Abstract

We present a design of the diffractive phase elements (DPE’s) that produce nondiffracting beams according to the beam-shaping scheme, in which the incident Gaussian-profile beam is converted into a Bessel-function J0 beam. An optimization method is applied to solving this special beam-shaping problem. Numerical investigation of the generating J0 Bessel beam shows that the designed DPE can satisfactorily produce the J0 Bessel beam.

© 1998 Optical Society of America

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References

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  1. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
    [CrossRef]
  2. J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [CrossRef] [PubMed]
  3. J. Turunen, A. Vasara, A. T. Friberg, “Holographic generation of diffraction-free beams,” Appl. Opt. 27, 3959–3962 (1988).
    [CrossRef] [PubMed]
  4. G. Indebetouw, “Nondiffracting optical fields: some remarks on their analysis and synthesis,” J. Opt. Soc. Am. A 6, 150–152 (1989).
    [CrossRef]
  5. R. M. Herman, T. A. Wiggins, “Production and uses of diffractionless beams,” J. Opt. Soc. Am. A 8, 932–942 (1991).
    [CrossRef]
  6. A. J. Cox, D. C. Dibble, “Holographic reproduction of a diffraction-free beam,” Appl. Opt. 30, 1330–1332 (1991).
    [CrossRef] [PubMed]
  7. N. Davidson, A. A. Friesem, E. Hasman, “Efficient formation of nondiffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
    [CrossRef]
  8. R. M. Herman, T. A. Wiggins, “Apodization of diffractionless beams,” Appl. Opt. 31, 5913–5915 (1992).
    [CrossRef] [PubMed]
  9. A. Vasara, J. Turunen, A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748–1754 (1989).
    [CrossRef] [PubMed]
  10. A. J. Cox, D. C. Dibble, “Nondiffracting beam from a spatially filtered Fabry–Perot resonator,” J. Opt. Soc. Am. A 9, 282–286 (1992).
    [CrossRef]
  11. K. Thewes, M. A. Karim, A. A. S. Awwal, “Diffraction-free beam generation using refracting systems,” Opt. Laser Technol. 23, 105–108 (1991).
    [CrossRef]
  12. K. M. Iftekharuddin, A. A. S. Awwal, M. K. Karim, “Gaussian-to-Bessel beam transformation using a split refracting system,” Appl. Opt. 32, 2252–2256 (1992).
    [CrossRef]
  13. Y. Lin, W. Seka, J. H. Eberly, H. Huang, D. L. Brown, “Experimental investigation of Bessel beam characteristics,” Appl. Opt. 31, 2708–2713 (1992).
    [CrossRef] [PubMed]
  14. H. Bartelt, “Computer-generated holographic component with optimum light efficiency,” Appl. Opt. 23, 1499–1502 (1984).
    [CrossRef] [PubMed]
  15. H. Bartelt, “Applications of the tandem component: an element with optimum light efficiency,” Appl. Opt. 24, 3811–3816 (1985).
    [CrossRef] [PubMed]
  16. R. Fletcher, Practical Methods of Optimization (Wiley, New York, 1980), pp. 33–62.

1992 (5)

1991 (3)

1989 (2)

1988 (1)

1987 (2)

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[CrossRef]

1985 (1)

1984 (1)

Awwal, A. A. S.

K. M. Iftekharuddin, A. A. S. Awwal, M. K. Karim, “Gaussian-to-Bessel beam transformation using a split refracting system,” Appl. Opt. 32, 2252–2256 (1992).
[CrossRef]

K. Thewes, M. A. Karim, A. A. S. Awwal, “Diffraction-free beam generation using refracting systems,” Opt. Laser Technol. 23, 105–108 (1991).
[CrossRef]

Bartelt, H.

Brown, D. L.

Cox, A. J.

Davidson, N.

N. Davidson, A. A. Friesem, E. Hasman, “Efficient formation of nondiffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
[CrossRef]

Dibble, D. C.

Durnin, J.

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

Fletcher, R.

R. Fletcher, Practical Methods of Optimization (Wiley, New York, 1980), pp. 33–62.

Friberg, A. T.

Friesem, A. A.

N. Davidson, A. A. Friesem, E. Hasman, “Efficient formation of nondiffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
[CrossRef]

Hasman, E.

N. Davidson, A. A. Friesem, E. Hasman, “Efficient formation of nondiffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
[CrossRef]

Herman, R. M.

Huang, H.

Iftekharuddin, K. M.

Indebetouw, G.

Karim, M. A.

K. Thewes, M. A. Karim, A. A. S. Awwal, “Diffraction-free beam generation using refracting systems,” Opt. Laser Technol. 23, 105–108 (1991).
[CrossRef]

Karim, M. K.

Lin, Y.

Miceli, J. J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Seka, W.

Thewes, K.

K. Thewes, M. A. Karim, A. A. S. Awwal, “Diffraction-free beam generation using refracting systems,” Opt. Laser Technol. 23, 105–108 (1991).
[CrossRef]

Turunen, J.

Vasara, A.

Wiggins, T. A.

Appl. Opt. (7)

J. Opt. Soc. Am. A (5)

Opt. Commun. (1)

N. Davidson, A. A. Friesem, E. Hasman, “Efficient formation of nondiffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
[CrossRef]

Opt. Laser Technol. (1)

K. Thewes, M. A. Karim, A. A. S. Awwal, “Diffraction-free beam generation using refracting systems,” Opt. Laser Technol. 23, 105–108 (1991).
[CrossRef]

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Other (1)

R. Fletcher, Practical Methods of Optimization (Wiley, New York, 1980), pp. 33–62.

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Figures (3)

Fig. 1
Fig. 1

Schematic representation of a diffractive optical system for producing a nondiffracting beam.

Fig. 2
Fig. 2

Phase distribution of the designed DPE1 for generating a J0 beam.

Fig. 3
Fig. 3

Radial intensity of the generating J0 beam on the output plane. Solid curve, radial intensity distribution of the ideal J0 beam; circles, calculated value for the J0 beam generated by the designed DPE1.

Equations (13)

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B(ρ, z)=exp(iβz)J0(αρ),
exp(iβl)J0(αρ)=exp[-iψ(ρ)]×0RG(r, ρ)u(r)exp[iϕ(r)]dr,
G(r, ρ)=2πiλlexpi2πlλexpiπ(r2+ρ2)λlJ02πrρλlr,
Bn exp(iψn)=m=1MGmnum exp(iϕm)
forn=1, 2, , N.
min D(Φ1)=n=1Nm=1MGmnum exp(iϕm)-B˜n2,
D(Φ1)ϕm=ium exp(-iϕm)n=1NGmn*(B˜n-Bn)×exp(iψn)+c.c.form=1, 2,, M,
grad(k)=D(Φ1(k))ϕ1(k), D(Φ1(k))ϕ2(k),, D(Φ1(k))ϕM(k);
D(Φ1(k+1))=min D(Φ1(k)+λp(k)).
H(k+1)=H(k)+1+WT·H(k)·WΔqT·W Δq·ΔqTΔqT·W-Δq·WT·H(k)ΔqT·W-H(k)·W·ΔqTΔqT·W,
wm=D(Φ1(k+1))ϕm(k+1)-D(Φ1(k))ϕm(k),form=1, 2,, M,
Δq=Φ1(k+1)-Φ1(k).
MSE=D(Φ1(k+1))mum2<,

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