Abstract

The combined effects of diffraction and Poynting vector walk-off in second-harmonic generation with pump beams that contain screw phase dislocations is addressed for what is believed to be the first time. We predict the spontaneous nucleation of multiple vortex twins whose subsequent explosion can yield quasi-aligned patterns of single-charge vortices.

© 1999 Optical Society of America

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References

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  1. J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974); A. Ashkin, J. M. Dziedzic, and T. Yamane, Nature 330, 769 (1987); M. Padgett and L. Allen, Phys. World 10(9), 35 (1997).
    [CrossRef] [PubMed]
  2. G. Indebetouw, J. Mod. Opt. 40, 73 (1993); B. Luther-Davies, J. Christou, V. Tikhonenko, and Y. S. Kivshar, J. Opt. Soc. Am. B 14, 3045 (1997); D. Rozas, C. T. Law, and G. A. Swartzlander, J. Opt. Soc. Am. B 14, 3055 (1997); Y. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).
    [CrossRef]
  3. T. Ackemann, E. Kriege, and W. Lange, Opt. Commun. 115, 339 (1995); A. V. Ilyenkov, A. I. Khiznyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, Appl. Phys. B 62, 471 (1996).
    [CrossRef]
  4. I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
    [CrossRef]
  5. J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
    [CrossRef]
  6. A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997); Opt. Commun. 150, 372 (1998).
    [CrossRef]
  7. D. V. Petrov and L. Torner, Phys. Rev. E 58, 7903 (1998).
    [CrossRef]
  8. P. D. Trapani, A. Berzanskis, S. Minardi, S. Sapone, and W. Chinaglia, Phys. Rev. Lett. 81, 5133 (1998).
    [CrossRef]
  9. I. Freund, Opt. Commun. 159, 99 (1999).
    [CrossRef]
  10. D. V. Petrov, G. Molina-Terriza, and L. Torner, Opt. Commun. 162, 357 (1999).
    [CrossRef]
  11. T. Frisch, Y. Pomeau, and S. Rica, Phys. Rev. Lett. 69, 1644 (1992).
    [CrossRef] [PubMed]
  12. K. Staliunas, Phys. Rev. A 48, 1573 (1992).
    [CrossRef]
  13. J. T. Malos, R. Dykstra, M. Vaupel, and C. O. Weiss, Opt. Lett. 22, 1056 (1997).
    [CrossRef] [PubMed]

1999 (2)

I. Freund, Opt. Commun. 159, 99 (1999).
[CrossRef]

D. V. Petrov, G. Molina-Terriza, and L. Torner, Opt. Commun. 162, 357 (1999).
[CrossRef]

1998 (2)

D. V. Petrov and L. Torner, Phys. Rev. E 58, 7903 (1998).
[CrossRef]

P. D. Trapani, A. Berzanskis, S. Minardi, S. Sapone, and W. Chinaglia, Phys. Rev. Lett. 81, 5133 (1998).
[CrossRef]

1997 (3)

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997); Opt. Commun. 150, 372 (1998).
[CrossRef]

J. T. Malos, R. Dykstra, M. Vaupel, and C. O. Weiss, Opt. Lett. 22, 1056 (1997).
[CrossRef] [PubMed]

1995 (1)

T. Ackemann, E. Kriege, and W. Lange, Opt. Commun. 115, 339 (1995); A. V. Ilyenkov, A. I. Khiznyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, Appl. Phys. B 62, 471 (1996).
[CrossRef]

1993 (2)

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

G. Indebetouw, J. Mod. Opt. 40, 73 (1993); B. Luther-Davies, J. Christou, V. Tikhonenko, and Y. S. Kivshar, J. Opt. Soc. Am. B 14, 3045 (1997); D. Rozas, C. T. Law, and G. A. Swartzlander, J. Opt. Soc. Am. B 14, 3055 (1997); Y. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).
[CrossRef]

1992 (2)

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

K. Staliunas, Phys. Rev. A 48, 1573 (1992).
[CrossRef]

1974 (1)

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974); A. Ashkin, J. M. Dziedzic, and T. Yamane, Nature 330, 769 (1987); M. Padgett and L. Allen, Phys. World 10(9), 35 (1997).
[CrossRef] [PubMed]

Ackemann, T.

T. Ackemann, E. Kriege, and W. Lange, Opt. Commun. 115, 339 (1995); A. V. Ilyenkov, A. I. Khiznyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, Appl. Phys. B 62, 471 (1996).
[CrossRef]

Allen, L.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

Basistiy, I. V.

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

Bazhenov, V. Y.

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

Berry, M. V.

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974); A. Ashkin, J. M. Dziedzic, and T. Yamane, Nature 330, 769 (1987); M. Padgett and L. Allen, Phys. World 10(9), 35 (1997).
[CrossRef] [PubMed]

Berzanskis, A.

P. D. Trapani, A. Berzanskis, S. Minardi, S. Sapone, and W. Chinaglia, Phys. Rev. Lett. 81, 5133 (1998).
[CrossRef]

A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997); Opt. Commun. 150, 372 (1998).
[CrossRef]

Chinaglia, W.

P. D. Trapani, A. Berzanskis, S. Minardi, S. Sapone, and W. Chinaglia, Phys. Rev. Lett. 81, 5133 (1998).
[CrossRef]

Courtial, J.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

Dholakia, K.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

Dykstra, R.

Freund, I.

I. Freund, Opt. Commun. 159, 99 (1999).
[CrossRef]

Frisch, T.

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

Indebetouw, G.

G. Indebetouw, J. Mod. Opt. 40, 73 (1993); B. Luther-Davies, J. Christou, V. Tikhonenko, and Y. S. Kivshar, J. Opt. Soc. Am. B 14, 3045 (1997); D. Rozas, C. T. Law, and G. A. Swartzlander, J. Opt. Soc. Am. B 14, 3055 (1997); Y. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).
[CrossRef]

Kriege, E.

T. Ackemann, E. Kriege, and W. Lange, Opt. Commun. 115, 339 (1995); A. V. Ilyenkov, A. I. Khiznyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, Appl. Phys. B 62, 471 (1996).
[CrossRef]

Lange, W.

T. Ackemann, E. Kriege, and W. Lange, Opt. Commun. 115, 339 (1995); A. V. Ilyenkov, A. I. Khiznyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, Appl. Phys. B 62, 471 (1996).
[CrossRef]

Malos, J. T.

Matijosius, A.

A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997); Opt. Commun. 150, 372 (1998).
[CrossRef]

Minardi, S.

P. D. Trapani, A. Berzanskis, S. Minardi, S. Sapone, and W. Chinaglia, Phys. Rev. Lett. 81, 5133 (1998).
[CrossRef]

Molina-Terriza, G.

D. V. Petrov, G. Molina-Terriza, and L. Torner, Opt. Commun. 162, 357 (1999).
[CrossRef]

Nye, J. F.

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974); A. Ashkin, J. M. Dziedzic, and T. Yamane, Nature 330, 769 (1987); M. Padgett and L. Allen, Phys. World 10(9), 35 (1997).
[CrossRef] [PubMed]

Padgett, M. J.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

Petrov, D. V.

D. V. Petrov, G. Molina-Terriza, and L. Torner, Opt. Commun. 162, 357 (1999).
[CrossRef]

D. V. Petrov and L. Torner, Phys. Rev. E 58, 7903 (1998).
[CrossRef]

Piskarskas, A.

A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997); Opt. Commun. 150, 372 (1998).
[CrossRef]

Pomeau, Y.

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

Rica, S.

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

Sapone, S.

P. D. Trapani, A. Berzanskis, S. Minardi, S. Sapone, and W. Chinaglia, Phys. Rev. Lett. 81, 5133 (1998).
[CrossRef]

Smilgevicius, V.

A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997); Opt. Commun. 150, 372 (1998).
[CrossRef]

Soskin, M. S.

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

Stabinis, A.

A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997); Opt. Commun. 150, 372 (1998).
[CrossRef]

Staliunas, K.

K. Staliunas, Phys. Rev. A 48, 1573 (1992).
[CrossRef]

Torner, L.

D. V. Petrov, G. Molina-Terriza, and L. Torner, Opt. Commun. 162, 357 (1999).
[CrossRef]

D. V. Petrov and L. Torner, Phys. Rev. E 58, 7903 (1998).
[CrossRef]

Trapani, P. D.

P. D. Trapani, A. Berzanskis, S. Minardi, S. Sapone, and W. Chinaglia, Phys. Rev. Lett. 81, 5133 (1998).
[CrossRef]

Vasnetsov, M. V.

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

Vaupel, M.

Weiss, C. O.

J. Mod. Opt. (1)

G. Indebetouw, J. Mod. Opt. 40, 73 (1993); B. Luther-Davies, J. Christou, V. Tikhonenko, and Y. S. Kivshar, J. Opt. Soc. Am. B 14, 3045 (1997); D. Rozas, C. T. Law, and G. A. Swartzlander, J. Opt. Soc. Am. B 14, 3055 (1997); Y. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).
[CrossRef]

Opt. Commun. (5)

T. Ackemann, E. Kriege, and W. Lange, Opt. Commun. 115, 339 (1995); A. V. Ilyenkov, A. I. Khiznyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, Appl. Phys. B 62, 471 (1996).
[CrossRef]

I. V. Basistiy, V. Y. Bazhenov, M. 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); Opt. Commun. 150, 372 (1998).
[CrossRef]

I. Freund, Opt. Commun. 159, 99 (1999).
[CrossRef]

D. V. Petrov, G. Molina-Terriza, and L. Torner, Opt. Commun. 162, 357 (1999).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (2)

K. Staliunas, Phys. Rev. A 48, 1573 (1992).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

Phys. Rev. E (1)

D. V. Petrov and L. Torner, Phys. Rev. E 58, 7903 (1998).
[CrossRef]

Phys. Rev. Lett. (2)

P. D. Trapani, A. Berzanskis, S. Minardi, S. Sapone, and W. Chinaglia, Phys. Rev. Lett. 81, 5133 (1998).
[CrossRef]

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

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

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974); A. Ashkin, J. M. Dziedzic, and T. Yamane, Nature 330, 769 (1987); M. Padgett and L. Allen, Phys. World 10(9), 35 (1997).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Locations of all the single-charge vortices that are present in the SH beam as a function of crystal length. Filled circles, positive vortices such as those of the pump FF beam; open circles, negative vortices. δ=2, β=0.

Fig. 2
Fig. 2

(a)–(c) Interferograms of the SH beam obtained at selected instances of the beam evolution. (d) Amplitude of the SH beam shown in (b). δ=2, β=0. Propagation distances: (a) ξ=1.2, (b) ξ=2.4, (c) ξ=3.

Fig. 3
Fig. 3

Interferograms of the SH beam obtained at fixed crystal length for different walk-off strengths. ξ=4, β=0. Walk-off: (a) δ=0.5, (b) δ=2, (c) δ=3, (d) δ=4.

Fig. 4
Fig. 4

Interferograms of the SH beam under conditions of nonvanishing wave-vector mismatch. Mismatch: (a), (b) β=3; (c), (d) β=-3. Propagation distances: (a), (c) ξ=4; (b), (d) ξ=5. In all cases δ=3.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

ia1ξ-α122a1+a1*a2 exp-iβξ=0,
ia2ξ-α222a2-iδa2x+a12 expiβξ=0,
a2x,y,ξ=-dx-dya2x,y,ξ=0×Kx-x,y-y,ξ+-dx-dy×0ξdξa12x,y,ξKx-x,y-y,ξ-ξ.
Ku,v,w=i2α2πw expu+δw2+v2i2α2w.
a1x,y,ξ=A0x+signmiym1+i2ξm+1 exp-x2+y21+i2ξ,
a2x,y,ξ=A021+i2ξ30ξx+δξ-ξ+iy21+i2ξ×exp-2x+δξ-ξ2+y21+i2ξexp-iβξdξ.
a2x1,y1,ξ1A02ξx2-y2+xδξ+δ2ξ2/3+i2 xy+iδyξ.
x-δξ2,  y±δξ23,

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