Abstract

We experimentally demonstrate the possibility of breaking up intense vortex light beams into stable and controllable sets of parametric solitons. We report observations performed in seeded second-harmonic generation, but the scheme can be extended to all parametric processes. The number of generated solitons is shown to be determined by a robust arithmetic rule.

© 2001 Optical Society of America

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References

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  1. V. E. Zacharov and S. Wabnitz, eds., Optical Solitons: Theoretical Challenges and Industrial Perspectives (EDP Sciences, Cambridge, Mass., 1999).
  2. M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
    [CrossRef]
  3. W. E. Toruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
    [CrossRef]
  4. W. E. Toruellas, G. Assanto, B. Lawrence, R. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
    [CrossRef]
  5. R. Schiek, Y. Baek, G. I. Stegeman, and W. Sohler, Opt. Lett. 24, 83 (1999).
    [CrossRef]
  6. B. Costantini, C. De Angelis, A. Barthelemy, B. Bourliaguet, and V. Kermene, Opt. Lett. 23, 424 (1998).
    [CrossRef]
  7. P. Di Trapani and W. Chinaglia, Opt. Lett. 23, 1653 (1998).
    [CrossRef]
  8. J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
    [CrossRef]
  9. V. I. Basisty, V. Yu. Bazhenov, N. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
    [CrossRef]
  10. K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, 3742 (1996).
    [CrossRef]
  11. A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997).
    [CrossRef]
  12. L. Torner and D. V. Petrov, Electron. Lett. 33, 608 (1997).
    [CrossRef]
  13. W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
    [CrossRef]
  14. D. V. Petrov, L. Torner, J. Martorell, R. Vilaseca, J. P. Torres, and C. Cojocaru, Opt. Lett. 23, 1444 (1998).
    [CrossRef]
  15. L. Torner, J. P. Torres, J. M. Soto-Crespo, and D. V. Petrov, Opt. Quantum Electron. 30, 809 (1998).
    [CrossRef]
  16. V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, JETP Lett. 52, 429 (1991).
  17. N. R. Heckenberg, R. McDuff, C. R. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
    [CrossRef]
  18. G. Molina-Terriza and L. Torner, J. Opt. Soc. Am. B 17, 1197 (2000).
    [CrossRef]

2000 (1)

1999 (1)

1998 (5)

1997 (3)

A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997).
[CrossRef]

L. Torner and D. V. Petrov, Electron. Lett. 33, 608 (1997).
[CrossRef]

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

1996 (2)

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, 3742 (1996).
[CrossRef]

W. E. Toruellas, G. Assanto, B. Lawrence, R. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
[CrossRef]

1995 (1)

W. E. Toruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

1993 (1)

V. I. Basisty, V. Yu. Bazhenov, N. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

1992 (1)

1991 (1)

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

1974 (1)

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

Allen, L.

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, 3742 (1996).
[CrossRef]

Assanto, G.

W. E. Toruellas, G. Assanto, B. Lawrence, R. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
[CrossRef]

Baek, Y.

Barthelemy, A.

Basisty, V. I.

V. I. Basisty, V. Yu. Bazhenov, N. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Bazhenov, V. Yu.

V. I. Basisty, V. Yu. Bazhenov, N. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

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

Berry, M. V.

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

Berzanskis, A.

A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997).
[CrossRef]

Bourliaguet, B.

Chinaglia, W.

Cojocaru, C.

Costantini, B.

De Angelis, C.

Dholakia, K.

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, 3742 (1996).
[CrossRef]

Di Trapani, P.

Firth, W. J.

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

Fuerst, R.

W. E. Toruellas, G. Assanto, B. Lawrence, R. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
[CrossRef]

Hagan, D. J.

W. E. Toruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

Heckenberg, N. R.

Kermene, V.

Lawrence, B.

W. E. Toruellas, G. Assanto, B. Lawrence, R. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
[CrossRef]

Martorell, J.

Matijosius, A.

A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997).
[CrossRef]

McDuff, R.

Menyuk, C. R.

W. E. Toruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

Molina-Terriza, G.

Nye, J. F.

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

Padgett, M. J.

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, 3742 (1996).
[CrossRef]

Petrov, D. V.

D. V. Petrov, L. Torner, J. Martorell, R. Vilaseca, J. P. Torres, and C. Cojocaru, Opt. Lett. 23, 1444 (1998).
[CrossRef]

L. Torner, J. P. Torres, J. M. Soto-Crespo, and D. V. Petrov, Opt. Quantum Electron. 30, 809 (1998).
[CrossRef]

L. Torner and D. V. Petrov, Electron. Lett. 33, 608 (1997).
[CrossRef]

Piskarskas, A.

A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997).
[CrossRef]

Schiek, R.

Segev, M.

M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
[CrossRef]

Simpson, N. B.

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, 3742 (1996).
[CrossRef]

Skryabin, D. V.

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

Smilgevicius, V.

A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997).
[CrossRef]

Smith, C. R.

Sohler, W.

Soskin, M. S.

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

Soskin, N. S.

V. I. Basisty, V. Yu. Bazhenov, N. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Soto-Crespo, J. M.

L. Torner, J. P. Torres, J. M. Soto-Crespo, and D. V. Petrov, Opt. Quantum Electron. 30, 809 (1998).
[CrossRef]

Stabinis, A.

A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997).
[CrossRef]

Stegeman, G. I.

R. Schiek, Y. Baek, G. I. Stegeman, and W. Sohler, Opt. Lett. 24, 83 (1999).
[CrossRef]

M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
[CrossRef]

W. E. Toruellas, G. Assanto, B. Lawrence, R. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
[CrossRef]

W. E. Toruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

Torner, L.

G. Molina-Terriza and L. Torner, J. Opt. Soc. Am. B 17, 1197 (2000).
[CrossRef]

D. V. Petrov, L. Torner, J. Martorell, R. Vilaseca, J. P. Torres, and C. Cojocaru, Opt. Lett. 23, 1444 (1998).
[CrossRef]

L. Torner, J. P. Torres, J. M. Soto-Crespo, and D. V. Petrov, Opt. Quantum Electron. 30, 809 (1998).
[CrossRef]

L. Torner and D. V. Petrov, Electron. Lett. 33, 608 (1997).
[CrossRef]

W. E. Toruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

Torres, J. P.

D. V. Petrov, L. Torner, J. Martorell, R. Vilaseca, J. P. Torres, and C. Cojocaru, Opt. Lett. 23, 1444 (1998).
[CrossRef]

L. Torner, J. P. Torres, J. M. Soto-Crespo, and D. V. Petrov, Opt. Quantum Electron. 30, 809 (1998).
[CrossRef]

Toruellas, W. E.

W. E. Toruellas, G. Assanto, B. Lawrence, R. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
[CrossRef]

W. E. Toruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

VanStryland, E. W.

W. E. Toruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

Vasnetsov, M. V.

V. I. Basisty, V. Yu. Bazhenov, N. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

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

Vilaseca, R.

Wang, Z.

W. E. Toruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

White, A. G.

Appl. Phys. Lett. (1)

W. E. Toruellas, G. Assanto, B. Lawrence, R. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
[CrossRef]

Electron. Lett. (1)

L. Torner and D. V. Petrov, Electron. Lett. 33, 608 (1997).
[CrossRef]

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

JETP Lett. (1)

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

Opt. Commun. (2)

V. I. Basisty, V. Yu. Bazhenov, N. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997).
[CrossRef]

Opt. Lett. (5)

Opt. Quantum Electron. (1)

L. Torner, J. P. Torres, J. M. Soto-Crespo, and D. V. Petrov, Opt. Quantum Electron. 30, 809 (1998).
[CrossRef]

Phys. Rev. A (1)

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, 3742 (1996).
[CrossRef]

Phys. Rev. Lett. (2)

W. E. Toruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

Phys. Today (1)

M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

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

Other (1)

V. E. Zacharov and S. Wabnitz, eds., Optical Solitons: Theoretical Challenges and Industrial Perspectives (EDP Sciences, Cambridge, Mass., 1999).

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Figures (3)

Fig. 1
Fig. 1

(a) FF input pump beam: external diameter dFF=60 μm, total peak power PFF=4.5 MW, topological charge mFF=1. (b) SH seed beam: dSH=80 μm, PSH=2.5 MW, mSH=-2. (c) SH output of the 30-mm-long LBO crystal. Each beam is 30 μm FWHM in diameter. (d) SH output of the same crystal but in the low-pump-depletion regime: PFF=62 kW and PSH=8 kW. The side of each figure measures 500 μm.

Fig. 2
Fig. 2

Soliton algebra. The number of solitons depends on the topological charges mFF and mSH of the pump and the seed beams, respectively. (a) mSH=-1, PFF=2 MW, PSH=0.7 MW. (b) mSH=-2, PFF=1.7 MW, PSH=0.6 MW. (c) mSH=-3, PFF=3.3 MW, PSH=0.3 MW. (d) Same conditions as for (c) but without seeding. In all cases mFF=1. Crystal length, 15  mm. All frames show the output SH intensity. The scale of images is the same as for Fig.  1.

Fig. 3
Fig. 3

(a), (b) Soliton signature. SH (left) and FF (right) intensities, output from the 30-mm-long LBO crystal pumped by an mFF=1 and seeded by an mSH=-3 beam. PFF=3.3 MW, PSH=0.3 MW. (c), (d) Diffraction-free propagation. SH output of the 15-mm (left) and the 30-mm (right)-long LBO crystals. Input conditions: mFF=1, mSH=-1, PFF=2 MW, PSH=0.7 MW. The scale is the same as for Fig.  1.

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