Abstract

The experimental resolution that is obtained with a near-field microscope by optical tunneling detection is far beyond the Rayleigh criterion. We discuss the principal physical characteristics of this superresolution. Three different examples are presented. They show that the resolution increases as the collector width and collector-to-object distance decrease. It is interesting to note that, in the near-field microscope, as in all local probe microscopes, the resolution cannot be defined from the characteristics of the microscope only. In all tunnel devices the detector cannot be separated from the object. The superresolution that can be obtained results from this fact. This paper also points out the importance of evanescent waves in near-field optics and makes the connection between resolving power and evanescent fields.

© 1992 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  4. D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–655 (1984).
    [Crossref]
  5. U. C. Fischer, “Optical characteristics of 0.1 μm circular apertures in a metal film as light sources for scanning ultramicroscopy,” J. Vac. Sci. Technol. B 3, 386–390 (1985).
    [Crossref]
  6. E. Betzig, A. Harootunian, A. Lewis, M. Isaacson, “Near field diffraction by a slit: implications for superresolution microscopy,” Appl. Opt. 25, 1890–1900 (1986).
    [Crossref] [PubMed]
  7. R. C. Reddick, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
    [Crossref]
  8. D. Courjon, K. Sarrayeddine, M. Spajer, “Scanning tunneling optical microscopy,” Opt. Commun. 71, 23–27 (1989).
    [Crossref]
  9. 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).
  10. J. M. Vigoureux, C. Girard, D. Courjon, “General principle of scanning tunneling microscopy,” Opt. Lett. 14, 1039–1041 (1989).
    [Crossref] [PubMed]
  11. J. M. Guerra, “Photon tunneling microscopy,” Appl. Opt. 29, 3741–3752 (1990).
    [Crossref] [PubMed]
  12. J. M. Guerra, “Photon tunneling microscopy, surface measurement and characterization,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 254–263 (1989).
  13. J. M. Guerra, W. T. Plummer, “Optical proximity imaging method and apparatus,” U.S. Patent4, 681, 451 (21July1987).
  14. J. M. Vigoureux, C. Courjon, “Detection of nonradiative fields in light of the Heisenberg uncertainty principle and the Rayleigh criterion,” Appl. Opt. 31, 3170–3177 (1992).
    [Crossref] [PubMed]
  15. C. Girard, D. Courjon, “Model for scanning tunneling optical microscopy: a microscopic self-consistent approach,” Phys. Rev. B 42, 9340–9349 (1990).
    [Crossref]
  16. O. Keller, B. Sonderkaer, “Elastic scattering of light from a few atomic dipoles on a flat metal surface,” in Optical Testing and Metrology, C.P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.954, 344–363 (1988).
  17. A. Johner, R. Shaaf, “Reflection of light at a flat interface under normal incidence: a renewed macroscopic description,” Phys. Rev. B 40, 10231–10239 (1989).
    [Crossref]
  18. E. Abbe, “Betrage zur Theorie der Microscope und der Microscopischen Wahrehmung,” Arch. Mikrosk. Anat. 9, 413–468 (1873).
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  21. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959), Chap. 8.
  22. 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]
  23. 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]
  24. E. Wolf, M. Nieto Vesperinas, “Analyticity of the angular spectrum amplitude of scattered fields and some of its consequences,” J. Opt. Soc. Am. A 2, 886–889 (1985).
    [Crossref]
  25. J M. Vigoureux, L. D’Hooge, D. Van Labeke, “Quantization of evanescent electromagnetic waves. Momentum of the electromagnetic field very close to a dielectric medium,” Phys. Rev. A 21, 347–355 (1980).
    [Crossref]
  26. O. Costa de Beauregard, “Energy momentum quanta in Fresnel’s evanescent waves,” Int. J. Theoret. Phys. 7(2), 129–143 (1973).
    [Crossref]
  27. J. M. Vigoureux, R. Payen, “Interactions matière-onde évanescente de Fresnel. I: Radiation spontanée par un électron au voisinage d’un dioptre plan; effect Cerenkov,” J. Phys. (Paris) 35, 617–630 (1974); “Interactions matière-onde évanescente de Fresnel. II: Absorption par un atome au voisinage d’un dioptre plan,” J. Phys. (Paris) 36, 631–642 (1975); “Interaction matière-onde évanescente de Fresnel. III: Diffusion au voisinage d’un dioptre plan,” J. Phys. (Paris) 36, 1327–1340 (1975).
    [Crossref]
  28. S. Huard, C. Imbert, “Mesure de l’impulsion échangée au cours de l’interaction onde évanescente-atome,” Opt. Commun. 24, 185–189 (1978).
    [Crossref]

1992 (1)

1990 (4)

1989 (4)

A. Johner, R. Shaaf, “Reflection of light at a flat interface under normal incidence: a renewed macroscopic description,” Phys. Rev. B 40, 10231–10239 (1989).
[Crossref]

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

D. Courjon, K. Sarrayeddine, M. Spajer, “Scanning tunneling optical microscopy,” Opt. Commun. 71, 23–27 (1989).
[Crossref]

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

1986 (1)

1985 (2)

U. C. Fischer, “Optical characteristics of 0.1 μm circular apertures in a metal film as light sources for scanning ultramicroscopy,” J. Vac. Sci. Technol. B 3, 386–390 (1985).
[Crossref]

E. Wolf, M. Nieto Vesperinas, “Analyticity of the angular spectrum amplitude of scattered fields and some of its consequences,” J. Opt. Soc. Am. A 2, 886–889 (1985).
[Crossref]

1984 (2)

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

D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–655 (1984).
[Crossref]

1980 (1)

J M. Vigoureux, L. D’Hooge, D. Van Labeke, “Quantization of evanescent electromagnetic waves. Momentum of the electromagnetic field very close to a dielectric medium,” Phys. Rev. A 21, 347–355 (1980).
[Crossref]

1978 (1)

S. Huard, C. Imbert, “Mesure de l’impulsion échangée au cours de l’interaction onde évanescente-atome,” Opt. Commun. 24, 185–189 (1978).
[Crossref]

1974 (1)

J. M. Vigoureux, R. Payen, “Interactions matière-onde évanescente de Fresnel. I: Radiation spontanée par un électron au voisinage d’un dioptre plan; effect Cerenkov,” J. Phys. (Paris) 35, 617–630 (1974); “Interactions matière-onde évanescente de Fresnel. II: Absorption par un atome au voisinage d’un dioptre plan,” J. Phys. (Paris) 36, 631–642 (1975); “Interaction matière-onde évanescente de Fresnel. III: Diffusion au voisinage d’un dioptre plan,” J. Phys. (Paris) 36, 1327–1340 (1975).
[Crossref]

1973 (1)

O. Costa de Beauregard, “Energy momentum quanta in Fresnel’s evanescent waves,” Int. J. Theoret. Phys. 7(2), 129–143 (1973).
[Crossref]

1972 (1)

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

1956 (1)

1896 (1)

Lord Rayleigh, “On the theory of optical images with special reference to the microscope,” Philos. Mag. 5(42), 167–195 (1896).

1879 (1)

Lord Rayleigh, “Investigations in optics with special reference to the spectroscope,” Philos. Mag. 5(8), 261–274 (1879).

1873 (1)

E. Abbe, “Betrage zur Theorie der Microscope und der Microscopischen Wahrehmung,” Arch. Mikrosk. Anat. 9, 413–468 (1873).
[Crossref]

Abbe, E.

E. Abbe, “Betrage zur Theorie der Microscope und der Microscopischen Wahrehmung,” Arch. Mikrosk. Anat. 9, 413–468 (1873).
[Crossref]

Ash, E. A.

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

Betzig, E.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959), Chap. 8.

Costa de Beauregard, O.

O. Costa de Beauregard, “Energy momentum quanta in Fresnel’s evanescent waves,” Int. J. Theoret. Phys. 7(2), 129–143 (1973).
[Crossref]

Courjon, C.

Courjon, D.

D’Hooge, L.

J M. Vigoureux, L. D’Hooge, D. Van Labeke, “Quantization of evanescent electromagnetic waves. Momentum of the electromagnetic field very close to a dielectric medium,” Phys. Rev. A 21, 347–355 (1980).
[Crossref]

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).

Denk, W.

D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–655 (1984).
[Crossref]

Ferrell, T. L.

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

Fischer, U. C.

U. C. Fischer, “Optical characteristics of 0.1 μm circular apertures in a metal film as light sources for scanning ultramicroscopy,” J. Vac. Sci. Technol. B 3, 386–390 (1985).
[Crossref]

Girard, C.

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).

Guerra, J. M.

J. M. Guerra, “Photon tunneling microscopy,” Appl. Opt. 29, 3741–3752 (1990).
[Crossref] [PubMed]

J. M. Guerra, “Photon tunneling microscopy, surface measurement and characterization,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 254–263 (1989).

J. M. Guerra, W. T. Plummer, “Optical proximity imaging method and apparatus,” U.S. Patent4, 681, 451 (21July1987).

Harootunian, A.

Huard, S.

S. Huard, C. Imbert, “Mesure de l’impulsion échangée au cours de l’interaction onde évanescente-atome,” Opt. Commun. 24, 185–189 (1978).
[Crossref]

Imbert, C.

S. Huard, C. Imbert, “Mesure de l’impulsion échangée au cours de l’interaction onde évanescente-atome,” Opt. Commun. 24, 185–189 (1978).
[Crossref]

Isaacson, M.

Johner, A.

A. Johner, R. Shaaf, “Reflection of light at a flat interface under normal incidence: a renewed macroscopic description,” Phys. Rev. B 40, 10231–10239 (1989).
[Crossref]

Keller, O.

O. Keller, B. Sonderkaer, “Elastic scattering of light from a few atomic dipoles on a flat metal surface,” in Optical Testing and Metrology, C.P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.954, 344–363 (1988).

Labani, B.

Lanz, M.

D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–655 (1984).
[Crossref]

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).

Lewis, A.

Massey, G. A.

Nicholls, G.

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

Nieto Vesperinas, M.

O’Keefe, J. A.

Payen, R.

J. M. Vigoureux, R. Payen, “Interactions matière-onde évanescente de Fresnel. I: Radiation spontanée par un électron au voisinage d’un dioptre plan; effect Cerenkov,” J. Phys. (Paris) 35, 617–630 (1974); “Interactions matière-onde évanescente de Fresnel. II: Absorption par un atome au voisinage d’un dioptre plan,” J. Phys. (Paris) 36, 631–642 (1975); “Interaction matière-onde évanescente de Fresnel. III: Diffusion au voisinage d’un dioptre plan,” J. Phys. (Paris) 36, 1327–1340 (1975).
[Crossref]

Plummer, W. T.

J. M. Guerra, W. T. Plummer, “Optical proximity imaging method and apparatus,” U.S. Patent4, 681, 451 (21July1987).

Pohl, D. W.

D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–655 (1984).
[Crossref]

Rayleigh, Lord

Lord Rayleigh, “On the theory of optical images with special reference to the microscope,” Philos. Mag. 5(42), 167–195 (1896).

Lord Rayleigh, “Investigations in optics with special reference to the spectroscope,” Philos. Mag. 5(8), 261–274 (1879).

Reddick, R. C.

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

Sarayeddine, K.

Sarrayeddine, K.

D. Courjon, K. Sarrayeddine, M. Spajer, “Scanning tunneling optical microscopy,” Opt. Commun. 71, 23–27 (1989).
[Crossref]

Shaaf, R.

A. Johner, R. Shaaf, “Reflection of light at a flat interface under normal incidence: a renewed macroscopic description,” Phys. Rev. B 40, 10231–10239 (1989).
[Crossref]

Sonderkaer, B.

O. Keller, B. Sonderkaer, “Elastic scattering of light from a few atomic dipoles on a flat metal surface,” in Optical Testing and Metrology, C.P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.954, 344–363 (1988).

Spajer, M.

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]

J M. Vigoureux, L. D’Hooge, D. Van Labeke, “Quantization of evanescent electromagnetic waves. Momentum of the electromagnetic field very close to a dielectric medium,” Phys. Rev. A 21, 347–355 (1980).
[Crossref]

Vigoureux, J M.

J M. Vigoureux, L. D’Hooge, D. Van Labeke, “Quantization of evanescent electromagnetic waves. Momentum of the electromagnetic field very close to a dielectric medium,” Phys. Rev. A 21, 347–355 (1980).
[Crossref]

Vigoureux, J. M.

J. M. Vigoureux, C. Courjon, “Detection of nonradiative fields in light of the Heisenberg uncertainty principle and the Rayleigh criterion,” Appl. Opt. 31, 3170–3177 (1992).
[Crossref] [PubMed]

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 principle of scanning tunneling microscopy,” Opt. Lett. 14, 1039–1041 (1989).
[Crossref] [PubMed]

J. M. Vigoureux, R. Payen, “Interactions matière-onde évanescente de Fresnel. I: Radiation spontanée par un électron au voisinage d’un dioptre plan; effect Cerenkov,” J. Phys. (Paris) 35, 617–630 (1974); “Interactions matière-onde évanescente de Fresnel. II: Absorption par un atome au voisinage d’un dioptre plan,” J. Phys. (Paris) 36, 631–642 (1975); “Interaction matière-onde évanescente de Fresnel. III: Diffusion au voisinage d’un dioptre plan,” J. Phys. (Paris) 36, 1327–1340 (1975).
[Crossref]

Warmack, R. J.

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

Wolf, E.

Appl. Opt. (5)

Appl. Phys. Lett. (1)

D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–655 (1984).
[Crossref]

Arch. Mikrosk. Anat. (1)

E. Abbe, “Betrage zur Theorie der Microscope und der Microscopischen Wahrehmung,” Arch. Mikrosk. Anat. 9, 413–468 (1873).
[Crossref]

Int. J. Theoret. Phys. (1)

O. Costa de Beauregard, “Energy momentum quanta in Fresnel’s evanescent waves,” Int. J. Theoret. Phys. 7(2), 129–143 (1973).
[Crossref]

J. Opt. Soc. Am. (1)

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

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

J. Phys. (Paris) (1)

J. M. Vigoureux, R. Payen, “Interactions matière-onde évanescente de Fresnel. I: Radiation spontanée par un électron au voisinage d’un dioptre plan; effect Cerenkov,” J. Phys. (Paris) 35, 617–630 (1974); “Interactions matière-onde évanescente de Fresnel. II: Absorption par un atome au voisinage d’un dioptre plan,” J. Phys. (Paris) 36, 631–642 (1975); “Interaction matière-onde évanescente de Fresnel. III: Diffusion au voisinage d’un dioptre plan,” J. Phys. (Paris) 36, 1327–1340 (1975).
[Crossref]

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

U. C. Fischer, “Optical characteristics of 0.1 μm circular apertures in a metal film as light sources for scanning ultramicroscopy,” J. Vac. Sci. Technol. B 3, 386–390 (1985).
[Crossref]

Nature (London) (1)

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

Opt. Commun. (2)

D. Courjon, K. Sarrayeddine, M. Spajer, “Scanning tunneling optical microscopy,” Opt. Commun. 71, 23–27 (1989).
[Crossref]

S. Huard, C. Imbert, “Mesure de l’impulsion échangée au cours de l’interaction onde évanescente-atome,” Opt. Commun. 24, 185–189 (1978).
[Crossref]

Opt. Lett. (1)

Philos. Mag. (2)

Lord Rayleigh, “On the theory of optical images with special reference to the microscope,” Philos. Mag. 5(42), 167–195 (1896).

Lord Rayleigh, “Investigations in optics with special reference to the spectroscope,” Philos. Mag. 5(8), 261–274 (1879).

Phys. Rev. A (1)

J M. Vigoureux, L. D’Hooge, D. Van Labeke, “Quantization of evanescent electromagnetic waves. Momentum of the electromagnetic field very close to a dielectric medium,” Phys. Rev. A 21, 347–355 (1980).
[Crossref]

Phys. Rev. B (3)

A. Johner, R. Shaaf, “Reflection of light at a flat interface under normal incidence: a renewed macroscopic description,” Phys. Rev. B 40, 10231–10239 (1989).
[Crossref]

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

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

Other (5)

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).

O. Keller, B. Sonderkaer, “Elastic scattering of light from a few atomic dipoles on a flat metal surface,” in Optical Testing and Metrology, C.P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.954, 344–363 (1988).

J. M. Guerra, “Photon tunneling microscopy, surface measurement and characterization,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1009, 254–263 (1989).

J. M. Guerra, W. T. Plummer, “Optical proximity imaging method and apparatus,” U.S. Patent4, 681, 451 (21July1987).

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959), Chap. 8.

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Figures (9)

Fig. 1
Fig. 1

Schematization of detection (a) with a classical microscope and (b) with a near-field microscope. In (a) the field is collected at a very long distance (z = Z) so that all evanescent components (high spatial frequencies) of the diffracted field are lost. In (b) the field is collected at a distance of ∊ ≪ λ by a small tip (represented here by a slit). The high spatial frequencies of the object are then scattered and partially transformed into propagating modes that can be propagated to the detector.

Fig. 2
Fig. 2

Comparison of the angular spectrum of two slits (2L = 0.12 μm; 2d = 0.16 μm so that the distance between the edges of the two is only 40 nm) with those that are captured with the devices shown in Figs. 1(a) and 1(b), respectively. The angular spectrum of the slits object at z = 0 (a) contains both propagating p and nonpropagating np components. With a classical microscope (b) only the propagating components can be detected at z = Z ≥ λ. (The value of the wavelength of the incident light is λ = 0.5 μm.) With the near-field microscope (c) part of the evanescent components np is collected and converted into propagating components so that information on the sub-Rayleigh details of the object can be received on the detector. Let us note that, when the distance z = ∊ decreases, the detected angular spectrum tends toward that (a) of the object.

Fig. 3
Fig. 3

Computed images of two nanometric slits (2L = 0.12 μm; 2d = 0.16 μm) obtained with the devices shown in Figs. 1(a) and 1(b), respectively. The classical microscope cannot resolve two nanometric holes (a), which are, however, resolved with the near-field microscope (b). The resolution that is obtained in (b) increases as the width 2l of the collector decreases. [The value of the wavelength of the incident light is λ = 0.5 μm. The figures in (b) were obtained with ∊ = 0.01 μm.]

Fig. 4
Fig. 4

Computed images of two nanometric holes that are obtained with the devices shown in Figs. 1(a) and 1(b), respectively. The classical microscope cannot resolve the two nanometric holes (a). The resolution of the near-field microscope (b) is studied with respect to the distance z = ∊ from the object to the collector. As explained in the text it increases as the distance ∊ decreases. (In these figures the width 2l of the collector is 2l = 0.08 μm. Other values are the same as in Fig. 3.)

Fig. 5
Fig. 5

Comparison between the images of two electric dipoles obtained with the devices in Figs. 1(a) and 1(b), respectively. The two dipoles are perpendicular to the xy plane. Their polarizability α = r3 (n2 − 1)/(n2 + 2) was chosen to be α = 0.3 × 10−6 μm−3 so that in this example the object corresponds to two spheres, the radius of which is ~ 10 nm. The distance between the two dipoles is 0.6 μm. The two dipoles cannot be seen with the first device [Fig. 1(a)], but they are resolved with a near-field microscope (b) and (c)]. It is important to emphasize here that in (c) the image does not correspond to the profile of the object because of the anisotropy of the dipole field. In (c) we show the intensity at z = ∊.

Fig. 6
Fig. 6

Two nanometric spheres A (radius a) observed with a monomode fiber. Tip B can be considered to be a third sphere (radius b).

Fig. 7
Fig. 7

Computed image of the two spheres A and A′ as seen by detector B (Fig. 6). The radii of A and A′ are a = 1 nm. The radius of B is b = 1 nm. The distance z between B and the plane of A and A′ is 2, 2.2, and 2.6 nm, respectively.

Fig. 8
Fig. 8

Variations of visibility V of two nanometric objects in the near-field microscope with respect to the distance z = ∊ between the object plane and the tip (collector) for different values of width 2l of the tip.

Fig. 9
Fig. 9

Variations of the visibility of two nanometric objects in the near-field microscope with respect to width 2l of the tip (collector) for different values of the distance z = ∊ between the objects and the tip.

Equations (30)

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Δ x = 0.61 λ n sin θ ,
E 1 ( x , z = 0 ) = E 0 ( x , z = 0 ) × [ C ( x , d - L , d + L ) + C ( x , - d - L , - d + L ) ] ,
E 1 ( k x , z = 0 ) = 4 E 0 cos k x d sin k x L k x ,
E d ( x , z = Z ) = 1 2 π - + d k x × exp ( - i k x x ) E 1 ( k x , z = 0 ) exp [ - i ( k 2 - k x 2 ) 1 / 2 Z ] ,
E d ( x , z = Z ) = 1 2 π - ω / c + ω / c d k x × exp ( i k x x ) E 1 ( k x , z = 0 ) exp [ - i ( k 2 - k x 2 ) 1 / 2 Z ] ,
E 2 ( x , z = ) = 1 2 π - + d k x × exp ( - i k x x ) E 1 ( k x , z = 0 ) exp [ - i ( k 2 - k x 2 ) 1 / 2 ] .
E 3 ( x , z = ) = E 2 ( x , z = ) C ( x , X - l , X + l ) ,
E 3 ( k x , z = ) = 1 2 π - + d k x E 1 ( k x , z = 0 ) exp [ - i ( k 2 - k x 2 ) 1 / 2 ] × 2 sin ( k x - k x ) l ( k x - k x ) exp [ + i ( k x - k x ) X .
E d ( x , z = Z ) = 1 ( 2 π ) 2 - ω / c + ω / c d k x exp ( - i k x x ) exp [ - i ( k 2 - k x 2 ) 1 / 2 ( Z - ) ] × - + d k x 4 E 0 cos k x d sin k x L k x exp [ - i ( k 2 - k x 2 ) 1 / 2 ] × 2 sin ( k x - k x ) l ( k x - k x ) exp [ + i ( k x - k x ) X ] .
lim 1 2 sin ( k x - k x ) l ( k x - k x ) = 2 π δ ( k x - k x ) .
E r ( r i , ω ) = T ( r i - r j , ω ) · μ ( r j , ω ) = T ( r i - r j , ω ) · α ( ω ) · E ( r j , ω ) ,
T ( r i - r j , ω ) = exp ( - i r i - r j ω c ) × [ T 3 ( r i - r j ) + i ω c T 2 ( r i - r j ) - ω 2 c 2 T 1 ( r i - r j ) ] .
T 3 ( r ) = 3 r · r - I r 2 r 5 ,
T 2 ( r ) = 3 r · r - I r 2 r 4 ,
T 1 ( r ) = r · r - I r 2 r 3 ,
E 3 ( x , y , z = ) = E 2 ( x , y , z = ) T ( x , y ; X , Y , R ) ,
E ( k x , k y ) = d x d y exp [ + i ( k x x + k y y ) ] × exp [ - i k z ( Z - ) ] E 3 ( x , y , z = ) ,
I ( x , y , z ) = d k x d k y E ( K x , k y ) 2 ,
E ( r i , ω ) = E 0 ( r i , ω ) + Σ T ( r i - r j , ω ) · α j ( ω ) · E ( r j , ω ) ,
α 1 ( ω ) = b 3 [ ( ω ) - 1 ( ω ) + 2 ]
α 2 ( ω ) = α 3 ( ω ) = a 3 [ 1 ( ω ) - 1 1 ( ω ) + 2 ]
F ( ω ) = F 0 · ( ω ) + B ( ω ) · F ( ω ) ,
F ( ω ) = [ E ( r 1 , ω ) , E ( r 2 , ω ) , E ( R , ω ) ] ,
F 0 ( ω ) = [ E 0 ( r 1 , ω ) , E 0 ( r 2 , ω ) , E 0 ( R , ω ) ] ,
B ( ω ) = [ 0 0 0 0 0 0 0 0 0 T ( r 1 - r 2 , ω ) T ( r 1 - R , ω ) T ( r 2 - r 1 , ω ) 0 0 0 0 0 0 0 0 0 T ( r 2 - R , ω ) T ( r - r 1 , ω ) T ( R - r 2 , ω ) 0 0 0 0 0 0 0 0 0 ] ,
F ( ω ) = [ I - B ( ω ) ] - 1 F 0 ( ω ) .
E B , x ( R , ω ) = [ i α M 3 x , i α ( ω ) δ x , α ] E 0 ( ω ) , E B , y ( R , ω ) = [ i α M 3 y , i α ( ω ) δ x , α ] E 0 ( ω ) , E B , z ( R , ω ) = [ i α M 3 x , i α ( ω ) δ x , α ] E 0 ( ω ) .
μ s ( R , ω ) = E 0 ( ω ) b 3 [ ( ω ) - 1 ( ω ) + 2 ] × [ i M 3 x , i x ( ω ) , i M 3 y , i x ( ω ) , i M 3 z , i x ( ω ) ] .
E s ( L , ω ) = exp ( - i L - R ω c ) · T 1 ( L - R , ω ) · μ s ( R , ω ) .
I ( L ) b 6 [ ( ω ) - 1 ( ω ) + 2 ] 2 E 0 2 ( ω ) [ | i M 3 x , i x ( ω ) T 1 x x ( L - R , ω ) | 2 + | M 3 y , i x ( ω ) T 1 y y ( L - R , ω ) | 2 ] .

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