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.

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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 Jr. 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, "M 2 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. Andres and J. Ibarra, "2-D Lau patterns: in-register incoherent joint superposition of 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. Chavez-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).

Other (16)

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 Jr. and J. H. Eberly, "Diffraction free beams," Phys. Rev. Lett. 58, 1499 -1501 (1987).
[CrossRef] [PubMed]

G. Indebetouw, "Nondiffracting optical fields: some remarks on their analysis and synthesis," J. Opt. Soc. Am. A 6, 150-152 (1989).
[CrossRef]

R. Borghi and M. Santarsiero, "M 2 factor of Bessel-Gauss beams," Opt. Lett. 22, 262-264 (1997).
[CrossRef] [PubMed]

S. Ruschin and A. Leizer, "Evanescent Bessel beams," J. Opt. Soc. Am. A 15, 1139-1143 (1998).
[CrossRef]

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]

V. E. Peet and R. V. Tsubin, "Third harmonic generation and multiphoton ionization in Bessel beams," Phys. Rev. A 56, 1613-1620 (1997).
[CrossRef]

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]

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.

E. Tepichin, P. Andres and J. Ibarra, "2-D Lau patterns: in-register incoherent joint superposition of Montgomery patterns," Opt. Commun. 125, 27-35 (1996).
[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]

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. Chavez-Cerda, M. A. Meneses-Nava and J. M. Hickmann, "Interference of travelling non- diffracting beams," Opt. Lett. 23, 1871-1873 (1998).
[CrossRef]

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

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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