Abstract

Solitary wave steering under interaction with continuous waves is studied. An analytical approach based on two conserved quantities of the wave evolution is used to study transverse wave number variations. The method is applicable to any number of transverse dimensions and any kind of nonlinearity. The analytical results provide useful information for the investigation of optimal parameters of interaction for efficient multidimensional steering. Numerical simulations for specific cases are used to confirm the analytical results.

© 2005 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beams," Phys. Rev. Lett. 13, 479-482 (1964).
    [CrossRef]
  6. P. L. Kelley, "Self-focusing of optical beams," Phys. Rev. Lett. 15, 1005-1008 (1965).
    [CrossRef]
  7. A. S. Davydov, "Solitons in molecular systems," Phys. Scr. 20, 387-394 (1979).
    [CrossRef]
  8. V. L. Ginzburg and L. P. Pitaevski, 'On the theory of superfluidity,' Zh. Eksp. Teor. Fiz. 34, 1245 (1958) V. L. Ginzburg and L. P. Pitaevski, [Sov. Phys. JETP 7, 858 (1958)].
  9. J. J. Rasmussen and K. Rypdal, "Blow-up in nonlinear Schrödinger equations--I," Phys. Scr. 33, 481-497 (1986).
    [CrossRef]
  10. L. Berge, "Wave collapse in physics: principles and applications to light and plasma waves," Phys. Rep. 303, 259-370 (1998).
    [CrossRef]
  11. J. H. Marburger and E. Dawes, "Dynamical formation of a small-scale filament," Phys. Rev. Lett. 21, 556-558 (1968).
    [CrossRef]
  12. G. Fibich, "Small beam nonparaxiality arrests self-focusing of optical beams," Phys. Rev. Lett. 76, 4356-4359 (1996).
    [CrossRef] [PubMed]
  13. A. P. Sheppard and M. Haelterman, "Nonparaxiality stabilizes three-dimensional soliton beams in Kerr media," Opt. Lett. 23, 1820-1822 (1998).
    [CrossRef]
  14. L.-C. Crasovan, J. P. Torres, D. Mihalache, and L. Torner, "Arresting wave collapse by wave self-rectification," Phys. Rev. Lett. 91, 063904-063907 (2003).
    [CrossRef] [PubMed]
  15. B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 56, 4725-4735 (1997).
    [CrossRef]
  16. D. Mihalache, D. Mazilu, B. A. Malomed, and L. Torner, "Asymmetric spatio-temporal optical solitons in media with quadratic nonlinearity," Opt. Commun. 152, 365-370 (1998).
    [CrossRef]
  17. L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, "Tandem light bullets," Opt. Commun. 199, 277-281 (2001).
    [CrossRef]
  18. M. Desaix, D. Anderson, and M. Lisak, "Variational approach to collapse of optical pulses," J. Opt. Soc. Am. B 8, 2082-2086 (1991).
    [CrossRef]
  19. G. Fibich and A. L. Gaeta, "Critical power for self-focusing in bulk media and in hollow waveguides," Opt. Lett. 25, 335-337 (2000).
    [CrossRef]
  20. L. Torner, W. E. Torruellas, G. I. Stegeman, and C. R. Menyuk, "Beam steering by chi(2) trapping," Opt. Lett. 20, 1952-1954 (1995).
    [CrossRef] [PubMed]
  21. L. Torner, D. Mazilu, and D. Mihalache, "Walking solitons in nonlinear quadratic media," Phys. Rev. Lett. 77, 2455-2458 (1996).
    [CrossRef] [PubMed]
  22. D. Mihalache, D. Mazilu, L.-C. Crasovan, and L. Torner, "Stationary walking solitons in bulk quadratic nonlinear media," Opt. Commun. 137, 113-117 (1997)
    [CrossRef]
  23. D. Mihalache, D. Mazilu, L.-C. Crasovan, L. Torner, B. A. Malomed, and F. Lederer, "Three-dimensional walking spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 7340-7347 (2000).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  30. K. I. Karpman and V. V. Solov'ev, "A perturbational approach to the two soliton systems," Physica D 3, 487-502 (1981).
    [CrossRef]
  31. Y. S. Kivshar and B. Luther-Davies, "Dark optical solitons: physics and applications," Phys. Rep. 298, 81-197 (1998).
    [CrossRef]
  32. A. B. Aceves, C. De Angelis, and S. Wabnitz, "Nonlinear dynamics of induced modulational instability in a self-focusing slab waveguide with normal dispersion," Opt. Lett. 17, 1758-1760 (1992).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2004 (1)

2003 (1)

L.-C. Crasovan, J. P. Torres, D. Mihalache, and L. Torner, "Arresting wave collapse by wave self-rectification," Phys. Rev. Lett. 91, 063904-063907 (2003).
[CrossRef] [PubMed]

2001 (1)

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, "Tandem light bullets," Opt. Commun. 199, 277-281 (2001).
[CrossRef]

2000 (2)

G. Fibich and A. L. Gaeta, "Critical power for self-focusing in bulk media and in hollow waveguides," Opt. Lett. 25, 335-337 (2000).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, L. Torner, B. A. Malomed, and F. Lederer, "Three-dimensional walking spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 7340-7347 (2000).
[CrossRef]

1998 (4)

D. Mihalache, D. Mazilu, B. A. Malomed, and L. Torner, "Asymmetric spatio-temporal optical solitons in media with quadratic nonlinearity," Opt. Commun. 152, 365-370 (1998).
[CrossRef]

Y. S. Kivshar and B. Luther-Davies, "Dark optical solitons: physics and applications," Phys. Rep. 298, 81-197 (1998).
[CrossRef]

L. Berge, "Wave collapse in physics: principles and applications to light and plasma waves," Phys. Rep. 303, 259-370 (1998).
[CrossRef]

A. P. Sheppard and M. Haelterman, "Nonparaxiality stabilizes three-dimensional soliton beams in Kerr media," Opt. Lett. 23, 1820-1822 (1998).
[CrossRef]

1997 (2)

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 56, 4725-4735 (1997).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, and L. Torner, "Stationary walking solitons in bulk quadratic nonlinear media," Opt. Commun. 137, 113-117 (1997)
[CrossRef]

1996 (4)

1995 (1)

1994 (1)

1993 (1)

1992 (3)

1991 (1)

1986 (1)

J. J. Rasmussen and K. Rypdal, "Blow-up in nonlinear Schrödinger equations--I," Phys. Scr. 33, 481-497 (1986).
[CrossRef]

1985 (1)

H. L. Pecseli, "Solitons and weakly nonlinear waves in plasmas," IEEE Trans. Plasma Sci. PS-13, 53-86 (1985).
[CrossRef]

1982 (1)

1981 (1)

K. I. Karpman and V. V. Solov'ev, "A perturbational approach to the two soliton systems," Physica D 3, 487-502 (1981).
[CrossRef]

1979 (2)

M. J. Ablowitz and H. J. Segur, "On the evolution of packets of water waves," J. Fluid Mech. 92, 691-715 (1979).
[CrossRef]

A. S. Davydov, "Solitons in molecular systems," Phys. Scr. 20, 387-394 (1979).
[CrossRef]

1975 (1)

H. C. Yuen and B. M. Lake, "Nonlinear deep water waves: theory and experiment," Phys. Fluids 18, 956-960 (1975).
[CrossRef]

1968 (2)

T. Taniuti and H. Washimi, "Self-trapping and instability of hydromagnetic waves along the magnetic field in a cold plasma," Phys. Rev. Lett. 21, 209-212 (1968).
[CrossRef]

J. H. Marburger and E. Dawes, "Dynamical formation of a small-scale filament," Phys. Rev. Lett. 21, 556-558 (1968).
[CrossRef]

1965 (1)

P. L. Kelley, "Self-focusing of optical beams," Phys. Rev. Lett. 15, 1005-1008 (1965).
[CrossRef]

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beams," Phys. Rev. Lett. 13, 479-482 (1964).
[CrossRef]

1958 (1)

V. L. Ginzburg and L. P. Pitaevski, 'On the theory of superfluidity,' Zh. Eksp. Teor. Fiz. 34, 1245 (1958) V. L. Ginzburg and L. P. Pitaevski, [Sov. Phys. JETP 7, 858 (1958)].

Ablowitz, M. J.

M. J. Ablowitz and H. J. Segur, "On the evolution of packets of water waves," J. Fluid Mech. 92, 691-715 (1979).
[CrossRef]

Aceves, A. B.

Agrawal, G. P.

Aitchison, J. S.

Akhmediev, N. N.

Anderson, D.

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 56, 4725-4735 (1997).
[CrossRef]

M. Desaix, D. Anderson, and M. Lisak, "Variational approach to collapse of optical pulses," J. Opt. Soc. Am. B 8, 2082-2086 (1991).
[CrossRef]

Berge, L.

L. Berge, "Wave collapse in physics: principles and applications to light and plasma waves," Phys. Rep. 303, 259-370 (1998).
[CrossRef]

Berntson, A.

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 56, 4725-4735 (1997).
[CrossRef]

Cao, X. D.

Carrasco, S.

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, "Tandem light bullets," Opt. Commun. 199, 277-281 (2001).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beams," Phys. Rev. Lett. 13, 479-482 (1964).
[CrossRef]

Christou, J.

Crasovan, L.-C.

L.-C. Crasovan, J. P. Torres, D. Mihalache, and L. Torner, "Arresting wave collapse by wave self-rectification," Phys. Rev. Lett. 91, 063904-063907 (2003).
[CrossRef] [PubMed]

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, "Tandem light bullets," Opt. Commun. 199, 277-281 (2001).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, L. Torner, B. A. Malomed, and F. Lederer, "Three-dimensional walking spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 7340-7347 (2000).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, and L. Torner, "Stationary walking solitons in bulk quadratic nonlinear media," Opt. Commun. 137, 113-117 (1997)
[CrossRef]

Davydov, A. S.

A. S. Davydov, "Solitons in molecular systems," Phys. Scr. 20, 387-394 (1979).
[CrossRef]

Dawes, E.

J. H. Marburger and E. Dawes, "Dynamical formation of a small-scale filament," Phys. Rev. Lett. 21, 556-558 (1968).
[CrossRef]

De Angelis, C.

Desaix, M.

Drummond, P.

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 56, 4725-4735 (1997).
[CrossRef]

Fibich, G.

G. Fibich and A. L. Gaeta, "Critical power for self-focusing in bulk media and in hollow waveguides," Opt. Lett. 25, 335-337 (2000).
[CrossRef]

G. Fibich, "Small beam nonparaxiality arrests self-focusing of optical beams," Phys. Rev. Lett. 76, 4356-4359 (1996).
[CrossRef] [PubMed]

Gaeta, A. L.

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beams," Phys. Rev. Lett. 13, 479-482 (1964).
[CrossRef]

Ginzburg, V. L.

V. L. Ginzburg and L. P. Pitaevski, 'On the theory of superfluidity,' Zh. Eksp. Teor. Fiz. 34, 1245 (1958) V. L. Ginzburg and L. P. Pitaevski, [Sov. Phys. JETP 7, 858 (1958)].

Haelterman, M.

Hasegawa, A.

He, H.

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 56, 4725-4735 (1997).
[CrossRef]

Hizanidis, K.

Kang, J. U.

Karlsson, M.

M. Karlsson, "Optical beams in saturable self-focusing media," Phys. Rev. A 46, 2726-2734 (1992).
[CrossRef] [PubMed]

Karpman, K. I.

K. I. Karpman and V. V. Solov'ev, "A perturbational approach to the two soliton systems," Physica D 3, 487-502 (1981).
[CrossRef]

Kelley, P. L.

P. L. Kelley, "Self-focusing of optical beams," Phys. Rev. Lett. 15, 1005-1008 (1965).
[CrossRef]

Kivshar, Y. S.

Y. S. Kivshar and B. Luther-Davies, "Dark optical solitons: physics and applications," Phys. Rep. 298, 81-197 (1998).
[CrossRef]

J. Christou, V. Tikhonenko, Y. S. Kivshar, and B. Luther-Davies, "Vortex soliton motion and steering," Opt. Lett. 21, 1649-1651 (1996).
[CrossRef] [PubMed]

Kodama, Y.

Kominis, Y.

Lake, B. M.

H. C. Yuen and B. M. Lake, "Nonlinear deep water waves: theory and experiment," Phys. Fluids 18, 956-960 (1975).
[CrossRef]

Lederer, F.

D. Mihalache, D. Mazilu, L.-C. Crasovan, L. Torner, B. A. Malomed, and F. Lederer, "Three-dimensional walking spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 7340-7347 (2000).
[CrossRef]

Lisak, M.

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 56, 4725-4735 (1997).
[CrossRef]

M. Desaix, D. Anderson, and M. Lisak, "Variational approach to collapse of optical pulses," J. Opt. Soc. Am. B 8, 2082-2086 (1991).
[CrossRef]

Luther-Davies, B.

Y. S. Kivshar and B. Luther-Davies, "Dark optical solitons: physics and applications," Phys. Rep. 298, 81-197 (1998).
[CrossRef]

J. Christou, V. Tikhonenko, Y. S. Kivshar, and B. Luther-Davies, "Vortex soliton motion and steering," Opt. Lett. 21, 1649-1651 (1996).
[CrossRef] [PubMed]

Malomed, B. A.

D. Mihalache, D. Mazilu, L.-C. Crasovan, L. Torner, B. A. Malomed, and F. Lederer, "Three-dimensional walking spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 7340-7347 (2000).
[CrossRef]

D. Mihalache, D. Mazilu, B. A. Malomed, and L. Torner, "Asymmetric spatio-temporal optical solitons in media with quadratic nonlinearity," Opt. Commun. 152, 365-370 (1998).
[CrossRef]

B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, "Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity," Phys. Rev. E 56, 4725-4735 (1997).
[CrossRef]

Marburger, J. H.

J. H. Marburger and E. Dawes, "Dynamical formation of a small-scale filament," Phys. Rev. Lett. 21, 556-558 (1968).
[CrossRef]

Mazilu, D.

D. Mihalache, D. Mazilu, L.-C. Crasovan, L. Torner, B. A. Malomed, and F. Lederer, "Three-dimensional walking spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 7340-7347 (2000).
[CrossRef]

D. Mihalache, D. Mazilu, B. A. Malomed, and L. Torner, "Asymmetric spatio-temporal optical solitons in media with quadratic nonlinearity," Opt. Commun. 152, 365-370 (1998).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, and L. Torner, "Stationary walking solitons in bulk quadratic nonlinear media," Opt. Commun. 137, 113-117 (1997)
[CrossRef]

L. Torner, D. Mazilu, and D. Mihalache, "Walking solitons in nonlinear quadratic media," Phys. Rev. Lett. 77, 2455-2458 (1996).
[CrossRef] [PubMed]

Menyuk, C. R.

Meyerhofer, D. D.

Mihalache, D.

L.-C. Crasovan, J. P. Torres, D. Mihalache, and L. Torner, "Arresting wave collapse by wave self-rectification," Phys. Rev. Lett. 91, 063904-063907 (2003).
[CrossRef] [PubMed]

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, "Tandem light bullets," Opt. Commun. 199, 277-281 (2001).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, L. Torner, B. A. Malomed, and F. Lederer, "Three-dimensional walking spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 7340-7347 (2000).
[CrossRef]

D. Mihalache, D. Mazilu, B. A. Malomed, and L. Torner, "Asymmetric spatio-temporal optical solitons in media with quadratic nonlinearity," Opt. Commun. 152, 365-370 (1998).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, and L. Torner, "Stationary walking solitons in bulk quadratic nonlinear media," Opt. Commun. 137, 113-117 (1997)
[CrossRef]

L. Torner, D. Mazilu, and D. Mihalache, "Walking solitons in nonlinear quadratic media," Phys. Rev. Lett. 77, 2455-2458 (1996).
[CrossRef] [PubMed]

Pecseli, H. L.

H. L. Pecseli, "Solitons and weakly nonlinear waves in plasmas," IEEE Trans. Plasma Sci. PS-13, 53-86 (1985).
[CrossRef]

Pitaevski, L. P.

V. L. Ginzburg and L. P. Pitaevski, 'On the theory of superfluidity,' Zh. Eksp. Teor. Fiz. 34, 1245 (1958) V. L. Ginzburg and L. P. Pitaevski, [Sov. Phys. JETP 7, 858 (1958)].

Rasmussen, J. J.

J. J. Rasmussen and K. Rypdal, "Blow-up in nonlinear Schrödinger equations--I," Phys. Scr. 33, 481-497 (1986).
[CrossRef]

Rypdal, K.

J. J. Rasmussen and K. Rypdal, "Blow-up in nonlinear Schrödinger equations--I," Phys. Scr. 33, 481-497 (1986).
[CrossRef]

Segur, H. J.

M. J. Ablowitz and H. J. Segur, "On the evolution of packets of water waves," J. Fluid Mech. 92, 691-715 (1979).
[CrossRef]

Sheppard, A. P.

Snyder, A. W.

Solov'ev, V. V.

K. I. Karpman and V. V. Solov'ev, "A perturbational approach to the two soliton systems," Physica D 3, 487-502 (1981).
[CrossRef]

Stegeman, G. I.

Taniuti, T.

T. Taniuti and H. Washimi, "Self-trapping and instability of hydromagnetic waves along the magnetic field in a cold plasma," Phys. Rev. Lett. 21, 209-212 (1968).
[CrossRef]

Tikhonenko, V.

Torner, L.

L.-C. Crasovan, J. P. Torres, D. Mihalache, and L. Torner, "Arresting wave collapse by wave self-rectification," Phys. Rev. Lett. 91, 063904-063907 (2003).
[CrossRef] [PubMed]

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, "Tandem light bullets," Opt. Commun. 199, 277-281 (2001).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, L. Torner, B. A. Malomed, and F. Lederer, "Three-dimensional walking spatiotemporal solitons in quadratic media," Phys. Rev. E 62, 7340-7347 (2000).
[CrossRef]

D. Mihalache, D. Mazilu, B. A. Malomed, and L. Torner, "Asymmetric spatio-temporal optical solitons in media with quadratic nonlinearity," Opt. Commun. 152, 365-370 (1998).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, and L. Torner, "Stationary walking solitons in bulk quadratic nonlinear media," Opt. Commun. 137, 113-117 (1997)
[CrossRef]

L. Torner, D. Mazilu, and D. Mihalache, "Walking solitons in nonlinear quadratic media," Phys. Rev. Lett. 77, 2455-2458 (1996).
[CrossRef] [PubMed]

L. Torner, W. E. Torruellas, G. I. Stegeman, and C. R. Menyuk, "Beam steering by chi(2) trapping," Opt. Lett. 20, 1952-1954 (1995).
[CrossRef] [PubMed]

Torres, J. P.

L.-C. Crasovan, J. P. Torres, D. Mihalache, and L. Torner, "Arresting wave collapse by wave self-rectification," Phys. Rev. Lett. 91, 063904-063907 (2003).
[CrossRef] [PubMed]

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, "Tandem light bullets," Opt. Commun. 199, 277-281 (2001).
[CrossRef]

Torruellas, W. E.

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beams," Phys. Rev. Lett. 13, 479-482 (1964).
[CrossRef]

Wabnitz, S.

Washimi, H.

T. Taniuti and H. Washimi, "Self-trapping and instability of hydromagnetic waves along the magnetic field in a cold plasma," Phys. Rev. Lett. 21, 209-212 (1968).
[CrossRef]

Yuen, H. C.

H. C. Yuen and B. M. Lake, "Nonlinear deep water waves: theory and experiment," Phys. Fluids 18, 956-960 (1975).
[CrossRef]

IEEE Trans. Plasma Sci. (1)

H. L. Pecseli, "Solitons and weakly nonlinear waves in plasmas," IEEE Trans. Plasma Sci. PS-13, 53-86 (1985).
[CrossRef]

J. Fluid Mech. (1)

M. J. Ablowitz and H. J. Segur, "On the evolution of packets of water waves," J. Fluid Mech. 92, 691-715 (1979).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Commun. (3)

D. Mihalache, D. Mazilu, B. A. Malomed, and L. Torner, "Asymmetric spatio-temporal optical solitons in media with quadratic nonlinearity," Opt. Commun. 152, 365-370 (1998).
[CrossRef]

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, "Tandem light bullets," Opt. Commun. 199, 277-281 (2001).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, and L. Torner, "Stationary walking solitons in bulk quadratic nonlinear media," Opt. Commun. 137, 113-117 (1997)
[CrossRef]

Opt. Lett. (8)

Phys. Fluids (1)

H. C. Yuen and B. M. Lake, "Nonlinear deep water waves: theory and experiment," Phys. Fluids 18, 956-960 (1975).
[CrossRef]

Phys. Rep. (2)

L. Berge, "Wave collapse in physics: principles and applications to light and plasma waves," Phys. Rep. 303, 259-370 (1998).
[CrossRef]

Y. S. Kivshar and B. Luther-Davies, "Dark optical solitons: physics and applications," Phys. Rep. 298, 81-197 (1998).
[CrossRef]

Phys. Rev. A (1)

M. Karlsson, "Optical beams in saturable self-focusing media," Phys. Rev. A 46, 2726-2734 (1992).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Steering of a 2D circular Gaussian beam under interaction with a CW.

Fig. 2
Fig. 2

Gaussian beam’s variation of (a) mass ( Δ P s ) and (b) transverse wave number ( Δ k l s , l = x , y ) due to the the presence of a CW with transverse wave number difference Δ k l ( l = x , y ) .

Fig. 3
Fig. 3

Evolution of a Gaussian beam with A = 2 , a r 2 = 2 ( P = P cr ) in the presence of a CW with α = 0.2 , Δ k y = 0 , Δ k x = a r 1 , and saturation parameter s = (a), 1 (b), 0.5 (c) 0.25.

Fig. 4
Fig. 4

Evolution of a Gaussian beam with A = 1 , a r 2 = 2 ( P = P cr 2 ) in the presence of a CW with Δ ϕ = 0 , Δ k y = 0 , Δ k x = a r 1 and α = (a), 0.1 (b), 0.2 (c) 0.3. The saturation parameter is s = 0 (Kerr-type nonlinearity).

Fig. 5
Fig. 5

Evolution of a Gaussian beam with A = 1 , a r 2 = 2 ( P = P cr 2 ) in the presence of a CW with α = 0.2 , Δ k y = 0 , Δ k x = a r 1 , and Δ ϕ = (a), π 2 (b) π. The saturation parameter is s = 0 (Kerr-type nonlinearity).

Fig. 6
Fig. 6

Evolution of a Gaussian beam with A = 1 , a r 2 = 2 ( P = P cr 2 ) in the presence of a CW with α = 0.2 , Δ ϕ = 0 , Δ k y = 0 , and Δ k x = (a), 0 (b) 1. The saturation parameter is s = 0 (Kerr-type nonlinearity).

Equations (13)

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i u z + Δ u + F ( u 2 ) u = 0 ,
P = u 2 d S ,
M = i ( u * u u u * ) d S ,
u = u s + u cw ,
u s = U ( k s z r ; λ ) exp ( i k s r 2 i k s 2 z 4 + i λ z )
u cw = α exp ( i k cw r + i k z cw z + i ϕ )
P = P s + P cw + Δ P s ,
Δ P s = ( u s u cw * + u s * u cw ) d S ,
M = M s + M cw + Δ M s ,
Δ M s = i ( u s * u cw u s u cw * ) d S ,
Δ k s = Δ P s P s Δ k , Δ k k cw k s .
u s = A exp ( x 2 + y 2 2 a r 2 ) exp ( i k x s x i k y s y + i σ ) .
Δ P s = 4 π α A a r 2 cos Δ ϕ exp ( a r 2 Δ k 2 2 ) ,

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