Abstract

When canonical vortices with different topological charges coexist in an optical beam, they inevitably become noncanonical during propagation. The noncanonical nature of optical vortices can be expressed in terms of morphological parameters, which can be represented in terms of a spinor, similar to the Jones vectors for polarization. This allows one to express the prefactor for a Gaussian beam containing two arbitrary vortices in terms of two terms. One is a product of two linearly propagating vortices. The other one, which is called the coupling term, represents the interaction between the vortices. The coupling term is independent of the vortex positions but depends on their initial morphological parameters. There are two situations where the interaction is zero. One is when the vortices are canonical with the same topological charge, and the other is when the vortices have the same anisotropy but with orthogonal orientations. The former situation is well known. The noninteraction of the latter situation is confirmed by a numerical simulation.

© 2004 Optical Society of America

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2003

2001

1999

It was pointed out in I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159, 99–117 (1999), that optical vortices can have phase functions that are not monotonic as a function of angle around the vortex. Such nongeneric vortices are not considered here.

1997

1996

1995

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of an- gular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).

1994

1993

I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).

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

F. S. Roux, “Diffractive optical implementation of rotation transform performed by using phase singularities,” Appl. Opt. 32, 3715–3719 (1993).

1992

A. W. Snyder, L. Poladian, and D. J. Mitchell, “Stable black self-guiding beams of circular symmetry in a bulk Kerr medium,” Opt. Lett. 17, 789–791 (1992).

G. A. Swartzlander, Jr. and C. T. Law, “The optical vortex soliton,” Phys. Rev. Lett. 69, 2503–2506 (1992).

1974

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).

Beijersbergen, M. W.

Berry, M. V.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).

Freilikher, V.

I. Freund and V. Freilikher, “Parameterization of anisotropic vortices,” J. Opt. Soc. Am. A 14, 1902–1910 (1997).

I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).

Freund, I.

It was pointed out in I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159, 99–117 (1999), that optical vortices can have phase functions that are not monotonic as a function of angle around the vortex. Such nongeneric vortices are not considered here.

I. Freund and V. Freilikher, “Parameterization of anisotropic vortices,” J. Opt. Soc. Am. A 14, 1902–1910 (1997).

I. Freund, “Optical vortices in Gaussian random wave fields: statistical probability densities,” J. Opt. Soc. Am. A 11, 1644–1652 (1994).

I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of an- gular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).

García-Ripoll, J. J.

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of an- gular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of an- gular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).

Indebetouw, G.

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

Karman, G. P.

Kim, G.-H.

Kim, J.-U.

Law, C. T.

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

G. A. Swartzlander, Jr. and C. T. Law, “The optical vortex soliton,” Phys. Rev. Lett. 69, 2503–2506 (1992).

Lee, H. J.

Mitchell, D. J.

Molina-Terriza, G.

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).

Patterson, C.

C. Patterson, “Diffractive optical elements with spiral phase dislocations,” J. Mod. Opt. 41, 757–765 (1994).

Pérez-García, V. M.

Poladian, L.

Roux, F. S.

Rozas, D.

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

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Jr., “Experimental observation of fluidlike motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of an- gular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).

Sacks, Z. S.

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Jr., “Experimental observation of fluidlike motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).

Schechner, Y. Y.

Shamir, J.

Shvartsman, N.

I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).

Snyder, A. W.

Suk, H.

Swartzlander Jr., G. A.

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Jr., “Experimental observation of fluidlike motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).

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

G. A. Swartzlander, Jr. and C. T. Law, “The optical vortex soliton,” Phys. Rev. Lett. 69, 2503–2506 (1992).

Torner, L.

van Duijl, A.

Woerdman, J. P.

Wright, E. M.

Appl. Opt.

J. Mod. Opt.

C. Patterson, “Diffractive optical elements with spiral phase dislocations,” J. Mod. Opt. 41, 757–765 (1994).

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

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

F. S. Roux, “Optical vortex density limitation,” Opt. Commun. 223, 31–37 (2003).

I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).

It was pointed out in I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159, 99–117 (1999), that optical vortices can have phase functions that are not monotonic as a function of angle around the vortex. Such nongeneric vortices are not considered here.

Opt. Lett.

Phys. Rev. Lett.

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Jr., “Experimental observation of fluidlike motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of an- gular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).

G. A. Swartzlander, Jr. and C. T. Law, “The optical vortex soliton,” Phys. Rev. Lett. 69, 2503–2506 (1992).

Proc. R. Soc. London Ser. A

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).

Other

F. S. Roux, “Canonical optical vortex dynamics,” J. Opt. Soc. Am. B (to be published).

Wu-Ki Tung, Group Theory in Physics (World Scientific, Philadelphia, 1985).

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