Abstract

We introduce an asymmetry in the core of a high charge optical vortex by using an appropriate computer generated hologram. The splitting of a high charge optical vortex core into unit charge vortices has been found to depend on the extent of the asymmetry. For a second order vortex, the trajectories of the split unit charged vortices and their separation have been recorded as a function of change in the asymmetry of the core. We find a good agreement between the experimentally obtained and numerically calculated results.

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]

2010 (1)

M. R. Dennis, R. P. King, B. Jack, K. O'Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6(2), 118–121 (2010).
[CrossRef]

2009 (2)

2007 (2)

2006 (4)

2005 (3)

2004 (3)

2003 (4)

R. P. Singh and S. R. Chowdhury, “Trajectory of an optical vortex: Canonical vs. non-canonical,” Opt. Commun. 215(4-6), 231–237 (2003).
[CrossRef]

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[CrossRef] [PubMed]

I. D. Maleev and G. A. Swartzlander., “Composite optical vortices,” J. Opt. Soc. Am. B 20(6), 1169–1176 (2003).
[CrossRef]

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[CrossRef] [PubMed]

2001 (4)

M. V. Berry and M. R. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. R. Soc. Lond. A 457(2013), 2251–2263 (2001).
[CrossRef]

S. Chávez-Cerda, J. C. Gutiérrez-Vega, and G. H. C. New, “Elliptic vortices of electromagnetic wave fields,” Opt. Lett. 26(22), 1803–1805 (2001).
[CrossRef]

G. Molina-Terriza, E. M. Wright, and L. Torner, “Propagation and control of noncanonical optical vortices,” Opt. Lett. 26(3), 163–165 (2001).
[CrossRef]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

2000 (1)

I. Freund, “Optical vortex trajectories,” Opt. Commun. 181(1-3), 19–33 (2000).
[CrossRef]

1999 (2)

I. Freund, “Saddle point wave fields,” Opt. Commun. 163(4-6), 230–242 (1999).
[CrossRef]

I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159(1-3), 99–117 (1999).
[CrossRef]

1998 (1)

Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298(2-3), 81–197 (1998).
[CrossRef]

1997 (2)

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78(11), 2108–2111 (1997).
[CrossRef]

D. Rozas, C. T. Law, and G. A. Swartzlander., “Propagation dynamics of optical vortices,” J. Opt. Soc. Am. B 14(11), 3054–3065 (1997).
[CrossRef]

1996 (1)

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77(22), 4544–4547 (1996).
[CrossRef] [PubMed]

1995 (1)

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42(1), 217–223 (1995).
[CrossRef]

1993 (2)

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5-6), 422–428 (1993).
[CrossRef]

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40(1), 73–87 (1993).
[CrossRef]

1992 (3)

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24(9), S951–S962 (1992).
[CrossRef]

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(11), 8185–8189 (1992).
[CrossRef] [PubMed]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221–223 (1992).
[CrossRef] [PubMed]

1990 (1)

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 429–431 (1990).

1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336(1605), 165–190 (1974).
[CrossRef]

1958 (1)

V. L. Ginzburg and L. P. Pitaevskii, “On the theory of superfluidity,” Sov. Phys. JETP 34, 858–863 (1958).

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(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Almazov, A. A.

Arnold, A. S.

Arsenovic, D.

Barnett, S. M.

Basistiy, I. V.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5-6), 422–428 (1993).
[CrossRef]

Baumann, S. M.

Bazhenov, V. Y.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5-6), 422–428 (1993).
[CrossRef]

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 429–431 (1990).

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(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Belic, M.

Berry, M. V.

M. V. Berry and M. R. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. R. Soc. Lond. A 457(2013), 2251–2263 (2001).
[CrossRef]

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336(1605), 165–190 (1974).
[CrossRef]

Chakraborty, R.

Chávez-Cerda, S.

Chen, Z.

Chowdhury, S. R.

R. P. Singh and S. R. Chowdhury, “Trajectory of an optical vortex: Canonical vs. non-canonical,” Opt. Commun. 215(4-6), 231–237 (2003).
[CrossRef]

Courtial, J.

Curtis, J. E.

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[CrossRef] [PubMed]

Dennis, M. R.

M. R. Dennis, R. P. King, B. Jack, K. O'Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6(2), 118–121 (2010).
[CrossRef]

M. R. Dennis, “Rows of optical vortices from elliptically perturbing a high-order beam,” Opt. Lett. 31(9), 1325–1327 (2006).
[CrossRef] [PubMed]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” N. J. Phys. 7, 55.1–55.11 (2005).
[CrossRef]

M. V. Berry and M. R. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. R. Soc. Lond. A 457(2013), 2251–2263 (2001).
[CrossRef]

Ellinas, D.

Foo, G.

Franke-Arnold, S.

Freund, I.

I. Freund, “Optical vortex trajectories,” Opt. Commun. 181(1-3), 19–33 (2000).
[CrossRef]

I. Freund, “Saddle point wave fields,” Opt. Commun. 163(4-6), 230–242 (1999).
[CrossRef]

I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159(1-3), 99–117 (1999).
[CrossRef]

Galvez, E. J.

Gan, X.

Ghosh, A.

Gibson, G.

Ginzburg, V. L.

V. L. Ginzburg and L. P. Pitaevskii, “On the theory of superfluidity,” Sov. Phys. JETP 34, 858–863 (1958).

Girkin, J. M.

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[CrossRef] [PubMed]

Gutiérrez-Vega, J. C.

He, H.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42(1), 217–223 (1995).
[CrossRef]

Heckenberg, N. R.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42(1), 217–223 (1995).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221–223 (1992).
[CrossRef] [PubMed]

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24(9), S951–S962 (1992).
[CrossRef]

Indebetouw, G.

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40(1), 73–87 (1993).
[CrossRef]

Jack, B.

M. R. Dennis, R. P. King, B. Jack, K. O'Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6(2), 118–121 (2010).
[CrossRef]

Jefimovs, K.

Jovic, D.

Kalb, D. M.

Khonina, S. N.

King, R. P.

M. R. Dennis, R. P. King, B. Jack, K. O'Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6(2), 118–121 (2010).
[CrossRef]

Kivshar, Y. S.

Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298(2-3), 81–197 (1998).
[CrossRef]

Kotlyar, V. V.

Law, C. T.

Leach, J.

Lembessis, V. E.

Liu, S.

Luther-Davies, B.

Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298(2-3), 81–197 (1998).
[CrossRef]

MacMillan, L. H.

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Maleev, I. D.

Mamaev, A. V.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78(11), 2108–2111 (1997).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77(22), 4544–4547 (1996).
[CrossRef] [PubMed]

McDuff, R.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24(9), S951–S962 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221–223 (1992).
[CrossRef] [PubMed]

Molina-Terriza, G.

New, G. H. C.

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336(1605), 165–190 (1974).
[CrossRef]

Öhberg, P.

O'Holleran, K.

M. R. Dennis, R. P. King, B. Jack, K. O'Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6(2), 118–121 (2010).
[CrossRef]

Padgett, M. J.

Palacios, D. M.

Pas’ko, V.

Petrovic, M.

Pitaevskii, L. P.

V. L. Ginzburg and L. P. Pitaevskii, “On the theory of superfluidity,” Sov. Phys. JETP 34, 858–863 (1958).

Roux, F. S.

F. S. Roux, “Optical vortex trajectories in anastigmatic and elliptical Gaussian beams,” S. Afr. J. Sci. 102, 601–605 (2006).

F. S. Roux, “Coupling of noncanonical optical vortices,” J. Opt. Soc. Am. B 21(3), 664–670 (2004).
[CrossRef]

Roychowdhury, S.

R. P. Singh and S. Roychowdhury, “Non-conservation of topological charge: Experiment with optical vortex,” J. Mod. Opt. 51, 177–181 (2004).

Rozas, D.

Rubinsztein-Dunlop, H.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42(1), 217–223 (1995).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24(9), S951–S962 (1992).
[CrossRef]

Saffman, M.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78(11), 2108–2111 (1997).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77(22), 4544–4547 (1996).
[CrossRef] [PubMed]

Senthilkumaran, P.

Singh, R. P.

R. P. Singh and S. Roychowdhury, “Non-conservation of topological charge: Experiment with optical vortex,” J. Mod. Opt. 51, 177–181 (2004).

R. P. Singh and S. R. Chowdhury, “Trajectory of an optical vortex: Canonical vs. non-canonical,” Opt. Commun. 215(4-6), 231–237 (2003).
[CrossRef]

Smith, C. P.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24(9), S951–S962 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221–223 (1992).
[CrossRef] [PubMed]

Soifer, V. A.

Soskin, M. S.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5-6), 422–428 (1993).
[CrossRef]

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 429–431 (1990).

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(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Strinic, A.

Swartzlander, G. A.

Torner, L.

Turunen, J.

Vasnetsov, M.

Vasnetsov, M. V.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5-6), 422–428 (1993).
[CrossRef]

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 429–431 (1990).

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Vyas, S.

Wegener, M. J.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24(9), S951–S962 (1992).
[CrossRef]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

White, A. G.

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Figures (8)

Fig. 1
Fig. 1

Schematic of the experimental setup. M1, M2, M3 mirrors; BS1, BS2 beam splitters; A1, A2 apertures; PC1, PC2 computers; NDF1, NDF2 neutral density filters; SLM, spatial light modulator; CCD, charge coupled device camera.

Fig. 2
Fig. 2

Images of a second order vortex and the characteristic interferogram. (a, b) experimental; (c, d) simulated.

Fig. 3
Fig. 3

Experimental results of the splitting of a second order optical vortex on increasing (top to bottom) the asymmetry i.e. asymmetry parameter α moving away from the value 1.0. (I, II) optical vortices and interferograms with decreasing α = 0.7, 0.5 and 0.3; (III, IV) optical vortices and interferograms with increasing α = 1.43, 2.0 and 3.33.

Fig. 4
Fig. 4

Simulated results for the same asymmetry parameter values as in Fig. 3.

Fig. 5
Fig. 5

Experimental (open symbols) and simulated (filled symbols) trajectories of the unit charge vortices after splitting from a doubly charge vortex as the asymmetry parameter (α) moves away from 1. (a) decreasing; (b) increasing.

Fig. 6
Fig. 6

Plot showing the increase of the distance between split vortices as the asymmetry parameter (α) moves away from the value 1.

Fig. 7
Fig. 7

Experimental results of the splitting of high-order optical vortex on increasing (top to bottom) the asymmetry, α = 1.00, 0.70, 0.50 and 0.30 (I, II) optical vortices of third order and their characteristic interferograms; (III, IV) optical vortices of fourth order and their characteristic interferograms.

Fig. 8
Fig. 8

Simulated results for the same asymmetry parameter values as in Fig. 7.

Equations (3)

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U ( x , y ) = 1 j λ z U i ( ξ , η ) exp [ j k z { 1 + ( x ξ ) 2 + ( y η ) 2 z 2 } 1 / 2 ] d ξ d η
U ( x , y ) = exp ( j k z ) j λ z U i ( ξ , η ) exp [ j k 2 z { ( x ξ ) 2 + ( y η ) 2 } ] d ξ d η
U i ( ξ , η )   = 2 { 1 + cos ( k ξ m θ ) } exp ( ξ 2 + η 2 σ 2 ) .        

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