Abstract

Recently a laser analog of vortex generation behind an obstacle in a flow was demonstrated. Vortex generation occurs when tilted waves of different transverse structures are simultaneously excited in a laser. We have generalized this phenomenon to higher-order standing waves. Here typical phenomena expected for optical vortices, such as the excitation and disappearance of single vortices out of and into dark lines and dark areas, as well as vortex-pair creation and annihilation become apparent.

© 1997 Optical Society of America

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References

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  1. K. Staliunas, Phys. Rev. A 48, 1573 (1993).
    [Crossref] [PubMed]
  2. M. Vaupel and C. O. Weiss, Phys. Rev. A 51, 4078 (1995).
    [Crossref] [PubMed]
  3. M. Vaupel, K. Staliunas, and C. O. Weiss, Phys. Rev. A 54, 880 (1996).
    [Crossref] [PubMed]
  4. C. T. Law and G. A. Swartzlander, Opt. Lett. 18, 586 (1993).
    [Crossref]
  5. A. V. Mamaev and M. Saffman, Phys. Rev. Lett. 76, 2262 (1996).
    [Crossref] [PubMed]
  6. V. Tikhonenko, J. Christou, B. Luther-Davies, and Y. S. Kivshar, Opt. Lett. 21, 1129 (1996).
    [Crossref] [PubMed]
  7. G. S. McDonald, K. S. Syed, and W. J. Firth, Opt. Commun. 95, 281 (1993).
    [Crossref]
  8. E. P. Gros, J. Math. Phys. 4, 195 (1963).
    [Crossref]
  9. T. Frisch, Y. Pomeau, and S. Rica, Phys. Rev. Lett. 69, 1644 (1992).
    [Crossref] [PubMed]
  10. J. T. Malos, K. Staliunas, M. Vaupel, and C. O. Weiss, Opt. Commun. 128, 123 (1996).
    [Crossref]
  11. C. P. Smith, Y. Dihardja, C. O. Weiss, L. A. Lugiato, and F. Prati, Opt. Commun. 102, 505 (1993).
    [Crossref]

1996 (4)

M. Vaupel, K. Staliunas, and C. O. Weiss, Phys. Rev. A 54, 880 (1996).
[Crossref] [PubMed]

A. V. Mamaev and M. Saffman, Phys. Rev. Lett. 76, 2262 (1996).
[Crossref] [PubMed]

V. Tikhonenko, J. Christou, B. Luther-Davies, and Y. S. Kivshar, Opt. Lett. 21, 1129 (1996).
[Crossref] [PubMed]

J. T. Malos, K. Staliunas, M. Vaupel, and C. O. Weiss, Opt. Commun. 128, 123 (1996).
[Crossref]

1995 (1)

M. Vaupel and C. O. Weiss, Phys. Rev. A 51, 4078 (1995).
[Crossref] [PubMed]

1993 (4)

K. Staliunas, Phys. Rev. A 48, 1573 (1993).
[Crossref] [PubMed]

C. T. Law and G. A. Swartzlander, Opt. Lett. 18, 586 (1993).
[Crossref]

G. S. McDonald, K. S. Syed, and W. J. Firth, Opt. Commun. 95, 281 (1993).
[Crossref]

C. P. Smith, Y. Dihardja, C. O. Weiss, L. A. Lugiato, and F. Prati, Opt. Commun. 102, 505 (1993).
[Crossref]

1992 (1)

T. Frisch, Y. Pomeau, and S. Rica, Phys. Rev. Lett. 69, 1644 (1992).
[Crossref] [PubMed]

1963 (1)

E. P. Gros, J. Math. Phys. 4, 195 (1963).
[Crossref]

Christou, J.

Dihardja, Y.

C. P. Smith, Y. Dihardja, C. O. Weiss, L. A. Lugiato, and F. Prati, Opt. Commun. 102, 505 (1993).
[Crossref]

Firth, W. J.

G. S. McDonald, K. S. Syed, and W. J. Firth, Opt. Commun. 95, 281 (1993).
[Crossref]

Frisch, T.

T. Frisch, Y. Pomeau, and S. Rica, Phys. Rev. Lett. 69, 1644 (1992).
[Crossref] [PubMed]

Gros, E. P.

E. P. Gros, J. Math. Phys. 4, 195 (1963).
[Crossref]

Kivshar, Y. S.

Law, C. T.

Lugiato, L. A.

C. P. Smith, Y. Dihardja, C. O. Weiss, L. A. Lugiato, and F. Prati, Opt. Commun. 102, 505 (1993).
[Crossref]

Luther-Davies, B.

Malos, J. T.

J. T. Malos, K. Staliunas, M. Vaupel, and C. O. Weiss, Opt. Commun. 128, 123 (1996).
[Crossref]

Mamaev, A. V.

A. V. Mamaev and M. Saffman, Phys. Rev. Lett. 76, 2262 (1996).
[Crossref] [PubMed]

McDonald, G. S.

G. S. McDonald, K. S. Syed, and W. J. Firth, Opt. Commun. 95, 281 (1993).
[Crossref]

Pomeau, Y.

T. Frisch, Y. Pomeau, and S. Rica, Phys. Rev. Lett. 69, 1644 (1992).
[Crossref] [PubMed]

Prati, F.

C. P. Smith, Y. Dihardja, C. O. Weiss, L. A. Lugiato, and F. Prati, Opt. Commun. 102, 505 (1993).
[Crossref]

Rica, S.

T. Frisch, Y. Pomeau, and S. Rica, Phys. Rev. Lett. 69, 1644 (1992).
[Crossref] [PubMed]

Saffman, M.

A. V. Mamaev and M. Saffman, Phys. Rev. Lett. 76, 2262 (1996).
[Crossref] [PubMed]

Smith, C. P.

C. P. Smith, Y. Dihardja, C. O. Weiss, L. A. Lugiato, and F. Prati, Opt. Commun. 102, 505 (1993).
[Crossref]

Staliunas, K.

M. Vaupel, K. Staliunas, and C. O. Weiss, Phys. Rev. A 54, 880 (1996).
[Crossref] [PubMed]

J. T. Malos, K. Staliunas, M. Vaupel, and C. O. Weiss, Opt. Commun. 128, 123 (1996).
[Crossref]

K. Staliunas, Phys. Rev. A 48, 1573 (1993).
[Crossref] [PubMed]

Swartzlander, G. A.

Syed, K. S.

G. S. McDonald, K. S. Syed, and W. J. Firth, Opt. Commun. 95, 281 (1993).
[Crossref]

Tikhonenko, V.

Vaupel, M.

M. Vaupel, K. Staliunas, and C. O. Weiss, Phys. Rev. A 54, 880 (1996).
[Crossref] [PubMed]

J. T. Malos, K. Staliunas, M. Vaupel, and C. O. Weiss, Opt. Commun. 128, 123 (1996).
[Crossref]

M. Vaupel and C. O. Weiss, Phys. Rev. A 51, 4078 (1995).
[Crossref] [PubMed]

Weiss, C. O.

J. T. Malos, K. Staliunas, M. Vaupel, and C. O. Weiss, Opt. Commun. 128, 123 (1996).
[Crossref]

M. Vaupel, K. Staliunas, and C. O. Weiss, Phys. Rev. A 54, 880 (1996).
[Crossref] [PubMed]

M. Vaupel and C. O. Weiss, Phys. Rev. A 51, 4078 (1995).
[Crossref] [PubMed]

C. P. Smith, Y. Dihardja, C. O. Weiss, L. A. Lugiato, and F. Prati, Opt. Commun. 102, 505 (1993).
[Crossref]

J. Math. Phys. (1)

E. P. Gros, J. Math. Phys. 4, 195 (1963).
[Crossref]

Opt. Commun. (3)

G. S. McDonald, K. S. Syed, and W. J. Firth, Opt. Commun. 95, 281 (1993).
[Crossref]

J. T. Malos, K. Staliunas, M. Vaupel, and C. O. Weiss, Opt. Commun. 128, 123 (1996).
[Crossref]

C. P. Smith, Y. Dihardja, C. O. Weiss, L. A. Lugiato, and F. Prati, Opt. Commun. 102, 505 (1993).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (3)

K. Staliunas, Phys. Rev. A 48, 1573 (1993).
[Crossref] [PubMed]

M. Vaupel and C. O. Weiss, Phys. Rev. A 51, 4078 (1995).
[Crossref] [PubMed]

M. Vaupel, K. Staliunas, and C. O. Weiss, Phys. Rev. A 54, 880 (1996).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

A. V. Mamaev and M. Saffman, Phys. Rev. Lett. 76, 2262 (1996).
[Crossref] [PubMed]

T. Frisch, Y. Pomeau, and S. Rica, Phys. Rev. Lett. 69, 1644 (1992).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) Zero- and first-order standing waves with different tilts in a cylindrical resonator. Vortices detach from the node line of the first-order standing wave and move outward. The picture is a snapshot in time of the flow, with the arrow giving the direction of the motion. (b) Representation of (a) by lines of RE=0 (darker lines) and IE=0 (lighter lines). The thin curves are 180° out of phase with the thick curves. The intersections of darker and lighter curves have zero intensity and are vortices. The charge of the vortex depends on whether the phase increases clockwise or anticlockwise.

Fig. 2
Fig. 2

(a) First- and second-order standing waves with different tilts in a cylindrical resonator. Vortices detach from the node line of the first-order standing wave and connect to the node lines of the second-order standing wave. Additional vortices flow in from infinity. The picture is a snapshot in time of the flow, with the arrow giving the direction of the motion. (b) Representation of (a) corresponding to Fig.  1(b).

Fig. 3
Fig. 3

Observation of vortex streets between first- and second-order transverse standing waves in an optical channel (laser with a cylindrical-optics resonator). A, The node line of the first-order standing wave; B, the node lines of the second-order standing wave; C, D, vortices detached from the first-order standing-wave node line, moving toward the two node lines of the second-order standing wave. The flow is from left to right.

Fig. 4
Fig. 4

Zero- and second-order standing waves, showing annihilation of vortices.

Equations (3)

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Ψx, y, t=Anx, y+expiΔωtAmx, y,
Anx, y=1/21+tanh-xHnyexp-y2,
Amx, y=1/21+tanhxHmyexp-y2,

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