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

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 Pure Appl. Opt. 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. Guti???errez-Vega, "Fractionalization of optical beams: II. Elegant Laguerre-Gaussian modes," Opt. Express 15, 6300-6313 (2007). [CrossRef] [PubMed]
9. J. B. Götte, K. O???Holleran, D. Preece, 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. Gutierrez-Vega and C. Lopez-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. Smilgevicius, 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," Nat. 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 429, 22-26 (1983).
21. I. Freund, "Poincare 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 singular 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. Gutierrez-Vega and M. A. Bandres, "Helmholtz-Gauss waves," J. Opt. Soc. Am. A 22, 289-298 (2005). [CrossRef]
28. C. Lopez-Mariscal, M. A. Bandres, and J. C. Gutierrez-Vega, "Observation of the experimental propagation properties of Helmholtz-Gauss beams," Opt. Eng. 45, 068001 (2006). [CrossRef]
29. R. Jauregui, and S. Hacyan, "Quantum-mechanical properties of Bessel beams," Phys. Rev. A 71, 033411 (2005). [CrossRef]

Europhys. Lett.

• 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.

• 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

• M. V. Berry, "Optical vortices evolving from helicoidal integer and fractional phase steps," J. Opt. A Pure Appl. Opt. 6, 259-269 (2004). [CrossRef]

J. Opt. A: Pure Appl. Opt.

• J. C. Gutierrez-Vega and C. Lopez-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

• J. C. Gutierrez-Vega and M. A. Bandres, "Helmholtz-Gauss waves," J. Opt. Soc. Am. A 22, 289-298 (2005). [CrossRef]

Nat. Phys.

• G. Molina-Terriza, J. P. Torres, and L. Torner, "Twisted photons," Nat. Phys. 3, 305-310 (2007). [CrossRef]

Nature

• D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003). [CrossRef] [PubMed]

New J. Phys.

• 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.

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

Opt. Commun.

• S. Orlov, K. Regelskis, V. Smilgevicius, 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.

• C. Lopez-Mariscal, M. A. Bandres, and J. C. Gutierrez-Vega, "Observation of the experimental propagation properties of Helmholtz-Gauss beams," Opt. Eng. 45, 068001 (2006). [CrossRef]

Opt. Express

• J. C. Guti???errez-Vega, "Fractionalization of optical beams: II. Elegant Laguerre-Gaussian modes," Opt. Express 15, 6300-6313 (2007). [CrossRef] [PubMed]
• J. B. Götte, K. O???Holleran, D. Preece, 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]

Opt. Lett.

• M. R. Dennis, "Rows of optical vortices from elliptically perturbing a high-order beam," Opt. Lett. 31, 1325-1327 (2006). [CrossRef] [PubMed]
• 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]
• I. Freund, "Poincare vortices," Opt. Lett. 26, 1996-1998 (2001). [CrossRef]

Phys. Rev. A

• I. Freund and N. Shvartsman, "Wave-field phase singularities: The sign principle," Phys. Rev. A 50, 5164-5174 (1994). [CrossRef] [PubMed]
• R. Jauregui, and S. Hacyan, "Quantum-mechanical properties of Bessel beams," Phys. Rev. A 71, 033411 (2005). [CrossRef]

Phys. Rev. Lett.

• 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

• J. Zagrodzinski, "Vortices in different branches of physics," Physica C 369, 45-54 (2002). [CrossRef]

Proc SPIE

• J. B. Hayes and S. Lange, "A heterodyne interferometer for testing laser diodes," Proc SPIE 429, 22-26 (1983).

Proc. R. Soc. A

• 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.

• 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

• 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).

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