Abstract

A new experimental setup is demonstrated to produce high-order Bessel beams. It is based on the field decomposition of the Bessel beam into its even and odd field components. The implementation is performed over the spectral components with a Mach-Zehnder interferometer that synthesizes the components into the desired Bessel beam. The main advantage of our setup is that the required annular transmittances have only discrete phase changes of π radians instead of a continuous change of phase.

© 2004 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  8. W.-X. Cong, N.-X. Chen, B.-Y. Gu, “Generation of nondiffracting beams by diffractive phase elements,” J. Opt. Soc. Am. A 15, 2362–2364 (1998).
    [Crossref]
  9. K. Uehara, H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125–129 (1989).
    [Crossref]
  10. P. Pääkkönen, J. Turunen, “Resonators with Bessel-Gauss modes,” Opt. Commun. 156, 359–366 (1998).
    [Crossref]
  11. J. Rogel-Salazar, G. H. C. New, S. Chávez-Cerda, “Bessel-Gauss beam optical resonator,” Opt. Commun. 190, 117–122 (2001).
    [Crossref]
  12. A. N. Khilo, E. G. Katranji, A. A. Ryzhevich, “Axicon-based Bessel resonator: analytical description and experiment,” J. Opt. Soc. Am. A 18, 1986–1992 (2001).
    [Crossref]
  13. J. C. Gutiérrez-Vega, R. Rodriguez-Masegosa, S. Chávez-Cerda, “Bessel-Gauss resonator with spherical output mirror: geometrical- and wave-optics analysis,” J. Opt. Soc. Am. A 20, 2113–2122 (2003).
    [Crossref]
  14. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, Cambridge, UK, 1987), pp. 651–654.
  15. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25, 1493–1495 (2000).
    [Crossref]
  16. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
    [Crossref]

2003 (1)

2001 (3)

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

J. Rogel-Salazar, G. H. C. New, S. Chávez-Cerda, “Bessel-Gauss beam optical resonator,” Opt. Commun. 190, 117–122 (2001).
[Crossref]

A. N. Khilo, E. G. Katranji, A. A. Ryzhevich, “Axicon-based Bessel resonator: analytical description and experiment,” J. Opt. Soc. Am. A 18, 1986–1992 (2001).
[Crossref]

2000 (1)

1998 (2)

1992 (1)

G. Scott, N. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
[Crossref]

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

1954 (1)

Chávez-Cerda, S.

J. C. Gutiérrez-Vega, R. Rodriguez-Masegosa, S. Chávez-Cerda, “Bessel-Gauss resonator with spherical output mirror: geometrical- and wave-optics analysis,” J. Opt. Soc. Am. A 20, 2113–2122 (2003).
[Crossref]

J. Rogel-Salazar, G. H. C. New, S. Chávez-Cerda, “Bessel-Gauss beam optical resonator,” Opt. Commun. 190, 117–122 (2001).
[Crossref]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25, 1493–1495 (2000).
[Crossref]

Chen, N.-X.

Cong, W.-X.

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

Eberly, J. H.

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

Friberg, A. T.

Gu, B.-Y.

Gutiérrez-Vega, J. C.

Indebetouw, G.

Iturbe-Castillo, M. D.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25, 1493–1495 (2000).
[Crossref]

Katranji, E. G.

Khilo, A. N.

Kikuchi, H.

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

McArdle, N.

G. Scott, N. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
[Crossref]

McLeod, J. H.

Micely, J. J.

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

New, G. H. C.

J. Rogel-Salazar, G. H. C. New, S. Chávez-Cerda, “Bessel-Gauss beam optical resonator,” Opt. Commun. 190, 117–122 (2001).
[Crossref]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

Pääkkönen, P.

P. Pääkkönen, J. Turunen, “Resonators with Bessel-Gauss modes,” Opt. Commun. 156, 359–366 (1998).
[Crossref]

Ramírez, G. A.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

Rodríguez-Dagnino, R. M.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

Rodriguez-Masegosa, R.

Rogel-Salazar, J.

J. Rogel-Salazar, G. H. C. New, S. Chávez-Cerda, “Bessel-Gauss beam optical resonator,” Opt. Commun. 190, 117–122 (2001).
[Crossref]

Ryzhevich, A. A.

Scott, G.

G. Scott, N. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
[Crossref]

Tepichín, E.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

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.

Watson, G. N.

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, Cambridge, UK, 1987), pp. 651–654.

Appl. Opt. (1)

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 (6)

Opt. Commun. (3)

P. Pääkkönen, J. Turunen, “Resonators with Bessel-Gauss modes,” Opt. Commun. 156, 359–366 (1998).
[Crossref]

J. Rogel-Salazar, G. H. C. New, S. Chávez-Cerda, “Bessel-Gauss beam optical resonator,” Opt. Commun. 190, 117–122 (2001).
[Crossref]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

Opt. Eng. (1)

G. Scott, N. McArdle, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng. 31, 2640–2643 (1992).
[Crossref]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

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

Other (1)

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, Cambridge, UK, 1987), pp. 651–654.

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Figures (5)

Fig. 1
Fig. 1

Simple experimental setup used to generate nondiffracting beams.

Fig. 2
Fig. 2

Amplitude and phase distributions of the first-order (a) and (d) Bessel cosine, (b) and (e) Bessel sine, and (c) and (f) Bessel beams. In the phase distributions, white regions represent a value of zero and black regions represent a value of π.

Fig. 3
Fig. 3

Mach-Zehnder setup to produce HOBBs. Transmittances T 1 and T 2 are placed at a focal distance from the lens.

Fig. 4
Fig. 4

(a) and (c) Photographic images of the first-order Bessel cosine and Bessel sine beams and (b) and (d) intensity variation with angular position for the fourth lobes.

Fig. 5
Fig. 5

Photographic sequence of the first-order Bessel beam at planes z = 1, 2, 3, 4, 5, and 6 m. Image size is 1.8 mm × 1.8 mm.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

Ux, y, z0=expikzz02π Aφexpiktx cos φ+y sin φdφ,
Uρ, ϕ, z=Jmktρexpimϕexpikzz,
kt=k sin θ0=kaa2+f2-1/2,
kz=k cos θ0=kfa2+f2-1/2.
U=U1+iU2=Jmktρcosmϕexpikzz+iJmktρsinmϕexpikzz.
T1φ=cosmφ, T2φ=sinmφ,

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