Abstract

The propagation features of several apertured Bessel beams are numerically calculated. The calculations show that the relations of axial intensity versus propagation distance are similar to the radial distribution of the aperture functions, which may be helpful in choosing the proper aperture functions in experiments.

© 1995 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. R. M. Herman, T. A. Wiggins, “Production and uses of diffractionless beams,” J. Opt. Soc. Am. A 8, 932–942 (1991).
    [CrossRef]
  5. L. C. Laycock, S. C. Webster, “Bessel beams: their generation and application,” GEC J. Res. 10, 36–51 (1992).
  6. T. Hidaka, “Generation of diffraction-free laser beam using a specific Fresnel zone plate,” Jpn. J. Appl. Phys. 30, 1738–1739 (1991).
    [CrossRef]
  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. 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]
  9. J. K. Jabczynski, “A diffraction-free resonator,” Opt. Commun. 77, 292–294 (1990).
    [CrossRef]
  10. K. Thewes, M. A. Karim, A. A. S. Awwal, “Diffraction-free beam generation using a refracting system,” Opt. Laser Technol. 23, 105–108 (1991).
    [CrossRef]
  11. R. P. Macdonald, J. Chrostowski, S. A. Boothroyd, B. A. Syrett, “Holographic formation of a diode laser nondiffracting beam,” Appl. Opt. 32, 6470–6474 (1993).
    [CrossRef] [PubMed]
  12. K. M. Iftekharuddin, A. A. S. Awwal, M. A. Karim, “Gaussian-to-Bessel beam transformation using a split refracting system,” Appl. Opt. 32, 2252–2256 (1993).
    [CrossRef]
  13. G. Scott, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2646 (1992).
    [CrossRef]
  14. F. Gori, G. Guattari, C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
    [CrossRef]
  15. P. L. Overfelt, C. S. Kenney, “Comparison of the propagation characteristics of Bessel, Bessel-Gauss, and Gaussian beams diffracted by a circular aperture,” J. Opt. Soc. Am. A 8, 732–745 (1991).
    [CrossRef]
  16. R. M. Herman, T. A. Wiggins, “Apodization of diffraction-less beam,” Appl. Opt. 31, 5913–5915 (1992).
    [CrossRef] [PubMed]
  17. F. Bloisi, L. Vicari, “Bessel beams propagation through axisymmetric optical systems,” J. Opt. 22, 3–5 (1991).
    [CrossRef]
  18. N. B. Baranova, B. Ya. Zeldovich, M. O. Scully, “Acceleration of charged particles by laser beams,” J. Exp. Theoret. Phys. 78, 249–258 (1994).
  19. J. Lu, T. K. Song, R. R. Kinnick, J. F. Greenleaf, “In vitro and in vivo real-time imaging with ultrasonic limited diffraction beams,” IEEE Trans. Med. Imaging 12, 819–829 (1993).
    [CrossRef] [PubMed]
  20. M. O. Scully, M. S. Zubairy, “Simple laser accelerator: optics and particle dynamics,” Phys. Rev. A 44, 2656–2663 (1991).
    [CrossRef] [PubMed]
  21. B. Hafizi, P. Sprangle, “Diffraction effects in directed radiation beams,” J. Opt. Soc. Am. A 8, 705–717 (1991).
    [CrossRef]
  22. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 8, p. 382.

1994 (1)

N. B. Baranova, B. Ya. Zeldovich, M. O. Scully, “Acceleration of charged particles by laser beams,” J. Exp. Theoret. Phys. 78, 249–258 (1994).

1993 (3)

1992 (4)

G. Scott, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2646 (1992).
[CrossRef]

R. M. Herman, T. A. Wiggins, “Apodization of diffraction-less beam,” Appl. Opt. 31, 5913–5915 (1992).
[CrossRef] [PubMed]

L. C. Laycock, S. C. Webster, “Bessel beams: their generation and application,” GEC J. Res. 10, 36–51 (1992).

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]

1991 (7)

T. Hidaka, “Generation of diffraction-free laser beam using a specific Fresnel zone plate,” Jpn. J. Appl. Phys. 30, 1738–1739 (1991).
[CrossRef]

R. M. Herman, T. A. Wiggins, “Production and uses of diffractionless beams,” J. Opt. Soc. Am. A 8, 932–942 (1991).
[CrossRef]

F. Bloisi, L. Vicari, “Bessel beams propagation through axisymmetric optical systems,” J. Opt. 22, 3–5 (1991).
[CrossRef]

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

M. O. Scully, M. S. Zubairy, “Simple laser accelerator: optics and particle dynamics,” Phys. Rev. A 44, 2656–2663 (1991).
[CrossRef] [PubMed]

B. Hafizi, P. Sprangle, “Diffraction effects in directed radiation beams,” J. Opt. Soc. Am. A 8, 705–717 (1991).
[CrossRef]

P. L. Overfelt, C. S. Kenney, “Comparison of the propagation characteristics of Bessel, Bessel-Gauss, and Gaussian beams diffracted by a circular aperture,” J. Opt. Soc. Am. A 8, 732–745 (1991).
[CrossRef]

1990 (1)

J. K. Jabczynski, “A diffraction-free resonator,” Opt. Commun. 77, 292–294 (1990).
[CrossRef]

1989 (1)

1988 (1)

1987 (3)

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]

F. Gori, G. Guattari, C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Awwal, A. A. S.

K. M. Iftekharuddin, A. A. S. Awwal, M. A. Karim, “Gaussian-to-Bessel beam transformation using a split refracting system,” Appl. Opt. 32, 2252–2256 (1993).
[CrossRef]

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

Baranova, N. B.

N. B. Baranova, B. Ya. Zeldovich, M. O. Scully, “Acceleration of charged particles by laser beams,” J. Exp. Theoret. Phys. 78, 249–258 (1994).

Bloisi, F.

F. Bloisi, L. Vicari, “Bessel beams propagation through axisymmetric optical systems,” J. Opt. 22, 3–5 (1991).
[CrossRef]

Boothroyd, S. A.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 8, p. 382.

Chrostowski, 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]

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.

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

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]

Gori, F.

F. Gori, G. Guattari, C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Greenleaf, J. F.

J. Lu, T. K. Song, R. R. Kinnick, J. F. Greenleaf, “In vitro and in vivo real-time imaging with ultrasonic limited diffraction beams,” IEEE Trans. Med. Imaging 12, 819–829 (1993).
[CrossRef] [PubMed]

Guattari, G.

F. Gori, G. Guattari, C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Hafizi, B.

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.

Hidaka, T.

T. Hidaka, “Generation of diffraction-free laser beam using a specific Fresnel zone plate,” Jpn. J. Appl. Phys. 30, 1738–1739 (1991).
[CrossRef]

Iftekharuddin, K. M.

Jabczynski, J. K.

J. K. Jabczynski, “A diffraction-free resonator,” Opt. Commun. 77, 292–294 (1990).
[CrossRef]

Karim, M. A.

K. M. Iftekharuddin, A. A. S. Awwal, M. A. Karim, “Gaussian-to-Bessel beam transformation using a split refracting system,” Appl. Opt. 32, 2252–2256 (1993).
[CrossRef]

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

Kenney, C. S.

Kinnick, R. R.

J. Lu, T. K. Song, R. R. Kinnick, J. F. Greenleaf, “In vitro and in vivo real-time imaging with ultrasonic limited diffraction beams,” IEEE Trans. Med. Imaging 12, 819–829 (1993).
[CrossRef] [PubMed]

Laycock, L. C.

L. C. Laycock, S. C. Webster, “Bessel beams: their generation and application,” GEC J. Res. 10, 36–51 (1992).

Lu, J.

J. Lu, T. K. Song, R. R. Kinnick, J. F. Greenleaf, “In vitro and in vivo real-time imaging with ultrasonic limited diffraction beams,” IEEE Trans. Med. Imaging 12, 819–829 (1993).
[CrossRef] [PubMed]

Macdonald, R. P.

Miceli, J. J.

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

Overfelt, P. L.

Padovani, C.

F. Gori, G. Guattari, C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Scott, G.

G. Scott, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2646 (1992).
[CrossRef]

Scully, M. O.

N. B. Baranova, B. Ya. Zeldovich, M. O. Scully, “Acceleration of charged particles by laser beams,” J. Exp. Theoret. Phys. 78, 249–258 (1994).

M. O. Scully, M. S. Zubairy, “Simple laser accelerator: optics and particle dynamics,” Phys. Rev. A 44, 2656–2663 (1991).
[CrossRef] [PubMed]

Song, T. K.

J. Lu, T. K. Song, R. R. Kinnick, J. F. Greenleaf, “In vitro and in vivo real-time imaging with ultrasonic limited diffraction beams,” IEEE Trans. Med. Imaging 12, 819–829 (1993).
[CrossRef] [PubMed]

Sprangle, P.

Syrett, B. A.

Thewes, K.

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

Turunen, J.

Vasara, A.

Vicari, L.

F. Bloisi, L. Vicari, “Bessel beams propagation through axisymmetric optical systems,” J. Opt. 22, 3–5 (1991).
[CrossRef]

Webster, S. C.

L. C. Laycock, S. C. Webster, “Bessel beams: their generation and application,” GEC J. Res. 10, 36–51 (1992).

Wiggins, T. A.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 8, p. 382.

Zeldovich, B. Ya.

N. B. Baranova, B. Ya. Zeldovich, M. O. Scully, “Acceleration of charged particles by laser beams,” J. Exp. Theoret. Phys. 78, 249–258 (1994).

Zubairy, M. S.

M. O. Scully, M. S. Zubairy, “Simple laser accelerator: optics and particle dynamics,” Phys. Rev. A 44, 2656–2663 (1991).
[CrossRef] [PubMed]

Appl. Opt. (4)

GEC J. Res. (1)

L. C. Laycock, S. C. Webster, “Bessel beams: their generation and application,” GEC J. Res. 10, 36–51 (1992).

IEEE Trans. Med. Imaging (1)

J. Lu, T. K. Song, R. R. Kinnick, J. F. Greenleaf, “In vitro and in vivo real-time imaging with ultrasonic limited diffraction beams,” IEEE Trans. Med. Imaging 12, 819–829 (1993).
[CrossRef] [PubMed]

J. Exp. Theoret. Phys. (1)

N. B. Baranova, B. Ya. Zeldovich, M. O. Scully, “Acceleration of charged particles by laser beams,” J. Exp. Theoret. Phys. 78, 249–258 (1994).

J. Opt. (1)

F. Bloisi, L. Vicari, “Bessel beams propagation through axisymmetric optical systems,” J. Opt. 22, 3–5 (1991).
[CrossRef]

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

Jpn. J. Appl. Phys. (1)

T. Hidaka, “Generation of diffraction-free laser beam using a specific Fresnel zone plate,” Jpn. J. Appl. Phys. 30, 1738–1739 (1991).
[CrossRef]

Opt. Commun. (3)

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]

J. K. Jabczynski, “A diffraction-free resonator,” Opt. Commun. 77, 292–294 (1990).
[CrossRef]

F. Gori, G. Guattari, C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Opt. Eng. (1)

G. Scott, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2646 (1992).
[CrossRef]

Opt. Laser Technol. (1)

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

Phys. Rev. A (1)

M. O. Scully, M. S. Zubairy, “Simple laser accelerator: optics and particle dynamics,” Phys. Rev. A 44, 2656–2663 (1991).
[CrossRef] [PubMed]

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)

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 8, p. 382.

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Figures (4)

Fig. 1
Fig. 1

Aperture functions shown by Eq. (3): a, hard hole; b, anti-Gaussian; c, Gaussian; d, Airy; e, triangle.

Fig. 2
Fig. 2

Axial intensities versus propagation distance corresponding to Fig. 1.

Fig. 3
Fig. 3

Axial intensities after an axicon versus propagation distance: a, uniform plane-wave incidence; b, Gaussian-beam incidence.

Fig. 4
Fig. 4

Axial intensities of the diffraction of the Bessel beam modified by, a, axicon and, b, negative axicon phase apertures. α = 20 mm−1.

Equations (9)

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A ( x 2 , y 2 , z ) = k i z - - A ( x 1 , y 1 , 0 ) exp ( i k R ) d x d y ,
R = [ ( x 1 - x 2 ) 2 + ( y 1 - y 2 ) 2 + z 2 ] 1 / 2 = z + r 2 + ρ 2 2 z - 2 r ρ cos ( θ - φ ) 2 z .
A ( r , z ) = exp ( i k z + i k r 2 2 z ) ( k i z ) × 0 ρ A ( ρ , 0 ) J 0 ( k ρ r z ) exp ( i k ρ 2 2 z ) d ρ ,
A ( ρ , 0 ) = F ( ρ ) J 0 ( α ρ ) ,
F ( ρ ) = { 1 hard hole , exp ( ξ 2 - 1 4 ) anti - Gaussian , exp ( - ξ 2 ) Gaussian , 2 J 1 ( 1.22 π ξ ) / ( 1.22 π ξ ) Airy , 1 - ξ triangle ,
I ( 0 , z ) = A ( 0 , z ) 2 = ( k z ) 2 | 0 a ρ F ( ρ ) J 0 ( α ρ ) exp ( i k ρ 2 2 z ) d ρ | 2 .
I ( 0 , z ) = ( k z ) 2 | 0 a ρ exp ( i k ρ 2 2 z - i α ρ ) d ρ | 2 .
I ( 0 , z ) = ( k z ) 2 | 0 a exp ( - ρ 2 / ω 2 ) ρ exp ( i k ρ 2 2 z - i α ρ ) d ρ | 2 .
F ( ρ ) = { exp ( - i α ρ ) axicon , exp ( i α ρ ) negative axicon .

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