Abstract

We introduce a simple, single beam method for determination of the topological charge of polychromatic optical vortices. It is based on astigmatic transformation of singular optical beams, where the intensity pattern of a vortex beam acquires a form of dark stripes in the focal plane of a cylindrical lens. The number of the dark stripes is equal to the modulus of the vortex topological charge, while the stripe tilt indicates the charge sign. We demonstrate experimentally the effectiveness of this technique by revealing complex topological structure of polychromatic singular beams.

© 2009 Optical Society of America

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  1. J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. London A 336, 165-190 (1974).
    [CrossRef]
  2. M. S. Soskin and M. V. Vasnetsov, "Singular optics," Prog. Opt. 42, 219 (Ed. E. Wolf, Elsevier, 2001).
    [CrossRef]
  3. M. R. Dennis, K. O’Holleran, and M. J. Padgett, "Singular Optics: Optical Vortices and Polarization Singularities," Prog. Opt. 52, 293 (Ed. E. Wolf, Elsevier, 2009).
    [CrossRef]
  4. N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkukov, "Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment)," JETP Lett. 33, 195-199 (1981).
  5. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, "Generation of optical phase singularities by computer-generated holograms," Opt. Lett. 17, 221-223 (1992).
    [CrossRef] [PubMed]
  6. H. I. Sztul and R. R. Alfano, "Double-slit interference with Laguerre-Gaussian Beams," Opt. Lett. 31, 999 (2006).
    [CrossRef] [PubMed]
  7. G. Gbur and T. D. Visser, "Coherence vortices in partially coherent beams," Opt. Commun. 222, 117-125 (2003).
    [CrossRef]
  8. D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Jr., "Spatial correlation singularity of a vortex field," Phys. Rev. Lett. 92, 143905 (2004).
    [CrossRef] [PubMed]
  9. J. Leach and M. J. Padgett, "Observation of chromatic effects near a white-light vortex," New J. Phys. 5, 1541-1547 (2003).
    [CrossRef]
  10. O. V. Angelsky, S. G. Hanson, A. P. Maksimyak, and P. P. Maksimyak, "On the feasibility for determining the amplitude zeroes in polychromatic fields," Opt. Express 13, 4396-4405 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4396.
    [CrossRef] [PubMed]
  11. A. V. Volyar, Yu. A. Egorov, A. F. Rubass, and T. A. Fadeeva, "Fine structure of white optical vortices in crystals," Tech. Phys. Lett. 30, 701-704 (2004).
    [CrossRef]
  12. M. S. Soskin, P. V. Polyanskii, and O. O. Arkhelyuk, "Computer-synthesized hologram-based rainbow optical vortices," New J. Phys. 6, 196 (2004).
    [CrossRef]
  13. I. Freund, "Poincaré vortices," Opt. Lett. 26, 1996 (2001).
    [CrossRef]
  14. V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Yu. S. Kivshar, "Mapping phases of singular scalar light fields," Opt. Lett. 33, 89-91 (2008).
    [CrossRef]
  15. V. Shvedov, W. Krolikowski, A. Volyar, D. N. Neshev, A. S. Desyatnikov and Yu. S. Kivshar, "Focusing and correlation properties of white-light optical vortices," Opt. Express 13, 7393-7398 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-19-7393.
    [CrossRef] [PubMed]
  16. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
    [CrossRef] [PubMed]
  17. G. Molina-Terriza, J. Recolons, J. P. Torres, and L. Torner, "Observation of the Dynamical Inversion of the Topological Charge of an Optical Vortex," Phys. Rev. Lett. 87, 023902 (2001).
    [CrossRef]
  18. J. Serna, F. Encinas-Sanz, and G. Nemes¸, "Complete spatial characterization of a pulsed doughnut-type beam by use of spherical optics and a cylindrical lens," J. Opt. Soc. Am. A 18, 1726-1733 (2001).
    [CrossRef]
  19. V. H. Denisenko, M. S. Soskin, and M. V. Vasnetsov, "Transformations of Laguerre-Gaussian modes carrying optical vortex and their orbital angular momentum by cylindrical lens," Proc. SPIE 4607, 54-58 (2002).
    [CrossRef]
  20. A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, "Transformation of higher-order optical vortices upon focusing by an astigmatic lens," Opt. Commun. 241, 237-247 (2004).
    [CrossRef]
  21. R. K. Singh, P. Senthilkumaran, and K. Singh, "Influence of astigmatism and defocusing on the focusing of a singular beam," Opt. Commun. 270, 128-138 (2006).
    [CrossRef]
  22. A. Volyar, V. Shvedov, T. Fadeyeva, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, "Generation of single-charge optical vortices with an uniaxial crystal," Opt. Express 14, 3724-3729 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-9-3724.
    [CrossRef]
  23. A. V. Volyar and T. A. Fadeeva, "Generation of singular beams in uniaxial crystals," Opt. Spectrosc. 94, 235-244 (2003).
    [CrossRef]
  24. D. N. Neshev, A. Dreischuh, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, "Observation of polychromatic vortex solitons," Opt. Lett. 33, 1851-1853 (2008).
    [CrossRef] [PubMed]

2008 (2)

2006 (3)

2005 (2)

2004 (4)

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Jr., "Spatial correlation singularity of a vortex field," Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef] [PubMed]

A. V. Volyar, Yu. A. Egorov, A. F. Rubass, and T. A. Fadeeva, "Fine structure of white optical vortices in crystals," Tech. Phys. Lett. 30, 701-704 (2004).
[CrossRef]

M. S. Soskin, P. V. Polyanskii, and O. O. Arkhelyuk, "Computer-synthesized hologram-based rainbow optical vortices," New J. Phys. 6, 196 (2004).
[CrossRef]

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, "Transformation of higher-order optical vortices upon focusing by an astigmatic lens," Opt. Commun. 241, 237-247 (2004).
[CrossRef]

2003 (3)

A. V. Volyar and T. A. Fadeeva, "Generation of singular beams in uniaxial crystals," Opt. Spectrosc. 94, 235-244 (2003).
[CrossRef]

G. Gbur and T. D. Visser, "Coherence vortices in partially coherent beams," Opt. Commun. 222, 117-125 (2003).
[CrossRef]

J. Leach and M. J. Padgett, "Observation of chromatic effects near a white-light vortex," New J. Phys. 5, 1541-1547 (2003).
[CrossRef]

2002 (1)

V. H. Denisenko, M. S. Soskin, and M. V. Vasnetsov, "Transformations of Laguerre-Gaussian modes carrying optical vortex and their orbital angular momentum by cylindrical lens," Proc. SPIE 4607, 54-58 (2002).
[CrossRef]

2001 (3)

1992 (2)

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, "Generation of optical phase singularities by computer-generated holograms," Opt. Lett. 17, 221-223 (1992).
[CrossRef] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

1981 (1)

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkukov, "Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment)," JETP Lett. 33, 195-199 (1981).

1974 (1)

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. London A 336, 165-190 (1974).
[CrossRef]

Alfano, R. R.

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Angelsky, O. V.

Arkhelyuk, O. O.

M. S. Soskin, P. V. Polyanskii, and O. O. Arkhelyuk, "Computer-synthesized hologram-based rainbow optical vortices," New J. Phys. 6, 196 (2004).
[CrossRef]

Baranova, N. B.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkukov, "Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment)," JETP Lett. 33, 195-199 (1981).

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Bekshaev, A. Ya.

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, "Transformation of higher-order optical vortices upon focusing by an astigmatic lens," Opt. Commun. 241, 237-247 (2004).
[CrossRef]

Berry, M. V.

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. London A 336, 165-190 (1974).
[CrossRef]

Denisenko, V. G.

Denisenko, V. H.

V. H. Denisenko, M. S. Soskin, and M. V. Vasnetsov, "Transformations of Laguerre-Gaussian modes carrying optical vortex and their orbital angular momentum by cylindrical lens," Proc. SPIE 4607, 54-58 (2002).
[CrossRef]

Desyatnikov, A. S.

Dreischuh, A.

Egorov, Yu. A.

A. V. Volyar, Yu. A. Egorov, A. F. Rubass, and T. A. Fadeeva, "Fine structure of white optical vortices in crystals," Tech. Phys. Lett. 30, 701-704 (2004).
[CrossRef]

Encinas-Sanz, F.

Fadeeva, T. A.

A. V. Volyar, Yu. A. Egorov, A. F. Rubass, and T. A. Fadeeva, "Fine structure of white optical vortices in crystals," Tech. Phys. Lett. 30, 701-704 (2004).
[CrossRef]

A. V. Volyar and T. A. Fadeeva, "Generation of singular beams in uniaxial crystals," Opt. Spectrosc. 94, 235-244 (2003).
[CrossRef]

Fadeyeva, T.

Freund, I.

Gbur, G.

G. Gbur and T. D. Visser, "Coherence vortices in partially coherent beams," Opt. Commun. 222, 117-125 (2003).
[CrossRef]

Hanson, S. G.

Heckenberg, N. R.

Kivshar, Yu. S.

Krolikowski, W.

Leach, J.

J. Leach and M. J. Padgett, "Observation of chromatic effects near a white-light vortex," New J. Phys. 5, 1541-1547 (2003).
[CrossRef]

Maksimyak, A. P.

Maksimyak, P. P.

Maleev, I. D.

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Jr., "Spatial correlation singularity of a vortex field," Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef] [PubMed]

Mamaev, A. V.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkukov, "Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment)," JETP Lett. 33, 195-199 (1981).

Marathay, A. S.

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Jr., "Spatial correlation singularity of a vortex field," Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef] [PubMed]

McDuff, R.

Minovich, A.

Molina-Terriza, G.

G. Molina-Terriza, J. Recolons, J. P. Torres, and L. Torner, "Observation of the Dynamical Inversion of the Topological Charge of an Optical Vortex," Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

Nemes¸, G.

Neshev, D. N.

Nye, J. F.

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. London A 336, 165-190 (1974).
[CrossRef]

Padgett, M. J.

J. Leach and M. J. Padgett, "Observation of chromatic effects near a white-light vortex," New J. Phys. 5, 1541-1547 (2003).
[CrossRef]

Palacios, D. M.

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Jr., "Spatial correlation singularity of a vortex field," Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef] [PubMed]

Pilipetskii, N. F.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkukov, "Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment)," JETP Lett. 33, 195-199 (1981).

Polyanskii, P. V.

M. S. Soskin, P. V. Polyanskii, and O. O. Arkhelyuk, "Computer-synthesized hologram-based rainbow optical vortices," New J. Phys. 6, 196 (2004).
[CrossRef]

Recolons, J.

G. Molina-Terriza, J. Recolons, J. P. Torres, and L. Torner, "Observation of the Dynamical Inversion of the Topological Charge of an Optical Vortex," Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

Rubass, A. F.

A. V. Volyar, Yu. A. Egorov, A. F. Rubass, and T. A. Fadeeva, "Fine structure of white optical vortices in crystals," Tech. Phys. Lett. 30, 701-704 (2004).
[CrossRef]

Senthilkumaran, P.

R. K. Singh, P. Senthilkumaran, and K. Singh, "Influence of astigmatism and defocusing on the focusing of a singular beam," Opt. Commun. 270, 128-138 (2006).
[CrossRef]

Serna, J.

Shkukov, V. V.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkukov, "Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment)," JETP Lett. 33, 195-199 (1981).

Shvedov, V.

Singh, K.

R. K. Singh, P. Senthilkumaran, and K. Singh, "Influence of astigmatism and defocusing on the focusing of a singular beam," Opt. Commun. 270, 128-138 (2006).
[CrossRef]

Singh, R. K.

R. K. Singh, P. Senthilkumaran, and K. Singh, "Influence of astigmatism and defocusing on the focusing of a singular beam," Opt. Commun. 270, 128-138 (2006).
[CrossRef]

Smith, C. P.

Soskin, M. S.

V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Yu. S. Kivshar, "Mapping phases of singular scalar light fields," Opt. Lett. 33, 89-91 (2008).
[CrossRef]

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, "Transformation of higher-order optical vortices upon focusing by an astigmatic lens," Opt. Commun. 241, 237-247 (2004).
[CrossRef]

M. S. Soskin, P. V. Polyanskii, and O. O. Arkhelyuk, "Computer-synthesized hologram-based rainbow optical vortices," New J. Phys. 6, 196 (2004).
[CrossRef]

V. H. Denisenko, M. S. Soskin, and M. V. Vasnetsov, "Transformations of Laguerre-Gaussian modes carrying optical vortex and their orbital angular momentum by cylindrical lens," Proc. SPIE 4607, 54-58 (2002).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Swartzlander, G. A.

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Jr., "Spatial correlation singularity of a vortex field," Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef] [PubMed]

Sztul, H. I.

Torner, L.

G. Molina-Terriza, J. Recolons, J. P. Torres, and L. Torner, "Observation of the Dynamical Inversion of the Topological Charge of an Optical Vortex," Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

Torres, J. P.

G. Molina-Terriza, J. Recolons, J. P. Torres, and L. Torner, "Observation of the Dynamical Inversion of the Topological Charge of an Optical Vortex," Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

Vasnetsov, M. V.

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, "Transformation of higher-order optical vortices upon focusing by an astigmatic lens," Opt. Commun. 241, 237-247 (2004).
[CrossRef]

V. H. Denisenko, M. S. Soskin, and M. V. Vasnetsov, "Transformations of Laguerre-Gaussian modes carrying optical vortex and their orbital angular momentum by cylindrical lens," Proc. SPIE 4607, 54-58 (2002).
[CrossRef]

Visser, T. D.

G. Gbur and T. D. Visser, "Coherence vortices in partially coherent beams," Opt. Commun. 222, 117-125 (2003).
[CrossRef]

Volyar, A.

Volyar, A. V.

A. V. Volyar, Yu. A. Egorov, A. F. Rubass, and T. A. Fadeeva, "Fine structure of white optical vortices in crystals," Tech. Phys. Lett. 30, 701-704 (2004).
[CrossRef]

A. V. Volyar and T. A. Fadeeva, "Generation of singular beams in uniaxial crystals," Opt. Spectrosc. 94, 235-244 (2003).
[CrossRef]

White, A. G.

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Zel’dovich, B. Ya.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkukov, "Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment)," JETP Lett. 33, 195-199 (1981).

J. Opt. Soc. Am. A (1)

JETP Lett. (1)

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkukov, "Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment)," JETP Lett. 33, 195-199 (1981).

New J. Phys. (2)

J. Leach and M. J. Padgett, "Observation of chromatic effects near a white-light vortex," New J. Phys. 5, 1541-1547 (2003).
[CrossRef]

M. S. Soskin, P. V. Polyanskii, and O. O. Arkhelyuk, "Computer-synthesized hologram-based rainbow optical vortices," New J. Phys. 6, 196 (2004).
[CrossRef]

Opt. Commun. (3)

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, "Transformation of higher-order optical vortices upon focusing by an astigmatic lens," Opt. Commun. 241, 237-247 (2004).
[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, "Influence of astigmatism and defocusing on the focusing of a singular beam," Opt. Commun. 270, 128-138 (2006).
[CrossRef]

G. Gbur and T. D. Visser, "Coherence vortices in partially coherent beams," Opt. Commun. 222, 117-125 (2003).
[CrossRef]

Opt. Express (3)

Opt. Lett. (5)

Opt. Spectrosc. (1)

A. V. Volyar and T. A. Fadeeva, "Generation of singular beams in uniaxial crystals," Opt. Spectrosc. 94, 235-244 (2003).
[CrossRef]

Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

G. Molina-Terriza, J. Recolons, J. P. Torres, and L. Torner, "Observation of the Dynamical Inversion of the Topological Charge of an Optical Vortex," Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Jr., "Spatial correlation singularity of a vortex field," Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef] [PubMed]

Proc. R. Soc. London A (1)

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. London A 336, 165-190 (1974).
[CrossRef]

Proc. SPIE (1)

V. H. Denisenko, M. S. Soskin, and M. V. Vasnetsov, "Transformations of Laguerre-Gaussian modes carrying optical vortex and their orbital angular momentum by cylindrical lens," Proc. SPIE 4607, 54-58 (2002).
[CrossRef]

Tech. Phys. Lett. (1)

A. V. Volyar, Yu. A. Egorov, A. F. Rubass, and T. A. Fadeeva, "Fine structure of white optical vortices in crystals," Tech. Phys. Lett. 30, 701-704 (2004).
[CrossRef]

Other (2)

M. S. Soskin and M. V. Vasnetsov, "Singular optics," Prog. Opt. 42, 219 (Ed. E. Wolf, Elsevier, 2001).
[CrossRef]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, "Singular Optics: Optical Vortices and Polarization Singularities," Prog. Opt. 52, 293 (Ed. E. Wolf, Elsevier, 2009).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Intensity patterns in the focal plane of a cylindrical lens calculated for vortex beams with topological charges (a, b) l=+1 and (c, d) l=-2; parameter p=1.2 in (a, c) and p=10.6 in (b, d).

Fig. 2.
Fig. 2.

Experimental setup: SC - supercontinuum beam, WP1 and WP2 - quarter-wave plates; MO1 and MO2 - 3× and 5× achromatic microscope objectives, respectively; KTP - sample of uniaxial crystal; P - polarizer; F - variable spectral filter (300–750 nm); CL - cylindrical lens. The coloring of the beam indicates its polychromatic content.

Fig. 3.
Fig. 3.

Vortex beam with topological charge (a–c) l=+1 and (d–f) l=-1. The original intensity distributions in (a) and (d) to compare with the focal pattern of the cylindrical lens in (b) and (e). The frames (c) and (f) are the images in (b) and (e), respectively, but stretched in vertical direction by a factor of 3.5. The spatial scale is defined by the 5.25 mm size of frames (a) and (d).

Fig. 4.
Fig. 4.

True colour images of (a) double-charge polychromatic vortex beam and (b–h) its spectral components. After focusing by a cylindrical lens all components form a similar spatial pattern (bottom frames), featuring two distinct dark stripes. The slight colouring in (d,e) is due to the weak peak of transmission of the variable filter at longer wavelengths.

Fig. 5.
Fig. 5.

True color intensity distribution of the polychromatic beam (a) and its spectral components (b–j) without the cylindrical lens (top rows) and in its focal plane (bottom rows). The vertical stretching of the latter is indicated by the spatial scales in (b).

Equations (1)

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E ( x , y , z = f ) 2 = p 4 ξ 2 + 2 s p ξ η + η 2 ( 1 + p 2 ) ( 1 + p 2 ) 3 / 2 exp ( 2 p 2 ξ 2 1 + p 2 2 p 2 η 2 ) .

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