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  1. J. Durnin, “Exact Solutions for Diffraction-Free Beams. I: The Scalar Theory,” J. Opt. Soc. Am. A 4, 651 (1987).
    [CrossRef]
  2. F. Gori, G. Guattari, C. Padovani, “Bessel-Gauss Beams,” Opt. Commun. 64, 491 (1987).
    [CrossRef]
  3. J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  4. R. C. Fairchild, J. R. Fienup, “Computer-Generated Aspheric Holographic Optical Elements,” Opt. Eng. 21, 133 (1982).
    [CrossRef]
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Appendix III.
  6. G. J. Swanson, W. B. Veldkamp, “Infrared Applications of Diffractive Optical Elements,” Proc. SPIE 883, 155 (1988).
    [CrossRef]
  7. M. V. Peres, C. Gomez-Reino, J. M. Cuadvado, “Diffraction Patterns and Zone Plates Produced by Linear Axicons,” Opt. Acta 33, 1161 (1986).
    [CrossRef]

1988 (1)

G. J. Swanson, W. B. Veldkamp, “Infrared Applications of Diffractive Optical Elements,” Proc. SPIE 883, 155 (1988).
[CrossRef]

1987 (3)

F. Gori, G. Guattari, C. Padovani, “Bessel-Gauss Beams,” Opt. Commun. 64, 491 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

J. Durnin, “Exact Solutions for Diffraction-Free Beams. I: The Scalar Theory,” J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

1986 (1)

M. V. Peres, C. Gomez-Reino, J. M. Cuadvado, “Diffraction Patterns and Zone Plates Produced by Linear Axicons,” Opt. Acta 33, 1161 (1986).
[CrossRef]

1982 (1)

R. C. Fairchild, J. R. Fienup, “Computer-Generated Aspheric Holographic Optical Elements,” Opt. Eng. 21, 133 (1982).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Appendix III.

Cuadvado, J. M.

M. V. Peres, C. Gomez-Reino, J. M. Cuadvado, “Diffraction Patterns and Zone Plates Produced by Linear Axicons,” Opt. Acta 33, 1161 (1986).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

J. Durnin, “Exact Solutions for Diffraction-Free Beams. I: The Scalar Theory,” J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

Eberly, J. H.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Fairchild, R. C.

R. C. Fairchild, J. R. Fienup, “Computer-Generated Aspheric Holographic Optical Elements,” Opt. Eng. 21, 133 (1982).
[CrossRef]

Fienup, J. R.

R. C. Fairchild, J. R. Fienup, “Computer-Generated Aspheric Holographic Optical Elements,” Opt. Eng. 21, 133 (1982).
[CrossRef]

Gomez-Reino, C.

M. V. Peres, C. Gomez-Reino, J. M. Cuadvado, “Diffraction Patterns and Zone Plates Produced by Linear Axicons,” Opt. Acta 33, 1161 (1986).
[CrossRef]

Gori, F.

F. Gori, G. Guattari, C. Padovani, “Bessel-Gauss Beams,” Opt. Commun. 64, 491 (1987).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, C. Padovani, “Bessel-Gauss Beams,” Opt. Commun. 64, 491 (1987).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Padovani, C.

F. Gori, G. Guattari, C. Padovani, “Bessel-Gauss Beams,” Opt. Commun. 64, 491 (1987).
[CrossRef]

Peres, M. V.

M. V. Peres, C. Gomez-Reino, J. M. Cuadvado, “Diffraction Patterns and Zone Plates Produced by Linear Axicons,” Opt. Acta 33, 1161 (1986).
[CrossRef]

Swanson, G. J.

G. J. Swanson, W. B. Veldkamp, “Infrared Applications of Diffractive Optical Elements,” Proc. SPIE 883, 155 (1988).
[CrossRef]

Veldkamp, W. B.

G. J. Swanson, W. B. Veldkamp, “Infrared Applications of Diffractive Optical Elements,” Proc. SPIE 883, 155 (1988).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Appendix III.

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

Opt. Acta (1)

M. V. Peres, C. Gomez-Reino, J. M. Cuadvado, “Diffraction Patterns and Zone Plates Produced by Linear Axicons,” Opt. Acta 33, 1161 (1986).
[CrossRef]

Opt. Commun. (1)

F. Gori, G. Guattari, C. Padovani, “Bessel-Gauss Beams,” Opt. Commun. 64, 491 (1987).
[CrossRef]

Opt. Eng. (1)

R. C. Fairchild, J. R. Fienup, “Computer-Generated Aspheric Holographic Optical Elements,” Opt. Eng. 21, 133 (1982).
[CrossRef]

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Proc. SPIE (1)

G. J. Swanson, W. B. Veldkamp, “Infrared Applications of Diffractive Optical Elements,” Proc. SPIE 883, 155 (1988).
[CrossRef]

Other (1)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Appendix III.

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Figures (4)

Fig. 1
Fig. 1

(a) Original experimental arrangement for the generation of an approximate Bessel beam; (b) the modified system based on a holographic optical element (HOE).

Fig. 2
Fig. 2

Axial intensity of the approximate Bessel beam produced by the system of Fig. 1(b) with D = 10 mm, ρ0 = 2 mm, and λ = 633 nm. The dashed line at L = 31.6 m corresponds to the geometric-optics estimate for the diffraction-free propagation range.

Fig. 3
Fig. 3

Calculated beam profiles (intensity vs y-coordinate in millimeters) at distances (a) z = 10 m, (b) z = 20 m, and (c) z = 30 m from the hologram plane in the modified HOE system with parameters as in Fig. 2.

Fig. 4
Fig. 4

Experimental beam profiles corresponding to the numerical results of Fig. 3: (a) z = 10 m; (b) z = 20 m; and (c) z = 30 m.

Equations (2)

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V ( r , t ) = exp ( i β z - w t ) J 0 ( α ρ ) ,
I ( ρ ) = ( 2 π λ z ) 2 | 0 D exp [ i 2 π ( ρ 2 / 2 λ z - ρ / ρ 0 ) ] × J 0 ( 2 π ρ ρ / λ z ) ρ d ρ | 2 ,

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