Abstract

The propagation of light through nanometer-sized structures is studied computationally by use of multiple-multipole method. A two-dimensional scanning near-field optical microscope structure is chosen as an example. The relevant near and far fields as well as some imaging properties are determined for the two principal polarizations. Strikingly different results are obtained for the two principal polarizations: for s polarization, strong field confinement in the gap region, high sensitivity of the radiation pattern to the presence of an object, and high contrast; for p polarization, higher signal level with low contrast. At small gap widths a substantial amount of radiation is coupled into the substrate at angles larger than the critical angle. Line scan simulations for λ = 488 nm indicate a resolution of approximately two times the optical slit width. Resolution and contrast can be optimized by the appropriate choice of detector orientation and angle of acceptance. Coherent superposition of the radiation emitted into different directions permits further improvements.

© 1994 Optical Society of America

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  1. See, for instance, H. Rohrer, “Limits and possibilities of miniaturization,” Jpn. J. Appl. Phys. 32, 1335–1341 (1993);“Local probe methods and miniaturization,” in Nanosources and Manipulation of Atoms under High Fields and Temperatures: Applications, NATO ASI Series E, Vol. 235, V. Thien Binh, N. Garcia, K. Dransfeld, eds. (Kluwer, Dordrecht, The Netherlands, 1993), pp. 1–12.
    [CrossRef]
  2. See, for instance, D. W. Pohl, D. Courjon, eds., Near Field Optics, NATO ASI Series E, Vol. 242 (Kluwer, Dordrecht, The Netherlands, 1993).
    [CrossRef]
  3. D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
    [CrossRef]
  4. U. Duerig, D. W. Pohl, F. Rohner, “Near-field optical scanning microscopy,” J. Appl. Phys. 59, 3318–3327 (1986).
    [CrossRef]
  5. E. Betzig, M. Isaacson, A. Lewis, “Collection mode nearfield scanning optical microscopy,” Appl. Phys. Lett. 51, 2088–2090 (1987).
    [CrossRef]
  6. E. Betzig, “Principles and applications of near-field scanning optical microscopy (NSOM),” Ref. 2, pp. 7–16.
  7. M. Vaez-Iravani, R. Toledo-Crow, “Amplitude, phase contrast and polarization imaging in near-field scanning optical microscopy,” Ref. 2, pp. 25–34.
  8. T. Hartmann, R. Gatz, W. Wiegräbe, A. Kramer, A. Hillebrand, K. Liebermann, W. Baumeister, R. Gucken-berger, “A scanning near-field optical microscope (SNOM) for biological applications” Ref. 2, pp. 35–44.
  9. D. Courjon, K. Sarayeddine, 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. Van Labeke, D. Barchiesi, “Theoretical problems in scanning near-field optical microscopy,” Ref. 2, pp. 157–178.
  13. H. P. Baltes, ed., Inverse Scattering Problems in Optics, Vol. 20 of Topics in Current Physics (Springer-Verlag, Berlin, 1980).
    [CrossRef]
  14. Ch. Hafner, L. H. Bomholdt, The 3d Electrodynamic Wave Simulator (Wiley, Chichester, UK, 1993).
  15. M. V. K. Chari, P. P. Silvester, eds., Finite Elements in Electric and Magnetic Field Problems (Wiley, Chichester, UK, 1980).
  16. A. R. Mitchell, D. F. Griffiths, The Finite Difference Method in Partial Differential Equations (Wiley, Chichester, UK, 1980).
  17. M. Cadilhac, R. Petit, “On the diffraction problem in electromagnetic theory: a discussion based on concepts of functional analysis including an example of practical application” in Huygens’ Principle 1690–1990: Theory and Applications, H. Blok, H. A. Ferwerda, H. K. Kuiken, eds. (Elsevier, Amsterdam, 1992), pp. 240–272.
  18. P. Regli, “Automatische Wahl der sphaerischen Entwick-lungsfunktionen fuer die 3D-MMP Methode,” Ph.D. dissertation 9946 (Swiss Federal Institute of Technology, Zurich, Switzerland, 1992).
  19. Ch. Hafner, The Generalized Multiple Multipole Technique for Computational Electromagnetics (Artech, Boston, Mass., 1990).
  20. Ch. Hafner, “Multiple multipole (MMP) computations of guided waves and waveguide discontinuities,” Int. J. Nu-mer. Model. Electron. Networks Devices Fields 3, 247–257 (1990).
    [CrossRef]
  21. J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, “Optical properties of metals,” Phys. Data 18(2), 71–81 (1981).
  22. See, for instance, P. J. Feibelman, “Surface electromagnetic fields,” Prog. Surf. Sci. 12, 287–408 (1982).
    [CrossRef]
  23. See, for instance, A. Wokaun, “Surface enhancement of optical fields: mechanism and applications,” Mol. Phys. 56, 1–33 (1985).
    [CrossRef]
  24. C. J. Bouwkamp, “Diffraction theory,” Rep. Prog. Phys.17, 35–100 (1954).
    [CrossRef]
  25. A. Sommerfeld, Optics (Academic, New York, 1954).
  26. R. W. P. King, T. T. Wu, The Scattering and Diffraction of Waves, Vol. 7 of Harvard Monographs in Applied Science (Harvard U. Press, Cambridge, Mass., 1959).
  27. C. J. Bouwkamp, “On Bethe’s theory of diffraction by small holes,” Philips Res. Rep.5, 321–332 (1950).
  28. K. S. Kelleher, G. Hyde, “Reflector antennas,” in Antenna Engineering Handbook, 2nd ed., R. C. Johnson, H. Jasik, eds. (McGraw-Hill, New York, 1961), p. 17–1.
  29. D. W. Pohl, U. Ch. Fischer, U. T. Duerig, “Scanning near-field optical microscopy (SNOM): basic principles and some recent developments,” in Scanning Microscopy Technologies and Applications, E. C. Teague, ed., Proc. Soc. Photo-Opt. Instrum. Eng.897, 84–90 (1988).
    [CrossRef]
  30. A. Dereux, D. W. Pohl, “The 90° prism as a model SNOM probe: near-field, tunneling, and light scattering properties,” Ref. 2, pp. 189–198.
  31. D. Barchiesi, D. Van Labeke, “Scanning tunneling optical microscopy (STOM): theoretical study of polarization effects with two models of tip,” Ref. 2, pp. 179–188.
  32. C. Girard, X. Bouju, A. Dereux, “Optical near-field detection and local spectroscopy of a surface: a self-consistent theoretical study,” Ref. 2, pp. 199–208.
  33. A. Dereux, “Théorie de l’optique de champe proche,” Ph.D. dissertation (Facultes Universitaires Notre Dame de la Paix, Namur, Belgium, 1991).
  34. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1970), p. 333.
  35. H. Raether, “Surface plasmons,” Springer Tracts Mod. Phys. 111 (1988).
  36. M. Kerker, ed., Selected Papers on Surface-Enhanced Raman Scattering, Vol. 10 of SPIE Milestone Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1990).
  37. U. Ch. Fischer, D. W. Pohl, “Observation of single-particle plasmons by near-field optical microscopy,” Phys. Rev. Lett. 62, 458–461 (1989).
    [CrossRef] [PubMed]
  38. C. J. Bouwkamp, H. B. G. Casimir, “On multipole expansions in the theory of electromagnetic radiation,” Physica 20, 539–554 (1954).
    [CrossRef]
  39. H. S. Green, E. Wolf, “A scalar representation of electromagnetic fields,” Proc. Phys. Soc. A 66, 1129–1137 (1953).
    [CrossRef]
  40. P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
  41. Ch. Hafner, “Beiträge zur Berechnung der Ausbrietung elektromagnetischer Wellen in zylindrischen Strukturen mit Hilfe des ‘Point-Matching’ —Verfahrens,” Ph.D. dissertation 6683 (Swiss Federal Institute of Technology, Zurich, Switzerland, 1980).
  42. G. H. Golub, C. F. van Loan, Matrix Computations (Johns Hopkins U. Press, Baltimore, Md., 1989).

1993 (1)

See, for instance, H. Rohrer, “Limits and possibilities of miniaturization,” Jpn. J. Appl. Phys. 32, 1335–1341 (1993);“Local probe methods and miniaturization,” in Nanosources and Manipulation of Atoms under High Fields and Temperatures: Applications, NATO ASI Series E, Vol. 235, V. Thien Binh, N. Garcia, K. Dransfeld, eds. (Kluwer, Dordrecht, The Netherlands, 1993), pp. 1–12.
[CrossRef]

1990 (1)

Ch. Hafner, “Multiple multipole (MMP) computations of guided waves and waveguide discontinuities,” Int. J. Nu-mer. Model. Electron. Networks Devices Fields 3, 247–257 (1990).
[CrossRef]

1989 (3)

D. Courjon, K. Sarayeddine, 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]

U. Ch. Fischer, D. W. Pohl, “Observation of single-particle plasmons by near-field optical microscopy,” Phys. Rev. Lett. 62, 458–461 (1989).
[CrossRef] [PubMed]

1988 (1)

H. Raether, “Surface plasmons,” Springer Tracts Mod. Phys. 111 (1988).

1987 (1)

E. Betzig, M. Isaacson, A. Lewis, “Collection mode nearfield scanning optical microscopy,” Appl. Phys. Lett. 51, 2088–2090 (1987).
[CrossRef]

1986 (1)

U. Duerig, D. W. Pohl, F. Rohner, “Near-field optical scanning microscopy,” J. Appl. Phys. 59, 3318–3327 (1986).
[CrossRef]

1985 (1)

See, for instance, A. Wokaun, “Surface enhancement of optical fields: mechanism and applications,” Mol. Phys. 56, 1–33 (1985).
[CrossRef]

1984 (1)

D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[CrossRef]

1982 (1)

See, for instance, P. J. Feibelman, “Surface electromagnetic fields,” Prog. Surf. Sci. 12, 287–408 (1982).
[CrossRef]

1981 (1)

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, “Optical properties of metals,” Phys. Data 18(2), 71–81 (1981).

1954 (1)

C. J. Bouwkamp, H. B. G. Casimir, “On multipole expansions in the theory of electromagnetic radiation,” Physica 20, 539–554 (1954).
[CrossRef]

1953 (1)

H. S. Green, E. Wolf, “A scalar representation of electromagnetic fields,” Proc. Phys. Soc. A 66, 1129–1137 (1953).
[CrossRef]

Barchiesi, D.

D. Van Labeke, D. Barchiesi, “Theoretical problems in scanning near-field optical microscopy,” Ref. 2, pp. 157–178.

D. Barchiesi, D. Van Labeke, “Scanning tunneling optical microscopy (STOM): theoretical study of polarization effects with two models of tip,” Ref. 2, pp. 179–188.

Baumeister, W.

T. Hartmann, R. Gatz, W. Wiegräbe, A. Kramer, A. Hillebrand, K. Liebermann, W. Baumeister, R. Gucken-berger, “A scanning near-field optical microscope (SNOM) for biological applications” Ref. 2, pp. 35–44.

Betzig, E.

E. Betzig, M. Isaacson, A. Lewis, “Collection mode nearfield scanning optical microscopy,” Appl. Phys. Lett. 51, 2088–2090 (1987).
[CrossRef]

E. Betzig, “Principles and applications of near-field scanning optical microscopy (NSOM),” Ref. 2, pp. 7–16.

Bomholdt, L. H.

Ch. Hafner, L. H. Bomholdt, The 3d Electrodynamic Wave Simulator (Wiley, Chichester, UK, 1993).

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1970), p. 333.

Bouju, X.

C. Girard, X. Bouju, A. Dereux, “Optical near-field detection and local spectroscopy of a surface: a self-consistent theoretical study,” Ref. 2, pp. 199–208.

Bouwkamp, C. J.

C. J. Bouwkamp, H. B. G. Casimir, “On multipole expansions in the theory of electromagnetic radiation,” Physica 20, 539–554 (1954).
[CrossRef]

C. J. Bouwkamp, “Diffraction theory,” Rep. Prog. Phys.17, 35–100 (1954).
[CrossRef]

C. J. Bouwkamp, “On Bethe’s theory of diffraction by small holes,” Philips Res. Rep.5, 321–332 (1950).

Cadilhac, M.

M. Cadilhac, R. Petit, “On the diffraction problem in electromagnetic theory: a discussion based on concepts of functional analysis including an example of practical application” in Huygens’ Principle 1690–1990: Theory and Applications, H. Blok, H. A. Ferwerda, H. K. Kuiken, eds. (Elsevier, Amsterdam, 1992), pp. 240–272.

Casimir, H. B. G.

C. J. Bouwkamp, H. B. G. Casimir, “On multipole expansions in the theory of electromagnetic radiation,” Physica 20, 539–554 (1954).
[CrossRef]

Courjon, D.

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

Denk, W.

D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[CrossRef]

Dereux, A.

C. Girard, X. Bouju, A. Dereux, “Optical near-field detection and local spectroscopy of a surface: a self-consistent theoretical study,” Ref. 2, pp. 199–208.

A. Dereux, “Théorie de l’optique de champe proche,” Ph.D. dissertation (Facultes Universitaires Notre Dame de la Paix, Namur, Belgium, 1991).

A. Dereux, D. W. Pohl, “The 90° prism as a model SNOM probe: near-field, tunneling, and light scattering properties,” Ref. 2, pp. 189–198.

Duerig, U.

U. Duerig, D. W. Pohl, F. Rohner, “Near-field optical scanning microscopy,” J. Appl. Phys. 59, 3318–3327 (1986).
[CrossRef]

Duerig, U. T.

D. W. Pohl, U. Ch. Fischer, U. T. Duerig, “Scanning near-field optical microscopy (SNOM): basic principles and some recent developments,” in Scanning Microscopy Technologies and Applications, E. C. Teague, ed., Proc. Soc. Photo-Opt. Instrum. Eng.897, 84–90 (1988).
[CrossRef]

Feibelman, P. J.

See, for instance, P. J. Feibelman, “Surface electromagnetic fields,” Prog. Surf. Sci. 12, 287–408 (1982).
[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]

Feshbach, H.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

Fischer, U. Ch.

U. Ch. Fischer, D. W. Pohl, “Observation of single-particle plasmons by near-field optical microscopy,” Phys. Rev. Lett. 62, 458–461 (1989).
[CrossRef] [PubMed]

D. W. Pohl, U. Ch. Fischer, U. T. Duerig, “Scanning near-field optical microscopy (SNOM): basic principles and some recent developments,” in Scanning Microscopy Technologies and Applications, E. C. Teague, ed., Proc. Soc. Photo-Opt. Instrum. Eng.897, 84–90 (1988).
[CrossRef]

Gatz, R.

T. Hartmann, R. Gatz, W. Wiegräbe, A. Kramer, A. Hillebrand, K. Liebermann, W. Baumeister, R. Gucken-berger, “A scanning near-field optical microscope (SNOM) for biological applications” Ref. 2, pp. 35–44.

Girard, C.

C. Girard, X. Bouju, A. Dereux, “Optical near-field detection and local spectroscopy of a surface: a self-consistent theoretical study,” Ref. 2, pp. 199–208.

Golub, G. H.

G. H. Golub, C. F. van Loan, Matrix Computations (Johns Hopkins U. Press, Baltimore, Md., 1989).

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]

Green, H. S.

H. S. Green, E. Wolf, “A scalar representation of electromagnetic fields,” Proc. Phys. Soc. A 66, 1129–1137 (1953).
[CrossRef]

Griffiths, D. F.

A. R. Mitchell, D. F. Griffiths, The Finite Difference Method in Partial Differential Equations (Wiley, Chichester, UK, 1980).

Gucken-berger, R.

T. Hartmann, R. Gatz, W. Wiegräbe, A. Kramer, A. Hillebrand, K. Liebermann, W. Baumeister, R. Gucken-berger, “A scanning near-field optical microscope (SNOM) for biological applications” Ref. 2, pp. 35–44.

Hafner, Ch.

Ch. Hafner, “Multiple multipole (MMP) computations of guided waves and waveguide discontinuities,” Int. J. Nu-mer. Model. Electron. Networks Devices Fields 3, 247–257 (1990).
[CrossRef]

Ch. Hafner, The Generalized Multiple Multipole Technique for Computational Electromagnetics (Artech, Boston, Mass., 1990).

Ch. Hafner, L. H. Bomholdt, The 3d Electrodynamic Wave Simulator (Wiley, Chichester, UK, 1993).

Ch. Hafner, “Beiträge zur Berechnung der Ausbrietung elektromagnetischer Wellen in zylindrischen Strukturen mit Hilfe des ‘Point-Matching’ —Verfahrens,” Ph.D. dissertation 6683 (Swiss Federal Institute of Technology, Zurich, Switzerland, 1980).

Hartmann, T.

T. Hartmann, R. Gatz, W. Wiegräbe, A. Kramer, A. Hillebrand, K. Liebermann, W. Baumeister, R. Gucken-berger, “A scanning near-field optical microscope (SNOM) for biological applications” Ref. 2, pp. 35–44.

Hillebrand, A.

T. Hartmann, R. Gatz, W. Wiegräbe, A. Kramer, A. Hillebrand, K. Liebermann, W. Baumeister, R. Gucken-berger, “A scanning near-field optical microscope (SNOM) for biological applications” Ref. 2, pp. 35–44.

Hyde, G.

K. S. Kelleher, G. Hyde, “Reflector antennas,” in Antenna Engineering Handbook, 2nd ed., R. C. Johnson, H. Jasik, eds. (McGraw-Hill, New York, 1961), p. 17–1.

Isaacson, M.

E. Betzig, M. Isaacson, A. Lewis, “Collection mode nearfield scanning optical microscopy,” Appl. Phys. Lett. 51, 2088–2090 (1987).
[CrossRef]

Kelleher, K. S.

K. S. Kelleher, G. Hyde, “Reflector antennas,” in Antenna Engineering Handbook, 2nd ed., R. C. Johnson, H. Jasik, eds. (McGraw-Hill, New York, 1961), p. 17–1.

King, R. W. P.

R. W. P. King, T. T. Wu, The Scattering and Diffraction of Waves, Vol. 7 of Harvard Monographs in Applied Science (Harvard U. Press, Cambridge, Mass., 1959).

Koch, E. E.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, “Optical properties of metals,” Phys. Data 18(2), 71–81 (1981).

Krafka, C.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, “Optical properties of metals,” Phys. Data 18(2), 71–81 (1981).

Kramer, A.

T. Hartmann, R. Gatz, W. Wiegräbe, A. Kramer, A. Hillebrand, K. Liebermann, W. Baumeister, R. Gucken-berger, “A scanning near-field optical microscope (SNOM) for biological applications” Ref. 2, pp. 35–44.

Lanz, M.

D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[CrossRef]

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.

E. Betzig, M. Isaacson, A. Lewis, “Collection mode nearfield scanning optical microscopy,” Appl. Phys. Lett. 51, 2088–2090 (1987).
[CrossRef]

Liebermann, K.

T. Hartmann, R. Gatz, W. Wiegräbe, A. Kramer, A. Hillebrand, K. Liebermann, W. Baumeister, R. Gucken-berger, “A scanning near-field optical microscope (SNOM) for biological applications” Ref. 2, pp. 35–44.

Lynch, D. W.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, “Optical properties of metals,” Phys. Data 18(2), 71–81 (1981).

Mitchell, A. R.

A. R. Mitchell, D. F. Griffiths, The Finite Difference Method in Partial Differential Equations (Wiley, Chichester, UK, 1980).

Morse, P. M.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

Petit, R.

M. Cadilhac, R. Petit, “On the diffraction problem in electromagnetic theory: a discussion based on concepts of functional analysis including an example of practical application” in Huygens’ Principle 1690–1990: Theory and Applications, H. Blok, H. A. Ferwerda, H. K. Kuiken, eds. (Elsevier, Amsterdam, 1992), pp. 240–272.

Pohl, D. W.

U. Ch. Fischer, D. W. Pohl, “Observation of single-particle plasmons by near-field optical microscopy,” Phys. Rev. Lett. 62, 458–461 (1989).
[CrossRef] [PubMed]

U. Duerig, D. W. Pohl, F. Rohner, “Near-field optical scanning microscopy,” J. Appl. Phys. 59, 3318–3327 (1986).
[CrossRef]

D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[CrossRef]

D. W. Pohl, U. Ch. Fischer, U. T. Duerig, “Scanning near-field optical microscopy (SNOM): basic principles and some recent developments,” in Scanning Microscopy Technologies and Applications, E. C. Teague, ed., Proc. Soc. Photo-Opt. Instrum. Eng.897, 84–90 (1988).
[CrossRef]

A. Dereux, D. W. Pohl, “The 90° prism as a model SNOM probe: near-field, tunneling, and light scattering properties,” Ref. 2, pp. 189–198.

Raether, H.

H. Raether, “Surface plasmons,” Springer Tracts Mod. Phys. 111 (1988).

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]

Regli, P.

P. Regli, “Automatische Wahl der sphaerischen Entwick-lungsfunktionen fuer die 3D-MMP Methode,” Ph.D. dissertation 9946 (Swiss Federal Institute of Technology, Zurich, Switzerland, 1992).

Rohner, F.

U. Duerig, D. W. Pohl, F. Rohner, “Near-field optical scanning microscopy,” J. Appl. Phys. 59, 3318–3327 (1986).
[CrossRef]

Rohrer, H.

See, for instance, H. Rohrer, “Limits and possibilities of miniaturization,” Jpn. J. Appl. Phys. 32, 1335–1341 (1993);“Local probe methods and miniaturization,” in Nanosources and Manipulation of Atoms under High Fields and Temperatures: Applications, NATO ASI Series E, Vol. 235, V. Thien Binh, N. Garcia, K. Dransfeld, eds. (Kluwer, Dordrecht, The Netherlands, 1993), pp. 1–12.
[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.

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

Sommerfeld, A.

A. Sommerfeld, Optics (Academic, New York, 1954).

Spajer, M.

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

Toledo-Crow, R.

M. Vaez-Iravani, R. Toledo-Crow, “Amplitude, phase contrast and polarization imaging in near-field scanning optical microscopy,” Ref. 2, pp. 25–34.

Vaez-Iravani, M.

M. Vaez-Iravani, R. Toledo-Crow, “Amplitude, phase contrast and polarization imaging in near-field scanning optical microscopy,” Ref. 2, pp. 25–34.

Van Labeke, D.

D. Van Labeke, D. Barchiesi, “Theoretical problems in scanning near-field optical microscopy,” Ref. 2, pp. 157–178.

D. Barchiesi, D. Van Labeke, “Scanning tunneling optical microscopy (STOM): theoretical study of polarization effects with two models of tip,” Ref. 2, pp. 179–188.

van Loan, C. F.

G. H. Golub, C. F. van Loan, Matrix Computations (Johns Hopkins U. Press, Baltimore, Md., 1989).

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]

Weaver, J. H.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, “Optical properties of metals,” Phys. Data 18(2), 71–81 (1981).

Wiegräbe, W.

T. Hartmann, R. Gatz, W. Wiegräbe, A. Kramer, A. Hillebrand, K. Liebermann, W. Baumeister, R. Gucken-berger, “A scanning near-field optical microscope (SNOM) for biological applications” Ref. 2, pp. 35–44.

Wokaun, A.

See, for instance, A. Wokaun, “Surface enhancement of optical fields: mechanism and applications,” Mol. Phys. 56, 1–33 (1985).
[CrossRef]

Wolf, E.

H. S. Green, E. Wolf, “A scalar representation of electromagnetic fields,” Proc. Phys. Soc. A 66, 1129–1137 (1953).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1970), p. 333.

Wu, T. T.

R. W. P. King, T. T. Wu, The Scattering and Diffraction of Waves, Vol. 7 of Harvard Monographs in Applied Science (Harvard U. Press, Cambridge, Mass., 1959).

Appl. Phys. Lett. (2)

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

A. Dereux, D. W. Pohl, “The 90° prism as a model SNOM probe: near-field, tunneling, and light scattering properties,” Ref. 2, pp. 189–198.

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[CrossRef]

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See, for instance, D. W. Pohl, D. Courjon, eds., Near Field Optics, NATO ASI Series E, Vol. 242 (Kluwer, Dordrecht, The Netherlands, 1993).
[CrossRef]

E. Betzig, “Principles and applications of near-field scanning optical microscopy (NSOM),” Ref. 2, pp. 7–16.

M. Vaez-Iravani, R. Toledo-Crow, “Amplitude, phase contrast and polarization imaging in near-field scanning optical microscopy,” Ref. 2, pp. 25–34.

T. Hartmann, R. Gatz, W. Wiegräbe, A. Kramer, A. Hillebrand, K. Liebermann, W. Baumeister, R. Gucken-berger, “A scanning near-field optical microscope (SNOM) for biological applications” Ref. 2, pp. 35–44.

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Figures (16)

Fig. 1
Fig. 1

Geometry of the two-dimensional-model SNOM. Fixed parameters: half-angle, height, and aperture width of the wedge: 22.5°, 1686 nm, and 30 nm, respectively; inclination of the bottom of the screen: 15°; dielectric constants: –34.5 + i8.5 (screen), 2.25 (wedge, substrate); wavelength: 488 nm.

Fig. 2
Fig. 2

Field pattern inside the glass wedge: gray-scale contours, |E|2 (log scale, factor of 3 between successive lines); arrows, time-averaged power flux 〈S〉(arrow lengths ∝ |〈S〉| saturated at the length indicated by the vertical bar), (a) s polarization, (b) p polarization.

Fig. 3
Fig. 3

Close-up of the apex zone shown in Fig. 2: gray-scale contours, |E|2 (log scale, factor of 2 between successive lines); arrows, 〈S〉.The arrow length in (a) (s polarization) is scaled by a factor of 17 with respect to (b) (p polarization).

Fig. 4
Fig. 4

|E|2 in the aperture exit plane: (a) two-dimensional-model SNOM, (b) ideal circular aperture. Dashed curves, cross section in the plane of polarization; solid curves, cross section perpendicular to the plane of polarization.

Fig. 5
Fig. 5

Transmitted radiation patterns for three successive gap widths: 33 nm (solid curves), 103 nm (dashed curves), and 203 nm (dotted curves). θC, critical angle of 41.8° in glass, (a) s polarization, (b) p polarization.

Fig. 6
Fig. 6

Angular power density B(θ) for θ = 0° and θ = 55° as a function of gap width: (a)s polarization, (b) p polarization; a.u., arbitrary units.

Fig. 7
Fig. 7

Near field perturbed by an ideally conducting object with a diameter of 20 nm located 30 nm from the center position. Same scale as in Fig. 3.

Fig. 8
Fig. 8

Transmitted radiation patterns for a gap width of 33 nm and an object of 20-nm diameter moving from the center to the right. The figures indicate the lateral distance in nanometers. (a), (c) s polarization, (b), (d) p polarization; (a), (b) ideal conductor, (c), (d) highly refractive ( = 11.56) object.

Fig. 9
Fig. 9

Scan and gray-scale images for an ideally conducting( = −∞, solid curves), a glass ( = 2.25, dotted curves), and a highly refracting ( = 11.56, dashed curves) object. Gap width 33 nm, object diameter 20 nm. (a), (c) s polarization, (b), (d) p polarization.

Fig. 10
Fig. 10

Scan and gray-scale images of two ideally conducting objects separated by 130 nm. Gap width 33 nm, object diameter 20 nm. (a), (c) s polarization, (b), (d) p polarization.

Fig. 11
Fig. 11

Total transmitted power as a function of the dielectric constant of an object 20 nm in diameter located at the center position with a gap width of 33 nm. The arrow indicates the level for an ideally conducting object, (a) s polarization, (b) p polarization.

Fig. 12
Fig. 12

(a) Transmitted radiation patterns for p polarization, a gap width of 33 nm, and objects 20 nm in diameter, with various dielectric constants located at center position; (b) corresponding scan images.

Fig. 13
Fig. 13

Contour plots of |E|2 (log scale, factor of 2 between successive lines) in the gap region for p polarization, object diameter of 20 nm, and gap width of 33 nm. (e), (f) Field along a lateral line through the center of the object (0 dB = 100% of incident radiation).

Fig. 14
Fig. 14

Scan images of an ideally conducting object, obtained from different signals, scaled to 1 at infinite distance. Solid curves, B(55°) + B(−55°); dotted curves, Pt, dashed–dotted curves, B(0°). Gap width 33 nm, object diameter 20 nm. (a) s polarization, (b) p polarization, a.u., arbitrary units.

Fig. 15
Fig. 15

Scan and gray-scale images of an ideally conducting object of diameter 20 nm, gap width 33 nm, and coherent superposition. Dashed curves, Δφ = 0°; solid curves, Δφ = 180°. (a), (c) s polarization, (b), (d) p polarization, (c), (d) Δφ = 180°. a.u., arbitrary units.

Fig. 16
Fig. 16

Schematic principle of the multiple-multipole method. Multipole expansions located in domain Dj approximate the electromagnetic field inside domain Di and vice versa. On each side of the boundary Dij the field close to a point on the interface is defined mainly by the closest multipole (indicated by the sectors for the field in domain Di).

Equations (8)

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P t = π / 2 π / 2 B ( θ ) d θ ,
B ( 55 ° ) + B ( 55 ° ) + 2 [ B ( 55 ° ) B ( 55 ° ) ] 1 / 2 × cos ( φ 55 φ 55 Δ φ ) .
( 2 + k 2 ) f e , m ( r ) = 0 .
E = × [ f e , 0 , 0 ] 1 i ω × × [ f m , 0 , 0 ] ,
H = × [ f m , 0 , 0 ] 1 i ω μ × × [ f e , 0 , 0 ] .
f ( i ) ( r ) j = 0 J a j ( i ) · g j ( r ) ,
ψ n ( ρ , φ , z ) = B n ( κ ρ ) exp ( in φ ) exp ( i γ z ) .
n ( r k ) × [ E i ( r k ) E j ( r k ) ] = 0 n ( r k ) × [ H i ( r k ) H j ( r k ) ] = 0 n ( r k ) · [ μ i ( r k ) H i ( r k ) μ j ( r k ) H j ( r k ) ] = 0 n ( r k ) · [ i ( r k ) E i ( r k ) j ( r k ) E j ( r k ) ] = 0 } r k D i j ,

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