Abstract

A theoretical model for calculating the images obtained in scanning-tunneling optical microscopy is proposed. We calculate the intensity detected by a small spherical tip above a regular glass lattice illuminated in total internal reflection. The model is based on a macroscopic approach. We show that the resolution is limited neither by the wavelength nor by the decay length of the evanescent wave but that it is determined by the tip–sample distance and by the signal-to-noise ratio. We also discuss the quality of the images. In general, the intensity profile does not reproduce the sample profile. We analyzed two kinds of filtering that can deform the true profile. We also show that for a small sample period a strong signal is obtained only in TM polarization.

© 1992 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970).
  2. H. K. Wickramasinghe, “Differential laser heterodyne micrometrology,” Opt. Eng. 24, 926–929 (1985).
    [Crossref]
  3. E. A. Ash, G. Nichols, “Super resolution aperture scanning microscope,” Nature (London) 237, 510–512 (1972).
    [Crossref]
  4. G. A. Massey, “Microscopy and pattern generation with scanned evanescent waves,” Appl. Opt. 23, 658–680 (1984).
    [Crossref] [PubMed]
  5. D. W. Pohl, “Optical near-field scanning microscope,” European Patent0112401 (December27, 1982); U.S. Patent4,604,520 (December20, 1983).
  6. A. Lewis, M. Isaacson, A. Murray, A. Harootunian, “Scanning optical spectral microscopy with 500 A resolution,” Biophys. J. 41, 405a (1983).
  7. D. W. Pohl, W. Denk, U. Dürig, “Optical stethoscopy: imaging with λ/20,” in Micron and Submicron Integrated Circuit Metrology, K. M. Monahan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.565, 56–61 (1985).
    [Crossref]
  8. U. C. Fisher, U. T. Durig, D. W. Pohl, “Near-field optical scanning microscopy in reflection,” Appl. Phys. Lett. 52, 249–251 (1988).
    [Crossref]
  9. D. Courjon, K. Sarayedine, M. Spajer, “Scanning tunneling optical microscopy,” Opt. Commun. 71, 23–28 (1989).
    [Crossref]
  10. F. de Fornel, J. P. Goudonnet, L. Salomon, E. Lesniewska, “An evanescent field optical microscope,” in Optical Storage and Scanning Technology, T. Wilson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1139, 77–84 (1989).
    [Crossref]
  11. R. C. Reddik, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
    [Crossref]
  12. D. Courjon, J. M. Vigoureux, M. Spajer, K. Sarayeddine, S. Leblanc, “External and internal reflection near-field microscopy: experiments and results,” Appl. Opt. 29, 3734–3740 (1990).
    [Crossref] [PubMed]
  13. J. M. Vigoureux, C. Girard, D. Courjon, “General principles of scanning tunneling optical microscopy,” Opt. Lett. 14, 1039–1041 (1989).
    [Crossref] [PubMed]
  14. 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]
  15. C. Girard, M. Spajer, “Model for reflection near-field optical microscopy,” Appl. Opt. 29, 3726–3732 (1989).
    [Crossref]
  16. C. Girard, D. Courjon, “Model for scanning tunneling optical microscopy: a microscopic self-consistent approach,” Phys. Rev. B 42, 9340–9349 (1990).
    [Crossref]
  17. J. M. Vigoureux, F. Depasse, C. Girard, “Superresolution of near-field optical microscopy defined from properties of confined electromagnetic waves,” Appl. Opt. (to be published).
  18. J. Tersoff, D. R. Hamann, “Theory of the scanning tunneling microscope,” Phys. Rev. B 31, 805–813 (1985).
    [Crossref]
  19. W. Sachs, C. Noguera, “Generalized expression for the tunneling current in scanning tunneling microscopy,” Phys. Rev. B 43, 11612–11622 (1991).
    [Crossref]
  20. R. Petit, ed., Electromagnetic Theory of Gratings, Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980).
    [Crossref]
  21. D. Maystre, “Rigorous vector theories of diffraction gratings,” in Progress in Optics XXI, E. Wolf, ed. (Elsevier, Amsterdam, 1984).
    [Crossref]
  22. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).
  23. P. Beckmann, “Scattering of light by rough surfaces,” in Progress in Optics VI, E. Wolf, ed. (North-Holland, Amsterdam, 1963), pp. 53–69.
  24. G. S. Agarwal, “Interaction of electromagnetic waves at rough dielectric surfaces,” Phys. Rev. B 15, 2371–2383 (1977).
    [Crossref]
  25. F. Toigo, A. Marvin, V. Celli, N. R. Hill, “Optical properties of rough surfaces: general theory and the small roughness limit,” Phys. Rev. B 13, 5618–5626 (1977).
    [Crossref]
  26. J. M. Elson, “Light scattering from semi-infinite media for non-normal incidence,” Phys. Rev. B 12, 2541–2542 (1975).
    [Crossref]
  27. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  28. W. C. Meixner, P. R. Antoniewski, “Effect of atomic size on the effective polarizability of physisorbed atoms,” Phys. Status Solidi B 86, 339–343 (1978).
    [Crossref]
  29. C. Girard, J. M. Vigoureux, D. Van Labeke, P. Grossel, “Effective polarizability of two interacting adsorbed atoms,” Chem. Phys. 114, 209–220 (1987).
    [Crossref]

1991 (1)

W. Sachs, C. Noguera, “Generalized expression for the tunneling current in scanning tunneling microscopy,” Phys. Rev. B 43, 11612–11622 (1991).
[Crossref]

1990 (3)

1989 (4)

C. Girard, M. Spajer, “Model for reflection near-field optical microscopy,” Appl. Opt. 29, 3726–3732 (1989).
[Crossref]

D. Courjon, K. Sarayedine, M. Spajer, “Scanning tunneling optical microscopy,” Opt. Commun. 71, 23–28 (1989).
[Crossref]

R. C. Reddik, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
[Crossref]

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

1988 (1)

U. C. Fisher, U. T. Durig, D. W. Pohl, “Near-field optical scanning microscopy in reflection,” Appl. Phys. Lett. 52, 249–251 (1988).
[Crossref]

1987 (1)

C. Girard, J. M. Vigoureux, D. Van Labeke, P. Grossel, “Effective polarizability of two interacting adsorbed atoms,” Chem. Phys. 114, 209–220 (1987).
[Crossref]

1985 (2)

J. Tersoff, D. R. Hamann, “Theory of the scanning tunneling microscope,” Phys. Rev. B 31, 805–813 (1985).
[Crossref]

H. K. Wickramasinghe, “Differential laser heterodyne micrometrology,” Opt. Eng. 24, 926–929 (1985).
[Crossref]

1984 (1)

1983 (1)

A. Lewis, M. Isaacson, A. Murray, A. Harootunian, “Scanning optical spectral microscopy with 500 A resolution,” Biophys. J. 41, 405a (1983).

1978 (1)

W. C. Meixner, P. R. Antoniewski, “Effect of atomic size on the effective polarizability of physisorbed atoms,” Phys. Status Solidi B 86, 339–343 (1978).
[Crossref]

1977 (2)

G. S. Agarwal, “Interaction of electromagnetic waves at rough dielectric surfaces,” Phys. Rev. B 15, 2371–2383 (1977).
[Crossref]

F. Toigo, A. Marvin, V. Celli, N. R. Hill, “Optical properties of rough surfaces: general theory and the small roughness limit,” Phys. Rev. B 13, 5618–5626 (1977).
[Crossref]

1975 (1)

J. M. Elson, “Light scattering from semi-infinite media for non-normal incidence,” Phys. Rev. B 12, 2541–2542 (1975).
[Crossref]

1972 (1)

E. A. Ash, G. Nichols, “Super resolution aperture scanning microscope,” Nature (London) 237, 510–512 (1972).
[Crossref]

Agarwal, G. S.

G. S. Agarwal, “Interaction of electromagnetic waves at rough dielectric surfaces,” Phys. Rev. B 15, 2371–2383 (1977).
[Crossref]

Antoniewski, P. R.

W. C. Meixner, P. R. Antoniewski, “Effect of atomic size on the effective polarizability of physisorbed atoms,” Phys. Status Solidi B 86, 339–343 (1978).
[Crossref]

Ash, E. A.

E. A. Ash, G. Nichols, “Super resolution aperture scanning microscope,” Nature (London) 237, 510–512 (1972).
[Crossref]

Beckmann, P.

P. Beckmann, “Scattering of light by rough surfaces,” in Progress in Optics VI, E. Wolf, ed. (North-Holland, Amsterdam, 1963), pp. 53–69.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970).

Celli, V.

F. Toigo, A. Marvin, V. Celli, N. R. Hill, “Optical properties of rough surfaces: general theory and the small roughness limit,” Phys. Rev. B 13, 5618–5626 (1977).
[Crossref]

Courjon, D.

de Fornel, F.

F. de Fornel, J. P. Goudonnet, L. Salomon, E. Lesniewska, “An evanescent field optical microscope,” in Optical Storage and Scanning Technology, T. Wilson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1139, 77–84 (1989).
[Crossref]

Denk, W.

D. W. Pohl, W. Denk, U. Dürig, “Optical stethoscopy: imaging with λ/20,” in Micron and Submicron Integrated Circuit Metrology, K. M. Monahan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.565, 56–61 (1985).
[Crossref]

Depasse, F.

J. M. Vigoureux, F. Depasse, C. Girard, “Superresolution of near-field optical microscopy defined from properties of confined electromagnetic waves,” Appl. Opt. (to be published).

Durig, U. T.

U. C. Fisher, U. T. Durig, D. W. Pohl, “Near-field optical scanning microscopy in reflection,” Appl. Phys. Lett. 52, 249–251 (1988).
[Crossref]

Dürig, U.

D. W. Pohl, W. Denk, U. Dürig, “Optical stethoscopy: imaging with λ/20,” in Micron and Submicron Integrated Circuit Metrology, K. M. Monahan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.565, 56–61 (1985).
[Crossref]

Elson, J. M.

J. M. Elson, “Light scattering from semi-infinite media for non-normal incidence,” Phys. Rev. B 12, 2541–2542 (1975).
[Crossref]

Ferrell, T. L.

R. C. Reddik, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
[Crossref]

Fisher, U. C.

U. C. Fisher, U. T. Durig, D. W. Pohl, “Near-field optical scanning microscopy in reflection,” Appl. Phys. Lett. 52, 249–251 (1988).
[Crossref]

Girard, C.

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]

C. Girard, D. Courjon, “Model for scanning tunneling optical microscopy: a microscopic self-consistent approach,” Phys. Rev. B 42, 9340–9349 (1990).
[Crossref]

C. Girard, M. Spajer, “Model for reflection near-field optical microscopy,” Appl. Opt. 29, 3726–3732 (1989).
[Crossref]

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

C. Girard, J. M. Vigoureux, D. Van Labeke, P. Grossel, “Effective polarizability of two interacting adsorbed atoms,” Chem. Phys. 114, 209–220 (1987).
[Crossref]

J. M. Vigoureux, F. Depasse, C. Girard, “Superresolution of near-field optical microscopy defined from properties of confined electromagnetic waves,” Appl. Opt. (to be published).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Goudonnet, J. P.

F. de Fornel, J. P. Goudonnet, L. Salomon, E. Lesniewska, “An evanescent field optical microscope,” in Optical Storage and Scanning Technology, T. Wilson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1139, 77–84 (1989).
[Crossref]

Grossel, P.

C. Girard, J. M. Vigoureux, D. Van Labeke, P. Grossel, “Effective polarizability of two interacting adsorbed atoms,” Chem. Phys. 114, 209–220 (1987).
[Crossref]

Hamann, D. R.

J. Tersoff, D. R. Hamann, “Theory of the scanning tunneling microscope,” Phys. Rev. B 31, 805–813 (1985).
[Crossref]

Harootunian, A.

A. Lewis, M. Isaacson, A. Murray, A. Harootunian, “Scanning optical spectral microscopy with 500 A resolution,” Biophys. J. 41, 405a (1983).

Hill, N. R.

F. Toigo, A. Marvin, V. Celli, N. R. Hill, “Optical properties of rough surfaces: general theory and the small roughness limit,” Phys. Rev. B 13, 5618–5626 (1977).
[Crossref]

Isaacson, M.

A. Lewis, M. Isaacson, A. Murray, A. Harootunian, “Scanning optical spectral microscopy with 500 A resolution,” Biophys. J. 41, 405a (1983).

Labani, B.

Leblanc, S.

Lesniewska, E.

F. de Fornel, J. P. Goudonnet, L. Salomon, E. Lesniewska, “An evanescent field optical microscope,” in Optical Storage and Scanning Technology, T. Wilson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1139, 77–84 (1989).
[Crossref]

Lewis, A.

A. Lewis, M. Isaacson, A. Murray, A. Harootunian, “Scanning optical spectral microscopy with 500 A resolution,” Biophys. J. 41, 405a (1983).

Marvin, A.

F. Toigo, A. Marvin, V. Celli, N. R. Hill, “Optical properties of rough surfaces: general theory and the small roughness limit,” Phys. Rev. B 13, 5618–5626 (1977).
[Crossref]

Massey, G. A.

Maystre, D.

D. Maystre, “Rigorous vector theories of diffraction gratings,” in Progress in Optics XXI, E. Wolf, ed. (Elsevier, Amsterdam, 1984).
[Crossref]

Meixner, W. C.

W. C. Meixner, P. R. Antoniewski, “Effect of atomic size on the effective polarizability of physisorbed atoms,” Phys. Status Solidi B 86, 339–343 (1978).
[Crossref]

Murray, A.

A. Lewis, M. Isaacson, A. Murray, A. Harootunian, “Scanning optical spectral microscopy with 500 A resolution,” Biophys. J. 41, 405a (1983).

Nichols, G.

E. A. Ash, G. Nichols, “Super resolution aperture scanning microscope,” Nature (London) 237, 510–512 (1972).
[Crossref]

Noguera, C.

W. Sachs, C. Noguera, “Generalized expression for the tunneling current in scanning tunneling microscopy,” Phys. Rev. B 43, 11612–11622 (1991).
[Crossref]

Pohl, D. W.

U. C. Fisher, U. T. Durig, D. W. Pohl, “Near-field optical scanning microscopy in reflection,” Appl. Phys. Lett. 52, 249–251 (1988).
[Crossref]

D. W. Pohl, W. Denk, U. Dürig, “Optical stethoscopy: imaging with λ/20,” in Micron and Submicron Integrated Circuit Metrology, K. M. Monahan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.565, 56–61 (1985).
[Crossref]

D. W. Pohl, “Optical near-field scanning microscope,” European Patent0112401 (December27, 1982); U.S. Patent4,604,520 (December20, 1983).

Reddik, R. C.

R. C. Reddik, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
[Crossref]

Sachs, W.

W. Sachs, C. Noguera, “Generalized expression for the tunneling current in scanning tunneling microscopy,” Phys. Rev. B 43, 11612–11622 (1991).
[Crossref]

Salomon, L.

F. de Fornel, J. P. Goudonnet, L. Salomon, E. Lesniewska, “An evanescent field optical microscope,” in Optical Storage and Scanning Technology, T. Wilson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1139, 77–84 (1989).
[Crossref]

Sarayeddine, K.

Sarayedine, K.

D. Courjon, K. Sarayedine, M. Spajer, “Scanning tunneling optical microscopy,” Opt. Commun. 71, 23–28 (1989).
[Crossref]

Spajer, M.

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Tersoff, J.

J. Tersoff, D. R. Hamann, “Theory of the scanning tunneling microscope,” Phys. Rev. B 31, 805–813 (1985).
[Crossref]

Toigo, F.

F. Toigo, A. Marvin, V. Celli, N. R. Hill, “Optical properties of rough surfaces: general theory and the small roughness limit,” Phys. Rev. B 13, 5618–5626 (1977).
[Crossref]

Van Labeke, D.

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]

C. Girard, J. M. Vigoureux, D. Van Labeke, P. Grossel, “Effective polarizability of two interacting adsorbed atoms,” Chem. Phys. 114, 209–220 (1987).
[Crossref]

Vigoureux, J. M.

D. Courjon, J. M. Vigoureux, M. Spajer, K. Sarayeddine, S. Leblanc, “External and internal reflection near-field microscopy: experiments and results,” Appl. Opt. 29, 3734–3740 (1990).
[Crossref] [PubMed]

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

C. Girard, J. M. Vigoureux, D. Van Labeke, P. Grossel, “Effective polarizability of two interacting adsorbed atoms,” Chem. Phys. 114, 209–220 (1987).
[Crossref]

J. M. Vigoureux, F. Depasse, C. Girard, “Superresolution of near-field optical microscopy defined from properties of confined electromagnetic waves,” Appl. Opt. (to be published).

Warmack, R. J.

R. C. Reddik, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
[Crossref]

Wickramasinghe, H. K.

H. K. Wickramasinghe, “Differential laser heterodyne micrometrology,” Opt. Eng. 24, 926–929 (1985).
[Crossref]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970).

Appl. Opt. (3)

Appl. Phys. Lett. (1)

U. C. Fisher, U. T. Durig, D. W. Pohl, “Near-field optical scanning microscopy in reflection,” Appl. Phys. Lett. 52, 249–251 (1988).
[Crossref]

Biophys. J. (1)

A. Lewis, M. Isaacson, A. Murray, A. Harootunian, “Scanning optical spectral microscopy with 500 A resolution,” Biophys. J. 41, 405a (1983).

Chem. Phys. (1)

C. Girard, J. M. Vigoureux, D. Van Labeke, P. Grossel, “Effective polarizability of two interacting adsorbed atoms,” Chem. Phys. 114, 209–220 (1987).
[Crossref]

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

Nature (London) (1)

E. A. Ash, G. Nichols, “Super resolution aperture scanning microscope,” Nature (London) 237, 510–512 (1972).
[Crossref]

Opt. Commun. (1)

D. Courjon, K. Sarayedine, M. Spajer, “Scanning tunneling optical microscopy,” Opt. Commun. 71, 23–28 (1989).
[Crossref]

Opt. Eng. (1)

H. K. Wickramasinghe, “Differential laser heterodyne micrometrology,” Opt. Eng. 24, 926–929 (1985).
[Crossref]

Opt. Lett. (1)

Phys. Rev. B (7)

R. C. Reddik, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
[Crossref]

J. Tersoff, D. R. Hamann, “Theory of the scanning tunneling microscope,” Phys. Rev. B 31, 805–813 (1985).
[Crossref]

W. Sachs, C. Noguera, “Generalized expression for the tunneling current in scanning tunneling microscopy,” Phys. Rev. B 43, 11612–11622 (1991).
[Crossref]

C. Girard, D. Courjon, “Model for scanning tunneling optical microscopy: a microscopic self-consistent approach,” Phys. Rev. B 42, 9340–9349 (1990).
[Crossref]

G. S. Agarwal, “Interaction of electromagnetic waves at rough dielectric surfaces,” Phys. Rev. B 15, 2371–2383 (1977).
[Crossref]

F. Toigo, A. Marvin, V. Celli, N. R. Hill, “Optical properties of rough surfaces: general theory and the small roughness limit,” Phys. Rev. B 13, 5618–5626 (1977).
[Crossref]

J. M. Elson, “Light scattering from semi-infinite media for non-normal incidence,” Phys. Rev. B 12, 2541–2542 (1975).
[Crossref]

Phys. Status Solidi B (1)

W. C. Meixner, P. R. Antoniewski, “Effect of atomic size on the effective polarizability of physisorbed atoms,” Phys. Status Solidi B 86, 339–343 (1978).
[Crossref]

Other (10)

J. M. Vigoureux, F. Depasse, C. Girard, “Superresolution of near-field optical microscopy defined from properties of confined electromagnetic waves,” Appl. Opt. (to be published).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

R. Petit, ed., Electromagnetic Theory of Gratings, Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980).
[Crossref]

D. Maystre, “Rigorous vector theories of diffraction gratings,” in Progress in Optics XXI, E. Wolf, ed. (Elsevier, Amsterdam, 1984).
[Crossref]

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

P. Beckmann, “Scattering of light by rough surfaces,” in Progress in Optics VI, E. Wolf, ed. (North-Holland, Amsterdam, 1963), pp. 53–69.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970).

D. W. Pohl, “Optical near-field scanning microscope,” European Patent0112401 (December27, 1982); U.S. Patent4,604,520 (December20, 1983).

F. de Fornel, J. P. Goudonnet, L. Salomon, E. Lesniewska, “An evanescent field optical microscope,” in Optical Storage and Scanning Technology, T. Wilson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1139, 77–84 (1989).
[Crossref]

D. W. Pohl, W. Denk, U. Dürig, “Optical stethoscopy: imaging with λ/20,” in Micron and Submicron Integrated Circuit Metrology, K. M. Monahan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.565, 56–61 (1985).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1

Principle of a STOM: geometry of the tip and of the sample grating.

Fig. 2
Fig. 2

Diffraction filtering coefficients. Normal incidence (θ = 0°) and a small wavelength (λ/a = 0.01). No filtering effects occur, and the two polarizations are equivalent. (a) |DTE|, (b) |DTM|, (c) JTE, (d) JTM. The grating index is n = 1.5.

Fig. 3
Fig. 3

Diffraction filtering coefficients. Evanescent excitation (θ = 45°) and a small wavelength (λ/a = 0.01). In this case some diffracted orders are evanescent and the various coefficients vary with m, leading to filtering and polarization effects that remain small. (a) |DTE|, (b) |DTM|, (c) JTE, (d) JTM. The grating index is n = 1.5.

Fig. 4
Fig. 4

Diffraction filtering coefficients. Evanescent excitation (θ = 45°) and a small sample period (λ/a = 3). In this case all the diffracted orders are evanescent. The various coefficients strongly vary with m, leading to important filtering and polarization effects: the TE coefficients are negligible, and in TM polarization the high harmonics are strongly enhanced. (a) |DTE|, (b) |DTM|, (C) JTE, (d) JTM. The grating index is n = 1.5.

Fig. 5
Fig. 5

Intensity map I(x, z) for a sample of index n = 1.5 and an incidence angle beyond the critical angle (θ = 45°). The exciting light has λ = 0.67 μm. The sample profile is rectangular with period a, width b, and height h = 0.01 μm. All the distances, x and z, are in micrometers. (a) a = 1.6 μm, b = a/3, TE polarization; (b) a = 1.6 μm, b = a/3, TM polarization; (c) a = 0.2 μm, b = a/4, TE polarization; (d) a = 0.2 μm, b = a/4, TM polarization.

Equations (30)

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

Δ x = 1.22 λ 2 n sin ( u ) ,
l 0 = λ 2 π [ n 2 sin 2 ( θ ) - 1 ] 1 / 2 .
k i = 2 π λ n sin ( θ ) .
E x inc = sin ( ϕ ) cos ( θ ) E inc , E y inc = cos ( ϕ ) E inc , E z inc = - sin ( ϕ ) sin ( θ ) E inc ,
f ( x ) = m = - + f ^ ( m ) exp ( 2 i π m x / a ) .
α = ( - 1 + 2 ) R 3 ,
I ( x , z ) = ω 4 c 4 α E d ( x , z ) 2 .
E d ( x , z ) = m = - + E ( m ) exp [ i ( k m x + q m z ) ]             for z > 0 , E d ( x , z ) = m = - + E ( m ) exp [ i ( k m x - p m z ) ]             for z < 0.
k m = k i + m 2 π a ,
sin ( θ m ) = n sin ( θ ) + m λ a .
q m = [ ( 2 π λ ) 2 - ( k m ) 2 ] 1 / 2 , p m = [ n 2 ( 2 π λ ) 2 - ( k m ) 2 ] 1 / 2 .
q m = 2 π λ { 1 - [ n sin ( θ ) + m λ a ] 2 } 1 / 2 ,
q m 2 π λ ( - i m λ a ) = - i m 2 π a .
l m = a 2 π m .
d tip - surface l 1 = a 2 π .
d tip - surface l 10 = a 20 π a 60 .
exp { i [ k m x + q m f ( x ) ] } = exp ( i k m x ) [ 1 + q m f ( x ) + ]
E ( m ) = E 0 ( m ) + E 1 ( m ) ,
E x 0 ( m ) = 2 n 2 q 0 p 0 + n 2 q 0 E x inc δ m 0 , E y 0 ( m ) = 2 p 0 p 0 + q 0 E y inc δ m 0 , E z 0 ( m ) = 2 n 2 q 0 p 0 + n 2 q 0 E z inc δ m 0 .
E x 1 ( m ) = i ( n 2 - 1 ) f ^ ( m ) E x inc 2 n 2 q 0 q m ( q m q 0 + k m k 0 ) ( p 0 + q 0 n 2 ) q 0 ( p m + n 2 q m ) , E y 1 ( m ) = i ( n 2 - 1 ) f ^ ( m ) E y inc ( 2 π λ ) 2 2 p 0 p 0 + q 0 1 p m + q m , E z 1 ( m ) = i ( n 2 - 1 ) f ^ ( m ) E z inc 2 n 2 p 0 k m ( q m q 0 + k m k 0 ) ( p 0 + q 0 n 2 ) k 0 ( p m + n 2 q m ) .
E d ( x , z ) = exp ( i k i x ) [ E 0 ( x ) + E 1 ( x , z ) ] .
E 1 ( x , z ) = E inc m = - + 2 π f ^ ( m ) λ C ( m , z ) D ( m ) exp ( 2 i m x / a ) .
C ( m , z ) = exp ( i z q m ) .
D x ( m ) = i ( n 2 - 1 ) sin ( ϕ ) 2 n 2 P 0 P 0 + Q 0 n 2 ( + Q m ) P m Q 0 + K m K 0 P m + n 2 Q m , D y ( m ) = i ( n 2 - 1 ) cos ( ϕ ) 2 P 0 P 0 + Q 0 1 P m + Q m , D z ( m ) = i ( n 2 - 1 ) sin ( ϕ ) 2 n 2 P 0 P 0 + Q 0 n 2 ( - K m ) P m Q 0 + K m K 0 P m + n 2 Q m ,
k m = ( 2 π / λ ) K m ,             q m = ( 2 π / λ ) Q m ,             p m = ( 2 π / λ ) P m .
D TE ( m ) = 1 P m + Q m .
D TM ( m ) = P m Q 0 + K m K 0 P m + n 2 Q m .
J TE ( m ) = D TE ( m ) 2 , J TM ( m ) = ( K m 2 + Q m 2 ) D TM ( m ) 2 .
K m 2 + Q m 2 = K m 2 + Q m 2 = 1 ,
K m 2 + Q m 2 = [ n sin ( θ ) + m λ / a ] 2 - 1 ,

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