Abstract

An experiment was performed in which a single ring from a Fabry–Perot transmission fringe pattern was used to create a nondiffracting beam. The transverse and axial intensity distributions of this beam were measured and found to be in good agreement with previously existing and newly derived theoretical expressions. The diffraction-free range was found from calculation to be proportional to the cavity finesse and length, and the central-spot radius of the beam was theoretically shown to be proportional to the square root of the wavelength and cavity length.

© 1992 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. 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]
  5. A. J. Cox, D. C. Dibble, “Holographic reproduction of a diffraction-free beam,” Appl. Opt. 30, 1330–1332 (1990).
    [Crossref]
  6. K. Uehara, H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125–129 (1989).
    [Crossref]
  7. G. Indebetouw, “Nondiffracting optical fields: some remarks on their analysis and synthesis,” J. Opt. Soc. Am. A 6, 150–152 (1989).
    [Crossref]
  8. C. W. McCutchen, “Generalized aperture and the three-dimensional diffraction image,”J. Opt. Soc. Am. 54, 240–244 (1964).
    [Crossref]
  9. P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988), pp. 524–529.
  10. J. H. Moore, C. C. Davis, M. A. Coplan, Building Scientific Apparatus (Addison-Wesley, London, 1983), p. 235.
  11. A. Yariv, Introduction to Optical Electronics, 2nd ed. (Holt, Rinehart & Winston, New York, 1976), p. 79.

1990 (1)

1989 (3)

1988 (1)

1987 (2)

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]

1964 (1)

Coplan, M. A.

J. H. Moore, C. C. Davis, M. A. Coplan, Building Scientific Apparatus (Addison-Wesley, London, 1983), p. 235.

Cox, A. J.

Davis, C. C.

J. H. Moore, C. C. Davis, M. A. Coplan, Building Scientific Apparatus (Addison-Wesley, London, 1983), p. 235.

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.

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

P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988), pp. 524–529.

Friberg, A. T.

Indebetouw, G.

Kikuchi, H.

K. Uehara, H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125–129 (1989).
[Crossref]

McCutchen, C. W.

Miceli, J. J.

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

Milonni, P. W.

P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988), pp. 524–529.

Moore, J. H.

J. H. Moore, C. C. Davis, M. A. Coplan, Building Scientific Apparatus (Addison-Wesley, London, 1983), p. 235.

Turunen, J.

Uehara, K.

K. Uehara, H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125–129 (1989).
[Crossref]

Vasara, A.

Yariv, A.

A. Yariv, Introduction to Optical Electronics, 2nd ed. (Holt, Rinehart & Winston, New York, 1976), p. 79.

Appl. Opt. (2)

Appl. Phys. B (1)

K. Uehara, H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125–129 (1989).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

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 (3)

P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988), pp. 524–529.

J. H. Moore, C. C. Davis, M. A. Coplan, Building Scientific Apparatus (Addison-Wesley, London, 1983), p. 235.

A. Yariv, Introduction to Optical Electronics, 2nd ed. (Holt, Rinehart & Winston, New York, 1976), p. 79.

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Figures (6)

Fig. 1
Fig. 1

Diagram of the apparatus used to create the first nondiffracting beam,2 consisting of an annular slit (AS) of radius r and slit width Δ and a lens (L) of focal length f and radius Ra.

Fig. 2
Fig. 2

Diagram of the apparatus used in the present experiment, consisting of a spatial filter (SF), étalon mirrors (M1 and M2), a lens (L1) with focal length f1, an annular spatial filter (ASF) passing resonant ring 1, and a lens (L2) with focal length f2. Symmetric rays below the Z axis were omitted for clarity.

Fig. 3
Fig. 3

Intensity versus radial distance from the optical axis for (a) the resonant ring pattern in the focal plane of lens L1 with the annular spatial filter removed and (b) ring 1 transmitted through the annular spatial filter and reimaged with a second lens.

Fig. 4
Fig. 4

(a)–(c) Intensity of nondiffracting beam versus radial distance from the optical axis. (d) Plot of J0(αρ)2 for comparison.

Fig. 5
Fig. 5

Axial intensity of nondiffracting beam versus z (a) for an aperture of lens L2 much larger than the beam and (b) with a 0.16-cm-radius aperture placed near L2 that partially blocked the beam.

Fig. 6
Fig. 6

Enlarged drawing of the resonant cavity showing a few important rays.

Equations (3)

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E ( r , t ) = E 0 exp [ i ( β z - ω t ) ] J 0 ( α ρ ) ,
Δ z = ( F d π R ) ( f 2 f 1 ) 2 ,
ρ 0 = 0.383 ( f 2 f 1 ) ( λ d ) 1 / 2 .

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