Abstract

Diffraction of the localized optical near field by a subwavelength-sized probe (metallic circular aperture) is studied by a nonglobal approach. The problem is closely relevant to the basic principle of a near-field scanning optical microscope (NSOM). We obtain analytic expressions of the diffracted far field from which the transfer function of the NSOM can be calculated. In particular, we find a resonance enhancement in the detection efficiency when the sample size is similar to the probe size. By lateral scanning of the aperture position at a constant height, we also obtain a NSOM image of a dielectric sphere sample.

© 1996 Optical Society of America

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References

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  1. M. Born, E. WolfPrinciples of Optics, 5th ed. (Pergamon, London, 1975).
  2. J. D. JacksonClassical Electrodynamics, 2nd ed. (Wiley, New York, 1975), Chaps. 9 and 16.
  3. Y. LeviatanJ. Appl. Phys. 60,1577 (1986).
    [CrossRef]
  4. E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, R. L. KostelakScience 251,1468 ( 1991;E. Betzig, J. K. TrautmanScience 257,189 (1992).
    [CrossRef] [PubMed]
  5. See, for example, D. W. Pohl, D. Courjon, eds., Near Field Optics (Kluwer, Dordrecht, The Netherlands, 1993).
  6. O. J. F. Martin, C. Girard, A. Dereux, Phys. Rev. Lett. 74, 526 ( 1995).
    [CrossRef] [PubMed]
  7. T. Saiki, M. Ohtsu, K. Jang, W. Jhe, “Direct observation of size-dependent features of the optical near field on a subwavelength spherical surface,” submitted to Opt. Lett.
  8. L. Novotny, D. W. Pohl, P. Regli, J. Opt. Soc. Am. A 11, 1768 (1994).
    [CrossRef]
  9. F. Depasse, M. A. Paesler, D. Courjon, J. M. Vigoureux, Opt. Lett. 20,234 (1995).
    [CrossRef] [PubMed]
  10. H. Chew, D. S. Wang, M. Kerker, Appl. Opt. 18,2679 (1979).
    [CrossRef] [PubMed]
  11. H. Hori, S. Jiang, M. Ohtsu, H. Ohsawain Technical Digest of the 18th International Quantum Electronics Conference (1992), p. 48.

1995

1994

1992

H. Hori, S. Jiang, M. Ohtsu, H. Ohsawain Technical Digest of the 18th International Quantum Electronics Conference (1992), p. 48.

1991

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, R. L. KostelakScience 251,1468 ( 1991;E. Betzig, J. K. TrautmanScience 257,189 (1992).
[CrossRef] [PubMed]

1986

Y. LeviatanJ. Appl. Phys. 60,1577 (1986).
[CrossRef]

1979

Betzig, E.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, R. L. KostelakScience 251,1468 ( 1991;E. Betzig, J. K. TrautmanScience 257,189 (1992).
[CrossRef] [PubMed]

Born, M.

M. Born, E. WolfPrinciples of Optics, 5th ed. (Pergamon, London, 1975).

Chew, H.

Courjon, D.

Depasse, F.

Dereux, A.

O. J. F. Martin, C. Girard, A. Dereux, Phys. Rev. Lett. 74, 526 ( 1995).
[CrossRef] [PubMed]

Girard, C.

O. J. F. Martin, C. Girard, A. Dereux, Phys. Rev. Lett. 74, 526 ( 1995).
[CrossRef] [PubMed]

Harris, T. D.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, R. L. KostelakScience 251,1468 ( 1991;E. Betzig, J. K. TrautmanScience 257,189 (1992).
[CrossRef] [PubMed]

Hori, H.

H. Hori, S. Jiang, M. Ohtsu, H. Ohsawain Technical Digest of the 18th International Quantum Electronics Conference (1992), p. 48.

Jackson, J. D.

J. D. JacksonClassical Electrodynamics, 2nd ed. (Wiley, New York, 1975), Chaps. 9 and 16.

Jang, K.

T. Saiki, M. Ohtsu, K. Jang, W. Jhe, “Direct observation of size-dependent features of the optical near field on a subwavelength spherical surface,” submitted to Opt. Lett.

Jhe, W.

T. Saiki, M. Ohtsu, K. Jang, W. Jhe, “Direct observation of size-dependent features of the optical near field on a subwavelength spherical surface,” submitted to Opt. Lett.

Jiang, S.

H. Hori, S. Jiang, M. Ohtsu, H. Ohsawain Technical Digest of the 18th International Quantum Electronics Conference (1992), p. 48.

Kerker, M.

Kostelak, R. L.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, R. L. KostelakScience 251,1468 ( 1991;E. Betzig, J. K. TrautmanScience 257,189 (1992).
[CrossRef] [PubMed]

Leviatan, Y.

Y. LeviatanJ. Appl. Phys. 60,1577 (1986).
[CrossRef]

Martin, O. J. F.

O. J. F. Martin, C. Girard, A. Dereux, Phys. Rev. Lett. 74, 526 ( 1995).
[CrossRef] [PubMed]

Novotny, L.

Ohsawa, H.

H. Hori, S. Jiang, M. Ohtsu, H. Ohsawain Technical Digest of the 18th International Quantum Electronics Conference (1992), p. 48.

Ohtsu, M.

H. Hori, S. Jiang, M. Ohtsu, H. Ohsawain Technical Digest of the 18th International Quantum Electronics Conference (1992), p. 48.

T. Saiki, M. Ohtsu, K. Jang, W. Jhe, “Direct observation of size-dependent features of the optical near field on a subwavelength spherical surface,” submitted to Opt. Lett.

Paesler, M. A.

Pohl, D. W.

Regli, P.

Saiki, T.

T. Saiki, M. Ohtsu, K. Jang, W. Jhe, “Direct observation of size-dependent features of the optical near field on a subwavelength spherical surface,” submitted to Opt. Lett.

Trautman, J. K.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, R. L. KostelakScience 251,1468 ( 1991;E. Betzig, J. K. TrautmanScience 257,189 (1992).
[CrossRef] [PubMed]

Vigoureux, J. M.

Wang, D. S.

Weiner, J. S.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, R. L. KostelakScience 251,1468 ( 1991;E. Betzig, J. K. TrautmanScience 257,189 (1992).
[CrossRef] [PubMed]

Wolf, E.

M. Born, E. WolfPrinciples of Optics, 5th ed. (Pergamon, London, 1975).

Appl. Opt.

J. Appl. Phys.

Y. LeviatanJ. Appl. Phys. 60,1577 (1986).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Phys. Rev. Lett.

O. J. F. Martin, C. Girard, A. Dereux, Phys. Rev. Lett. 74, 526 ( 1995).
[CrossRef] [PubMed]

Science

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, R. L. KostelakScience 251,1468 ( 1991;E. Betzig, J. K. TrautmanScience 257,189 (1992).
[CrossRef] [PubMed]

Technical Digest of the 18th International Quantum Electronics Conference

H. Hori, S. Jiang, M. Ohtsu, H. Ohsawain Technical Digest of the 18th International Quantum Electronics Conference (1992), p. 48.

Other

See, for example, D. W. Pohl, D. Courjon, eds., Near Field Optics (Kluwer, Dordrecht, The Netherlands, 1993).

M. Born, E. WolfPrinciples of Optics, 5th ed. (Pergamon, London, 1975).

J. D. JacksonClassical Electrodynamics, 2nd ed. (Wiley, New York, 1975), Chaps. 9 and 16.

T. Saiki, M. Ohtsu, K. Jang, W. Jhe, “Direct observation of size-dependent features of the optical near field on a subwavelength spherical surface,” submitted to Opt. Lett.

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Figures (3)

Fig. 1
Fig. 1

Plot of the diffracted field intensity versus distance D, with fixed sphere radius a and aperture radius b (ka = kb = 0.5). The characteristic decay length is found to be ~a, independently of the wavelength of the illuminating light under the condition of total internal reflection (p polarization is assumed). Inset: A simple sketch of the system modeled.

Fig. 2
Fig. 2

Diffracted field intensity as a function of a (i.e., transfer function of the NSOM) for a given b (kb = 0.5) when Da is fixed (kDka = 0.25). The detected intensity is expected to be resonantly enhanced when a is approximately equal to b.

Fig. 3
Fig. 3

Calculated NSOM image of a small dielectric sphere obtained by lateral scanning of the aperture at a constant height above the prism. The sphere is placed upon the xy plane (prism) and irradiated by p-polarized light under the condition of total internal reflection, with the relevant parameters given by ka = 0.5, kb = 0.5, and kDka = 0.25. The image is in good agreement with the recent experimental observation.7

Equations (3)

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ψ ( r , t ) = 1 4 π s exp i ( k R ω t ) R n ^ [ ψ ( r ) + i k ( 1 + i k R ) R ^ ψ ( r ) ] d α ,
E sc = E 0 l , m { i k b l α E ( l , m ) × [ h l ( 1 ) ( k r ) Y l l m ( r ^ ) ] + α l α M ( l , m ) [ h l ( 1 ) ( k r ) Y l l m ( r ^ ) ] }
ψ D = ψ 0 exp ( i k R ) 4 R i k a cos θ ln | [ 1 sin tan 1 ( a / D ) 1 + sin tan 1 ( a / D ) ] × [ 1 + sin tan 1 ( a / D 2 + b 2 ) 1 sin tan 1 ( a / D 2 + b 2 ) ] | ,

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