Abstract

In principle, diffractive elements can be designed to control a propagating wave in three dimensions, but no general procedure has been proposed. We present an iterative method that is suitable for the design of such diffractive elements. The resulting complex amplitude distribution will approach any arbitrary requirement, as much as is permitted by basic physical principles. The problem of “nondiffracting-beam” propagation is analyzed as a special case, and intensity peaks are generated that propagate as much as 4 m with a bounded width. The generality of the method, as compared with other techniques, is demonstrated by the design of an array of nondiffracting beams.

© 1994 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
    [CrossRef]
  2. D. C. Youla, H. Webb, IEEE Trans. Med. Imaging TMI-1, 81 (1982), and references therein.
    [CrossRef]
  3. P. Sprangle, B. Hafizi, Phys. Rev. Lett. 66, 873 (1991); J. Durnin, J. J. Miceli, J. H. Eberly, Phys. Rev. Lett. 66, 874 (1991).
    [CrossRef]
  4. J. Amako, H. Miura, T. Sonehara, Appl. Opt. 32, 4323 (1993).
    [CrossRef] [PubMed]
  5. H. Bartlet, Appl. Opt. 23, 1499 (1984).
    [CrossRef]
  6. J. Durnin, J. J. Miceli, J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  7. A. Vasara, J. Turunen, A. T. Friberg, J. Opt. Soc. Am. A 6, 150 (1989).
    [CrossRef]
  8. N. Davidson, A. A. Friesam, E. Hasman, Opt. Commun. 88, 326 (1992).
    [CrossRef]
  9. A. J. Cox, J. D’Anna, Opt. Lett. 17, 232 (1992).
    [CrossRef] [PubMed]
  10. J. A. Davis, J. Guertin, D. M. Cottrell, Appl. Opt. 32, 6368 (1993).
    [CrossRef] [PubMed]
  11. J. Rosen, Opt. Lett. 19, 369 (1994).
    [CrossRef] [PubMed]
  12. J. Rosen, A. Yariv, Opt. Lett. 19, 843 (1994).
    [CrossRef] [PubMed]

1994

1993

1992

A. J. Cox, J. D’Anna, Opt. Lett. 17, 232 (1992).
[CrossRef] [PubMed]

N. Davidson, A. A. Friesam, E. Hasman, Opt. Commun. 88, 326 (1992).
[CrossRef]

1991

P. Sprangle, B. Hafizi, Phys. Rev. Lett. 66, 873 (1991); J. Durnin, J. J. Miceli, J. H. Eberly, Phys. Rev. Lett. 66, 874 (1991).
[CrossRef]

1989

1987

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

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

1984

1982

D. C. Youla, H. Webb, IEEE Trans. Med. Imaging TMI-1, 81 (1982), and references therein.
[CrossRef]

Amako, J.

Bartlet, H.

Cottrell, D. M.

Cox, A. J.

D’Anna, J.

Davidson, N.

N. Davidson, A. A. Friesam, E. Hasman, Opt. Commun. 88, 326 (1992).
[CrossRef]

Davis, J. A.

Durnin, J.

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

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

Eberly, J. H.

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

Friberg, A. T.

Friesam, A. A.

N. Davidson, A. A. Friesam, E. Hasman, Opt. Commun. 88, 326 (1992).
[CrossRef]

Guertin, J.

Hafizi, B.

P. Sprangle, B. Hafizi, Phys. Rev. Lett. 66, 873 (1991); J. Durnin, J. J. Miceli, J. H. Eberly, Phys. Rev. Lett. 66, 874 (1991).
[CrossRef]

Hasman, E.

N. Davidson, A. A. Friesam, E. Hasman, Opt. Commun. 88, 326 (1992).
[CrossRef]

Miceli, J. J.

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

Miura, H.

Rosen, J.

Sonehara, T.

Sprangle, P.

P. Sprangle, B. Hafizi, Phys. Rev. Lett. 66, 873 (1991); J. Durnin, J. J. Miceli, J. H. Eberly, Phys. Rev. Lett. 66, 874 (1991).
[CrossRef]

Turunen, J.

Vasara, A.

Webb, H.

D. C. Youla, H. Webb, IEEE Trans. Med. Imaging TMI-1, 81 (1982), and references therein.
[CrossRef]

Yariv, A.

Youla, D. C.

D. C. Youla, H. Webb, IEEE Trans. Med. Imaging TMI-1, 81 (1982), and references therein.
[CrossRef]

Appl. Opt.

IEEE Trans. Med. Imaging

D. C. Youla, H. Webb, IEEE Trans. Med. Imaging TMI-1, 81 (1982), and references therein.
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

N. Davidson, A. A. Friesam, E. Hasman, Opt. Commun. 88, 326 (1992).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

P. Sprangle, B. Hafizi, Phys. Rev. Lett. 66, 873 (1991); J. Durnin, J. J. Miceli, J. H. Eberly, Phys. Rev. Lett. 66, 874 (1991).
[CrossRef]

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Basic scheme for WF synthesis in the region D.

Fig. 2
Fig. 2

Nondiffracting beam after two iterations: (a) propagation of the central peak amplitude, (b) amplitude transverse field distribution along the z axis.

Fig. 3
Fig. 3

Nondiffracting array: (a) amplitude and (b) phase of the diffractive element; typical (c) intensity distribution and (d) intensity profile.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

F ( ξ , η , z ) = FrT [ f ( x , y ) ] .
| | f - g | | = inf x C z | | f - x | | ,
g = P z f = FrT - 1 [ P ¯ z FrT ( f ) ] ,
f C = i = 1 n C i .
f m = J m f 0 = J f m - 1             m = 0 , 1 , 2 ,
Δ ( z ) = π z 2 k r 2 + 4 π z ,
c 1 ( ξ , η ) = ( M - 1 - ) rect ( ξ / 3 ) rect ( η / 3 ) + 1 rect ( ξ / 7 ) rect ( η / 7 ) + ,
P z * [ F ( ξ , η ) ] = { M if ( ξ , η ) P min [ F ( ξ , η ) , c 1 ( ξ , η ) ] exp [ i Φ ( ξ , η ) ] otherwise ,
f 0 = { M if ( ξ , η ) = ( 0 , 0 ) exp [ i ψ ( ξ , η ) ] otherwise
c 5 ( ξ , η ) = c 1 ( ξ , η ) * [ δ ( ξ - 32 , η - 32 ) + δ ( ξ - 32 , η + 32 ) + δ ( ξ + 32 , η - 32 ) + δ ( ξ + 33 , η + 33 ) + δ ( ξ , η ) ]

Metrics