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Optics Express

Optics Express

  • Editor: J. H. Eberly
  • Vol. 3, Iss. 13 — Dec. 21, 1998
  • pp: 524–529
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Experimental observation of interfering Bessel beams

S. Chávez-Cerda, E. Tepichin, M. A. Meneses-Nava, G. Ramirez, and J. Miguel Hickmann  »View Author Affiliations


Optics Express, Vol. 3, Issue 13, pp. 524-529 (1998)
http://dx.doi.org/10.1364/OE.3.000524


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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.

© Optical Society of America

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.

In order to provide a better understanding of our experimental results, initially we will do a brief theoretical discussion. Mathematically the SBB may be represented by the following equation obtained from a Hankel transform applied to the light produced by a double annular slit:

Irz=J02(k0r)+a2J02(k1r)+2aJ02(k0r)J02(k1r)cos((kz0kz1)z+θ)
(1)

where r=x2+y2 is the radial coordinate, ki is the normalized radius of the annular slits and kiz2 = k 2 - kir2, with i = 0, 1 referring to the two annular slits. The symbols a and θ are, respectively, an amplitude factor and a phase difference relating the two Bessel beams. From this equation we notice that along the longitudinal axis the intensity will oscillate due to the presence of the last term. In order to simplify from now on we will deal with the particular case where there is no phase difference nor amplitude between the two Bessel beams, i.e. θ = 0 and a = 1 without loss of generality.

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. Experimental setup.
Figure 4. A sequence of photografic shots showing the SBB evolution in the first period.

Figure 5. A sequence of photografic shots showing the subsequent central mini-mums and maximums along the evolution of the SBB.

In order to compare the theory with our experimental results in Fig. 6 we show a density plot obtained through a numerical simulation of the evolution using the experimental parameters for the distances corresponding to a minimum (a) and to a maximum (b) at the beam’s center. The area depicted in the picture is equivalent to the area shown in the experimental picture shots. We observe an almost perfect match between both results.

Figure 6. Simulated density plots to the positions corresponding to a central minimum (a) and maximum (b).

One of the authors (JMH) owe a debt to R. Pinheiro and H. Alencar. He also thanks the partial support by CNPq, FINEP, CAPES, FAPEAL, Brazilian agencies, and the TWAS (Third World Academy of Science) besides the INAOE (Instituto Nacional de Astrofísica Óptica y Electrónica) by the support during his stay in México. This work was partially supported by CONACYT (Consejo Nacional de Ciencia y Tecnología) under the grant number 3943P-E9607.

References

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, “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).

OCIS Codes
(140.3300) Lasers and laser optics : Laser beam shaping
(260.1960) Physical optics : Diffraction theory

ToC Category:
Research Papers

History
Published: December 21, 1998

Citation
Sabino Chavez-Cerda, Eduardo Tepichin, Antonio Meneses-Nava, G. Ramirez, and Jandir Miguel Hickmann, "Experimental observation of interfering Bessel beams," Opt. Express 3, 524-529 (1998)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-3-13-524


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References

  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).

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