Pardo, “Diffraction and scattering by lamellar amplitude multilayer gratings in the X-UV region,” Opt. Commun. 86, 245–254 (1991).
[CrossRef]

Ashcroft, N. W.

D. M. Wood, N. W. Ashcroft, “Quantum size effect in the optical properties of small metallic particles,” Phys. Rev. B 25, 6255–6274 (1982).
[CrossRef]

Baida, F.

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

Bainier, C.

D. Courjon, C. Bainier, M. Spajer, “Imaging of submicron index variations by scanning optical tunneling,” J. Vac. Sci. Technol. B 10, 2436–2439 (1992).
[CrossRef]

Balkanski, M.

R. F. Wallis, M. Balkanski, Many-Body Aspects of Solid State Spectroscopy (North-Holland, Amsterdam, 1986).

Barchiesi, D.

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

D. Barchiesi, D. Van Labeke, “PSTM: an alternative to measure local variation of optical index,” Microsc. Microanal. Microstruct. 5, 435–446 (1994).
[CrossRef]

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

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

Betzig, E.

E. Betzig, P. L. Finn, J. S. Weiner, “Combined shear force and near-field scanning optical microscopy,” Appl. Phys. Lett. 60, 2484–2486 (1992).
[CrossRef]

Bolger, B.

M. H. P. Moers, R. G. Tack, O. F. J. Noordman, F. B. Segerink, N. F. Van-Hulst, B. Bolger, “Combined photon scanning tunneling microscope and atomic force microscope using silicon nitride probes,” in Near Field Optics, D. W. Pohl, D. Courjon, eds. (Kluwer, Dordrecht, The Netherlands, 1993), pp. 79–86.
[CrossRef]

Bourillot, E.

Carminati, R.

J.-J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near field data,” Opt. Commun. 11620–24 (1995).
[CrossRef]

R. Carminati, J.-J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope: concept of transfer function,” Opt. Commun. 116, 316–321 (1995).
[CrossRef]

F. de Fornel, P. M. Adam, L. Salomon, J.-P. Goudonnet, A. Sentenac, J.-J. Greffet, R. Carminati, “Analysis of image formation with a photon scanning tunneling microscope,” J. Opt. Soc. Am. A (to be published).

Chen, Y.

M. Garcia-Parajo, J. Rosiu, Y. Chen, “On the way to a multi-task near field optical microscope: simultaneous STM/SNOM and PSTM imaging,” Microsc. Microanal. Microstruct. 5, 399–407 (1994).
[CrossRef]

R. Toledo-Crow, P. C. Yang, Y. Chen, M. Vaez-Iravani, “Near-field differential scanning optical microscope with atomic force regulation,” Appl. Phys. Lett. 60, 2957–2959 (1992).
[CrossRef]

Cites, J.

J. Cites, M. F. M. Sanghadasa, C. S. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrel, “Analysis of photon scanning tunneling microscope images,” J. Appl. Phys. 71, 7–10 (1992).
[CrossRef]

Courjon, D.

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

D. Courjon, C. Bainier, M. Spajer, “Imaging of submicron index variations by scanning optical tunneling,” J. Vac. Sci. Technol. B 10, 2436–2439 (1992).
[CrossRef]

de Fornel, F.

E. Bourillot, F. de Fornel, J.-P. Goudonnet, D. Persegol, A. Kevorkian, D. Delacourt, “Analysis of photonscanning tunneling microscope images of inhomogeneous samples: determination of the local refractive index of channel waveguides,” J. Opt. Soc. Am. A 12, 95–106 (1995).
[CrossRef]

E. Bourillot, F. de Fornel, L. Salomon, P. M. Adam, J.-P. Goudonnet, “Observation de structures guidantes en microscopie à effet tunnel photonique,” J. Opt. (Paris) 23, 57–62 (1992).
[CrossRef]

F. de Fornel, P. M. Adam, L. Salomon, J.-P. Goudonnet, A. Sentenac, J.-J. Greffet, R. Carminati, “Analysis of image formation with a photon scanning tunneling microscope,” J. Opt. Soc. Am. A (to be published).

Delacourt, D.

Dereux, A.

O. J. F. Martin, C. Girard, A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
[CrossRef] [PubMed]

C. Girard, A. Dereux, “Optical spectroscopy of a surface at a nanometer scale: a theoretical study in real space,” Phys. Rev. B 49, 11,334–11,351 (1994).
[CrossRef]

C. Girard, A. Dereux, O. Martin, M. Devel, “Importance of confined field in near-field optical imaging of subwavelength objects,” Phys. Rev. B 50, 14,467–14,473 (1994).
[CrossRef]

Devel, M.

C. Girard, A. Dereux, O. Martin, M. Devel, “Importance of confined field in near-field optical imaging of subwavelength objects,” Phys. Rev. B 50, 14,467–14,473 (1994).
[CrossRef]

Elson, J. M.

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
[CrossRef]

Ferrel, T. L.

J. Cites, M. F. M. Sanghadasa, C. S. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrel, “Analysis of photon scanning tunneling microscope images,” J. Appl. Phys. 71, 7–10 (1992).
[CrossRef]

Finn, P. L.

E. Betzig, P. L. Finn, J. S. Weiner, “Combined shear force and near-field scanning optical microscopy,” Appl. Phys. Lett. 60, 2484–2486 (1992).
[CrossRef]

Garcia, N.

Garcia-Parajo, M.

M. Garcia-Parajo, J. Rosiu, Y. Chen, “On the way to a multi-task near field optical microscope: simultaneous STM/SNOM and PSTM imaging,” Microsc. Microanal. Microstruct. 5, 399–407 (1994).
[CrossRef]

Girard, C.

O. J. F. Martin, C. Girard, A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
[CrossRef] [PubMed]

C. Girard, A. Dereux, O. Martin, M. Devel, “Importance of confined field in near-field optical imaging of subwavelength objects,” Phys. Rev. B 50, 14,467–14,473 (1994).
[CrossRef]

C. Girard, A. Dereux, “Optical spectroscopy of a surface at a nanometer scale: a theoretical study in real space,” Phys. Rev. B 49, 11,334–11,351 (1994).
[CrossRef]

Gottfried, K.

K. Gottfried, Quantum Mechanics (Benjamin, New York, 1966).

Goudonnet, J.-P.

E. Bourillot, F. de Fornel, J.-P. Goudonnet, D. Persegol, A. Kevorkian, D. Delacourt, “Analysis of photonscanning tunneling microscope images of inhomogeneous samples: determination of the local refractive index of channel waveguides,” J. Opt. Soc. Am. A 12, 95–106 (1995).
[CrossRef]

E. Bourillot, F. de Fornel, L. Salomon, P. M. Adam, J.-P. Goudonnet, “Observation de structures guidantes en microscopie à effet tunnel photonique,” J. Opt. (Paris) 23, 57–62 (1992).
[CrossRef]

F. de Fornel, P. M. Adam, L. Salomon, J.-P. Goudonnet, A. Sentenac, J.-J. Greffet, R. Carminati, “Analysis of image formation with a photon scanning tunneling microscope,” J. Opt. Soc. Am. A (to be published).

Greffet, J.-J.

A. Sentenac, J.-J. Greffet, “Study of the features of the PSTM images by means of a perturbative approach,” Ultramicroscopy 57, 246–250 (1995).
[CrossRef]

R. Carminati, J.-J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope: concept of transfer function,” Opt. Commun. 116, 316–321 (1995).
[CrossRef]

J.-J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near field data,” Opt. Commun. 11620–24 (1995).
[CrossRef]

F. Pincemin, A. Sentenac, J.-J. Greffet, “Near field scattered by a dielectric rod below a metallic surface,” J. Opt. Soc. Am. A 11, 1117–1127 (1994).
[CrossRef]

J.-J. Greffet, “Scattering of s-polarized electromagnetic waves by a 2D obstacle near an interface,” Opt. Commun. 72, 274–278 (1989).
[CrossRef]

F. de Fornel, P. M. Adam, L. Salomon, J.-P. Goudonnet, A. Sentenac, J.-J. Greffet, R. Carminati, “Analysis of image formation with a photon scanning tunneling microscope,” J. Opt. Soc. Am. A (to be published).

Heinzelmann, H.

H. Heinzelmann, D. W. Pohl, “Scanning near-field optical microscopy,” Appl. Phys. A 59, 89–101 (1994).
[CrossRef]

Hugonin, J.-P.

N. Joachimowicz, C. Pichot, J.-P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag. 29, 1742–1752 (1991).
[CrossRef]

Joachimowicz, N.

N. Joachimowicz, C. Pichot, J.-P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag. 29, 1742–1752 (1991).
[CrossRef]

Kevorkian, A.

Maradudin, A. A

Maradudin, A. A.

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]

Martin, O.

C. Girard, A. Dereux, O. Martin, M. Devel, “Importance of confined field in near-field optical imaging of subwavelength objects,” Phys. Rev. B 50, 14,467–14,473 (1994).
[CrossRef]

Martin, O. J. F.

O. J. F. Martin, C. Girard, A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
[CrossRef] [PubMed]

McGurn, A. R.

Méndez, E. R.

Mills, D. L.

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]

Moers, M. H. P.

M. H. P. Moers, R. G. Tack, O. F. J. Noordman, F. B. Segerink, N. F. Van-Hulst, B. Bolger, “Combined photon scanning tunneling microscope and atomic force microscope using silicon nitride probes,” in Near Field Optics, D. W. Pohl, D. Courjon, eds. (Kluwer, Dordrecht, The Netherlands, 1993), pp. 79–86.
[CrossRef]

Nevière, M.

M. Nevière, P. Vincent, “Diffraction gratings as components for photon scanning tunneling microscope image interpretation,” in Near Field Optics, D. W. Pohl, D. Courjon, eds. (Kluwer, Dordrecht, The Netherlands, 1993), pp. 377–378.
[CrossRef]

Nieto-Vesperinas, M.

Noordman, O. F. J.

M. H. P. Moers, R. G. Tack, O. F. J. Noordman, F. B. Segerink, N. F. Van-Hulst, B. Bolger, “Combined photon scanning tunneling microscope and atomic force microscope using silicon nitride probes,” in Near Field Optics, D. W. Pohl, D. Courjon, eds. (Kluwer, Dordrecht, The Netherlands, 1993), pp. 79–86.
[CrossRef]

Novak, F.

D. W. Oxtoby, F. Novak, S. A. Rice, “The Ewald–Oseen theorem in the x-ray frequency region: a microscopic analysis,” J. Chem. Phys. 76, 5278–5282 (1982).
[CrossRef]

Novotny, L.

O’Donnell, K. A.

Oxtoby, D. W.

D. W. Oxtoby, F. Novak, S. A. Rice, “The Ewald–Oseen theorem in the x-ray frequency region: a microscopic analysis,” J. Chem. Phys. 76, 5278–5282 (1982).
[CrossRef]

Pardo, B.

A. Sammar, J.-M. Andre, B. Pardo, “Diffraction and scattering by lamellar amplitude multilayer gratings in the X-UV region,” Opt. Commun. 86, 245–254 (1991).
[CrossRef]

Persegol, D.

Pichot, C.

N. Joachimowicz, C. Pichot, J.-P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag. 29, 1742–1752 (1991).
[CrossRef]

Pincemin, F.

Pohl, D. W.

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]

H. Heinzelmann, D. W. Pohl, “Scanning near-field optical microscopy,” Appl. Phys. A 59, 89–101 (1994).
[CrossRef]

D. W. Pohl, “Scanning near-field optical microscopy,” in Advances in Optical and Electron Microscopy, (C. Sheppard, T. Mulvey, eds. (Academic, London, 1990).

Reddick, R. C.

J. Cites, M. F. M. Sanghadasa, C. S. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrel, “Analysis of photon scanning tunneling microscope images,” J. Appl. Phys. 71, 7–10 (1992).
[CrossRef]

Regli, P.

Rice, S. A.

D. W. Oxtoby, F. Novak, S. A. Rice, “The Ewald–Oseen theorem in the x-ray frequency region: a microscopic analysis,” J. Chem. Phys. 76, 5278–5282 (1982).
[CrossRef]

Rosiu, J.

M. Garcia-Parajo, J. Rosiu, Y. Chen, “On the way to a multi-task near field optical microscope: simultaneous STM/SNOM and PSTM imaging,” Microsc. Microanal. Microstruct. 5, 399–407 (1994).
[CrossRef]

Salomon, L.

E. Bourillot, F. de Fornel, L. Salomon, P. M. Adam, J.-P. Goudonnet, “Observation de structures guidantes en microscopie à effet tunnel photonique,” J. Opt. (Paris) 23, 57–62 (1992).
[CrossRef]

F. de Fornel, P. M. Adam, L. Salomon, J.-P. Goudonnet, A. Sentenac, J.-J. Greffet, R. Carminati, “Analysis of image formation with a photon scanning tunneling microscope,” J. Opt. Soc. Am. A (to be published).

Sammar, A.

A. Sammar, J.-M. Andre, B. Pardo, “Diffraction and scattering by lamellar amplitude multilayer gratings in the X-UV region,” Opt. Commun. 86, 245–254 (1991).
[CrossRef]

Sanghadasa, M. F. M.

J. Cites, M. F. M. Sanghadasa, C. S. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrel, “Analysis of photon scanning tunneling microscope images,” J. Appl. Phys. 71, 7–10 (1992).
[CrossRef]

Schollwock, U.

U. Schollwock, H. Wagner, “A perturbation theory approach to scanning near field optical microscopy,” in Near Field Optics, D. W. Pohl, D. Courjon, eds. (Kluwer, Dordrecht, The Netherlands, 1993), pp. 247–254.
[CrossRef]

Segerink, F. B.

M. H. P. Moers, R. G. Tack, O. F. J. Noordman, F. B. Segerink, N. F. Van-Hulst, B. Bolger, “Combined photon scanning tunneling microscope and atomic force microscope using silicon nitride probes,” in Near Field Optics, D. W. Pohl, D. Courjon, eds. (Kluwer, Dordrecht, The Netherlands, 1993), pp. 79–86.
[CrossRef]

Sentenac, A.

J.-J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near field data,” Opt. Commun. 11620–24 (1995).
[CrossRef]

A. Sentenac, J.-J. Greffet, “Study of the features of the PSTM images by means of a perturbative approach,” Ultramicroscopy 57, 246–250 (1995).
[CrossRef]

F. Pincemin, A. Sentenac, J.-J. Greffet, “Near field scattered by a dielectric rod below a metallic surface,” J. Opt. Soc. Am. A 11, 1117–1127 (1994).
[CrossRef]

F. de Fornel, P. M. Adam, L. Salomon, J.-P. Goudonnet, A. Sentenac, J.-J. Greffet, R. Carminati, “Analysis of image formation with a photon scanning tunneling microscope,” J. Opt. Soc. Am. A (to be published).

Spajer, M.

D. Courjon, C. Bainier, M. Spajer, “Imaging of submicron index variations by scanning optical tunneling,” J. Vac. Sci. Technol. B 10, 2436–2439 (1992).
[CrossRef]

Sung, C. S.

J. Cites, M. F. M. Sanghadasa, C. S. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrel, “Analysis of photon scanning tunneling microscope images,” J. Appl. Phys. 71, 7–10 (1992).
[CrossRef]

Tack, R. G.

M. H. P. Moers, R. G. Tack, O. F. J. Noordman, F. B. Segerink, N. F. Van-Hulst, B. Bolger, “Combined photon scanning tunneling microscope and atomic force microscope using silicon nitride probes,” in Near Field Optics, D. W. Pohl, D. Courjon, eds. (Kluwer, Dordrecht, The Netherlands, 1993), pp. 79–86.
[CrossRef]

Toledo-Crow, R.

R. Toledo-Crow, P. C. Yang, Y. Chen, M. Vaez-Iravani, “Near-field differential scanning optical microscope with atomic force regulation,” Appl. Phys. Lett. 60, 2957–2959 (1992).
[CrossRef]

Vaez-Iravani, M.

R. Toledo-Crow, P. C. Yang, Y. Chen, M. Vaez-Iravani, “Near-field differential scanning optical microscope with atomic force regulation,” Appl. Phys. Lett. 60, 2957–2959 (1992).
[CrossRef]

Van Labeke, D.

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

D. Barchiesi, D. Van Labeke, “PSTM: an alternative to measure local variation of optical index,” Microsc. Microanal. Microstruct. 5, 435–446 (1994).
[CrossRef]

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

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

Van-Hulst, N. F.

M. H. P. Moers, R. G. Tack, O. F. J. Noordman, F. B. Segerink, N. F. Van-Hulst, B. Bolger, “Combined photon scanning tunneling microscope and atomic force microscope using silicon nitride probes,” in Near Field Optics, D. W. Pohl, D. Courjon, eds. (Kluwer, Dordrecht, The Netherlands, 1993), pp. 79–86.
[CrossRef]

Vincent, P.

M. Nevière, P. Vincent, “Diffraction gratings as components for photon scanning tunneling microscope image interpretation,” in Near Field Optics, D. W. Pohl, D. Courjon, eds. (Kluwer, Dordrecht, The Netherlands, 1993), pp. 377–378.
[CrossRef]

Wagner, H.

U. Schollwock, H. Wagner, “A perturbation theory approach to scanning near field optical microscopy,” in Near Field Optics, D. W. Pohl, D. Courjon, eds. (Kluwer, Dordrecht, The Netherlands, 1993), pp. 247–254.
[CrossRef]

Wallis, R. F.

R. F. Wallis, M. Balkanski, Many-Body Aspects of Solid State Spectroscopy (North-Holland, Amsterdam, 1986).

Warmack, R. J.

J. Cites, M. F. M. Sanghadasa, C. S. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrel, “Analysis of photon scanning tunneling microscope images,” J. Appl. Phys. 71, 7–10 (1992).
[CrossRef]

Weiner, J. S.

E. Betzig, P. L. Finn, J. S. Weiner, “Combined shear force and near-field scanning optical microscopy,” Appl. Phys. Lett. 60, 2484–2486 (1992).
[CrossRef]

West, C. S.

Wood, D. M.

D. M. Wood, N. W. Ashcroft, “Quantum size effect in the optical properties of small metallic particles,” Phys. Rev. B 25, 6255–6274 (1982).
[CrossRef]

Yang, P. C.

R. Toledo-Crow, P. C. Yang, Y. Chen, M. Vaez-Iravani, “Near-field differential scanning optical microscope with atomic force regulation,” Appl. Phys. Lett. 60, 2957–2959 (1992).
[CrossRef]

Appl. Phys. A (1)

H. Heinzelmann, D. W. Pohl, “Scanning near-field optical microscopy,” Appl. Phys. A 59, 89–101 (1994).
[CrossRef]

Appl. Phys. Lett. (2)

E. Betzig, P. L. Finn, J. S. Weiner, “Combined shear force and near-field scanning optical microscopy,” Appl. Phys. Lett. 60, 2484–2486 (1992).
[CrossRef]

R. Toledo-Crow, P. C. Yang, Y. Chen, M. Vaez-Iravani, “Near-field differential scanning optical microscope with atomic force regulation,” Appl. Phys. Lett. 60, 2957–2959 (1992).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

N. Joachimowicz, C. Pichot, J.-P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag. 29, 1742–1752 (1991).
[CrossRef]

J. Appl. Phys. (1)

J. Cites, M. F. M. Sanghadasa, C. S. Sung, R. C. Reddick, R. J. Warmack, T. L. Ferrel, “Analysis of photon scanning tunneling microscope images,” J. Appl. Phys. 71, 7–10 (1992).
[CrossRef]

J. Chem. Phys. (1)

D. W. Oxtoby, F. Novak, S. A. Rice, “The Ewald–Oseen theorem in the x-ray frequency region: a microscopic analysis,” J. Chem. Phys. 76, 5278–5282 (1982).
[CrossRef]

J. Opt. (Paris) (1)

E. Bourillot, F. de Fornel, L. Salomon, P. M. Adam, J.-P. Goudonnet, “Observation de structures guidantes en microscopie à effet tunnel photonique,” J. Opt. (Paris) 23, 57–62 (1992).
[CrossRef]

J. Opt. Soc. Am. A (7)

J. Vac. Sci. Technol. B (1)

D. Courjon, C. Bainier, M. Spajer, “Imaging of submicron index variations by scanning optical tunneling,” J. Vac. Sci. Technol. B 10, 2436–2439 (1992).
[CrossRef]

Microsc. Microanal. Microstruct. (2)

D. Barchiesi, D. Van Labeke, “PSTM: an alternative to measure local variation of optical index,” Microsc. Microanal. Microstruct. 5, 435–446 (1994).
[CrossRef]

M. Garcia-Parajo, J. Rosiu, Y. Chen, “On the way to a multi-task near field optical microscope: simultaneous STM/SNOM and PSTM imaging,” Microsc. Microanal. Microstruct. 5, 399–407 (1994).
[CrossRef]

Opt. Commun. (6)

G. S. Agarwal, “Scattering from rough surfaces,” Opt. Commun. 14, 161–166 (1975).
[CrossRef]

A. Sammar, J.-M. Andre, B. Pardo, “Diffraction and scattering by lamellar amplitude multilayer gratings in the X-UV region,” Opt. Commun. 86, 245–254 (1991).
[CrossRef]

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

J.-J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near field data,” Opt. Commun. 11620–24 (1995).
[CrossRef]

J.-J. Greffet, “Scattering of s-polarized electromagnetic waves by a 2D obstacle near an interface,” Opt. Commun. 72, 274–278 (1989).
[CrossRef]

R. Carminati, J.-J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope: concept of transfer function,” Opt. Commun. 116, 316–321 (1995).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (6)

C. Girard, A. Dereux, “Optical spectroscopy of a surface at a nanometer scale: a theoretical study in real space,” Phys. Rev. B 49, 11,334–11,351 (1994).
[CrossRef]

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]

G. S. Agarwal, “Integral equation treatment of scattering from rough surfaces,” Phys. Rev. B 14, 846–848 (1976).
[CrossRef]

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
[CrossRef]

D. M. Wood, N. W. Ashcroft, “Quantum size effect in the optical properties of small metallic particles,” Phys. Rev. B 25, 6255–6274 (1982).
[CrossRef]

C. Girard, A. Dereux, O. Martin, M. Devel, “Importance of confined field in near-field optical imaging of subwavelength objects,” Phys. Rev. B 50, 14,467–14,473 (1994).
[CrossRef]

Phys. Rev. Lett. (1)

O. J. F. Martin, C. Girard, A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
[CrossRef] [PubMed]

Ultramicroscopy (1)

A. Sentenac, J.-J. Greffet, “Study of the features of the PSTM images by means of a perturbative approach,” Ultramicroscopy 57, 246–250 (1995).
[CrossRef]

Other (7)

U. Schollwock, H. Wagner, “A perturbation theory approach to scanning near field optical microscopy,” in Near Field Optics, D. W. Pohl, D. Courjon, eds. (Kluwer, Dordrecht, The Netherlands, 1993), pp. 247–254.
[CrossRef]

F. de Fornel, P. M. Adam, L. Salomon, J.-P. Goudonnet, A. Sentenac, J.-J. Greffet, R. Carminati, “Analysis of image formation with a photon scanning tunneling microscope,” J. Opt. Soc. Am. A (to be published).

M. H. P. Moers, R. G. Tack, O. F. J. Noordman, F. B. Segerink, N. F. Van-Hulst, B. Bolger, “Combined photon scanning tunneling microscope and atomic force microscope using silicon nitride probes,” in Near Field Optics, D. W. Pohl, D. Courjon, eds. (Kluwer, Dordrecht, The Netherlands, 1993), pp. 79–86.
[CrossRef]

D. W. Pohl, “Scanning near-field optical microscopy,” in Advances in Optical and Electron Microscopy, (C. Sheppard, T. Mulvey, eds. (Academic, London, 1990).

M. Nevière, P. Vincent, “Diffraction gratings as components for photon scanning tunneling microscope image interpretation,” in Near Field Optics, D. W. Pohl, D. Courjon, eds. (Kluwer, Dordrecht, The Netherlands, 1993), pp. 377–378.
[CrossRef]

K. Gottfried, Quantum Mechanics (Benjamin, New York, 1966).

R. F. Wallis, M. Balkanski, Many-Body Aspects of Solid State Spectroscopy (North-Holland, Amsterdam, 1986).

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Figures (6)

Fig. 1
Fig. 1

Scattering geometry.

Fig. 2
Fig. 2

Samples used in the numerical simulation: (a) surface defect, (b) subsurface particle. The geometry is two dimensional.

Fig. 3
Fig. 3

(a) Normalized near-field intensity along a line at a constant height z0 = 70 nm above sample (a) in Fig. 2 for s polarization and θi = 0°. The dielectric constants of the upper medium and of the substrate are 1 = 1 and 3 = 2.25, respectively. The defect has width L = 316 nm and height h. Three defects with the same value of the product Δ × h were used. (b) Same as (a) for p polarization. Throughout the figures, ɛ is identical to in the text.

Fig. 4
Fig. 4

(a) Same as Fig. 3(a) with θi = 45°; (b) same as (a) for p polarization.

Fig. 5
Fig. 5

(a) Normalized near-field intensity along a line at a constant height z0 = 40 nm above sample (b) in Fig. 2 for s polarization and θi = 0° The dielectric constants of the upper medium and of the substrate are 1 = 1 and 3 = 2.25, respectively. The defect has a width L = 316 nm and a depth h. Three defects with the same value of the product Δ × h were used. (b) Same as (a) for p polarization.

Fig. 6
Fig. 6

(a) Same as Fig. 5(a) with θi = 45° (b) same as (a) for p polarization.

Tables (3)

Tables Icon

Table 1 Influence of Dielectric Contrast on the Accuracy of the Perturbative Expressiona

Tables Icon

Table 2 Influence of Height of the Defect on the Accuracy of the Perturbative Expressiona

Tables Icon

Table 3 Influence of Width of the Defect on the Accuracy of the Perturbative Expressiona

Equations (44)

Equations on this page are rendered with MathJax. Learn more.

f ( z ) = { 1 for z > 0 3 for z < 0 .
× × E ( r ) ( r ) k 0 2 E ( r ) = 0 ,
× × E f ( r ) f ( z ) k 0 2 E f ( r ) = 0 ,
E s = E E f .
× × E s ( r ) f ( z ) k 0 2 E s ( r ) = [ ( r ) f ( z ) ] k 0 2 E ( r ) .
× × G ¯ ¯ ( r r , z , z ) f ( z ) k 0 2 G ¯ ¯ ( r r , z , z ) = I ¯ ¯ δ ( r r ) δ ( z z ) ,
E s ( r ) = k 0 2 [ ( r ) f ( z ) ] G ¯ ¯ ( r r , z , z ) E ( r ) d r .
E ( r ) = E f ( r ) + Ω 2 k 0 2 [ ( r ) 1 ] G ¯ ¯ ( r r , z , z ) × E ( r ) d r .
k 0 2 [ ( r ) 1 ] E ( r ) d r
k 0 2 [ ( r ) 1 ] G ¯ ¯ ( r r , z , z ) E ( r ) d r
E ( r ) = E f ( r ) + Ω 2 k 0 2 [ ( r ) 1 ] G ¯ ¯ ( r r , z , z ) × E f ( r ) d r .
E ( r ) = E ( 0 ) ( r ) + d r k 0 2 G ¯ ¯ ( r r , z , 0 ) E ( 0 ) ( r , 0 ) × 0 S ( r ) [ ( r , z ) 1 ] d z ,
Δ ¯ ( r ) = 1 S ( r ) 0 S ( r ) [ ( r , z ) 1 ] d z ,
E ( r ) = E ( 0 ) ( r ) + k 0 2 G ¯ ¯ ( r r , z , 0 ) E ( 0 ) ( r , 0 ) × Δ ¯ ( r ) S ( r ) d r .
sup | E ( r ) E ( 0 ) ( r ) E ( 0 ) ( r ) | 1 ,
sup | d r k 0 2 G ¯ ¯ ( r r , z , 0 ) E ( 0 ) ( r , 0 ) 0 S ( r ) [ ( r , z ) 1 ] d z E ( 0 ) ( r ) | 1 .
G ¯ ¯ ( r r ) = ( I ¯ ¯ + 1 k 0 2 ) G 0 ( r , r ) ,
G 0 ( r , r ) = exp ( i k 0 | r r | | ) 4 π | r r | ·
| d r k 0 2 G ¯ ¯ ( r r , z , 0 ) E ( 0 ) ( r , 0 ) 0 S ( r ) [ ( r , z ) 1 ] d z E ( 0 ) ( r ) | < k 0 2 Δ h Γ 4 π d .
π Δ h Γ λ 2 d 1 ,
E ( r ) = E ( 0 ) ( r ) + k 0 2 4 π 2 ( 2 1 ) g ¯ ¯ ( k , z , 0 ) E 0 S ( k k i ) × exp ( i k · r ) d k .
S ( k ) = 4 π 2 h 2 [ δ ( k k g ) + δ ( k + k g ) ] ,
E ( r ) = E ( 0 ) ( r ) + k 0 2 h ( 2 1 ) { g ¯ ¯ ( k i + k g , z , 0 ) E 0 × exp [ i ( k i + k g ) · r ] + g ¯ ¯ ( k i k g , z , 0 ) E 0 × exp [ i ( k i k g ) · r ] } .
sup | E ( 1 ) ( r ) E ( 0 ) ( r ) | 1 ,
k 0 2 h ( 2 1 ) sup | g i j | 1 ,
2 π h λ ( 2 1 ) 1 .
2 π 2 h λ 2 ( 2 1 ) exp ( k g z ) k g 1 ( s polarization ) .
h ( 2 1 ) k g exp ( k g z ) 1 ( p polarization ) .
Δ h Γ λ 2 d 1 ,
sup | I ( x , z 0 ) I ref ( x , z 0 ) | I ref ( x , z 0 ) ,
G ¯ ¯ ( r r , z , z ) = 1 4 π 2 g ¯ ¯ ( k , z , z ) × exp [ i k · ( r r ) ] d k .
g ¯ ¯ ( k , z , z ) = f ¯ ¯ ( k , z ) exp ( i γ 1 z ) + h ¯ ¯ ( k , z ) exp ( i γ 1 z ) ,
E ( 0 ) ( r ) = E 0 + exp ( i k i · r + i γ 1 i z ) + E 0 exp ( i k i · r i γ 1 i z ) ,
E ( 0 ) ( r ) = E 0 + exp ( i k i · r + i γ 1 i z ) .
E ( 1 ) ( r ) = k 0 2 4 π 2 d k f ¯ ¯ ( k , z ) E 0 + exp ( i k · r ) × d r exp [ i ( k i k ) · r ] × 0 S ( r ) d z [ ( r ) 1 ] exp [ i ( γ 1 i γ 1 ) z ] + k 0 2 4 π 2 d k h ¯ ¯ ( k , z ) E 0 + exp ( i k · r ) × d r exp [ i ( k i k ) · r ] × 0 S ( r ) d z [ ( r ) 1 ] exp [ i ( γ 1 i γ 1 ) z ] .
G ¯ ¯ ( r r , z , z ) = 1 4 π 2 g ¯ ¯ ( k , z , z ) × exp [ i k · ( r r ) ] d k .
2 π h / λ 1 ,
| k | h 1 .
E ( r ) = E ( 0 ) ( r ) + k 0 2 ( 1 ) S ( r ) G ¯ ¯ ( r r , z , 0 ) × E ( 0 ) ( r , 0 ) d r .
G ¯ ¯ ( r r , z , z ) = 1 4 π 2 g ¯ ¯ ( k , z , z ) × exp [ i k · ( r r ) ] d k .
E ( 0 ) ( r , 0 ) = E 0 exp ( i k i · r ) ,
E ( r ) = E ( 0 ) ( r ) + k 0 2 4 π 2 ( 1 ) d k g ¯ ¯ ( k , z , 0 ) E 0 × exp ( i k · r ) d r S ( r ) exp [ i ( k i k ) · r ] .
S ( k ) = S ( r ) exp ( i k · r ) d r ,
E ( r ) = E ( 0 ) ( r ) + k 0 2 4 π 2 ( 1 ) g ¯ ¯ ( k , z , 0 ) E 0 S ( k k i ) × exp ( i k · r ) d k .

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