Abstract

Spatial effects of interference and interaction of light modes in the subwavelength part of the near-field optical microscopy probe have been theoretically studied. It was found that the mode interference can lead to higher spatial compression of light (wavelength is equal to 500nm in free space) within the transverse size of 25nm inside the probe output aperture of 100nm in diameter. The results predict a principal possibility of higher spatial resolution in the near-field optical microscopy technique.

© 2007 Optical Society of America

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  1. D. W. Pohl, W. Denk, and M. Lanz, "Optical stethoscopy: image recording with resolution lambda/20," Appl. Phys. Lett. 44, 651-654 (1984).
    [CrossRef]
  2. E. Betzig and R. J. Chichester, "Single molecules observed by near-field scanning optical microscopy," Science 262, 1422-1425 (1993).
    [CrossRef] [PubMed]
  3. B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, "Scanning near-field optical microscopy with aperture probes: fundamentals and applications," J. Chem. Phys. 112, 7761-7776 (2000).
    [CrossRef]
  4. E. Betzig and J. K. Trautman, "Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit," Science 257, 189-195 (1992).
    [CrossRef] [PubMed]
  5. E. Betzig and J. K. Trautman, "Polarization contrast in near-field scanning optical microscopy," Appl. Opt. 31, 4563-4568 (1992).
    [CrossRef] [PubMed]
  6. Th. Lacoste, Th. Huser, R. Prioli, and H. Heinzelmann, "Contrast enhancement using polarization-modulation scanning near-field optical microscopy (PM-SNOM)," Ultramicroscopy 71, 333-340 (1998).
    [CrossRef]
  7. H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163-173 (1944).
    [CrossRef]
  8. C. J. Bouwkamp, "Diffraction theory," Rep. Prog. Phys. 17, 35-100 (1954).
    [CrossRef]
  9. A. Roberts, "Small-hole coupling of radiation into a near-field probe," J. Appl. Phys. 70, 4045-4049 (1991).
    [CrossRef]
  10. L. Novotny, D. W. Pohl, and P. Regli, "Light propagation through nanometer-sized structures: the two-dimensional-aperture scanning near-field optical microscope," J. Opt. Soc. Am. A 11, 1768-1778 (1994).
    [CrossRef]
  11. A. L. Gutman, "To the calculation of waveguides with gradually varied cross-section," Radiotekhnika 12, 20-28 (1957) (in Russian).
  12. T. I. Kuznetsova, V. S. Lebedev, and A. M. Tsvelik, "Optical fields inside a conical waveguide with a subwavelength-sized exit hole," J. Opt. A, Pure Appl. Opt. 6, 338-348 (2004).
    [CrossRef]
  13. B. Z. Katsenellenbaum, M. K. A. Thumm, L. Mercader Del Rio, M. Pereyaslavets, and M. Sorolla Ayza, Theory of Nonuniform Waveguides: the Cross-Section Method (IEE, 1998).
    [CrossRef]
  14. B. Z. Katzenellenbaum, "The non-uniform waveguides with slowly changing parameters," Dokl. Akad. Nauk SSSR 102, 711-718 (1955) (in Russian).
  15. N. M. Arslanov and S. A. Moiseev, "Light propagation in scanning near-field optical microscopy probe," in International Workshop on Quantum Optics 2003, V. V. Samartsev, ed., Proc. SPIE 5402, 25-35 (2003).
  16. N. M. Arslanov, "The optimal form of the scanning near-field optical microscopy probe with subwavelength aperture," J. Opt. A, Pure Appl. Opt. 8, 338-344 (2006).
    [CrossRef]
  17. N. M. Arslanov and S. A. Moiseev, "Propagation of the TM and TE electromagnetic fields in the near-field optical microscopy narrowing probe with 50nm aperture radius," Investigated in Russia 237, 2423-2440 (2005) (in Russian); see http://zhurnal.ape.relarn.ru/articles/2005/237.pdf.
  18. Ya. L. Alpert, "To the question about the electromagnetic waves propagation in the pipes," Zh. Tekh. Fiz. 10, 1358-1364 (1940) (in Russian).
  19. M. Born and E. Wolf, Principles of Optics (Pergamon, 1975).
  20. L. Novotny and C. Hafner, "Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function," Phys. Rev. E 50, 4094-4106 (1994).
    [CrossRef]
  21. M. A. Leontovich, Investigations of Spreading Radiowave (Microwave) (Akad. Nauk SSSR, Moscow, 1948), Part. II (in Russian).
  22. R. Stockle, C. Fokas, V. Deckert, and R. Zenobi, "High-quality near-field optical probes by tube etching," Appl. Phys. Lett. 75, 160-170 (1999).
    [CrossRef]
  23. J. A. Veerman, A. M. Otter, L. Kuipers, and N. F. van Hulst, "High definition aperture probes for near-field optical microscopy fabricated by focused ion beam milling," Appl. Phys. Lett. 72, 3115-3125 (1998).
    [CrossRef]
  24. D. Zeisel, S. Nettesheim, B. Dutoit, and R. Zenobi, "Pulsed laser-induced desorption and optical imaging on a nanometer scale with scanning near-field microscopy using chemically etched fiber tips," Appl. Phys. Lett. 68, 2491-2492 (1996).
    [CrossRef]
  25. L. A. Vainstein, The Diffraction Theory and Method of Factorization (Soviet Radio, 1966).
  26. L. A. Vainstein, "Irradiation of the asymmetrical electromagnetic waves from the open end of circular waveguide," Dokl. Akad. Nauk SSSR 74, 485-488 (1950) (in Russian).

2006 (1)

N. M. Arslanov, "The optimal form of the scanning near-field optical microscopy probe with subwavelength aperture," J. Opt. A, Pure Appl. Opt. 8, 338-344 (2006).
[CrossRef]

2005 (1)

N. M. Arslanov and S. A. Moiseev, "Propagation of the TM and TE electromagnetic fields in the near-field optical microscopy narrowing probe with 50nm aperture radius," Investigated in Russia 237, 2423-2440 (2005) (in Russian); see http://zhurnal.ape.relarn.ru/articles/2005/237.pdf.

2004 (1)

T. I. Kuznetsova, V. S. Lebedev, and A. M. Tsvelik, "Optical fields inside a conical waveguide with a subwavelength-sized exit hole," J. Opt. A, Pure Appl. Opt. 6, 338-348 (2004).
[CrossRef]

2000 (1)

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, "Scanning near-field optical microscopy with aperture probes: fundamentals and applications," J. Chem. Phys. 112, 7761-7776 (2000).
[CrossRef]

1999 (1)

R. Stockle, C. Fokas, V. Deckert, and R. Zenobi, "High-quality near-field optical probes by tube etching," Appl. Phys. Lett. 75, 160-170 (1999).
[CrossRef]

1998 (2)

J. A. Veerman, A. M. Otter, L. Kuipers, and N. F. van Hulst, "High definition aperture probes for near-field optical microscopy fabricated by focused ion beam milling," Appl. Phys. Lett. 72, 3115-3125 (1998).
[CrossRef]

Th. Lacoste, Th. Huser, R. Prioli, and H. Heinzelmann, "Contrast enhancement using polarization-modulation scanning near-field optical microscopy (PM-SNOM)," Ultramicroscopy 71, 333-340 (1998).
[CrossRef]

1996 (1)

D. Zeisel, S. Nettesheim, B. Dutoit, and R. Zenobi, "Pulsed laser-induced desorption and optical imaging on a nanometer scale with scanning near-field microscopy using chemically etched fiber tips," Appl. Phys. Lett. 68, 2491-2492 (1996).
[CrossRef]

1994 (2)

L. Novotny and C. Hafner, "Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function," Phys. Rev. E 50, 4094-4106 (1994).
[CrossRef]

L. Novotny, D. W. Pohl, and P. Regli, "Light propagation through nanometer-sized structures: the two-dimensional-aperture scanning near-field optical microscope," J. Opt. Soc. Am. A 11, 1768-1778 (1994).
[CrossRef]

1993 (1)

E. Betzig and R. J. Chichester, "Single molecules observed by near-field scanning optical microscopy," Science 262, 1422-1425 (1993).
[CrossRef] [PubMed]

1992 (2)

E. Betzig and J. K. Trautman, "Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit," Science 257, 189-195 (1992).
[CrossRef] [PubMed]

E. Betzig and J. K. Trautman, "Polarization contrast in near-field scanning optical microscopy," Appl. Opt. 31, 4563-4568 (1992).
[CrossRef] [PubMed]

1991 (1)

A. Roberts, "Small-hole coupling of radiation into a near-field probe," J. Appl. Phys. 70, 4045-4049 (1991).
[CrossRef]

1984 (1)

D. W. Pohl, W. Denk, and M. Lanz, "Optical stethoscopy: image recording with resolution lambda/20," Appl. Phys. Lett. 44, 651-654 (1984).
[CrossRef]

1957 (1)

A. L. Gutman, "To the calculation of waveguides with gradually varied cross-section," Radiotekhnika 12, 20-28 (1957) (in Russian).

1955 (1)

B. Z. Katzenellenbaum, "The non-uniform waveguides with slowly changing parameters," Dokl. Akad. Nauk SSSR 102, 711-718 (1955) (in Russian).

1954 (1)

C. J. Bouwkamp, "Diffraction theory," Rep. Prog. Phys. 17, 35-100 (1954).
[CrossRef]

1950 (1)

L. A. Vainstein, "Irradiation of the asymmetrical electromagnetic waves from the open end of circular waveguide," Dokl. Akad. Nauk SSSR 74, 485-488 (1950) (in Russian).

1944 (1)

H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163-173 (1944).
[CrossRef]

1940 (1)

Ya. L. Alpert, "To the question about the electromagnetic waves propagation in the pipes," Zh. Tekh. Fiz. 10, 1358-1364 (1940) (in Russian).

Alpert, Ya. L.

Ya. L. Alpert, "To the question about the electromagnetic waves propagation in the pipes," Zh. Tekh. Fiz. 10, 1358-1364 (1940) (in Russian).

Arslanov, N. M.

N. M. Arslanov, "The optimal form of the scanning near-field optical microscopy probe with subwavelength aperture," J. Opt. A, Pure Appl. Opt. 8, 338-344 (2006).
[CrossRef]

N. M. Arslanov and S. A. Moiseev, "Propagation of the TM and TE electromagnetic fields in the near-field optical microscopy narrowing probe with 50nm aperture radius," Investigated in Russia 237, 2423-2440 (2005) (in Russian); see http://zhurnal.ape.relarn.ru/articles/2005/237.pdf.

N. M. Arslanov and S. A. Moiseev, "Light propagation in scanning near-field optical microscopy probe," in International Workshop on Quantum Optics 2003, V. V. Samartsev, ed., Proc. SPIE 5402, 25-35 (2003).

Ayza, M. Sorolla

B. Z. Katsenellenbaum, M. K. A. Thumm, L. Mercader Del Rio, M. Pereyaslavets, and M. Sorolla Ayza, Theory of Nonuniform Waveguides: the Cross-Section Method (IEE, 1998).
[CrossRef]

Bethe, H. A.

H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163-173 (1944).
[CrossRef]

Betzig, E.

E. Betzig and R. J. Chichester, "Single molecules observed by near-field scanning optical microscopy," Science 262, 1422-1425 (1993).
[CrossRef] [PubMed]

E. Betzig and J. K. Trautman, "Polarization contrast in near-field scanning optical microscopy," Appl. Opt. 31, 4563-4568 (1992).
[CrossRef] [PubMed]

E. Betzig and J. K. Trautman, "Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit," Science 257, 189-195 (1992).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975).

Bouwkamp, C. J.

C. J. Bouwkamp, "Diffraction theory," Rep. Prog. Phys. 17, 35-100 (1954).
[CrossRef]

Chichester, R. J.

E. Betzig and R. J. Chichester, "Single molecules observed by near-field scanning optical microscopy," Science 262, 1422-1425 (1993).
[CrossRef] [PubMed]

Deckert, V.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, "Scanning near-field optical microscopy with aperture probes: fundamentals and applications," J. Chem. Phys. 112, 7761-7776 (2000).
[CrossRef]

R. Stockle, C. Fokas, V. Deckert, and R. Zenobi, "High-quality near-field optical probes by tube etching," Appl. Phys. Lett. 75, 160-170 (1999).
[CrossRef]

Denk, W.

D. W. Pohl, W. Denk, and M. Lanz, "Optical stethoscopy: image recording with resolution lambda/20," Appl. Phys. Lett. 44, 651-654 (1984).
[CrossRef]

Dutoit, B.

D. Zeisel, S. Nettesheim, B. Dutoit, and R. Zenobi, "Pulsed laser-induced desorption and optical imaging on a nanometer scale with scanning near-field microscopy using chemically etched fiber tips," Appl. Phys. Lett. 68, 2491-2492 (1996).
[CrossRef]

Fokas, C.

R. Stockle, C. Fokas, V. Deckert, and R. Zenobi, "High-quality near-field optical probes by tube etching," Appl. Phys. Lett. 75, 160-170 (1999).
[CrossRef]

Gutman, A. L.

A. L. Gutman, "To the calculation of waveguides with gradually varied cross-section," Radiotekhnika 12, 20-28 (1957) (in Russian).

Hafner, C.

L. Novotny and C. Hafner, "Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function," Phys. Rev. E 50, 4094-4106 (1994).
[CrossRef]

Hecht, B.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, "Scanning near-field optical microscopy with aperture probes: fundamentals and applications," J. Chem. Phys. 112, 7761-7776 (2000).
[CrossRef]

Heinzelmann, H.

Th. Lacoste, Th. Huser, R. Prioli, and H. Heinzelmann, "Contrast enhancement using polarization-modulation scanning near-field optical microscopy (PM-SNOM)," Ultramicroscopy 71, 333-340 (1998).
[CrossRef]

Huser, Th.

Th. Lacoste, Th. Huser, R. Prioli, and H. Heinzelmann, "Contrast enhancement using polarization-modulation scanning near-field optical microscopy (PM-SNOM)," Ultramicroscopy 71, 333-340 (1998).
[CrossRef]

Katsenellenbaum, B. Z.

B. Z. Katsenellenbaum, M. K. A. Thumm, L. Mercader Del Rio, M. Pereyaslavets, and M. Sorolla Ayza, Theory of Nonuniform Waveguides: the Cross-Section Method (IEE, 1998).
[CrossRef]

Katzenellenbaum, B. Z.

B. Z. Katzenellenbaum, "The non-uniform waveguides with slowly changing parameters," Dokl. Akad. Nauk SSSR 102, 711-718 (1955) (in Russian).

Kuipers, L.

J. A. Veerman, A. M. Otter, L. Kuipers, and N. F. van Hulst, "High definition aperture probes for near-field optical microscopy fabricated by focused ion beam milling," Appl. Phys. Lett. 72, 3115-3125 (1998).
[CrossRef]

Kuznetsova, T. I.

T. I. Kuznetsova, V. S. Lebedev, and A. M. Tsvelik, "Optical fields inside a conical waveguide with a subwavelength-sized exit hole," J. Opt. A, Pure Appl. Opt. 6, 338-348 (2004).
[CrossRef]

Lacoste, Th.

Th. Lacoste, Th. Huser, R. Prioli, and H. Heinzelmann, "Contrast enhancement using polarization-modulation scanning near-field optical microscopy (PM-SNOM)," Ultramicroscopy 71, 333-340 (1998).
[CrossRef]

Lanz, M.

D. W. Pohl, W. Denk, and M. Lanz, "Optical stethoscopy: image recording with resolution lambda/20," Appl. Phys. Lett. 44, 651-654 (1984).
[CrossRef]

Lebedev, V. S.

T. I. Kuznetsova, V. S. Lebedev, and A. M. Tsvelik, "Optical fields inside a conical waveguide with a subwavelength-sized exit hole," J. Opt. A, Pure Appl. Opt. 6, 338-348 (2004).
[CrossRef]

Leontovich, M. A.

M. A. Leontovich, Investigations of Spreading Radiowave (Microwave) (Akad. Nauk SSSR, Moscow, 1948), Part. II (in Russian).

Martin, O. J. F.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, "Scanning near-field optical microscopy with aperture probes: fundamentals and applications," J. Chem. Phys. 112, 7761-7776 (2000).
[CrossRef]

Mercader Del Rio, L.

B. Z. Katsenellenbaum, M. K. A. Thumm, L. Mercader Del Rio, M. Pereyaslavets, and M. Sorolla Ayza, Theory of Nonuniform Waveguides: the Cross-Section Method (IEE, 1998).
[CrossRef]

Moiseev, S. A.

N. M. Arslanov and S. A. Moiseev, "Propagation of the TM and TE electromagnetic fields in the near-field optical microscopy narrowing probe with 50nm aperture radius," Investigated in Russia 237, 2423-2440 (2005) (in Russian); see http://zhurnal.ape.relarn.ru/articles/2005/237.pdf.

N. M. Arslanov and S. A. Moiseev, "Light propagation in scanning near-field optical microscopy probe," in International Workshop on Quantum Optics 2003, V. V. Samartsev, ed., Proc. SPIE 5402, 25-35 (2003).

Nettesheim, S.

D. Zeisel, S. Nettesheim, B. Dutoit, and R. Zenobi, "Pulsed laser-induced desorption and optical imaging on a nanometer scale with scanning near-field microscopy using chemically etched fiber tips," Appl. Phys. Lett. 68, 2491-2492 (1996).
[CrossRef]

Novotny, L.

L. Novotny, D. W. Pohl, and P. Regli, "Light propagation through nanometer-sized structures: the two-dimensional-aperture scanning near-field optical microscope," J. Opt. Soc. Am. A 11, 1768-1778 (1994).
[CrossRef]

L. Novotny and C. Hafner, "Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function," Phys. Rev. E 50, 4094-4106 (1994).
[CrossRef]

Otter, A. M.

J. A. Veerman, A. M. Otter, L. Kuipers, and N. F. van Hulst, "High definition aperture probes for near-field optical microscopy fabricated by focused ion beam milling," Appl. Phys. Lett. 72, 3115-3125 (1998).
[CrossRef]

Pereyaslavets, M.

B. Z. Katsenellenbaum, M. K. A. Thumm, L. Mercader Del Rio, M. Pereyaslavets, and M. Sorolla Ayza, Theory of Nonuniform Waveguides: the Cross-Section Method (IEE, 1998).
[CrossRef]

Pohl, D. W.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, "Scanning near-field optical microscopy with aperture probes: fundamentals and applications," J. Chem. Phys. 112, 7761-7776 (2000).
[CrossRef]

L. Novotny, D. W. Pohl, and P. Regli, "Light propagation through nanometer-sized structures: the two-dimensional-aperture scanning near-field optical microscope," J. Opt. Soc. Am. A 11, 1768-1778 (1994).
[CrossRef]

D. W. Pohl, W. Denk, and M. Lanz, "Optical stethoscopy: image recording with resolution lambda/20," Appl. Phys. Lett. 44, 651-654 (1984).
[CrossRef]

Prioli, R.

Th. Lacoste, Th. Huser, R. Prioli, and H. Heinzelmann, "Contrast enhancement using polarization-modulation scanning near-field optical microscopy (PM-SNOM)," Ultramicroscopy 71, 333-340 (1998).
[CrossRef]

Regli, P.

Roberts, A.

A. Roberts, "Small-hole coupling of radiation into a near-field probe," J. Appl. Phys. 70, 4045-4049 (1991).
[CrossRef]

Sick, B.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, "Scanning near-field optical microscopy with aperture probes: fundamentals and applications," J. Chem. Phys. 112, 7761-7776 (2000).
[CrossRef]

Stockle, R.

R. Stockle, C. Fokas, V. Deckert, and R. Zenobi, "High-quality near-field optical probes by tube etching," Appl. Phys. Lett. 75, 160-170 (1999).
[CrossRef]

Thumm, M. K. A.

B. Z. Katsenellenbaum, M. K. A. Thumm, L. Mercader Del Rio, M. Pereyaslavets, and M. Sorolla Ayza, Theory of Nonuniform Waveguides: the Cross-Section Method (IEE, 1998).
[CrossRef]

Trautman, J. K.

E. Betzig and J. K. Trautman, "Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit," Science 257, 189-195 (1992).
[CrossRef] [PubMed]

E. Betzig and J. K. Trautman, "Polarization contrast in near-field scanning optical microscopy," Appl. Opt. 31, 4563-4568 (1992).
[CrossRef] [PubMed]

Tsvelik, A. M.

T. I. Kuznetsova, V. S. Lebedev, and A. M. Tsvelik, "Optical fields inside a conical waveguide with a subwavelength-sized exit hole," J. Opt. A, Pure Appl. Opt. 6, 338-348 (2004).
[CrossRef]

Vainstein, L. A.

L. A. Vainstein, "Irradiation of the asymmetrical electromagnetic waves from the open end of circular waveguide," Dokl. Akad. Nauk SSSR 74, 485-488 (1950) (in Russian).

L. A. Vainstein, The Diffraction Theory and Method of Factorization (Soviet Radio, 1966).

van Hulst, N. F.

J. A. Veerman, A. M. Otter, L. Kuipers, and N. F. van Hulst, "High definition aperture probes for near-field optical microscopy fabricated by focused ion beam milling," Appl. Phys. Lett. 72, 3115-3125 (1998).
[CrossRef]

Veerman, J. A.

J. A. Veerman, A. M. Otter, L. Kuipers, and N. F. van Hulst, "High definition aperture probes for near-field optical microscopy fabricated by focused ion beam milling," Appl. Phys. Lett. 72, 3115-3125 (1998).
[CrossRef]

Wild, U. P.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, "Scanning near-field optical microscopy with aperture probes: fundamentals and applications," J. Chem. Phys. 112, 7761-7776 (2000).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975).

Zeisel, D.

D. Zeisel, S. Nettesheim, B. Dutoit, and R. Zenobi, "Pulsed laser-induced desorption and optical imaging on a nanometer scale with scanning near-field microscopy using chemically etched fiber tips," Appl. Phys. Lett. 68, 2491-2492 (1996).
[CrossRef]

Zenobi, R.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, "Scanning near-field optical microscopy with aperture probes: fundamentals and applications," J. Chem. Phys. 112, 7761-7776 (2000).
[CrossRef]

R. Stockle, C. Fokas, V. Deckert, and R. Zenobi, "High-quality near-field optical probes by tube etching," Appl. Phys. Lett. 75, 160-170 (1999).
[CrossRef]

D. Zeisel, S. Nettesheim, B. Dutoit, and R. Zenobi, "Pulsed laser-induced desorption and optical imaging on a nanometer scale with scanning near-field microscopy using chemically etched fiber tips," Appl. Phys. Lett. 68, 2491-2492 (1996).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

R. Stockle, C. Fokas, V. Deckert, and R. Zenobi, "High-quality near-field optical probes by tube etching," Appl. Phys. Lett. 75, 160-170 (1999).
[CrossRef]

J. A. Veerman, A. M. Otter, L. Kuipers, and N. F. van Hulst, "High definition aperture probes for near-field optical microscopy fabricated by focused ion beam milling," Appl. Phys. Lett. 72, 3115-3125 (1998).
[CrossRef]

D. Zeisel, S. Nettesheim, B. Dutoit, and R. Zenobi, "Pulsed laser-induced desorption and optical imaging on a nanometer scale with scanning near-field microscopy using chemically etched fiber tips," Appl. Phys. Lett. 68, 2491-2492 (1996).
[CrossRef]

D. W. Pohl, W. Denk, and M. Lanz, "Optical stethoscopy: image recording with resolution lambda/20," Appl. Phys. Lett. 44, 651-654 (1984).
[CrossRef]

Dokl. Akad. Nauk SSSR (2)

B. Z. Katzenellenbaum, "The non-uniform waveguides with slowly changing parameters," Dokl. Akad. Nauk SSSR 102, 711-718 (1955) (in Russian).

L. A. Vainstein, "Irradiation of the asymmetrical electromagnetic waves from the open end of circular waveguide," Dokl. Akad. Nauk SSSR 74, 485-488 (1950) (in Russian).

Investigated in Russia (1)

N. M. Arslanov and S. A. Moiseev, "Propagation of the TM and TE electromagnetic fields in the near-field optical microscopy narrowing probe with 50nm aperture radius," Investigated in Russia 237, 2423-2440 (2005) (in Russian); see http://zhurnal.ape.relarn.ru/articles/2005/237.pdf.

J. Appl. Phys. (1)

A. Roberts, "Small-hole coupling of radiation into a near-field probe," J. Appl. Phys. 70, 4045-4049 (1991).
[CrossRef]

J. Chem. Phys. (1)

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, "Scanning near-field optical microscopy with aperture probes: fundamentals and applications," J. Chem. Phys. 112, 7761-7776 (2000).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (2)

N. M. Arslanov, "The optimal form of the scanning near-field optical microscopy probe with subwavelength aperture," J. Opt. A, Pure Appl. Opt. 8, 338-344 (2006).
[CrossRef]

T. I. Kuznetsova, V. S. Lebedev, and A. M. Tsvelik, "Optical fields inside a conical waveguide with a subwavelength-sized exit hole," J. Opt. A, Pure Appl. Opt. 6, 338-348 (2004).
[CrossRef]

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

Phys. Rev. (1)

H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163-173 (1944).
[CrossRef]

Phys. Rev. E (1)

L. Novotny and C. Hafner, "Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function," Phys. Rev. E 50, 4094-4106 (1994).
[CrossRef]

Radiotekhnika (1)

A. L. Gutman, "To the calculation of waveguides with gradually varied cross-section," Radiotekhnika 12, 20-28 (1957) (in Russian).

Rep. Prog. Phys. (1)

C. J. Bouwkamp, "Diffraction theory," Rep. Prog. Phys. 17, 35-100 (1954).
[CrossRef]

Science (2)

E. Betzig and J. K. Trautman, "Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit," Science 257, 189-195 (1992).
[CrossRef] [PubMed]

E. Betzig and R. J. Chichester, "Single molecules observed by near-field scanning optical microscopy," Science 262, 1422-1425 (1993).
[CrossRef] [PubMed]

Ultramicroscopy (1)

Th. Lacoste, Th. Huser, R. Prioli, and H. Heinzelmann, "Contrast enhancement using polarization-modulation scanning near-field optical microscopy (PM-SNOM)," Ultramicroscopy 71, 333-340 (1998).
[CrossRef]

Zh. Tekh. Fiz. (1)

Ya. L. Alpert, "To the question about the electromagnetic waves propagation in the pipes," Zh. Tekh. Fiz. 10, 1358-1364 (1940) (in Russian).

Other (5)

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975).

B. Z. Katsenellenbaum, M. K. A. Thumm, L. Mercader Del Rio, M. Pereyaslavets, and M. Sorolla Ayza, Theory of Nonuniform Waveguides: the Cross-Section Method (IEE, 1998).
[CrossRef]

N. M. Arslanov and S. A. Moiseev, "Light propagation in scanning near-field optical microscopy probe," in International Workshop on Quantum Optics 2003, V. V. Samartsev, ed., Proc. SPIE 5402, 25-35 (2003).

M. A. Leontovich, Investigations of Spreading Radiowave (Microwave) (Akad. Nauk SSSR, Moscow, 1948), Part. II (in Russian).

L. A. Vainstein, The Diffraction Theory and Method of Factorization (Soviet Radio, 1966).

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Figures (11)

Fig. 1
Fig. 1

Light field at the output aperture of a NFO microscopy probe. The main light transformations occur at the subwavelength probe part.

Fig. 2
Fig. 2

Dependence of the wavenumber’s real part Re h on radius a. Re h determines the propagation velocities of the modes in the regular waveguide. The arrows show the critical radius for each light mode in the probe with ideal metallic walls.

Fig. 3
Fig. 3

Dependence of the wavenumber’s imaginary part Im h on radius a. The behavior of Im h determines the steep increasing of the decrements corresponding to the different light modes in the narrowing probe. The decrements of the modes EH 11 and TE 01 have steep increasing at 220 nm ; HE 21 mode at 160 nm ; TM 01 mode at 135 nm .

Fig. 4
Fig. 4

Results of the numerical calculations of the field mode powers TM 0 m ( m = 1 , 2 ) (wavelength of light λ = 500 nm ) in the probe output with aluminum coating. Length of the probe ( L ) was changed from L = 1172 nm to L = 8 nm with initial radius a ( z = 0 ) = 500 nm and output radius a ( L ) = 50 nm , which correspond to the various inclinations α of the probe.

Fig. 5
Fig. 5

Numerical calculations of the light field T M 1 m spatial structure inside the output aperture of the probe with inclination angle α = 30 ° for ε = 34.5 + 8 i , ε 0 = 2.16 , λ = 500 nm , a 1 = 500 nm , a 2 = 50 nm in arbitrary units. The light spatial structure of the intensities I z and I r closely agrees with experimental data given in Ref. [2]. The TM field radial and longitudinal component intensities have been found on the output probe aperture cross section by taking into account the main light modes TM 11 , TM 12 , and TM 13 . The arrows show the intensity widths of the field components.

Fig. 6
Fig. 6

Spatial structure of the longitudinal I z and radial component I r (and total I z + I r ) in the light intensity inside the probe output aperture with inclination angle α = 25 ° for ϵ = 34.5 + 8 i , ϵ 0 = 2.16 , λ 0 = 500 nm , a 1 = 500 nm , a 2 = 50 nm .

Fig. 7
Fig. 7

Spatial structure of the longitudinal I z and radial component I r (and total I z + I r ) in the light intensity inside the probe output aperture with inclination angle α = 55 ° for ϵ = 34.5 + 8 i , ϵ 0 = 2.16 , λ 0 = 500 nm , a 1 = 500 nm , a 2 = 50 nm .

Fig. 8
Fig. 8

Numerical calculations of the squared field amplitudes J 1 = P 1 ( z ) 2 , J 2 = P 2 ( z ) 2 corresponding to the first and second field modes; the interference term J 12 = 2 P 1 ( z ) P 2 ( z ) cos ( θ 1 θ 2 ) becomes significant at the angles α > 55 ° [see expressions (16, 17)].

Fig. 9
Fig. 9

Mode phases ϑ 1 and ϑ 2 , depending on the inclination angle α and their difference ϑ 12 . It is seen that the phase difference between the two lowest light modes ensures the spatial compression at the inclination angle α 75 ° , where the interfering mode amplitudes became comparable on magnitude. The phase difference is lost for the angle α > 80 ° .

Fig. 10
Fig. 10

Light field spatial structure inside the output aperture of the probe with inclination angle α = 75 ° . The TM field radial and longitudinal component intensities I r and I z , respectively, are shown (in arbitrary units) on the output probe aperture cross section, taking into account main modes TM 11 , TM 12 , and TM 13 . The arrows show the intensity widths of the field components, which are less than the aperture diameter, and one can determine the higher-spatial-resolution NFO microscopy technique due to the field mode interference.

Fig. 11
Fig. 11

d z ( L ) is the spatial width of longitudinal field intensity I z ; d r ( L ) is the spatial width of the radial component of the field intensity I r . The Raleigh criteria of the line resolution were taken into account. As seen from the figure, there is the minimum spatial width of longitudinal field intensity I z at the angle α 75 ° .

Equations (35)

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E ( z ) = P j ( z ) E j ( z ) , H ( z ) = P j ( z ) H j ( z ) ,
S d S ( [ H m E j ] + [ H j E m ] ) = 2 k h m δ j m ,
E y j ( d d z i h j ) P j = j P j z E y j ,
E x j ( d d z i h j ) P j = j P j z E x j ,
H y j ( d d z i h j ) P j = j P j z H y j ,
H x j ( d d z i h j ) P j = j P j z H x j .
d d z P j ( z ) i h j ( z ) P j ( z ) = ν = ν = S j m ( z ) P m ( z ) ,
S j m = 1 2 k h j S d S ( E x j d d z H y m E y j d d z H x m + H y j d d z E x m H x j d d z E y m ) .
div { [ H j d d z E m ] [ d d z H m E j ] } = i k ( d ϵ d z E m E j d μ d z H j H m ) ,
d d z H m = ( d d z H ̃ m + i ζ H ̃ m d d z h m ) e i h m ζ ,
S j m ( z ) = 1 2 h j ( z ) [ h j ( z ) h m ( z ) ] d S ( d d z ϵ E m E j d d z μ H j H m ) .
E r j = E r j , H z j = H z j , H φ j = H φ j ,
S j m ( z ) = a ( z ) 2 h j ( z ) [ h j ( z ) h m ( z ) ] d a ( z ) d z C d φ ( 1 ϵ 0 ϵ ) ( H z j H z m H φ j H φ m + ϵ 0 E r j E r m ) .
h j ( z ) = [ k 0 2 ϵ 0 α j 2 ( z ) ] 1 2 ,
E φ = ξ H z , E z = ξ H φ .
h j ( z ) = [ k 0 2 ϵ 0 ν j 2 a ( z ) 2 + ξ 2 i k 0 ϵ 0 a ( z ) ] 1 2 ,
h j ( z ) = [ k 0 2 ϵ 0 μ j 2 a ( z ) 2 + ξ 2 a ( z ) i k 0 ( μ n j 2 n 2 ) ( μ n j 4 a ( z ) 4 + h 0 2 ( z ) n 2 a ( z ) 2 ) ] 1 2 .
I ( r ) = j P j ( z ) 2 E j 2 ( r ) + ( j < j P j ( z ) P j * ( z ) E j ( r ) E j * ( r ) + c.c. ) .
I z ( r , φ , z ) P 1 ( z ) 2 J 0 ( α 01 r ) 2 + P 2 ( z ) 2 J 0 ( α 02 r ) 2 + 2 P 1 ( z ) P 2 ( z ) J 0 ( α 01 r ) J 0 ( α 02 r ) cos ( θ 1 θ 2 ) ,
I r ( r , φ , z ) P 1 ( z ) 2 J 1 ( α 01 r ) 2 + P 2 ( z ) 2 J 1 ( α 02 r ) 2 + 2 P 1 ( z ) P 2 ( z ) J 1 ( α 01 r ) J 1 ( α 02 r ) cos ( θ 1 θ 2 ) ,
S 12 ( z ) = S 21 ( z ) ( h 2 ( z ) h 1 ( z ) ) a ( z ) a k r S 21 ( z ) ,
i h Π e r φ i k 0 μ 0 Π m r 1 = ξ α 2 Π m ,
α 2 Π e = ξ ( i k 0 ε 0 Π e r + i h Π m r φ ) .
Δ Π n + α n 2 Π n = 0
α n 2 d S Π n TM Π n TM = 1 , α n 2 d S Π n TE Π n TE = ε 0 ,
i Φ e r φ i k 0 Π m r = ξ α 2 Π m ,
α 2 Φ e = ξ ( i k 0 ε 0 Φ e r + i h 2 Π m r φ ) ,
Δ Φ e + α 2 Φ e = 0 ,
Δ Π m + α 2 Π m = 0 .
α 2 = α 0 2 + ξ α 1 2 + , h 2 = k 0 2 ε 0 α 2 = h 0 2 ξ α 1 2 ,
Φ = Φ 0 e + ξ Φ 1 e + , Π m = Π 0 m + ξ Π 1 m + ,
S d S ( V Δ U U Δ V ) = c d S ( V U n U V n ) ,
α 1 2 = i k 0 μ 0 ( α 0 4 c r d φ Π 0 m 2 + h 0 2 c r d φ Π 0 m 2 Π 0 m r 2 φ 2 ) = 2 a i k 0 ( μ n j 2 n 2 ) ( α 0 4 + h 0 2 n 2 a 2 ) .
α 1 2 = i k 0 ε 0 c r d φ ( Π 0 e r ) 2 = 2 i k 0 ε 0 a .
h 1 2 = k 0 2 ε 0 α 0 2 ξ α 1 2 ,

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