Abstract

We predict that vortex dipoles nested in light beams trapped in graded-index media can undergo closed Berry trajectories, yielding periodic vortex annihilations and revivals along the light-propagation direction. The vortex revivals from vortex-free wave fronts are mediated by Freund stationary point bundles that carry the necessary Poincaré–Hopf indices. Vortex spiraling and spontaneous generation of circular-edge dislocations are also found to occur.

© 2001 Optical Society of America

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References

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2001 (4)

Yu. S. Kivshar and E. A. Ostrovskaya, Opt. Photon. News 12(4), 27 (2001).

I. Freund and D. A. Kessler, Opt. Commun. 187, 71 (2001).
[CrossRef]

G. Molina-Terriza, E. M. Wright, and L. Torner, Opt. Lett. 26, 163 (2001).
[CrossRef]

I. Freund, Opt. Lett. 26, 545 (2001).
[CrossRef]

2000 (2)

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, JETP Lett. 71, 130 (2000).
[CrossRef]

I. Freund, Opt. Commun. 181, 19 (2000).
[CrossRef]

1999 (1)

A. Ashkin, Opt. Photon. News 10(5), 41 (1999).
[CrossRef]

1998 (2)

Yu. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, and L. M. Pismen, Opt. Commun. 152, 198 (1998).
[CrossRef]

M. V. Berry, Proc. SPIE 3487, 1 (1998).
[CrossRef]

1997 (1)

1994 (1)

B. Luther-Davies, R. Powles, and V. Tikhonenko, Opt. Lett. 22, 1816 (1994).
[CrossRef]

1993 (1)

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

1992 (1)

1991 (1)

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, JETP Lett. 52, 429 (1991).

1981 (1)

J. F. Nye, Proc. R. Soc. London Ser. A 378, 219 (1981).
[CrossRef]

1974 (1)

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

Ashkin, A.

A. Ashkin, Opt. Photon. News 10(5), 41 (1999).
[CrossRef]

Bazhenov, V. Yu.

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, JETP Lett. 52, 429 (1991).

Berry, M. V.

M. V. Berry, Proc. SPIE 3487, 1 (1998).
[CrossRef]

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

Christou, J.

Yu. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, and L. M. Pismen, Opt. Commun. 152, 198 (1998).
[CrossRef]

Freund, I.

I. Freund, Opt. Lett. 26, 545 (2001).
[CrossRef]

I. Freund and D. A. Kessler, Opt. Commun. 187, 71 (2001).
[CrossRef]

I. Freund, Opt. Commun. 181, 19 (2000).
[CrossRef]

Heckenberg, N. R.

Indebetouw, G.

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

Kessler, D. A.

I. Freund and D. A. Kessler, Opt. Commun. 187, 71 (2001).
[CrossRef]

Kivshar, Yu. S.

Yu. S. Kivshar and E. A. Ostrovskaya, Opt. Photon. News 12(4), 27 (2001).

Yu. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, and L. M. Pismen, Opt. Commun. 152, 198 (1998).
[CrossRef]

Law, C. T.

Luther-Davies, B.

Yu. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, and L. M. Pismen, Opt. Commun. 152, 198 (1998).
[CrossRef]

B. Luther-Davies, R. Powles, and V. Tikhonenko, Opt. Lett. 22, 1816 (1994).
[CrossRef]

Marienko, I. G.

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, JETP Lett. 71, 130 (2000).
[CrossRef]

McDuff, R.

Molina-Terriza, G.

Nye, J. F.

J. F. Nye, Proc. R. Soc. London Ser. A 378, 219 (1981).
[CrossRef]

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

Ostrovskaya, E. A.

Yu. S. Kivshar and E. A. Ostrovskaya, Opt. Photon. News 12(4), 27 (2001).

Pismen, L. M.

Yu. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, and L. M. Pismen, Opt. Commun. 152, 198 (1998).
[CrossRef]

Powles, R.

B. Luther-Davies, R. Powles, and V. Tikhonenko, Opt. Lett. 22, 1816 (1994).
[CrossRef]

Rozas, D.

Smith, C. P.

Soskin, M. S.

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, JETP Lett. 71, 130 (2000).
[CrossRef]

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, JETP Lett. 52, 429 (1991).

Swartzlander, G. A.

Tikhonenko, V.

Yu. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, and L. M. Pismen, Opt. Commun. 152, 198 (1998).
[CrossRef]

B. Luther-Davies, R. Powles, and V. Tikhonenko, Opt. Lett. 22, 1816 (1994).
[CrossRef]

Torner, L.

Vasnetsov, M. V.

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, JETP Lett. 71, 130 (2000).
[CrossRef]

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, JETP Lett. 52, 429 (1991).

White, A. G.

Wright, E. M.

J. Mod. Opt. (1)

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

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

JETP Lett. (2)

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, JETP Lett. 71, 130 (2000).
[CrossRef]

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, JETP Lett. 52, 429 (1991).

Opt. Commun. (3)

Yu. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, and L. M. Pismen, Opt. Commun. 152, 198 (1998).
[CrossRef]

I. Freund, Opt. Commun. 181, 19 (2000).
[CrossRef]

I. Freund and D. A. Kessler, Opt. Commun. 187, 71 (2001).
[CrossRef]

Opt. Lett. (4)

Opt. Photon. News (2)

A. Ashkin, Opt. Photon. News 10(5), 41 (1999).
[CrossRef]

Yu. S. Kivshar and E. A. Ostrovskaya, Opt. Photon. News 12(4), 27 (2001).

Proc. R. Soc. London Ser. A (2)

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

J. F. Nye, Proc. R. Soc. London Ser. A 378, 219 (1981).
[CrossRef]

Proc. SPIE (1)

M. V. Berry, Proc. SPIE 3487, 1 (1998).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Trajectories followed by single vortices, vortex twins, and well-separated vortex dipoles nested in a symmetrical host beam. The trajectories are shown by white lines superimposed upon the intensity pattern of the input light beam. Initial conditions: (a) single canonical vortex, A=1, x1,y1=1,0; (b) two canonical vortex twins; (c) two vortex twins with A1=1-i, A2=1; (d) vortex dipole, A1=1, A2=-1. In (b)–(d), x1,y1=1,0 and x2,y2=-0.25,0. wx=wy=1.

Fig. 2
Fig. 2

Annihilation and spontaneous revival of a vortex dipole. The plots show the sequence of the light-intensity pattern at different propagation distances, z/π: (a) 0, (b) 0.25, (c) 0.4, (d) 0.5; z is in units of Rayleigh lengths of the host beam. The plus and minus signs in (a) and (d) represent vortex topological charges. In (c), the dashed circle depicts the location of a circular-edge dislocation. A1=1,A2=-1,xs=0.35, and wx=wy=1.

Fig. 3
Fig. 3

(a) Berry vortex trajectories. (b) Projection on the xz plane of the main Freund stationary point bundles for the Poincaré–Hopf index flows. Only bundles crossing vortex trajectories are displayed. (c) Full xz cross section of (b) at the location of the circular-edge dislocation. Point M in (b) indicates the features depicted in (c). (d) same as (a) but for a slightly tilted foliation relative to the propagation axis. See the text for the meaning of all features. In (b), the small vertical arrows mark the foliations displayed in Fig.  2.

Fig. 4
Fig. 4

Propagation in an elliptical host beam. The plots show interferograms of the beam and a titled plane wave. (a) Circular-edge dislocation corresponding to Fig.  2(b). (b) Conical-edge dislocation that appears when wx=1, wy=2, and xs=0.5 at z=π. (c) Sequence illustrating the periodic inversion of the topological charge of a single vortex A0=1,wx=1,wy=2; snapshots at z=0,π/2,π.

Equations (2)

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iEz+122E+gx,y;E,E*E=0,
Δzrev=cos-12xs21-2xs2.

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