Abstract

We report for the first time, to our knowledge, the characteristics of a so-called nondiffracting beam produced by illumination of a binary-phase reflective holographic optical element with light from a diode laser. The Bessel beam has an intensity profile whose pattern changes little over distances of order 1 m and has a 1/e amplitude radius for the central lobe of ~ 100 μm. This beam may have application for alignment of integrated optic elements in which unguided diffraction-free beams are used to align glass-slab elements containing interconnection holograms to a computer board. The aligning Bessel beam would be produced on reflection from a hologram on the glass-substrate interconnecting element. A single hologram may be used for different substrates having different lengths and functionality because of the large depth of field of the Bessel beam.

© 1993 Optical Society of America

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References

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    [Crossref]
  2. J. Turunen, A. Vasara, A. T. Friberg, “Holographic generation of diffraction-free beams,” Appl. Opt. 27, 3959–3962(1988).
    [Crossref] [PubMed]
  3. R. M. Herman, T. A. Wiggins, “Production and uses of diffractionless beams,” J. Opt. Soc. Am. A 8, 932–942 (1991).
    [Crossref]
  4. L. C. Laycock, S. C. Webster, “Bessel beams: their generation and application,” GEC J. Res. 10, 36–51 (1992).
  5. T. Hidaka, “Generation of a diffraction-free laser beam using a specific Fresnel zone plate,” Jpn. J. Appl. Phys. 30, 1738–1739 (1991).
    [Crossref]
  6. 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]
  7. 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]
  8. H. Dammann, “Spectral characteristic of stepped-phase gratings,” Optik 53, 409–417 (1979).
  9. 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]
  10. J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [Crossref] [PubMed]
  11. F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
    [Crossref]
  12. 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).
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  14. E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987), p. 418.
  15. R. M. Herman, T. A. Wiggins, “Apodization of diffraction-less beams,” Appl. Opt. 31, 5913–5915 (1992).
    [Crossref] [PubMed]
  16. A. J. Cox, J. D’Anna, “Constant-axial-intensity nondiffracting beam,” Opt. Lett. 17, 232–234 (1992).
    [Crossref] [PubMed]
  17. P. Sprangle, B. Hafizi, “Comment on nondiffracting beams,” Phys. Rev. Lett. 66, 837 (1991).
    [Crossref] [PubMed]
  18. K.-H. Brenner, F. Sauer, “Diffractive–reflective optical interconnects,” Appl. Opt. 27, 4251–4254 (1988).
    [Crossref] [PubMed]
  19. R. K. Kostuk, Y. T. Huang, D. Heterington, M. Kato, “Reducing alignment and chromatic sensitivity of holographic optical interconnects with substrate-mode holograms,” Appl. Opt. 28, 4939–4944 (1989).
    [Crossref] [PubMed]

1992 (5)

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]

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]

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

A. J. Cox, J. D’Anna, “Constant-axial-intensity nondiffracting beam,” Opt. Lett. 17, 232–234 (1992).
[Crossref] [PubMed]

1991 (4)

1989 (2)

1988 (2)

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]

1979 (1)

H. Dammann, “Spectral characteristic of stepped-phase gratings,” Optik 53, 409–417 (1979).

1954 (1)

Brenner, K.-H.

Brown, D. L.

Cox, A. J.

D’Anna, J.

Dammann, H.

H. Dammann, “Spectral characteristic of stepped-phase gratings,” Optik 53, 409–417 (1979).

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, 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]

Eberly, J. H.

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]

Guattari, G.

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

Hafizi, B.

P. Sprangle, B. Hafizi, “Comment on nondiffracting beams,” Phys. Rev. Lett. 66, 837 (1991).
[Crossref] [PubMed]

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]

Hecht, E.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987), p. 418.

Herman, R. M.

Heterington, D.

Hidaka, T.

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

Huang, H.

Huang, Y. T.

Kato, M.

Kenney, C. S.

Kostuk, R. K.

Laycock, L. C.

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

Lin, Y.

McLeod, J. H.

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]

Sauer, F.

Seka, W.

Sprangle, P.

P. Sprangle, B. Hafizi, “Comment on nondiffracting beams,” Phys. Rev. Lett. 66, 837 (1991).
[Crossref] [PubMed]

Turunen, J.

Vasara, A.

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.

Appl. Opt. (5)

GEC J. Res. (1)

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

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Jpn. J. Appl. Phys. (1)

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

Opt. Commun. (2)

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]

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

Opt. Lett. (1)

Optik (1)

H. Dammann, “Spectral characteristic of stepped-phase gratings,” Optik 53, 409–417 (1979).

Phys. Rev. Lett. (2)

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

P. Sprangle, B. Hafizi, “Comment on nondiffracting beams,” Phys. Rev. Lett. 66, 837 (1991).
[Crossref] [PubMed]

Other (1)

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987), p. 418.

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Figures (6)

Fig. 1
Fig. 1

Ray-optics diagram showing the different intersection points along the optical axis of rays originating from common annuli on the hologram surface. Annuli of larger radii have greater area and therefore route more light. Since the intersection point becomes further away from the hologram face for annuli for larger radii, the intensity along the optical axis grows linearly with distance from the hologram face.

Fig. 2
Fig. 2

Schematic of experimental arrangement. The figure shows a scale view of the center region of the hologram used in the experiments as well as a predicted intensity profile for the Bessel beam. The plane mirror together with the rest of the apparatus created a Michelson interferometer and was used only during interference experiments described in the text. The insert at the lower left shows the Bessel function variation J02(x); the argument x is indicated on the abscissa. ND, neutral density.

Fig. 3
Fig. 3

Data points are the measured peak-to-peak distance from the central spot to the first ring of the Bessel beam at various distances along the beam’s propagation length. The solid curve shows the calculated spot size of a Gaussian beam whose beam waist is equal to that of the central peak in the Bessel beam. The measured peak-to-peak data are also shown at a scale of 10:1 (×10). The measured data are approximately 1.6 times larger than the 1/e amplitude radius for the central peak in the Bessel beam.

Fig. 4
Fig. 4

Measured intensity of the beam’s central spot averaged over five trials (data points). The solid curve is the theoretical variation obtained with Eq. (3).

Fig. 5
Fig. 5

Photographs of the beam taken at a distance of 50 cm from the hologram face: (a) photo of the Bessel beam, (b) an oscilloscope trace of a horizontal section through the center of the ring structure in (a); (c), (d) Michelson interferograms of the Bessel beam. With the central spot as the zeroth ring, in (c) the odd-numbered rings are suppressed, while (d) shows the even-numbered rings suppressed.

Fig. 6
Fig. 6

Alignment system for accurately positioning an integrated light-guided glass substrate to the optical sources and detectors beneath it by use of a nondiffracting beam.

Equations (3)

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t ( r ) = exp ( - i 2 π r / r 0 ) r R = 0 r > R ,
ϕ ( r , f ) = r r 0 + ( f 2 + r 2 ) 1 / 2 λ .
I ( ρ ) = ( π λ z ) 2 | 0 R exp [ i k ( ρ 2 + r 2 + z 0 2 ) 1 / 2 ] J 0 ( r ρ k / z ) r d r | 2 ,

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