Abstract

Focusing light through an interface leads to an aberrated intensity distribution that is highly extended with a relatively low peak intensity. We present a method, using a well-chosen annular aperture, that can greatly improve the localization of the intensity about a prescribed point on the axis. Also, the intensity at that point can be increased significantly. By continuously varying the annulus radii, we can scan the intensity peak through the second medium. This localization and scanning method has possible applications in three-dimensional imaging and lithography.

© 1998 Optical Society of America

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References

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  1. P. Török, P. Varga, Z. Laczik, and G. R. Booker, J. Opt. Soc. Am. A 12, 325 (1995).
    [CrossRef]
  2. S. H. Wiersma and T. D. Visser, J. Opt. Soc. Am. A 13, 320 (1996).
    [CrossRef]
  3. S. H. Wiersma, P. Török, T. D. Visser, and P. Varga, J. Opt. Soc. Am. A 14, 1482 (1997).
    [CrossRef]
  4. V. Dhayalan, “Focusing on Electromagnetic waves,” Ph.D. dissertation (University of Bergen, Bergen, Norway, 1996).
  5. M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, Cambridge, 1997).

1997 (1)

1996 (1)

1995 (1)

J. Opt. Soc. Am. A (3)

Other (2)

V. Dhayalan, “Focusing on Electromagnetic waves,” Ph.D. dissertation (University of Bergen, Bergen, Norway, 1996).

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, Cambridge, 1997).

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Figures (4)

Fig. 1
Fig. 1

Intensity distribution (in arbitrary units) along the z axis (in micrometers) for an unobscured lens with a semiaperture angle Ω1=45° and a focal length of 10-2 m. The lens is positioned in air (n1=1). The interface with the second medium n2=1.51 is located 300  µm in front of the focus of the lens. The wavelength in air is λ0=632.8 nm.

Fig. 2
Fig. 2

Intensity Iz=-203 µm as a function of θlow and θhigh. All other parameters are as in Fig.  1.

Fig. 3
Fig. 3

Intensity distribution along the z axis (in micrometers) for an optimized annular aperture with 28.04°<θ1<36.71°. All other parameters and the normalization are as in Fig.  1.

Fig. 4
Fig. 4

Stationary phase θstat (dashed curve) and the two interval limits θlow (lower curve) and θhigh (upper curve) that give optimal intensity as a function of axial position z (in micrometers). All parameters are as in Fig.  1.

Equations (5)

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Exz=Cz0Ω1expik2s-ik1tgθ1, zdθ1,
Cz=f2f-d2zf-d-1expik1f,
gθ1, z=1s3-ik2s2ηs+ηp cos θ2tan θ1.
tθ1=f-dcos θ1,
sθ1, z=t2+z2-2zf-d1/2.

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