Abstract

The propagation dynamics of an optical vortex pair is experimentally confirmed to experience enhanced rotation in a self-defocusing medium. We measured this effect to be 3.5 times larger than in linear media. The enhancement is attributed to nonlinear refraction within the dark vortex cores, permitting the vortices to propagate as vortex filaments.

© 2000 Optical Society of America

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References

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    [CrossRef]
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  9. A. W. Snyder, L. Poladian, and D. J. Mitchell, Opt. Lett. 17, 789 (1992).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  19. L. G. Gouy, Ann. Chim. Phys. Ser. 6 24, 145 (1891).
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1999

1998

1997

D. Rozas, C. T. Law, and G. A. Swartzlander, J. Opt. Soc. Am. B 14, 3054 (1997).
[CrossRef]

A. V. Ilyenkov, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, J. Nonlin. Opt. Phys. Mater. 6, 169 (1997).
[CrossRef]

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Phys. Rev. Lett. 79, 3399 (1997).
[CrossRef]

1996

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, Appl. Phys. B 62, 465 (1996).
[CrossRef]

1995

T. Ackemann, E. Kriege, and W. Lange, Opt. Commun. 115, 339 (1995).
[CrossRef]

1994

1993

G. Indebetow, J. Mod. Opt. 40, 73 (1993).
[CrossRef]

1992

1990

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, Pis’ma Zh. Eksp. Teor. Fiz. 52, 1037 (1990) [JETP Lett. 52, 429 (1990)].

1981

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, Pis’ma Zh. Eks. Teor. Fiz. 33, 206 (1981); JETP Lett. 33, 195 (1981).

1974

W. H. Carter, Opt. Acta 21, 871 (1974).
[CrossRef]

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

1965

R. Betchov, J. Fluid Mech. Part 3,  22, 471 (1965).
[CrossRef]

1961

G. Goubau and F. Schwering, IRE Trans. Antennas Propag. 9, 248 (1961).
[CrossRef]

1891

L. G. Gouy, Ann. Chim. Phys. Ser. 6 24, 145 (1891).

Ackemann, T.

T. Ackemann, E. Kriege, and W. Lange, Opt. Commun. 115, 339 (1995).
[CrossRef]

Baranova, N. B.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, Pis’ma Zh. Eks. Teor. Fiz. 33, 206 (1981); JETP Lett. 33, 195 (1981).

Bazhenov, V. Yu.

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, Pis’ma Zh. Eksp. Teor. Fiz. 52, 1037 (1990) [JETP Lett. 52, 429 (1990)].

Berry, M. V.

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Betchov, R.

R. Betchov, J. Fluid Mech. Part 3,  22, 471 (1965).
[CrossRef]

Carter, W. H.

W. H. Carter, Opt. Acta 21, 871 (1974).
[CrossRef]

Deykoon, A. M.

Goubau, G.

G. Goubau and F. Schwering, IRE Trans. Antennas Propag. 9, 248 (1961).
[CrossRef]

Gouy, L. G.

L. G. Gouy, Ann. Chim. Phys. Ser. 6 24, 145 (1891).

Heckenberg, N. R.

Ilyenkov, A. V.

A. V. Ilyenkov, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, J. Nonlin. Opt. Phys. Mater. 6, 169 (1997).
[CrossRef]

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, Appl. Phys. B 62, 465 (1996).
[CrossRef]

Indebetow, G.

G. Indebetow, J. Mod. Opt. 40, 73 (1993).
[CrossRef]

Khizhnyak, A. I.

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, Appl. Phys. B 62, 465 (1996).
[CrossRef]

Kreminskaya, L. V.

A. V. Ilyenkov, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, J. Nonlin. Opt. Phys. Mater. 6, 169 (1997).
[CrossRef]

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, Appl. Phys. B 62, 465 (1996).
[CrossRef]

Kriege, E.

T. Ackemann, E. Kriege, and W. Lange, Opt. Commun. 115, 339 (1995).
[CrossRef]

Lange, W.

T. Ackemann, E. Kriege, and W. Lange, Opt. Commun. 115, 339 (1995).
[CrossRef]

Law, C. T.

D. Rozas, C. T. Law, and G. A. Swartzlander, J. Opt. Soc. Am. B 14, 3054 (1997).
[CrossRef]

G. A. Swartzlander and C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef]

Luther-Davies, B.

Mamaev, A. V.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, Pis’ma Zh. Eks. Teor. Fiz. 33, 206 (1981); JETP Lett. 33, 195 (1981).

McDuff, R.

Mitchell, D. J.

Nye, J. F.

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Pilipetskii, N. F.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, Pis’ma Zh. Eks. Teor. Fiz. 33, 206 (1981); JETP Lett. 33, 195 (1981).

Poladian, L.

Powles, R.

Rozas, D.

Sacks, Z. S.

Z. S. Sacks, D. Rozas, and G. A. Swartzlander, J. Opt. Soc. Am. B 15, 2226 (1998).
[CrossRef]

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Phys. Rev. Lett. 79, 3399 (1997).
[CrossRef]

Schwering, F.

G. Goubau and F. Schwering, IRE Trans. Antennas Propag. 9, 248 (1961).
[CrossRef]

Shkunov, V. V.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, Pis’ma Zh. Eks. Teor. Fiz. 33, 206 (1981); JETP Lett. 33, 195 (1981).

Smith, C. P.

Snyder, A. W.

Sommerfeld, A.

A. Sommerfeld, Mechanics of Deformable Bodies (Academic, London, 1950), p. 156.

Soskin, M. S.

A. M. Deykoon, M. S. Soskin, and G. A. Swartzlander, Opt. Lett. 24, 1224 (1999).
[CrossRef]

A. V. Ilyenkov, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, J. Nonlin. Opt. Phys. Mater. 6, 169 (1997).
[CrossRef]

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, Appl. Phys. B 62, 465 (1996).
[CrossRef]

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, Pis’ma Zh. Eksp. Teor. Fiz. 52, 1037 (1990) [JETP Lett. 52, 429 (1990)].

Swartzlander, G. A.

A. M. Deykoon, M. S. Soskin, and G. A. Swartzlander, Opt. Lett. 24, 1224 (1999).
[CrossRef]

Z. S. Sacks, D. Rozas, and G. A. Swartzlander, J. Opt. Soc. Am. B 15, 2226 (1998).
[CrossRef]

D. Rozas, C. T. Law, and G. A. Swartzlander, J. Opt. Soc. Am. B 14, 3054 (1997).
[CrossRef]

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Phys. Rev. Lett. 79, 3399 (1997).
[CrossRef]

G. A. Swartzlander and C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef]

G. A. Swartzlander, in Optical Vortices, M. Vasnetsov and K. Staliunas, eds., Vol. 228 of Horizons in World Physics (Nova, Commack, N.Y., 1999), pp. 107–124.

Tikhonenko, V.

Vasnetsov, M. V.

A. V. Ilyenkov, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, J. Nonlin. Opt. Phys. Mater. 6, 169 (1997).
[CrossRef]

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, Appl. Phys. B 62, 465 (1996).
[CrossRef]

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, Pis’ma Zh. Eksp. Teor. Fiz. 52, 1037 (1990) [JETP Lett. 52, 429 (1990)].

White, A. G.

Zel’dovich, B. Ya.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, Pis’ma Zh. Eks. Teor. Fiz. 33, 206 (1981); JETP Lett. 33, 195 (1981).

Ann. Chim. Phys. Ser. 6

L. G. Gouy, Ann. Chim. Phys. Ser. 6 24, 145 (1891).

Appl. Phys. B

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, Appl. Phys. B 62, 465 (1996).
[CrossRef]

IRE Trans. Antennas Propag.

G. Goubau and F. Schwering, IRE Trans. Antennas Propag. 9, 248 (1961).
[CrossRef]

J. Fluid Mech.

R. Betchov, J. Fluid Mech. Part 3,  22, 471 (1965).
[CrossRef]

J. Mod. Opt.

G. Indebetow, J. Mod. Opt. 40, 73 (1993).
[CrossRef]

J. Nonlin. Opt. Phys. Mater.

A. V. Ilyenkov, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, J. Nonlin. Opt. Phys. Mater. 6, 169 (1997).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Acta

W. H. Carter, Opt. Acta 21, 871 (1974).
[CrossRef]

Opt. Commun.

T. Ackemann, E. Kriege, and W. Lange, Opt. Commun. 115, 339 (1995).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

G. A. Swartzlander and C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef]

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Phys. Rev. Lett. 79, 3399 (1997).
[CrossRef]

Pis’ma Zh. Eks. Teor. Fiz.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, Pis’ma Zh. Eks. Teor. Fiz. 33, 206 (1981); JETP Lett. 33, 195 (1981).

Pis’ma Zh. Eksp. Teor. Fiz.

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, Pis’ma Zh. Eksp. Teor. Fiz. 52, 1037 (1990) [JETP Lett. 52, 429 (1990)].

Proc. R. Soc. London Ser. A

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Other

G. A. Swartzlander, in Optical Vortices, M. Vasnetsov and K. Staliunas, eds., Vol. 228 of Horizons in World Physics (Nova, Commack, N.Y., 1999), pp. 107–124.

A. Sommerfeld, Mechanics of Deformable Bodies (Academic, London, 1950), p. 156.

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Figures (5)

Fig. 1
Fig. 1

(a) Intensity and (b) phase profiles of two identical small-core vortices near the center of a Gaussian beam in the initial transverse plane z=0.

Fig. 2
Fig. 2

Experimental setup: Ar, argon-ion laser λ=514 nm; H, holographic recording of two identical small-core vortices; M1, M2, mirrors, C, vertical glass cell of length lC=29 cm filled with weakly absorbing liquid (dyed methanol); L1, L2, lenses of focal distance d=50 mm; CCD, CCD camera and frame grabber; S1, S2, shutters.

Fig. 3
Fig. 3

Output intensity profiles for incident powers of P0=a 0.01, (b) 0.4, (c) 1.9, and (d) 2.5 W. In the plane of the hologram (not shown), dV=84±4 µm and the initial vortex alignment is -11.5° below the x axis.

Fig. 4
Fig. 4

Transverse intensity profile for the nonlinear case, P0=0.54 W, showing optical blooming at the edge of the beam as well as a radiation ring surrounding the vortices. The intensity along the dashed line is plotted at the bottom.

Fig. 5
Fig. 5

(a) Plots of measured values of angular displacement ϕV versus incident power P0 for initial vortex separations of dV=84±4 µm and dV=135±4 µm. (b) Vortex trajectories for dV=135±4 µm and the initial vortex alignment along the x axis.

Equations (2)

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Er,θ,z=EBGr,zj=1NAjrj,zexpimjθj,
Ajrj,ztanhrj/wjexpiΔnkz,

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