Abstract

We experimentally verified the interference resulting of the superposition of two Bessel beams propagating in free space and showed for first time the self imaging effect using nondiffracting beams. Our results are supported by numerical simulations and possible applications are discussed.

© 1998 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, and J. H. Eberly, “Diffraction free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [Crossref] [PubMed]
  3. G. Indebetouw, “Nondiffracting optical fields: some remarks on their analysis and synthesis,” J. Opt. Soc. Am. A 6, 150–152 (1989).
    [Crossref]
  4. R. Borghi and M. Santarsiero, “M2 factor of Bessel-Gauss beams,” Opt. Lett. 22, 262–264 (1997).
    [Crossref] [PubMed]
  5. S. Ruschin and A. Leizer, “Evanescent Bessel beams,” J. Opt. Soc. Am. A 15, 1139–1143 (1998).
    [Crossref]
  6. D. Ding and Z. Lu, “The second harmonic component in the Bessel beams,” Appl. Phys. Lett. 68, 608–610 (1996).
    [Crossref]
  7. X. Liu, “Comment on ‘The second harmonic component in the Bessel beams,’” Appl. Phys. Lett.,  71, 722 (1997).
    [Crossref]
  8. V. E. Peet and R. V. Tsubin, “Third harmonic generation and multiphoton ionization in Bessel beams,” Phys. Rev. A 56, 1613–1620 (1997).
    [Crossref]
  9. S. Klewitz, P. Leiderer, S. Herminghaus, and S. Sogomonian, “Tunable stimulated Raman scattering by pumping with Bessel beams,” Opt. Lett. 21, 248–250 (1996).
    [Crossref] [PubMed]
  10. K. Patorsky “The self-imaging phenomenon and its applications,” in Progress in Optics XXVII,E. Wolf, ed., p. 3–108 (Elsevier, Amsterdan, 1990) and references there in.
  11. E. Tepichin, P. Andrés, and J. Ibarra, “2-D Lau patterns: in-register incoherent joint superposi-tionof Montgomery patterns,” Opt. Commun. 125, 27–35 (1996).
    [Crossref]
  12. Yu. B. Ovchinnikov, I. Manek, and R. Grimm, “Surface trap for Cs atoms based on evanescent-wave cooling,” Phys. Rev. Lett. 79, 2225–2228 (1997).
    [Crossref]
  13. I. Manek, Yu. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Comm. 147, 67–70 (1998).
    [Crossref]
  14. J. Yin and Y. Zhu, “Dark-hollow-beam gravito-optical atom trap above an apex of a hollow optical fiber,” Opt. Comm. 152, 421–428 (1998).
    [Crossref]
  15. S. Chávez-Cerda, M. A. Meneses-Nava, and J. M. Hickmann, “Interference of travelling non-diffracting beams,” Opt. Lett. 23, 1871–1873 (1998).
    [Crossref]
  16. W-H Lee, “Computer generated holograms: techniques and applications,” in Progress in Optics XVI, p. 121 (1978).

1998 (4)

S. Ruschin and A. Leizer, “Evanescent Bessel beams,” J. Opt. Soc. Am. A 15, 1139–1143 (1998).
[Crossref]

I. Manek, Yu. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Comm. 147, 67–70 (1998).
[Crossref]

J. Yin and Y. Zhu, “Dark-hollow-beam gravito-optical atom trap above an apex of a hollow optical fiber,” Opt. Comm. 152, 421–428 (1998).
[Crossref]

S. Chávez-Cerda, M. A. Meneses-Nava, and J. M. Hickmann, “Interference of travelling non-diffracting beams,” Opt. Lett. 23, 1871–1873 (1998).
[Crossref]

1997 (4)

Yu. B. Ovchinnikov, I. Manek, and R. Grimm, “Surface trap for Cs atoms based on evanescent-wave cooling,” Phys. Rev. Lett. 79, 2225–2228 (1997).
[Crossref]

R. Borghi and M. Santarsiero, “M2 factor of Bessel-Gauss beams,” Opt. Lett. 22, 262–264 (1997).
[Crossref] [PubMed]

X. Liu, “Comment on ‘The second harmonic component in the Bessel beams,’” Appl. Phys. Lett.,  71, 722 (1997).
[Crossref]

V. E. Peet and R. V. Tsubin, “Third harmonic generation and multiphoton ionization in Bessel beams,” Phys. Rev. A 56, 1613–1620 (1997).
[Crossref]

1996 (3)

S. Klewitz, P. Leiderer, S. Herminghaus, and S. Sogomonian, “Tunable stimulated Raman scattering by pumping with Bessel beams,” Opt. Lett. 21, 248–250 (1996).
[Crossref] [PubMed]

E. Tepichin, P. Andrés, and J. Ibarra, “2-D Lau patterns: in-register incoherent joint superposi-tionof Montgomery patterns,” Opt. Commun. 125, 27–35 (1996).
[Crossref]

D. Ding and Z. Lu, “The second harmonic component in the Bessel beams,” Appl. Phys. Lett. 68, 608–610 (1996).
[Crossref]

1989 (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, and J. H. Eberly, “Diffraction free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Andrés, P.

E. Tepichin, P. Andrés, and J. Ibarra, “2-D Lau patterns: in-register incoherent joint superposi-tionof Montgomery patterns,” Opt. Commun. 125, 27–35 (1996).
[Crossref]

Borghi, R.

Chávez-Cerda, S.

Ding, D.

D. Ding and Z. Lu, “The second harmonic component in the Bessel beams,” Appl. Phys. Lett. 68, 608–610 (1996).
[Crossref]

Durnin, J.

J. Durnin, J. J. Miceli, and 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.

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

Grimm, R.

I. Manek, Yu. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Comm. 147, 67–70 (1998).
[Crossref]

Yu. B. Ovchinnikov, I. Manek, and R. Grimm, “Surface trap for Cs atoms based on evanescent-wave cooling,” Phys. Rev. Lett. 79, 2225–2228 (1997).
[Crossref]

Herminghaus, S.

Hickmann, J. M.

Ibarra, J.

E. Tepichin, P. Andrés, and J. Ibarra, “2-D Lau patterns: in-register incoherent joint superposi-tionof Montgomery patterns,” Opt. Commun. 125, 27–35 (1996).
[Crossref]

Indebetouw, G.

Klewitz, S.

Lee, W-H

W-H Lee, “Computer generated holograms: techniques and applications,” in Progress in Optics XVI, p. 121 (1978).

Leiderer, P.

Leizer, A.

Liu, X.

X. Liu, “Comment on ‘The second harmonic component in the Bessel beams,’” Appl. Phys. Lett.,  71, 722 (1997).
[Crossref]

Lu, Z.

D. Ding and Z. Lu, “The second harmonic component in the Bessel beams,” Appl. Phys. Lett. 68, 608–610 (1996).
[Crossref]

Manek, I.

I. Manek, Yu. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Comm. 147, 67–70 (1998).
[Crossref]

Yu. B. Ovchinnikov, I. Manek, and R. Grimm, “Surface trap for Cs atoms based on evanescent-wave cooling,” Phys. Rev. Lett. 79, 2225–2228 (1997).
[Crossref]

Meneses-Nava, M. A.

Miceli, J. J.

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

Ovchinnikov, Yu. B.

I. Manek, Yu. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Comm. 147, 67–70 (1998).
[Crossref]

Yu. B. Ovchinnikov, I. Manek, and R. Grimm, “Surface trap for Cs atoms based on evanescent-wave cooling,” Phys. Rev. Lett. 79, 2225–2228 (1997).
[Crossref]

Patorsky, K.

K. Patorsky “The self-imaging phenomenon and its applications,” in Progress in Optics XXVII,E. Wolf, ed., p. 3–108 (Elsevier, Amsterdan, 1990) and references there in.

Peet, V. E.

V. E. Peet and R. V. Tsubin, “Third harmonic generation and multiphoton ionization in Bessel beams,” Phys. Rev. A 56, 1613–1620 (1997).
[Crossref]

Ruschin, S.

Santarsiero, M.

Sogomonian, S.

Tepichin, E.

E. Tepichin, P. Andrés, and J. Ibarra, “2-D Lau patterns: in-register incoherent joint superposi-tionof Montgomery patterns,” Opt. Commun. 125, 27–35 (1996).
[Crossref]

Tsubin, R. V.

V. E. Peet and R. V. Tsubin, “Third harmonic generation and multiphoton ionization in Bessel beams,” Phys. Rev. A 56, 1613–1620 (1997).
[Crossref]

Yin, J.

J. Yin and Y. Zhu, “Dark-hollow-beam gravito-optical atom trap above an apex of a hollow optical fiber,” Opt. Comm. 152, 421–428 (1998).
[Crossref]

Zhu, Y.

J. Yin and Y. Zhu, “Dark-hollow-beam gravito-optical atom trap above an apex of a hollow optical fiber,” Opt. Comm. 152, 421–428 (1998).
[Crossref]

Appl. Phys. Lett. (2)

D. Ding and Z. Lu, “The second harmonic component in the Bessel beams,” Appl. Phys. Lett. 68, 608–610 (1996).
[Crossref]

X. Liu, “Comment on ‘The second harmonic component in the Bessel beams,’” Appl. Phys. Lett.,  71, 722 (1997).
[Crossref]

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

Opt. Comm. (2)

I. Manek, Yu. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Comm. 147, 67–70 (1998).
[Crossref]

J. Yin and Y. Zhu, “Dark-hollow-beam gravito-optical atom trap above an apex of a hollow optical fiber,” Opt. Comm. 152, 421–428 (1998).
[Crossref]

Opt. Commun. (1)

E. Tepichin, P. Andrés, and J. Ibarra, “2-D Lau patterns: in-register incoherent joint superposi-tionof Montgomery patterns,” Opt. Commun. 125, 27–35 (1996).
[Crossref]

Opt. Lett. (3)

Phys. Rev. A (1)

V. E. Peet and R. V. Tsubin, “Third harmonic generation and multiphoton ionization in Bessel beams,” Phys. Rev. A 56, 1613–1620 (1997).
[Crossref]

Phys. Rev. Lett. (2)

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

Yu. B. Ovchinnikov, I. Manek, and R. Grimm, “Surface trap for Cs atoms based on evanescent-wave cooling,” Phys. Rev. Lett. 79, 2225–2228 (1997).
[Crossref]

Other (2)

W-H Lee, “Computer generated holograms: techniques and applications,” in Progress in Optics XVI, p. 121 (1978).

K. Patorsky “The self-imaging phenomenon and its applications,” in Progress in Optics XXVII,E. Wolf, ed., p. 3–108 (Elsevier, Amsterdan, 1990) and references there in.

Supplementary Material (1)

» Media 1: MOV (1509 KB)     

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Figures (6)

Figure 1.
Figure 1.

The evolution of the SBB: density plot showing the simulated evolution of two Bessel beams in phase with same normalized amplitude and spatial frequencies k 0 = 4 and k 1 = k 0/5.

Figure 2.
Figure 2.

Animation showing the simulated evolution of two Bessel beams in phase with same normalized amplitude and spatial frequencies k 0 = 4 and k 1 = k 0/5. [Media 1]

Figure 3.
Figure 3.

Experimental setup.

Figure 4.
Figure 4.

A sequence of photografic shots showing the SBB evolution in the first period.

Figure 5.
Figure 5.

A sequence of photografic shots showing the subsequent central mini-mums and maximums along the evolution of the SBB.

Figure 6.
Figure 6.

Simulated density plots to the positions corresponding to a central minimum (a) and maximum (b).

Equations (1)

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I r z = J 0 2 ( k 0 r ) + a 2 J 0 2 ( k 1 r ) + 2 a J 0 2 ( k 0 r ) J 0 2 ( k 1 r ) cos ( ( k z 0 k z 1 ) z + θ )

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