Abstract

We present a measurement of the intensity around the focus of a N.A.-0.95 lens using a tapered optical fiber probe. An asymmetry introduced by the vector nature of the incident polarized light is evident, although it is inconsistent with that predicted theoretically by considering the magnitude squared of the electric field. The sensitivity of the probe to different components of the electromagnetic field is considered, and it is shown that the measurement is consistent with vector diffraction theory when the probe properties are taken into account.

© 2002 Optical Society of America

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  1. S. K. Rhodes, A. Barty, A. Roberts, K. A. Nugent, “Sub-wavelength characterisation of optical focal structures,” Opt. Commun. 145, 9–14 (1998).
    [CrossRef]
  2. E. Betzig, M. Isaacson, A. Lewis, “Collection mode near-field scanning optical microscopy,” Appl. Phys. Lett. 51, 2088–2090 (1987).
    [CrossRef]
  3. M. Gu, D. Day, “Use of two-photon excitation for erasable-rewritable three-dimensional bit optical data storage in a photorefractive polymer,” Opt. Lett. 24, 288–290 (1999).
    [CrossRef]
  4. G. P. Karman, A. van Duijl, M. W. Beijersbergen, J. P. Woerdman, “Measurement of the three-dimensional intensity distribution in the neighborhood of a paraxial focus,” Appl. Opt. 36, 8091–8095 (1997).
    [CrossRef]
  5. M. Müller, A. H. Buist, G. J. Brakenhoff, J. Squier, “Method for complex focal field measurement of a high-numerical-aperture lens under cw pulsed conditions,” Opt. Commun. 138, 16–20 (1997).
    [CrossRef]
  6. Y. Li, H. Platzer, “An experimental investigation of diffraction patterns in low-Fresnel-number focusing systems,” Opt. Acta 30, 1621–1643 (1983).
    [CrossRef]
  7. R. Juškaitis, T. Wilson, “The measurement of the amplitude point spread function of microscope objective lenses,” J. Microsc. (Oxford) 189, 9–11 (1997).
  8. R. Wilson, R. Juškaitis, P. Higdon, “The imaging of di-electric point scatterers in conventional and confocal polarization microscopes,” Opt. Commun. 141, 298–313 (1997).
    [CrossRef]
  9. A. I. Carswell, “Measurements of the longitudinal component of the electromagnetic field at the focus of a coherent beam,” Phys. Rev. Lett. 15, 647–649 (1965).
    [CrossRef]
  10. R. Oron, J. L. Guedalia, N. Davidson, A. A. Friesem, E. Hasman, “Anomaly in a high-numerical-aperture diffractive focusing lens,” Opt. Lett. 25, 439–441 (2000).
    [CrossRef]
  11. H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
    [CrossRef]
  12. E. Betzig, R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262, 1422–1428 (1993).
    [CrossRef] [PubMed]
  13. J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, N. F. van Hulst, “Single molecule mapping of the optical field distribution of probes for near-field microscopy,” J. Microsc. (Oxford) 194, 477–482 (1999).
    [CrossRef]
  14. B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
    [CrossRef]
  15. M. Mansuripur, “Distribution of light at and near the focus of high-numerical aperture objectives,” J. Opt. Soc. Am. A 3, 2086–2093 (1986).
    [CrossRef]
  16. M. Mansuripur, “Distribution of light at and near the focus of high-numerical-aperture objectives: erratum,” J. Opt. Soc. Am. A 10, 382–383 (1993).
    [CrossRef]
  17. R. Kant, “An analytical solution of vector diffraction for focusing optical systems,” J. Mod. Opt. 40, 337–347 (1993).
    [CrossRef]
  18. R. Kant, “An analytical solution of vector diffraction for focusing optical systems with Seidel aberrations. I. Spherical aberration, curvature of field, and distortion,” J. Mod. Opt. 40, 2293–2310 (1993).
    [CrossRef]
  19. S. K. Rhodes, “High-resolution studies of electromagnetic fields in focal regions,” Ph.D. thesis (University of Melbourne, Melbourne, Australia, 2001).
  20. J. A. Veerman, A. M. Otter, L. Kuipers, N. F. van Hulst, “High definition aperture probes for near-field optical microscopy fabricated by focused ion beam milling,” Appl. Phys. Lett. 72, 3115–3117 (1998).
    [CrossRef]

2000 (1)

1999 (2)

J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, N. F. van Hulst, “Single molecule mapping of the optical field distribution of probes for near-field microscopy,” J. Microsc. (Oxford) 194, 477–482 (1999).
[CrossRef]

M. Gu, D. Day, “Use of two-photon excitation for erasable-rewritable three-dimensional bit optical data storage in a photorefractive polymer,” Opt. Lett. 24, 288–290 (1999).
[CrossRef]

1998 (2)

J. A. Veerman, A. M. Otter, L. Kuipers, N. F. van Hulst, “High definition aperture probes for near-field optical microscopy fabricated by focused ion beam milling,” Appl. Phys. Lett. 72, 3115–3117 (1998).
[CrossRef]

S. K. Rhodes, A. Barty, A. Roberts, K. A. Nugent, “Sub-wavelength characterisation of optical focal structures,” Opt. Commun. 145, 9–14 (1998).
[CrossRef]

1997 (4)

M. Müller, A. H. Buist, G. J. Brakenhoff, J. Squier, “Method for complex focal field measurement of a high-numerical-aperture lens under cw pulsed conditions,” Opt. Commun. 138, 16–20 (1997).
[CrossRef]

R. Juškaitis, T. Wilson, “The measurement of the amplitude point spread function of microscope objective lenses,” J. Microsc. (Oxford) 189, 9–11 (1997).

R. Wilson, R. Juškaitis, P. Higdon, “The imaging of di-electric point scatterers in conventional and confocal polarization microscopes,” Opt. Commun. 141, 298–313 (1997).
[CrossRef]

G. P. Karman, A. van Duijl, M. W. Beijersbergen, J. P. Woerdman, “Measurement of the three-dimensional intensity distribution in the neighborhood of a paraxial focus,” Appl. Opt. 36, 8091–8095 (1997).
[CrossRef]

1993 (4)

M. Mansuripur, “Distribution of light at and near the focus of high-numerical-aperture objectives: erratum,” J. Opt. Soc. Am. A 10, 382–383 (1993).
[CrossRef]

E. Betzig, R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262, 1422–1428 (1993).
[CrossRef] [PubMed]

R. Kant, “An analytical solution of vector diffraction for focusing optical systems,” J. Mod. Opt. 40, 337–347 (1993).
[CrossRef]

R. Kant, “An analytical solution of vector diffraction for focusing optical systems with Seidel aberrations. I. Spherical aberration, curvature of field, and distortion,” J. Mod. Opt. 40, 2293–2310 (1993).
[CrossRef]

1987 (1)

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

1986 (1)

1983 (1)

Y. Li, H. Platzer, “An experimental investigation of diffraction patterns in low-Fresnel-number focusing systems,” Opt. Acta 30, 1621–1643 (1983).
[CrossRef]

1965 (1)

A. I. Carswell, “Measurements of the longitudinal component of the electromagnetic field at the focus of a coherent beam,” Phys. Rev. Lett. 15, 647–649 (1965).
[CrossRef]

1959 (1)

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

1944 (1)

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
[CrossRef]

Barty, A.

S. K. Rhodes, A. Barty, A. Roberts, K. A. Nugent, “Sub-wavelength characterisation of optical focal structures,” Opt. Commun. 145, 9–14 (1998).
[CrossRef]

Beijersbergen, M. W.

Bethe, H. A.

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
[CrossRef]

Betzig, E.

E. Betzig, R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262, 1422–1428 (1993).
[CrossRef] [PubMed]

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

Brakenhoff, G. J.

M. Müller, A. H. Buist, G. J. Brakenhoff, J. Squier, “Method for complex focal field measurement of a high-numerical-aperture lens under cw pulsed conditions,” Opt. Commun. 138, 16–20 (1997).
[CrossRef]

Buist, A. H.

M. Müller, A. H. Buist, G. J. Brakenhoff, J. Squier, “Method for complex focal field measurement of a high-numerical-aperture lens under cw pulsed conditions,” Opt. Commun. 138, 16–20 (1997).
[CrossRef]

Carswell, A. I.

A. I. Carswell, “Measurements of the longitudinal component of the electromagnetic field at the focus of a coherent beam,” Phys. Rev. Lett. 15, 647–649 (1965).
[CrossRef]

Chichester, R. J.

E. Betzig, R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262, 1422–1428 (1993).
[CrossRef] [PubMed]

Davidson, N.

Day, D.

Friesem, A. A.

Garcia-Parajo, M. F.

J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, N. F. van Hulst, “Single molecule mapping of the optical field distribution of probes for near-field microscopy,” J. Microsc. (Oxford) 194, 477–482 (1999).
[CrossRef]

Gu, M.

Guedalia, J. L.

Hasman, E.

Higdon, P.

R. Wilson, R. Juškaitis, P. Higdon, “The imaging of di-electric point scatterers in conventional and confocal polarization microscopes,” Opt. Commun. 141, 298–313 (1997).
[CrossRef]

Isaacson, M.

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

Juškaitis, R.

R. Wilson, R. Juškaitis, P. Higdon, “The imaging of di-electric point scatterers in conventional and confocal polarization microscopes,” Opt. Commun. 141, 298–313 (1997).
[CrossRef]

R. Juškaitis, T. Wilson, “The measurement of the amplitude point spread function of microscope objective lenses,” J. Microsc. (Oxford) 189, 9–11 (1997).

Kant, R.

R. Kant, “An analytical solution of vector diffraction for focusing optical systems,” J. Mod. Opt. 40, 337–347 (1993).
[CrossRef]

R. Kant, “An analytical solution of vector diffraction for focusing optical systems with Seidel aberrations. I. Spherical aberration, curvature of field, and distortion,” J. Mod. Opt. 40, 2293–2310 (1993).
[CrossRef]

Karman, G. P.

Kuipers, L.

J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, N. F. van Hulst, “Single molecule mapping of the optical field distribution of probes for near-field microscopy,” J. Microsc. (Oxford) 194, 477–482 (1999).
[CrossRef]

J. A. Veerman, A. M. Otter, L. Kuipers, N. F. van Hulst, “High definition aperture probes for near-field optical microscopy fabricated by focused ion beam milling,” Appl. Phys. Lett. 72, 3115–3117 (1998).
[CrossRef]

Lewis, A.

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

Li, Y.

Y. Li, H. Platzer, “An experimental investigation of diffraction patterns in low-Fresnel-number focusing systems,” Opt. Acta 30, 1621–1643 (1983).
[CrossRef]

Mansuripur, M.

Müller, M.

M. Müller, A. H. Buist, G. J. Brakenhoff, J. Squier, “Method for complex focal field measurement of a high-numerical-aperture lens under cw pulsed conditions,” Opt. Commun. 138, 16–20 (1997).
[CrossRef]

Nugent, K. A.

S. K. Rhodes, A. Barty, A. Roberts, K. A. Nugent, “Sub-wavelength characterisation of optical focal structures,” Opt. Commun. 145, 9–14 (1998).
[CrossRef]

Oron, R.

Otter, A. M.

J. A. Veerman, A. M. Otter, L. Kuipers, N. F. van Hulst, “High definition aperture probes for near-field optical microscopy fabricated by focused ion beam milling,” Appl. Phys. Lett. 72, 3115–3117 (1998).
[CrossRef]

Platzer, H.

Y. Li, H. Platzer, “An experimental investigation of diffraction patterns in low-Fresnel-number focusing systems,” Opt. Acta 30, 1621–1643 (1983).
[CrossRef]

Rhodes, S. K.

S. K. Rhodes, A. Barty, A. Roberts, K. A. Nugent, “Sub-wavelength characterisation of optical focal structures,” Opt. Commun. 145, 9–14 (1998).
[CrossRef]

S. K. Rhodes, “High-resolution studies of electromagnetic fields in focal regions,” Ph.D. thesis (University of Melbourne, Melbourne, Australia, 2001).

Richards, B.

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Roberts, A.

S. K. Rhodes, A. Barty, A. Roberts, K. A. Nugent, “Sub-wavelength characterisation of optical focal structures,” Opt. Commun. 145, 9–14 (1998).
[CrossRef]

Squier, J.

M. Müller, A. H. Buist, G. J. Brakenhoff, J. Squier, “Method for complex focal field measurement of a high-numerical-aperture lens under cw pulsed conditions,” Opt. Commun. 138, 16–20 (1997).
[CrossRef]

van Duijl, A.

van Hulst, N. F.

J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, N. F. van Hulst, “Single molecule mapping of the optical field distribution of probes for near-field microscopy,” J. Microsc. (Oxford) 194, 477–482 (1999).
[CrossRef]

J. A. Veerman, A. M. Otter, L. Kuipers, N. F. van Hulst, “High definition aperture probes for near-field optical microscopy fabricated by focused ion beam milling,” Appl. Phys. Lett. 72, 3115–3117 (1998).
[CrossRef]

Veerman, J. A.

J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, N. F. van Hulst, “Single molecule mapping of the optical field distribution of probes for near-field microscopy,” J. Microsc. (Oxford) 194, 477–482 (1999).
[CrossRef]

J. A. Veerman, A. M. Otter, L. Kuipers, N. F. van Hulst, “High definition aperture probes for near-field optical microscopy fabricated by focused ion beam milling,” Appl. Phys. Lett. 72, 3115–3117 (1998).
[CrossRef]

Wilson, R.

R. Wilson, R. Juškaitis, P. Higdon, “The imaging of di-electric point scatterers in conventional and confocal polarization microscopes,” Opt. Commun. 141, 298–313 (1997).
[CrossRef]

Wilson, T.

R. Juškaitis, T. Wilson, “The measurement of the amplitude point spread function of microscope objective lenses,” J. Microsc. (Oxford) 189, 9–11 (1997).

Woerdman, J. P.

Wolf, E.

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

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

J. A. Veerman, A. M. Otter, L. Kuipers, N. F. van Hulst, “High definition aperture probes for near-field optical microscopy fabricated by focused ion beam milling,” Appl. Phys. Lett. 72, 3115–3117 (1998).
[CrossRef]

J. Microsc. (Oxford) (2)

J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, N. F. van Hulst, “Single molecule mapping of the optical field distribution of probes for near-field microscopy,” J. Microsc. (Oxford) 194, 477–482 (1999).
[CrossRef]

R. Juškaitis, T. Wilson, “The measurement of the amplitude point spread function of microscope objective lenses,” J. Microsc. (Oxford) 189, 9–11 (1997).

J. Mod. Opt. (2)

R. Kant, “An analytical solution of vector diffraction for focusing optical systems,” J. Mod. Opt. 40, 337–347 (1993).
[CrossRef]

R. Kant, “An analytical solution of vector diffraction for focusing optical systems with Seidel aberrations. I. Spherical aberration, curvature of field, and distortion,” J. Mod. Opt. 40, 2293–2310 (1993).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Acta (1)

Y. Li, H. Platzer, “An experimental investigation of diffraction patterns in low-Fresnel-number focusing systems,” Opt. Acta 30, 1621–1643 (1983).
[CrossRef]

Opt. Commun. (3)

S. K. Rhodes, A. Barty, A. Roberts, K. A. Nugent, “Sub-wavelength characterisation of optical focal structures,” Opt. Commun. 145, 9–14 (1998).
[CrossRef]

M. Müller, A. H. Buist, G. J. Brakenhoff, J. Squier, “Method for complex focal field measurement of a high-numerical-aperture lens under cw pulsed conditions,” Opt. Commun. 138, 16–20 (1997).
[CrossRef]

R. Wilson, R. Juškaitis, P. Higdon, “The imaging of di-electric point scatterers in conventional and confocal polarization microscopes,” Opt. Commun. 141, 298–313 (1997).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (1)

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
[CrossRef]

Phys. Rev. Lett. (1)

A. I. Carswell, “Measurements of the longitudinal component of the electromagnetic field at the focus of a coherent beam,” Phys. Rev. Lett. 15, 647–649 (1965).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Science (1)

E. Betzig, R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262, 1422–1428 (1993).
[CrossRef] [PubMed]

Other (1)

S. K. Rhodes, “High-resolution studies of electromagnetic fields in focal regions,” Ph.D. thesis (University of Melbourne, Melbourne, Australia, 2001).

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Figures (3)

Fig. 1
Fig. 1

Apparatus used for mapping focal structures. The He–Ne laser source passes through a spatial filter before illuminating the lens under investigation. The intensity is mapped by the tapered fiber probe being scanned through the focal region. The light coupled into the probe is amplified and read into the computer, which simultaneously controls the positioning of the probe through the stepper motor and the piezoelectric tube. The axis convention shown is maintained for all figures shown in this paper.

Fig. 2
Fig. 2

Experimentally acquired meridional plane contour plots of the focal distribution of a 0.95-N.A. microscope objective in (a) the plane parallel to the incident polarization vector (the xz plane) and (b) the orthogonal plane (the yz plane). Contours have been selected to maximize the visibility of subsidiary maxima.

Fig. 3
Fig. 3

Computed detected signal assuming the Bethe small-hole model for coupling through the probe aperture. The two figures correspond to the experimentally determined plots in Fig. 2; the contours selected are the same.

Equations (16)

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S=c27π2k2R6(4H02+E02),
e(r)=-ik2πΩa(σx, σy)σz×exp(ik[Φ(σx, σy)+σ·r])dσxdσy,
ax=fσzσz+σy2σx2+σy2(1-σz),
ay=fσzσxσyσx2+σy2(σz-1),
ay=-fσzσx,
Φ(ρ, ϕ)=lmnAlmnρn cosm ϕ,
ex=-ikf2πF1σzσz+σy2σx2+σy2(1-σz)×exp{ik[Φ(σx, σy)+σzz]},
ey=-ikf2πF(σz-1)σzσxσyσx2+σy2×exp{ik[Φ(σx, σy)+σzz]},
ez=-ikf2πF-σxσzexp{ik[Φ(σx, σy)+σzz]},
ex=-i[I0+I2 cos (2ϕP)],
ey=-iI2 sin (2ϕP),
ez=-2I2 cos (ϕP),
I0=2s=0as0isCs1/2(cos θP)js(krP),
I1=2 sin θPs=0as1isCs3/2(cos θP)js+1(krP),
I3=2 sin2 θPs=0as2isCs5/2(cos θP)js+2(krP),
S=|hx|2+|hy|2+|ez|24.

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