Abstract

The diffraction patterns of a conical lens illuminated by plane and spherical waves have been intensively investigated. A practical method is described to transform the Bessel profile of a zero-order Bessel beam into a caustic one through the use of a combination of a conical lens and a cylindrical lens, which in turn transforms the field generated by the conical lens. The cylindrical lens was illuminated by a zero-order Bessel beam, producing a lips caustic beam. It is shown that this type of wave tends to regenerate during propagation, although the waves are severely perturbed.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. F. Nye, “The relation between the spherical aberration of a lens and the spun cusp diffraction catastrophe,” J. Opt. A: Pure Appl. Opt. 7, 95-102 (2005).
    [CrossRef]
  2. A. M. Deykoon, M. S. Soskin, and G. A. Swartzlander, Jr., “Nonlinear optical catastrophe from a smooth initial beam,” Opt. Lett. 24, 1224-1226 (1999).
    [CrossRef]
  3. R. Arimoto, C. Saloma, T. Tanaka, and S. Kawata, “Imaging properties of axicon in a scanning optical system,” Appl. Opt. 31, 6653-6657 (1992).
    [CrossRef] [PubMed]
  4. A. Thaning, Z. Jaroszewicz, and A. T. Friberg, “Diffractive axicons in oblique illumination: analysis and experiments and comparison with elliptical axicons,” Appl. Opt. 42, 9-17(2003).
    [CrossRef] [PubMed]
  5. M. Anguiano-Morales, A. Martínez, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Self-healing property of a caustic optical beam,” Appl. Opt. 46, 8284-8290 (2007).
    [CrossRef] [PubMed]
  6. M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex,” JETP Lett. 71, 130-133(2000).
    [CrossRef]
  7. J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am. 44, 592-597 (1954).
    [CrossRef]
  8. Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207-211(1998).
    [CrossRef]
  9. M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Conical dynamics of Bessel beams,” Opt. Eng. 46, 078001 (2007).
    [CrossRef]
  10. M. V. Perez, C. Gomez-Reino, and J. M. Cuadrado, “Diffraction patterns and zone plates produced by thin linear axicons,” Opt. Acta 33, 1161-1176 (1986).
    [CrossRef]

2007

M. Anguiano-Morales, A. Martínez, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Self-healing property of a caustic optical beam,” Appl. Opt. 46, 8284-8290 (2007).
[CrossRef] [PubMed]

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Conical dynamics of Bessel beams,” Opt. Eng. 46, 078001 (2007).
[CrossRef]

2005

J. F. Nye, “The relation between the spherical aberration of a lens and the spun cusp diffraction catastrophe,” J. Opt. A: Pure Appl. Opt. 7, 95-102 (2005).
[CrossRef]

2003

2000

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex,” JETP Lett. 71, 130-133(2000).
[CrossRef]

1999

1998

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207-211(1998).
[CrossRef]

1992

1986

M. V. Perez, C. Gomez-Reino, and J. M. Cuadrado, “Diffraction patterns and zone plates produced by thin linear axicons,” Opt. Acta 33, 1161-1176 (1986).
[CrossRef]

1954

Anguiano-Morales, M.

M. Anguiano-Morales, A. Martínez, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Self-healing property of a caustic optical beam,” Appl. Opt. 46, 8284-8290 (2007).
[CrossRef] [PubMed]

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Conical dynamics of Bessel beams,” Opt. Eng. 46, 078001 (2007).
[CrossRef]

Arimoto, R.

Bouchal, Z.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207-211(1998).
[CrossRef]

Chávez-Cerda,

Chávez-Cerda, S.

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Conical dynamics of Bessel beams,” Opt. Eng. 46, 078001 (2007).
[CrossRef]

Chlup, M.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207-211(1998).
[CrossRef]

Cuadrado, J. M.

M. V. Perez, C. Gomez-Reino, and J. M. Cuadrado, “Diffraction patterns and zone plates produced by thin linear axicons,” Opt. Acta 33, 1161-1176 (1986).
[CrossRef]

Deykoon, A. M.

Friberg, A. T.

Gomez-Reino, C.

M. V. Perez, C. Gomez-Reino, and J. M. Cuadrado, “Diffraction patterns and zone plates produced by thin linear axicons,” Opt. Acta 33, 1161-1176 (1986).
[CrossRef]

Iturbe-Castillo, M. D.

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Conical dynamics of Bessel beams,” Opt. Eng. 46, 078001 (2007).
[CrossRef]

M. Anguiano-Morales, A. Martínez, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Self-healing property of a caustic optical beam,” Appl. Opt. 46, 8284-8290 (2007).
[CrossRef] [PubMed]

Jaroszewicz, Z.

Kawata, S.

Marienko, I. G.

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex,” JETP Lett. 71, 130-133(2000).
[CrossRef]

Martínez, A.

McLeod, J. H.

Méndez-Otero, M. M.

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Conical dynamics of Bessel beams,” Opt. Eng. 46, 078001 (2007).
[CrossRef]

Nye, J. F.

J. F. Nye, “The relation between the spherical aberration of a lens and the spun cusp diffraction catastrophe,” J. Opt. A: Pure Appl. Opt. 7, 95-102 (2005).
[CrossRef]

Perez, M. V.

M. V. Perez, C. Gomez-Reino, and J. M. Cuadrado, “Diffraction patterns and zone plates produced by thin linear axicons,” Opt. Acta 33, 1161-1176 (1986).
[CrossRef]

Saloma, C.

Soskin, M. S.

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex,” JETP Lett. 71, 130-133(2000).
[CrossRef]

A. M. Deykoon, M. S. Soskin, and G. A. Swartzlander, Jr., “Nonlinear optical catastrophe from a smooth initial beam,” Opt. Lett. 24, 1224-1226 (1999).
[CrossRef]

Swartzlander, G. A.

Tanaka, T.

Thaning, A.

Vasnetsov, M. V.

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex,” JETP Lett. 71, 130-133(2000).
[CrossRef]

Wagner, J.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207-211(1998).
[CrossRef]

Appl. Opt.

J. Opt. A: Pure Appl. Opt.

J. F. Nye, “The relation between the spherical aberration of a lens and the spun cusp diffraction catastrophe,” J. Opt. A: Pure Appl. Opt. 7, 95-102 (2005).
[CrossRef]

J. Opt. Soc. Am.

JETP Lett.

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex,” JETP Lett. 71, 130-133(2000).
[CrossRef]

Opt. Acta

M. V. Perez, C. Gomez-Reino, and J. M. Cuadrado, “Diffraction patterns and zone plates produced by thin linear axicons,” Opt. Acta 33, 1161-1176 (1986).
[CrossRef]

Opt. Commun.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207-211(1998).
[CrossRef]

Opt. Eng.

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Conical dynamics of Bessel beams,” Opt. Eng. 46, 078001 (2007).
[CrossRef]

Opt. Lett.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Schematic illustration of the generation of a Bessel beam using a conical lens. A collimated beam is incident on a conical lens, which has an opening angle γ. Beyond the conical lens, the beam is deviated toward the z axis at an angle θ, and in the interference zone a Bessel beam is formed. For z > z Max , a hollow beam is obtained.

Fig. 2
Fig. 2

Schematic diagram of the experimental setup to generate a caustic beam. The conical lens is illuminated with a plane wave with normal incidence. At a distance z 0 from the conical lens, a cylindrical lens is placed, so the field after passing through the second lens is detected at some observation point denoted by z p .

Fig. 3
Fig. 3

Experimentally obtained caustics by means of the combination of a conical lens and a cylindrical lens, in the region z p < f , where z p is (a)  80 mm and (b)  100 mm .

Fig. 4
Fig. 4

Experimentally obtained caustics at z p of (a)  145 mm and (b)  160 mm from the cylindrical lens.

Fig. 5
Fig. 5

Transverse intensity distributions of the focal segments generated by means of the combination of a conical lens and a cylindrical lens in the region z p > f , where z p is (a)  170 mm and (b)  400 mm from the cylindrical lens.

Fig. 6
Fig. 6

Numeric results of the diffraction pattern of the conical lens and the cylindrical lens when z p is (a)  100 mm ( z p < f ) and (b)  400 mm ( z p > f ).

Fig. 7
Fig. 7

Experimental results for an obstructed lips caustic beam when z p is (a)  170 mm , (b)  370 mm , (c)  400 mm , and (d)  430 mm from the cylindrical lens.

Fig. 8
Fig. 8

Intensity distribution recorded beyond the conical lens, at z p = 430 mm .

Fig. 9
Fig. 9

Evolution of a truncated hexagonal array when z p is (a)  170 mm and (b)  430 mm from conical lens.

Equations (4)

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

r z Max = tan [ ( n 1 ) γ ] .
z Max = r ( n 1 ) γ ,
t CL = exp ( i k x 2 2 f ) .
H 0 ( 2 ) ( k ρ ) e i k z .

Metrics