Abstract

The vortex emergence process as an integer order Bessel field progresses continuously onto the contiguous higher order Bessel field is studied in detail. We assess the progressive migration of phase singularities and explain the predicted increase in fractional orbital angular momentum content of the beam in terms of this gradual process.

© 2008 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Vortex structure of elegant Laguerre–Gaussian beams of fractional order

Israel Martinez-Castellanos and Julio C. Gutiérrez-Vega
J. Opt. Soc. Am. A 30(11) 2395-2400 (2013)

Light beams with fractional orbital angular momentum and their vortex structure

Jörg B. Götte, Kevin O’Holleran, Daryl Preece, Florian Flossmann, Sonja Franke-Arnold, Stephen M. Barnett, and Miles J. Padgett
Opt. Express 16(2) 993-1006 (2008)

References

  • View by:
  • |
  • |
  • |

  1. M.S. Soskin and M. V. Vasnetsov, “Singular Optics”, Prog. Opt. 42, 219–276 (2001).
    [Crossref]
  2. J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micro-manipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
    [Crossref]
  3. D. G. Grier, “A revolution in optical manipulation, ” Nature 424, 810–816 (2003).
    [Crossref] [PubMed]
  4. J. Zagrodzinski, “Vortices in different branches of physics,” Physica C 369, 45–54 (2002).
    [Crossref]
  5. M. V. Berry, in Les Houches Lecture Series Session XXXV, (North-Holland, Amsterdam, 1981), pp.453–543.
  6. M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A 6, 259–269 (2004).
    [Crossref]
  7. J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
    [Crossref]
  8. J. C. Gutiérrez-Vega, “Fractionalization of optical beams: II. Elegant Laguerre–Gaussian modes,” Opt. Express 15, 6300–6313 (2007).
    [Crossref] [PubMed]
  9. J. B. Götte, K. óHolleran, Preece D., F. Flossmann, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express 16, 993–1006 (2008).
    [Crossref] [PubMed]
  10. J. C. Gutiérrez-Vega and C. López-Mariscal, “Nondiffracting vortex beams with continuous orbital angular momentum order dependence,” J. Opt. A: Pure Appl.Opt. 10, 015009 (2008).
    [Crossref]
  11. S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
    [Crossref]
  12. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nature Phys. 3, 305–310 (2007).
    [Crossref]
  13. J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54, 1723–1738 (2007).
    [Crossref]
  14. S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W.’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
    [Crossref] [PubMed]
  15. H. Bechmann-Pasquinucci and A. Peres, “Quantum cryptography with 3-state systems,” Phys. Rev. Lett. 85, 3313–3316 (2000).
    [Crossref] [PubMed]
  16. S. Barreiro, J. W. R. Tabosa, J. P. Torres, Y. Deyanova, and L. Torner, “Four-wave mixing of light beams with engineered orbital angular momentum in cold cesium atoms,” Opt. Lett. 29, 1515–1517 (2004).
    [Crossref] [PubMed]
  17. X. F. Ren, G. P. Guo, Y. F. Huang, and G. C. Guo, “Plasmon-assisted transmission of highdimensional orbital angular momentum entangled states,” Europhys. Lett. 76, 753–759 (2006).
    [Crossref]
  18. J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
    [Crossref]
  19. M. R. Dennis, “Rows of optical vortices from elliptically perturbing a high-order beam,” Opt. Lett. 31, 1325–1327 (2006).
    [Crossref] [PubMed]
  20. J. B. Hayes and S. Lange, “A heterodyne interferometer for testing laser diodes,” Proc SPIE 0429, 22–26 (1983).
  21. I. Freund, “Poincaré vortices,” Opt. Lett. 26, 1996–1998 (2001).
    [Crossref]
  22. V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, “Mapping phases of ingular scalar light fields,” Opt Lett. 33, 89–91 (2008).
    [Crossref]
  23. K. Creath, “Phase-measurement interferometry techniques, “ Prog. Opt. 26, 349–393 (1988).
    [Crossref]
  24. J. F. Nye, J. V. Hajnal, and J. H. Hannay, “Phase saddles and dislocations in two-dimensional waves such as the tides,” Proc. R. Soc. A 417, 7–20 (1988).
    [Crossref]
  25. I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50, 5164–5174 (1994).
    [Crossref] [PubMed]
  26. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1964).
  27. J. C. Gutiérrez-Vega and M. A. Bandres, “Helmholtz-Gauss waves,” J. Opt. Soc. Am. A 22, 289–298 (2005).
    [Crossref]
  28. C. López-Mariscal, M. A. Bandrés, and J. C. Gutiérrez-Vega, “Observation of the experimental propagation properties of Helmholtz-Gauss beams,” Opt. Eng. 45, 068001 (2006).
    [Crossref]
  29. R. Jaúregui and S. Hacyan, “Quantum-mechanical properties of Bessel beams,” Phys. Rev. A 71, 033411 (2005).
    [Crossref]

2008 (3)

J. B. Götte, K. óHolleran, Preece D., F. Flossmann, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express 16, 993–1006 (2008).
[Crossref] [PubMed]

J. C. Gutiérrez-Vega and C. López-Mariscal, “Nondiffracting vortex beams with continuous orbital angular momentum order dependence,” J. Opt. A: Pure Appl.Opt. 10, 015009 (2008).
[Crossref]

V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, “Mapping phases of ingular scalar light fields,” Opt Lett. 33, 89–91 (2008).
[Crossref]

2007 (3)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nature Phys. 3, 305–310 (2007).
[Crossref]

J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54, 1723–1738 (2007).
[Crossref]

J. C. Gutiérrez-Vega, “Fractionalization of optical beams: II. Elegant Laguerre–Gaussian modes,” Opt. Express 15, 6300–6313 (2007).
[Crossref] [PubMed]

2006 (3)

X. F. Ren, G. P. Guo, Y. F. Huang, and G. C. Guo, “Plasmon-assisted transmission of highdimensional orbital angular momentum entangled states,” Europhys. Lett. 76, 753–759 (2006).
[Crossref]

M. R. Dennis, “Rows of optical vortices from elliptically perturbing a high-order beam,” Opt. Lett. 31, 1325–1327 (2006).
[Crossref] [PubMed]

C. López-Mariscal, M. A. Bandrés, and J. C. Gutiérrez-Vega, “Observation of the experimental propagation properties of Helmholtz-Gauss beams,” Opt. Eng. 45, 068001 (2006).
[Crossref]

2005 (4)

R. Jaúregui and S. Hacyan, “Quantum-mechanical properties of Bessel beams,” Phys. Rev. A 71, 033411 (2005).
[Crossref]

J. C. Gutiérrez-Vega and M. A. Bandres, “Helmholtz-Gauss waves,” J. Opt. Soc. Am. A 22, 289–298 (2005).
[Crossref]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[Crossref]

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W.’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref] [PubMed]

2004 (3)

S. Barreiro, J. W. R. Tabosa, J. P. Torres, Y. Deyanova, and L. Torner, “Four-wave mixing of light beams with engineered orbital angular momentum in cold cesium atoms,” Opt. Lett. 29, 1515–1517 (2004).
[Crossref] [PubMed]

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A 6, 259–269 (2004).
[Crossref]

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
[Crossref]

2003 (1)

D. G. Grier, “A revolution in optical manipulation, ” Nature 424, 810–816 (2003).
[Crossref] [PubMed]

2002 (2)

J. Zagrodzinski, “Vortices in different branches of physics,” Physica C 369, 45–54 (2002).
[Crossref]

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[Crossref]

2001 (3)

M.S. Soskin and M. V. Vasnetsov, “Singular Optics”, Prog. Opt. 42, 219–276 (2001).
[Crossref]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micro-manipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[Crossref]

I. Freund, “Poincaré vortices,” Opt. Lett. 26, 1996–1998 (2001).
[Crossref]

2000 (1)

H. Bechmann-Pasquinucci and A. Peres, “Quantum cryptography with 3-state systems,” Phys. Rev. Lett. 85, 3313–3316 (2000).
[Crossref] [PubMed]

1994 (1)

I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50, 5164–5174 (1994).
[Crossref] [PubMed]

1988 (2)

K. Creath, “Phase-measurement interferometry techniques, “ Prog. Opt. 26, 349–393 (1988).
[Crossref]

J. F. Nye, J. V. Hajnal, and J. H. Hannay, “Phase saddles and dislocations in two-dimensional waves such as the tides,” Proc. R. Soc. A 417, 7–20 (1988).
[Crossref]

1983 (1)

J. B. Hayes and S. Lange, “A heterodyne interferometer for testing laser diodes,” Proc SPIE 0429, 22–26 (1983).

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1964).

Aiello, A.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W.’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref] [PubMed]

Arlt, J.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micro-manipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[Crossref]

Bandres, M. A.

Bandrés, M. A.

C. López-Mariscal, M. A. Bandrés, and J. C. Gutiérrez-Vega, “Observation of the experimental propagation properties of Helmholtz-Gauss beams,” Opt. Eng. 45, 068001 (2006).
[Crossref]

Barnett, S. M.

Barreiro, S.

Bechmann-Pasquinucci, H.

H. Bechmann-Pasquinucci and A. Peres, “Quantum cryptography with 3-state systems,” Phys. Rev. Lett. 85, 3313–3316 (2000).
[Crossref] [PubMed]

Berry, M. V.

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A 6, 259–269 (2004).
[Crossref]

M. V. Berry, in Les Houches Lecture Series Session XXXV, (North-Holland, Amsterdam, 1981), pp.453–543.

Courtial, J.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[Crossref]

Creath, K.

K. Creath, “Phase-measurement interferometry techniques, “ Prog. Opt. 26, 349–393 (1988).
[Crossref]

D., Preece

Denisenko, V. G.

V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, “Mapping phases of ingular scalar light fields,” Opt Lett. 33, 89–91 (2008).
[Crossref]

Dennis, M. R.

M. R. Dennis, “Rows of optical vortices from elliptically perturbing a high-order beam,” Opt. Lett. 31, 1325–1327 (2006).
[Crossref] [PubMed]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[Crossref]

Desyatnikov, A. S.

V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, “Mapping phases of ingular scalar light fields,” Opt Lett. 33, 89–91 (2008).
[Crossref]

Deyanova, Y.

Dholakia, K.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micro-manipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[Crossref]

Eliel, E. R.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W.’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref] [PubMed]

Flossmann, F.

Franke-Arnold, S.

Freund, I.

I. Freund, “Poincaré vortices,” Opt. Lett. 26, 1996–1998 (2001).
[Crossref]

I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50, 5164–5174 (1994).
[Crossref] [PubMed]

Garces-Chavez, V.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micro-manipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[Crossref]

Götte, J. B.

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation, ” Nature 424, 810–816 (2003).
[Crossref] [PubMed]

Guo, G. C.

X. F. Ren, G. P. Guo, Y. F. Huang, and G. C. Guo, “Plasmon-assisted transmission of highdimensional orbital angular momentum entangled states,” Europhys. Lett. 76, 753–759 (2006).
[Crossref]

Guo, G. P.

X. F. Ren, G. P. Guo, Y. F. Huang, and G. C. Guo, “Plasmon-assisted transmission of highdimensional orbital angular momentum entangled states,” Europhys. Lett. 76, 753–759 (2006).
[Crossref]

Gutiérrez-Vega, J. C.

J. C. Gutiérrez-Vega and C. López-Mariscal, “Nondiffracting vortex beams with continuous orbital angular momentum order dependence,” J. Opt. A: Pure Appl.Opt. 10, 015009 (2008).
[Crossref]

J. C. Gutiérrez-Vega, “Fractionalization of optical beams: II. Elegant Laguerre–Gaussian modes,” Opt. Express 15, 6300–6313 (2007).
[Crossref] [PubMed]

C. López-Mariscal, M. A. Bandrés, and J. C. Gutiérrez-Vega, “Observation of the experimental propagation properties of Helmholtz-Gauss beams,” Opt. Eng. 45, 068001 (2006).
[Crossref]

J. C. Gutiérrez-Vega and M. A. Bandres, “Helmholtz-Gauss waves,” J. Opt. Soc. Am. A 22, 289–298 (2005).
[Crossref]

Hacyan, S.

R. Jaúregui and S. Hacyan, “Quantum-mechanical properties of Bessel beams,” Phys. Rev. A 71, 033411 (2005).
[Crossref]

Hajnal, J. V.

J. F. Nye, J. V. Hajnal, and J. H. Hannay, “Phase saddles and dislocations in two-dimensional waves such as the tides,” Proc. R. Soc. A 417, 7–20 (1988).
[Crossref]

Hannay, J. H.

J. F. Nye, J. V. Hajnal, and J. H. Hannay, “Phase saddles and dislocations in two-dimensional waves such as the tides,” Proc. R. Soc. A 417, 7–20 (1988).
[Crossref]

Hayes, J. B.

J. B. Hayes and S. Lange, “A heterodyne interferometer for testing laser diodes,” Proc SPIE 0429, 22–26 (1983).

Hooft, G. W.’t

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W.’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref] [PubMed]

Huang, Y. F.

X. F. Ren, G. P. Guo, Y. F. Huang, and G. C. Guo, “Plasmon-assisted transmission of highdimensional orbital angular momentum entangled states,” Europhys. Lett. 76, 753–759 (2006).
[Crossref]

Jaúregui, R.

R. Jaúregui and S. Hacyan, “Quantum-mechanical properties of Bessel beams,” Phys. Rev. A 71, 033411 (2005).
[Crossref]

Kivshar, Y. S.

V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, “Mapping phases of ingular scalar light fields,” Opt Lett. 33, 89–91 (2008).
[Crossref]

Krolikowski, W.

V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, “Mapping phases of ingular scalar light fields,” Opt Lett. 33, 89–91 (2008).
[Crossref]

Lange, S.

J. B. Hayes and S. Lange, “A heterodyne interferometer for testing laser diodes,” Proc SPIE 0429, 22–26 (1983).

Leach, J.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[Crossref]

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
[Crossref]

López-Mariscal, C.

J. C. Gutiérrez-Vega and C. López-Mariscal, “Nondiffracting vortex beams with continuous orbital angular momentum order dependence,” J. Opt. A: Pure Appl.Opt. 10, 015009 (2008).
[Crossref]

C. López-Mariscal, M. A. Bandrés, and J. C. Gutiérrez-Vega, “Observation of the experimental propagation properties of Helmholtz-Gauss beams,” Opt. Eng. 45, 068001 (2006).
[Crossref]

Ma, X.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W.’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref] [PubMed]

Minovich, A.

V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, “Mapping phases of ingular scalar light fields,” Opt Lett. 33, 89–91 (2008).
[Crossref]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nature Phys. 3, 305–310 (2007).
[Crossref]

Nye, J. F.

J. F. Nye, J. V. Hajnal, and J. H. Hannay, “Phase saddles and dislocations in two-dimensional waves such as the tides,” Proc. R. Soc. A 417, 7–20 (1988).
[Crossref]

Oemrawsingh, S. S. R.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W.’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref] [PubMed]

óHolleran, K.

Orlov, S.

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[Crossref]

Padgett, M. J.

J. B. Götte, K. óHolleran, Preece D., F. Flossmann, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express 16, 993–1006 (2008).
[Crossref] [PubMed]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[Crossref]

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
[Crossref]

Peres, A.

H. Bechmann-Pasquinucci and A. Peres, “Quantum cryptography with 3-state systems,” Phys. Rev. Lett. 85, 3313–3316 (2000).
[Crossref] [PubMed]

Regelskis, K.

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[Crossref]

Ren, X. F.

X. F. Ren, G. P. Guo, Y. F. Huang, and G. C. Guo, “Plasmon-assisted transmission of highdimensional orbital angular momentum entangled states,” Europhys. Lett. 76, 753–759 (2006).
[Crossref]

Shvartsman, N.

I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50, 5164–5174 (1994).
[Crossref] [PubMed]

Sibbett, W.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micro-manipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[Crossref]

Smilgevicius, V.

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[Crossref]

Soskin, M. S.

V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, “Mapping phases of ingular scalar light fields,” Opt Lett. 33, 89–91 (2008).
[Crossref]

Soskin, M.S.

M.S. Soskin and M. V. Vasnetsov, “Singular Optics”, Prog. Opt. 42, 219–276 (2001).
[Crossref]

Stabinis, A.

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[Crossref]

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1964).

Tabosa, J. W. R.

Torner, L.

Torres, J. P.

Vasnetsov, M. V.

M.S. Soskin and M. V. Vasnetsov, “Singular Optics”, Prog. Opt. 42, 219–276 (2001).
[Crossref]

Voigt, D.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W.’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref] [PubMed]

Woerdman, J. P.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W.’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref] [PubMed]

Yao, E.

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
[Crossref]

Zagrodzinski, J.

J. Zagrodzinski, “Vortices in different branches of physics,” Physica C 369, 45–54 (2002).
[Crossref]

Zambrini, R.

J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54, 1723–1738 (2007).
[Crossref]

Europhys. Lett. (1)

X. F. Ren, G. P. Guo, Y. F. Huang, and G. C. Guo, “Plasmon-assisted transmission of highdimensional orbital angular momentum entangled states,” Europhys. Lett. 76, 753–759 (2006).
[Crossref]

J. Mod. Opt. (1)

J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54, 1723–1738 (2007).
[Crossref]

J. Opt. A (1)

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A 6, 259–269 (2004).
[Crossref]

J. Opt. A: Pure Appl.Opt. (1)

J. C. Gutiérrez-Vega and C. López-Mariscal, “Nondiffracting vortex beams with continuous orbital angular momentum order dependence,” J. Opt. A: Pure Appl.Opt. 10, 015009 (2008).
[Crossref]

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

Nature (1)

D. G. Grier, “A revolution in optical manipulation, ” Nature 424, 810–816 (2003).
[Crossref] [PubMed]

Nature Phys. (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nature Phys. 3, 305–310 (2007).
[Crossref]

New J. Phys. (2)

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
[Crossref]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[Crossref]

Opt Lett. (1)

V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, “Mapping phases of ingular scalar light fields,” Opt Lett. 33, 89–91 (2008).
[Crossref]

Opt. Commun. (2)

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[Crossref]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micro-manipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[Crossref]

Opt. Eng. (1)

C. López-Mariscal, M. A. Bandrés, and J. C. Gutiérrez-Vega, “Observation of the experimental propagation properties of Helmholtz-Gauss beams,” Opt. Eng. 45, 068001 (2006).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (2)

I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50, 5164–5174 (1994).
[Crossref] [PubMed]

R. Jaúregui and S. Hacyan, “Quantum-mechanical properties of Bessel beams,” Phys. Rev. A 71, 033411 (2005).
[Crossref]

Phys. Rev. Lett. (2)

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W.’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of Two Photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref] [PubMed]

H. Bechmann-Pasquinucci and A. Peres, “Quantum cryptography with 3-state systems,” Phys. Rev. Lett. 85, 3313–3316 (2000).
[Crossref] [PubMed]

Physica C (1)

J. Zagrodzinski, “Vortices in different branches of physics,” Physica C 369, 45–54 (2002).
[Crossref]

Proc SPIE (1)

J. B. Hayes and S. Lange, “A heterodyne interferometer for testing laser diodes,” Proc SPIE 0429, 22–26 (1983).

Proc. R. Soc. A (1)

J. F. Nye, J. V. Hajnal, and J. H. Hannay, “Phase saddles and dislocations in two-dimensional waves such as the tides,” Proc. R. Soc. A 417, 7–20 (1988).
[Crossref]

Prog. Opt. (2)

K. Creath, “Phase-measurement interferometry techniques, “ Prog. Opt. 26, 349–393 (1988).
[Crossref]

M.S. Soskin and M. V. Vasnetsov, “Singular Optics”, Prog. Opt. 42, 219–276 (2001).
[Crossref]

Other (2)

M. V. Berry, in Les Houches Lecture Series Session XXXV, (North-Holland, Amsterdam, 1981), pp.453–543.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1964).

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 (6)

Fig. 1.
Fig. 1.

Amplitudes and phase of the Bessel coefficients cm of the wave field U α=M+μ for different values of μ. The arrows in the small circles represent the phase of the coefficients, i.e.[μ -(m-M)]π/2, where zero phase corresponds to an arrow pointing along the positive x axis.

Fig. 2.
Fig. 2.

Experimental setup. The wavefield generated by the SLM is set to interfere with the reference plane wave in the lower branch. The compensating plate tunes the relative phases of both fields. BE: Beam Expander, SF: Spatial Filter, HWP: Half-wave Plate, SLM: Spatial Light Modulator, CP: Compensating Plate, LP: Linear Polarizer, CCD: Camera.

Fig. 3.
Fig. 3.

Phase maps Φ(r) of the field Uα (r) for several orders in the range α ∈ (5,6). In third row, the position of the vortices are determined by the crossings of the zero contours ReUα (r)=0 (red lines) and ImUα (r)=0 (blue lines).

Fig. 4.
Fig. 4.

Fine structure of the phase distribution Φ(R,θ) near the first three nodal circles R=βM,n =1,2,3 for the slightly perturbed field U M+μ (R,θ) with M=3,4 and μ=±0.0001.The radial excursion is δ=0.0001. The position of the vortices are determined by the crossings of the zero contours ReUα (r)=0 (red lines) and ImUα (r)=0 (blue lines).White and black dots represent positive and negative vortices, respectively.

Fig. 5.
Fig. 5.

The theoretical trajectories of the vortices within the centralmost region of Uα (r)as its order increases continuously from α=3 to 7. The distances are measured in units of k 0 r.

Fig. 6.
Fig. 6.

Curves Jα (k 0 y)=0 on the (α,k 0 y) plane representing the vertical displacement of the vortices along the y axis as the beam order increases. The trapping of the vortices coming from the negative y axis reveals the mechanism of addition of a new vortex to the on-axis high-order dislocation each time the order is increased by one unit.

Equations (19)

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

U α ( r ) = ( i ) α 2 π π π exp ( iαϕ ) exp [ i k 0 r cos ( ϕ θ ) ] .
U α ( r ) = m = c m ( α ) J m ( k 0 r ) exp ( imθ )
= m = [ i ( m α ) sin [ π ( m α ) ] π ( m α ) ] J m ( k 0 r ) exp ( imθ )
S ( r ) = Im ( U α * U α ) = U α 2 Φ ,
L ¯ z ( α ) = α 1 2 π sin ( 2 απ )
α M + μ
tan [ Φ ( r ) ] = tan ( δΦ 2 ) [ I 2 ( r ) I 3 ( r ) ] + [ I 1 ( r ) I 4 ( r ) ] [ I 2 ( r ) I 3 ( r ) ] + [ I 1 ( r ) I 4 ( r ) ]
tan ( δΦ 2 ) = 3 [ I 2 ( r ) I 3 ( r ) ] [ I 1 ( r ) I 4 ( r ) ] [ I 2 ( r ) I 3 ( r ) ] + [ I 1 ( r ) I 4 ( r ) ]
c m = i ( m M μ ) sin [ π ( m M μ ) ] π ( m M μ ) = small μ { 1 , m = M , μ ( i m M m M ) , m = M ± 1 , M ± 2 , . . . .
U M + μ R θ J M ( R ) exp ( iMθ ) μ m m M ( i m M m M ) J m ( R ) exp ( imθ )
U M + μ R θ + i μ 3 U M 3 - μ 2 U M 2 i μ U M 1 + U M iμU M + 1 + μ 2 U M + 2 + i μ 3 U M + 3 +
U M + μ R θ small r c 0 U 0 + c M U M = i M μ M + R M 2 M M ! exp ( iMθ ) ,
θ n = 2 π M n + { π 2 , if M = 1 , 3 , 5 , ..., 0 , if M = 2 , 6 , 10 , ..., M , if M = 4 , 8 , 12 ..., n = 1 , 2 , ..., M ,
J m ( R ) J m ( β M , n ) + J m ( β M , n ) ( R β M , n ) ,
U M + μ ( R , θ ) R β M , n δ J m ( β M , n ) exp ( imθ ) μ m { ; } m M ( i m M m M ) [ J m ( β M , n ) + J m ( β M , n ) δ ] exp ( imθ ) ,
U α ( x = 0 , y ) = i α J α ( k 0 y ) ,
Φ α ( r , z = 0 ) = exp ( r 2 w 0 2 ) U α ( r , k 0 ) ,
Φ α ( r , z ) = exp ( i k 0 2 z 2 ) GB ( r , z ) U α ( x μ , y μ , k 0 ) ,
GB ( r ) = exp ( ikz ) μ exp ( r 2 μ w 0 2 ) ,

Metrics