Abstract

A method of finding the three-dimensional distribution of light in the focal region of small-fnumber lenses that have arbitrary surface curvatures is described. The Fresnel approximation is not used, and the effects of aberration are included. A comparison of the numerical results with experimental measurements for a commercially obtained plano–convex lens is provided.

© 2000 Optical Society of America

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References

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  1. A. Boivin and E. Wolf, Phys. Rev. B 138, 1561 (1965).
    [Crossref]
  2. C. J. R. Sheppard and H. J. Matthews, J. Opt. Soc. Am. A 4, 1354 (1987).
    [Crossref]
  3. J. W. Goodman, Introduction to Fourier Optics (McGraw Hill, New York, 1996).
  4. S. Chi and C. Guo, Opt. Lett. 20, 1598 (1995).
    [Crossref] [PubMed]
  5. A. Nussbaum, Optical System Design (Prentice-Hall, Englewood Cliffs, N.J., 1998), p. 58.

1995 (1)

1987 (1)

1965 (1)

A. Boivin and E. Wolf, Phys. Rev. B 138, 1561 (1965).
[Crossref]

Boivin, A.

A. Boivin and E. Wolf, Phys. Rev. B 138, 1561 (1965).
[Crossref]

Chi, S.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw Hill, New York, 1996).

Guo, C.

Matthews, H. J.

Nussbaum, A.

A. Nussbaum, Optical System Design (Prentice-Hall, Englewood Cliffs, N.J., 1998), p. 58.

Sheppard, C. J. R.

Wolf, E.

A. Boivin and E. Wolf, Phys. Rev. B 138, 1561 (1965).
[Crossref]

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

Opt. Lett. (1)

Phys. Rev. B (1)

A. Boivin and E. Wolf, Phys. Rev. B 138, 1561 (1965).
[Crossref]

Other (2)

A. Nussbaum, Optical System Design (Prentice-Hall, Englewood Cliffs, N.J., 1998), p. 58.

J. W. Goodman, Introduction to Fourier Optics (McGraw Hill, New York, 1996).

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Figures (4)

Fig. 1
Fig. 1

Top, ray propagation geometry through a thick lens; lower left, angles of incidence and refraction at the first surface; lower right, angles of incidence and refraction at the second surface.

Fig. 2
Fig. 2

Normalized intensity of the wave front as a function of the ray height in plane P2.

Fig. 3
Fig. 3

Left, on-axis intensity distribution as a function of the distance from plane P2: Solid curve, theory; filled circles, experiment. Right, same at left but displayed with logarithmic ordinates.

Fig. 4
Fig. 4

Transverse profile of the beam measured at the focus and at two points, 2 mm before and after the focus.

Equations (14)

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θ1=tan-11/df1r/dr,
θi1r=π/2-θ1r
θr1r=sin-11ncostan-11df1r/dr.
f1r1+d2 cosθi1r1-θr1r1=T-f2r2,
d2 sinθi1r1-θr1r1=r1-r2.
θ2=tan-11/df2r/dr,
θi2r=π/2-θ2r+θi1-θr1,
θr2r=sin-1n sin θi2.
θ3=θr2-π/2-θ2,
d3=f2r2/cos θ3,
r3=r2-f2r2tan θ3.
ϕr1=2πλf1r1+nd2+d3.
U2x2,y2=ziλU1x1,y1expikρρ2dx1dy1,
ρ=z2+x1-x22+y1-y221/2.

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