Abstract

A novel method of designing the longitudinal intensity profile of a diffracted beam in free space is proposed. By use of this method illumination of an arbitrarily synthesized aperture can yield a desired intensity distribution, including a constant (nondiffracting) curve, along a chosen limited range.

© 1994 Optical Society of America

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References

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  1. J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
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    [CrossRef] [PubMed]
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  9. J. K. Jabczynski, Opt. Commun. 77, 292 (1990).
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  10. R. M. Herman, T. A. Wiggins, J. Opt. Soc. Am. A 8, 932 (1991).
    [CrossRef]
  11. A. J. Cox, D. C. Dibble, J. Opt. Soc. Am. A 9, 282 (1992).
    [CrossRef]
  12. J. W. Goodman, Introduction to Fourier Optics, 1st ed. (McGraw-Hill, New York, 1968), Chap. 3, p. 42.
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  15. B. Colombeau, C. Froehly, M. Vampouille, Opt. Commun. 28, 35 (1979).
    [CrossRef]

1993

1992

1991

1990

F. Bloisi, L. Vicari, Opt. Commun. 75, 353 (1990).
[CrossRef]

J. K. Jabczynski, Opt. Commun. 77, 292 (1990).
[CrossRef]

1989

1987

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

F. Gori, G. Guattari, C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

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

1979

B. Colombeau, C. Froehly, M. Vampouille, Opt. Commun. 28, 35 (1979).
[CrossRef]

Bloisi, F.

F. Bloisi, L. Vicari, Opt. Commun. 75, 353 (1990).
[CrossRef]

Colombeau, B.

B. Colombeau, C. Froehly, M. Vampouille, Opt. Commun. 28, 35 (1979).
[CrossRef]

Cox, A. J.

D’Anna, J.

Dibble, D. C.

Durnin, J.

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

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

Eberly, J. H.

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

Friberg, A. T.

Froehly, C.

B. Colombeau, C. Froehly, M. Vampouille, Opt. Commun. 28, 35 (1979).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 1st ed. (McGraw-Hill, New York, 1968), Chap. 3, p. 42.

Gori, F.

F. Gori, G. Guattari, C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Herman, R. M.

Indebetouw, G.

Jabczynski, J. K.

J. K. Jabczynski, Opt. Commun. 77, 292 (1990).
[CrossRef]

Kenney, C. S.

Miceli, J. J.

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

Overfelt, P. L.

Padovani, C.

F. Gori, G. Guattari, C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Rosen, J.

Turunen, J.

Vampouille, M.

B. Colombeau, C. Froehly, M. Vampouille, Opt. Commun. 28, 35 (1979).
[CrossRef]

Vasara, A.

Vicari, L.

F. Bloisi, L. Vicari, Opt. Commun. 75, 353 (1990).
[CrossRef]

Wiggins, T. A.

J. Opt. Soc. Am. A

Opt. Commun.

B. Colombeau, C. Froehly, M. Vampouille, Opt. Commun. 28, 35 (1979).
[CrossRef]

F. Gori, G. Guattari, C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

F. Bloisi, L. Vicari, Opt. Commun. 75, 353 (1990).
[CrossRef]

J. K. Jabczynski, Opt. Commun. 77, 292 (1990).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

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

Other

J. W. Goodman, Introduction to Fourier Optics, 1st ed. (McGraw-Hill, New York, 1968), Chap. 3, p. 42.

H. Stark, ed., Image Recovery Theory and Application, 1st ed. (Academic, New York, 1987), Chap. 8, p. 277.

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Figures (3)

Fig. 1
Fig. 1

Transverse intensity distribution of the beam obtained from (a)–(d) the EPOCS algorithm and (e)–(h) the Bessel beam J0(αr) at z = 0 [(a), (e)], z = 52 cm [(b), (f)], z = 104 cm (c), (g)], and z = 156 cm [(d), (h)].

Fig. 2
Fig. 2

Intensity distribution along the propagation axis of the beam obtained from (a) the EPOCS algorithm and (b) the Bessel aperture J0(αr).

Fig. 3
Fig. 3

Intensity distribution along the propagation axis of the beam diffracted from a phase-only aperture (solid curve) calculated by the EPOCS. The dotted curve is the requested profile I0(z), and the insets show the transverse cross sections of the intensity at three points along the z axis.

Equations (8)

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u ( z ) = 1 j λ 0 2 π 0 f ( r , θ ) h ( r , z ) r d r d θ ,
u ( ζ ) = ζ 2 j λ 0 2 π 0 f ( ρ , θ ) exp ( j k ρ + ζ ) ρ + ζ d ρ d θ ,
c ( ζ ) = 2 j λ u ( ζ ) ζ = - T ( v ) H * ( v ) exp ( j 2 π v ζ ) d v ,
t ( ρ ) = 0 2 π f ( ρ , θ ) d θ ,             h ( ρ ) = exp ( - j k ρ ) ρ .
P 2 [ c i ( ζ ) ] = { 2 λ [ I 0 ( ζ ) ζ ] 1 / 2 exp [ j Ψ i ( ζ ) ] ζ Δ ζ c i ( ζ ) otherwise ,
e i = 1 Δ ζ Δ ζ c i ( ζ ) - P 2 [ c i ( ζ ) ] 2 d ζ .
P 1 [ t i ( ρ ) ] = { J 0 ( α ρ ) 0 < ρ < w 0 s exp [ j ϕ i ( ρ ) ] t i ( ρ ) > s w 0 < ρ < r 0 t i ( ρ ) t i ( ρ ) s w 0 < ρ < r 0 0 ρ > r 0 .
P 1 [ t i ( ρ ) ] = { exp [ j ϕ i ( ρ ) ] ρ < r 0 0 otherwise ,

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