Abstract

Optical fields with scale- and shape-invariant transverse intensity profiles consisting of a prescribed distribution of bright spots are introduced. Approximations of such fields are demonstrated by means of binary annular-aperture diffractive elements.

© 1998 Optical Society of America

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References

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  1. J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
    [CrossRef]
  2. J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  3. J. Turunen, A. Vasara, and A. T. Friberg, J. Opt. Soc. Am. A 8, 282 (1991).
    [CrossRef]
  4. J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Wiley-VCH, Berlin, 1997), Sec. 1.3.6 and Chap. 6.
  5. S. A. Collins, J. Opt. Soc. Am. 60, 1168 (1970).

1991

1987

J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

1970

Collins, S. A.

Durnin, J.

J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Friberg, A. T.

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Turunen, J.

Vasara, A.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Phys. Rev. Lett.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Other

J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Wiley-VCH, Berlin, 1997), Sec. 1.3.6 and Chap. 6.

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Figures (4)

Fig. 1
Fig. 1

Basic arrangement for the generation of propagation-invariant spot arrays: DE, diffractive element with a thin annular aperture; L, collimating lens.

Fig. 2
Fig. 2

(a) Amplitude and (b) phase of the angular spectrum of a double-Bessel field with a1=a2.

Fig. 3
Fig. 3

Evolution of the intensity profile of the double-Bessel field behind lens L.

Fig. 4
Fig. 4

Experimental results: transverse intensity distributions and cross sections (at x=0) of the double-Bessel field at (a) z=20 mm and (b) z=120 mm.

Equations (7)

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Ux,y,z=expiβz02πAϕ×expiαx cos ϕ+y sin ϕdϕ,
AϕAϕexp-iαΔx cos ϕ+Δy sin ϕ.
Ux,y,z=2π expiβzm=1MamJ0αx-Δxm2+y-Δym21/2,
αΔxm-Δxn2+Δym-Δyn21/2x0,
Aϕ=m=1Mam exp-iαΔxm cos ϕ+Δym sin ϕ,
S=I1+I2=8π2a21+J022αΔx+2J02αΔxcosΔφ,
Ux,y,z=expikf+ziλf×R-w/2R+w/2r expikf-zr2/2f2×02πAϕexp-ikrx cos ϕ+y sin ϕ/fdϕdr.

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