Abstract

We numerically investigate the excitation, propagation, and characteristic features of spatial solitonlike waves formed by three-wave mixing in a birefringent bulk medium in the presence of spatial walk-off. Effects such as angular steering, all-optical switching, and beam pointing stabilization are addressed in the cases of normal and tilted input beams.

© 1997 Optical Society of America

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  1. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
    [Crossref] [PubMed]
  2. R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138 (1996).
    [Crossref]
  3. Y. N. Karamzin and A. P. Sukhorukov, “Mutual focusing of high-power light beams in media with quadratic nonlinearity,” Sov. Phys. JETP 41, 414 (1976).
  4. R. deSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, and E. W. Van Stryland, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28 (1992).
    [Crossref] [PubMed]
  5. See, for example, G. I. Stegeman, R. Schiek, L. Torner, W. E. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. W. Van Stryland, D. J. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.
  6. K. Hayata and M. Koshiba, “Multidimensional solitons in quadratic nonlinear media,” Phys. Rev. Lett. 71, 3275 (1993).
    [Crossref] [PubMed]
  7. M. J. Werner and P. D. Drummond, “Simulton solutions for the parametric amplifier,” J. Opt. Soc. Am. B 10, 2390 (1993); “Strongly coupled nonlinear parametric solitary waves,” Opt. Lett. 19, 613 (1994).
    [Crossref] [PubMed]
  8. P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005 (1965).
    [Crossref]
  9. C. R. Menyuk, R. Schiek, and L. Torner, “Solitary waves due to χ(2):χ(2) cascading,” J. Opt. Soc. Am. B 11, 234 (1994).
  10. L. Torner, C. R. Menyuk, and G. I. Stegeman, “Excitation of solitons with cascaded χ(2) nonlinearities,” Opt. Lett. 19, 1615 (1994).
    [Crossref] [PubMed]
  11. L. Torner, C. R. Menyuk, and G. I. Stegeman, “Bright solitons with second-order nonlinearities,” J. Opt. Soc. Am. B 12, 889 (1995).
    [Crossref]
  12. L. Torner, D. Mihalache, D. Mazilu, and N. N. Akhmediev, “Stability of spatial solitary waves in quadratic media,” Opt. Lett. 20, 2183 (1995).
    [Crossref] [PubMed]
  13. A. V. Buryak and Y. S. Kivshar, “Spatial optical solitons governed by quadratic nonlinearity,” Opt. Lett. 19, 1612 (1994).
    [Crossref] [PubMed]
  14. L. Torner, “Stationary solitary waves with second-order nonlinearities,” Opt. Commun. 114, 136 (1995).
    [Crossref]
  15. D. E. Pelinovsky, A. V. Buryak, and Y. S. Kivshar, “Instabilities of solitons governed by quadratic nonlinearities,” Phys. Rev. Lett. 75, 591 (1995).
    [Crossref] [PubMed]
  16. L. Torner, D. Mazilu, and D. Mihalache, “Walking solitons in quadratic nonlinear media,” Phys. Rev. Lett. 77, 2455 (1996).
    [Crossref] [PubMed]
  17. L. Torner, C. R. Menyuk, W. E. Torruellas, and G. I. Stegeman, “Two-dimensional solitons with second-order nonlinearities,” Opt. Lett. 20, 13 (1995).
    [Crossref] [PubMed]
  18. L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruellas, and G. I. Stegeman, “Stationary trapping of light beams in bulk second-order nonlinear media,” Opt. Commun. 121, 149 (1995).
    [Crossref]
  19. L. Torner and E. M. Wright, “Soliton excitation and mutual locking of light beams in bulk quadratic nonlinear crystals,” J. Opt. Soc. Am. B 13, 864 (1996).
    [Crossref]
  20. A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, “Self-trapping of light beams and parametric solitons in diffractive quadratic media,” Phys. Rev. A 52, 1670 (1995).
    [Crossref] [PubMed]
  21. V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, “Self-guided beams in a diffractive χ(2) medium: variational approach,” Opt. Commun. 118, 345 (1995).
    [Crossref]
  22. L. Bergé, V. K. Mezentsev, J. J. Rasmussen, and J. Wyller, “Formation of stable solitons in quadratic nonlinear media,” Phys. Rev. A 52, R28 (1995).
    [Crossref] [PubMed]
  23. D.-M. Baboiu, G. I. Stegeman, and L. Torner, “Interaction of one-dimensional bright solitary waves in quadratic media,” Opt. Lett. 20, 2282 (1995).
    [Crossref] [PubMed]
  24. C. Etrich, U. Peschel, F. Lederer, and B. Malomed, “Collision of solitary waves in media with a second-order nonlinearity,” Phys. Rev. A 52, 3444 (1995).
    [Crossref]
  25. D. Mihalache, F. Lederer, D. Mazilu, and L. C. Crasovan, “Multiple-humped bright solitary waves in second-order nonlinear media,” Opt. Eng. 35, 1616 (1996).
    [Crossref]
  26. M. Haelterman, S. Trillo, and P. Ferro, “Higher-order self-guided mode solitary waves in diffractive quadratic media,” Opt. Lett. 22, 84 (1997).
    [Crossref] [PubMed]
  27. L. Torner, W. E. Torruellas, G. I. Stegeman, and C. R. Menyuk, “Beam steering by χ(2) trapping,” Opt. Lett. 20, 1952 (1995).
    [Crossref] [PubMed]
  28. L. Torner, J. P. Torres, and C. R. Menyuk, “Fission and self-deflection of spatial solitons by cascading,” Opt. Lett. 21, 462 (1996).
  29. C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, “Origin of the persistent oscillations of solitary waves in nonlinear quadratic media,” Phys. Rev. E 54, 4321 (1996).
    [Crossref]
  30. W. E. Torruellas, Z. Wang, L. Torner, and G. I. Stegeman, “Observation of mutual trapping and dragging of two-dimensional spatial solitary waves in a quadratic medium,” Opt. Lett. 20, 1949 (1995).
    [Crossref] [PubMed]
  31. W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, “All-optical switching by spatial walk-off compensation and solitary-wave locking,” Appl. Phys. Lett. 68, 1449 (1996).
    [Crossref]
  32. R. A. Fuerst, B. L. Lawrence, W. E. Torruellas, and G. I. Stegeman, “Beam reshaping by use of spatial solitons in the quadratic nonlinear medium KTP,” Opt. Lett. 22, 19 (1997).
    [Crossref] [PubMed]
  33. G. Leo, G. Assanto, and W. E. Torruellas, “Beam pointing control with spatial solitary waves in quadratic nonlinear media,” Opt. Commun. 134, 223 (1997).
    [Crossref]
  34. G. Leo, G. Assanto, and W. E. Torruellas, “Intensity controlled interactions between vectorial spatial solitary waves in quadratic nonlinear media,” Opt. Lett. 22, 7 (1997).
    [Crossref] [PubMed]
  35. R. Mollame, S. Trillo, and G. Assanto, “Polarization controlled soliton switching in type II second-harmonic generation,” Opt. Lett. 21, 1969 (1996).
    [Crossref] [PubMed]
  36. H. T. Tran, “Self-induced phase matching and three-wave bright spatial solitons in quadratic media,” Opt. Commun. 118, 581 (1995).
    [Crossref]
  37. B. A. Malomed, D. Anderson, and M. Lisak, “Three-wave interaction solitons in a dispersive medium with quadratic nonlinearity,” Opt. Commun. 126, 251 (1996).
    [Crossref]
  38. A. V. Buryak, Y. S. Kivshar, and S. Trillo, “Stability of three-wave parametric solitons in diffractive quadratic media,” Phys. Rev. Lett. 77, 5210 (1996).
    [Crossref] [PubMed]
  39. G. Leo and G. Assanto, “Multiple branching of vectorial spatial solitary waves in quadratic media,” Opt. Commun. (to be published).

1997 (4)

1996 (10)

R. Mollame, S. Trillo, and G. Assanto, “Polarization controlled soliton switching in type II second-harmonic generation,” Opt. Lett. 21, 1969 (1996).
[Crossref] [PubMed]

B. A. Malomed, D. Anderson, and M. Lisak, “Three-wave interaction solitons in a dispersive medium with quadratic nonlinearity,” Opt. Commun. 126, 251 (1996).
[Crossref]

A. V. Buryak, Y. S. Kivshar, and S. Trillo, “Stability of three-wave parametric solitons in diffractive quadratic media,” Phys. Rev. Lett. 77, 5210 (1996).
[Crossref] [PubMed]

L. Torner, D. Mazilu, and D. Mihalache, “Walking solitons in quadratic nonlinear media,” Phys. Rev. Lett. 77, 2455 (1996).
[Crossref] [PubMed]

L. Torner, J. P. Torres, and C. R. Menyuk, “Fission and self-deflection of spatial solitons by cascading,” Opt. Lett. 21, 462 (1996).

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, “Origin of the persistent oscillations of solitary waves in nonlinear quadratic media,” Phys. Rev. E 54, 4321 (1996).
[Crossref]

D. Mihalache, F. Lederer, D. Mazilu, and L. C. Crasovan, “Multiple-humped bright solitary waves in second-order nonlinear media,” Opt. Eng. 35, 1616 (1996).
[Crossref]

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, “All-optical switching by spatial walk-off compensation and solitary-wave locking,” Appl. Phys. Lett. 68, 1449 (1996).
[Crossref]

R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138 (1996).
[Crossref]

L. Torner and E. M. Wright, “Soliton excitation and mutual locking of light beams in bulk quadratic nonlinear crystals,” J. Opt. Soc. Am. B 13, 864 (1996).
[Crossref]

1995 (15)

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, “Self-trapping of light beams and parametric solitons in diffractive quadratic media,” Phys. Rev. A 52, 1670 (1995).
[Crossref] [PubMed]

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, “Self-guided beams in a diffractive χ(2) medium: variational approach,” Opt. Commun. 118, 345 (1995).
[Crossref]

L. Bergé, V. K. Mezentsev, J. J. Rasmussen, and J. Wyller, “Formation of stable solitons in quadratic nonlinear media,” Phys. Rev. A 52, R28 (1995).
[Crossref] [PubMed]

D.-M. Baboiu, G. I. Stegeman, and L. Torner, “Interaction of one-dimensional bright solitary waves in quadratic media,” Opt. Lett. 20, 2282 (1995).
[Crossref] [PubMed]

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, “Collision of solitary waves in media with a second-order nonlinearity,” Phys. Rev. A 52, 3444 (1995).
[Crossref]

L. Torner, C. R. Menyuk, and G. I. Stegeman, “Bright solitons with second-order nonlinearities,” J. Opt. Soc. Am. B 12, 889 (1995).
[Crossref]

L. Torner, D. Mihalache, D. Mazilu, and N. N. Akhmediev, “Stability of spatial solitary waves in quadratic media,” Opt. Lett. 20, 2183 (1995).
[Crossref] [PubMed]

L. Torner, “Stationary solitary waves with second-order nonlinearities,” Opt. Commun. 114, 136 (1995).
[Crossref]

D. E. Pelinovsky, A. V. Buryak, and Y. S. Kivshar, “Instabilities of solitons governed by quadratic nonlinearities,” Phys. Rev. Lett. 75, 591 (1995).
[Crossref] [PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[Crossref] [PubMed]

W. E. Torruellas, Z. Wang, L. Torner, and G. I. Stegeman, “Observation of mutual trapping and dragging of two-dimensional spatial solitary waves in a quadratic medium,” Opt. Lett. 20, 1949 (1995).
[Crossref] [PubMed]

L. Torner, C. R. Menyuk, W. E. Torruellas, and G. I. Stegeman, “Two-dimensional solitons with second-order nonlinearities,” Opt. Lett. 20, 13 (1995).
[Crossref] [PubMed]

L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruellas, and G. I. Stegeman, “Stationary trapping of light beams in bulk second-order nonlinear media,” Opt. Commun. 121, 149 (1995).
[Crossref]

L. Torner, W. E. Torruellas, G. I. Stegeman, and C. R. Menyuk, “Beam steering by χ(2) trapping,” Opt. Lett. 20, 1952 (1995).
[Crossref] [PubMed]

H. T. Tran, “Self-induced phase matching and three-wave bright spatial solitons in quadratic media,” Opt. Commun. 118, 581 (1995).
[Crossref]

1994 (3)

1993 (2)

1992 (1)

1976 (1)

Y. N. Karamzin and A. P. Sukhorukov, “Mutual focusing of high-power light beams in media with quadratic nonlinearity,” Sov. Phys. JETP 41, 414 (1976).

1965 (1)

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005 (1965).
[Crossref]

Akhmediev, N. N.

Anderson, D.

B. A. Malomed, D. Anderson, and M. Lisak, “Three-wave interaction solitons in a dispersive medium with quadratic nonlinearity,” Opt. Commun. 126, 251 (1996).
[Crossref]

Assanto, G.

G. Leo, G. Assanto, and W. E. Torruellas, “Beam pointing control with spatial solitary waves in quadratic nonlinear media,” Opt. Commun. 134, 223 (1997).
[Crossref]

G. Leo, G. Assanto, and W. E. Torruellas, “Intensity controlled interactions between vectorial spatial solitary waves in quadratic nonlinear media,” Opt. Lett. 22, 7 (1997).
[Crossref] [PubMed]

R. Mollame, S. Trillo, and G. Assanto, “Polarization controlled soliton switching in type II second-harmonic generation,” Opt. Lett. 21, 1969 (1996).
[Crossref] [PubMed]

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, “All-optical switching by spatial walk-off compensation and solitary-wave locking,” Appl. Phys. Lett. 68, 1449 (1996).
[Crossref]

See, for example, G. I. Stegeman, R. Schiek, L. Torner, W. E. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. W. Van Stryland, D. J. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

G. Leo and G. Assanto, “Multiple branching of vectorial spatial solitary waves in quadratic media,” Opt. Commun. (to be published).

Baboiu, D.

See, for example, G. I. Stegeman, R. Schiek, L. Torner, W. E. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. W. Van Stryland, D. J. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

Baboiu, D.-M.

Baek, Y.

R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138 (1996).
[Crossref]

See, for example, G. I. Stegeman, R. Schiek, L. Torner, W. E. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. W. Van Stryland, D. J. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

Bergé, L.

L. Bergé, V. K. Mezentsev, J. J. Rasmussen, and J. Wyller, “Formation of stable solitons in quadratic nonlinear media,” Phys. Rev. A 52, R28 (1995).
[Crossref] [PubMed]

Buryak, A. V.

A. V. Buryak, Y. S. Kivshar, and S. Trillo, “Stability of three-wave parametric solitons in diffractive quadratic media,” Phys. Rev. Lett. 77, 5210 (1996).
[Crossref] [PubMed]

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, “Self-trapping of light beams and parametric solitons in diffractive quadratic media,” Phys. Rev. A 52, 1670 (1995).
[Crossref] [PubMed]

D. E. Pelinovsky, A. V. Buryak, and Y. S. Kivshar, “Instabilities of solitons governed by quadratic nonlinearities,” Phys. Rev. Lett. 75, 591 (1995).
[Crossref] [PubMed]

A. V. Buryak and Y. S. Kivshar, “Spatial optical solitons governed by quadratic nonlinearity,” Opt. Lett. 19, 1612 (1994).
[Crossref] [PubMed]

Crasovan, L. C.

D. Mihalache, F. Lederer, D. Mazilu, and L. C. Crasovan, “Multiple-humped bright solitary waves in second-order nonlinear media,” Opt. Eng. 35, 1616 (1996).
[Crossref]

deSalvo, R.

Drummond, P. D.

Etrich, C.

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, “Origin of the persistent oscillations of solitary waves in nonlinear quadratic media,” Phys. Rev. E 54, 4321 (1996).
[Crossref]

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, “Collision of solitary waves in media with a second-order nonlinearity,” Phys. Rev. A 52, 3444 (1995).
[Crossref]

Ferro, P.

Fuerst, R. A.

R. A. Fuerst, B. L. Lawrence, W. E. Torruellas, and G. I. Stegeman, “Beam reshaping by use of spatial solitons in the quadratic nonlinear medium KTP,” Opt. Lett. 22, 19 (1997).
[Crossref] [PubMed]

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, “All-optical switching by spatial walk-off compensation and solitary-wave locking,” Appl. Phys. Lett. 68, 1449 (1996).
[Crossref]

Haelterman, M.

Hagan, D. J.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[Crossref] [PubMed]

R. deSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, and E. W. Van Stryland, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28 (1992).
[Crossref] [PubMed]

See, for example, G. I. Stegeman, R. Schiek, L. Torner, W. E. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. W. Van Stryland, D. J. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

Hayata, K.

K. Hayata and M. Koshiba, “Multidimensional solitons in quadratic nonlinear media,” Phys. Rev. Lett. 71, 3275 (1993).
[Crossref] [PubMed]

Karamzin, Y. N.

Y. N. Karamzin and A. P. Sukhorukov, “Mutual focusing of high-power light beams in media with quadratic nonlinearity,” Sov. Phys. JETP 41, 414 (1976).

Kelley, P. L.

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005 (1965).
[Crossref]

Kivshar, Y. S.

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, “Origin of the persistent oscillations of solitary waves in nonlinear quadratic media,” Phys. Rev. E 54, 4321 (1996).
[Crossref]

A. V. Buryak, Y. S. Kivshar, and S. Trillo, “Stability of three-wave parametric solitons in diffractive quadratic media,” Phys. Rev. Lett. 77, 5210 (1996).
[Crossref] [PubMed]

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, “Self-guided beams in a diffractive χ(2) medium: variational approach,” Opt. Commun. 118, 345 (1995).
[Crossref]

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, “Self-trapping of light beams and parametric solitons in diffractive quadratic media,” Phys. Rev. A 52, 1670 (1995).
[Crossref] [PubMed]

D. E. Pelinovsky, A. V. Buryak, and Y. S. Kivshar, “Instabilities of solitons governed by quadratic nonlinearities,” Phys. Rev. Lett. 75, 591 (1995).
[Crossref] [PubMed]

A. V. Buryak and Y. S. Kivshar, “Spatial optical solitons governed by quadratic nonlinearity,” Opt. Lett. 19, 1612 (1994).
[Crossref] [PubMed]

Koshiba, M.

K. Hayata and M. Koshiba, “Multidimensional solitons in quadratic nonlinear media,” Phys. Rev. Lett. 71, 3275 (1993).
[Crossref] [PubMed]

Lawrence, B. L.

R. A. Fuerst, B. L. Lawrence, W. E. Torruellas, and G. I. Stegeman, “Beam reshaping by use of spatial solitons in the quadratic nonlinear medium KTP,” Opt. Lett. 22, 19 (1997).
[Crossref] [PubMed]

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, “All-optical switching by spatial walk-off compensation and solitary-wave locking,” Appl. Phys. Lett. 68, 1449 (1996).
[Crossref]

Lederer, F.

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, “Origin of the persistent oscillations of solitary waves in nonlinear quadratic media,” Phys. Rev. E 54, 4321 (1996).
[Crossref]

D. Mihalache, F. Lederer, D. Mazilu, and L. C. Crasovan, “Multiple-humped bright solitary waves in second-order nonlinear media,” Opt. Eng. 35, 1616 (1996).
[Crossref]

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, “Collision of solitary waves in media with a second-order nonlinearity,” Phys. Rev. A 52, 3444 (1995).
[Crossref]

Leo, G.

G. Leo, G. Assanto, and W. E. Torruellas, “Beam pointing control with spatial solitary waves in quadratic nonlinear media,” Opt. Commun. 134, 223 (1997).
[Crossref]

G. Leo, G. Assanto, and W. E. Torruellas, “Intensity controlled interactions between vectorial spatial solitary waves in quadratic nonlinear media,” Opt. Lett. 22, 7 (1997).
[Crossref] [PubMed]

G. Leo and G. Assanto, “Multiple branching of vectorial spatial solitary waves in quadratic media,” Opt. Commun. (to be published).

Lisak, M.

B. A. Malomed, D. Anderson, and M. Lisak, “Three-wave interaction solitons in a dispersive medium with quadratic nonlinearity,” Opt. Commun. 126, 251 (1996).
[Crossref]

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, “Self-guided beams in a diffractive χ(2) medium: variational approach,” Opt. Commun. 118, 345 (1995).
[Crossref]

Malomed, B.

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, “Collision of solitary waves in media with a second-order nonlinearity,” Phys. Rev. A 52, 3444 (1995).
[Crossref]

Malomed, B. A.

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, “Origin of the persistent oscillations of solitary waves in nonlinear quadratic media,” Phys. Rev. E 54, 4321 (1996).
[Crossref]

B. A. Malomed, D. Anderson, and M. Lisak, “Three-wave interaction solitons in a dispersive medium with quadratic nonlinearity,” Opt. Commun. 126, 251 (1996).
[Crossref]

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, “Self-guided beams in a diffractive χ(2) medium: variational approach,” Opt. Commun. 118, 345 (1995).
[Crossref]

Mazilu, D.

D. Mihalache, F. Lederer, D. Mazilu, and L. C. Crasovan, “Multiple-humped bright solitary waves in second-order nonlinear media,” Opt. Eng. 35, 1616 (1996).
[Crossref]

L. Torner, D. Mazilu, and D. Mihalache, “Walking solitons in quadratic nonlinear media,” Phys. Rev. Lett. 77, 2455 (1996).
[Crossref] [PubMed]

L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruellas, and G. I. Stegeman, “Stationary trapping of light beams in bulk second-order nonlinear media,” Opt. Commun. 121, 149 (1995).
[Crossref]

L. Torner, D. Mihalache, D. Mazilu, and N. N. Akhmediev, “Stability of spatial solitary waves in quadratic media,” Opt. Lett. 20, 2183 (1995).
[Crossref] [PubMed]

Menyuk, C. R.

Mezentsev, V. K.

L. Bergé, V. K. Mezentsev, J. J. Rasmussen, and J. Wyller, “Formation of stable solitons in quadratic nonlinear media,” Phys. Rev. A 52, R28 (1995).
[Crossref] [PubMed]

Mihalache, D.

D. Mihalache, F. Lederer, D. Mazilu, and L. C. Crasovan, “Multiple-humped bright solitary waves in second-order nonlinear media,” Opt. Eng. 35, 1616 (1996).
[Crossref]

L. Torner, D. Mazilu, and D. Mihalache, “Walking solitons in quadratic nonlinear media,” Phys. Rev. Lett. 77, 2455 (1996).
[Crossref] [PubMed]

L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruellas, and G. I. Stegeman, “Stationary trapping of light beams in bulk second-order nonlinear media,” Opt. Commun. 121, 149 (1995).
[Crossref]

L. Torner, D. Mihalache, D. Mazilu, and N. N. Akhmediev, “Stability of spatial solitary waves in quadratic media,” Opt. Lett. 20, 2183 (1995).
[Crossref] [PubMed]

Mollame, R.

Pelinovsky, D. E.

D. E. Pelinovsky, A. V. Buryak, and Y. S. Kivshar, “Instabilities of solitons governed by quadratic nonlinearities,” Phys. Rev. Lett. 75, 591 (1995).
[Crossref] [PubMed]

Peschel, U.

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, “Origin of the persistent oscillations of solitary waves in nonlinear quadratic media,” Phys. Rev. E 54, 4321 (1996).
[Crossref]

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, “Collision of solitary waves in media with a second-order nonlinearity,” Phys. Rev. A 52, 3444 (1995).
[Crossref]

Rasmussen, J. J.

L. Bergé, V. K. Mezentsev, J. J. Rasmussen, and J. Wyller, “Formation of stable solitons in quadratic nonlinear media,” Phys. Rev. A 52, R28 (1995).
[Crossref] [PubMed]

Schiek, R.

R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138 (1996).
[Crossref]

C. R. Menyuk, R. Schiek, and L. Torner, “Solitary waves due to χ(2):χ(2) cascading,” J. Opt. Soc. Am. B 11, 234 (1994).

See, for example, G. I. Stegeman, R. Schiek, L. Torner, W. E. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. W. Van Stryland, D. J. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

Sheik-Bahae, M.

Steblina, V. V.

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, “Self-trapping of light beams and parametric solitons in diffractive quadratic media,” Phys. Rev. A 52, 1670 (1995).
[Crossref] [PubMed]

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, “Self-guided beams in a diffractive χ(2) medium: variational approach,” Opt. Commun. 118, 345 (1995).
[Crossref]

Stegeman, G.

Stegeman, G. I.

R. A. Fuerst, B. L. Lawrence, W. E. Torruellas, and G. I. Stegeman, “Beam reshaping by use of spatial solitons in the quadratic nonlinear medium KTP,” Opt. Lett. 22, 19 (1997).
[Crossref] [PubMed]

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, “All-optical switching by spatial walk-off compensation and solitary-wave locking,” Appl. Phys. Lett. 68, 1449 (1996).
[Crossref]

R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138 (1996).
[Crossref]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[Crossref] [PubMed]

L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruellas, and G. I. Stegeman, “Stationary trapping of light beams in bulk second-order nonlinear media,” Opt. Commun. 121, 149 (1995).
[Crossref]

D.-M. Baboiu, G. I. Stegeman, and L. Torner, “Interaction of one-dimensional bright solitary waves in quadratic media,” Opt. Lett. 20, 2282 (1995).
[Crossref] [PubMed]

L. Torner, W. E. Torruellas, G. I. Stegeman, and C. R. Menyuk, “Beam steering by χ(2) trapping,” Opt. Lett. 20, 1952 (1995).
[Crossref] [PubMed]

W. E. Torruellas, Z. Wang, L. Torner, and G. I. Stegeman, “Observation of mutual trapping and dragging of two-dimensional spatial solitary waves in a quadratic medium,” Opt. Lett. 20, 1949 (1995).
[Crossref] [PubMed]

L. Torner, C. R. Menyuk, W. E. Torruellas, and G. I. Stegeman, “Two-dimensional solitons with second-order nonlinearities,” Opt. Lett. 20, 13 (1995).
[Crossref] [PubMed]

L. Torner, C. R. Menyuk, and G. I. Stegeman, “Bright solitons with second-order nonlinearities,” J. Opt. Soc. Am. B 12, 889 (1995).
[Crossref]

L. Torner, C. R. Menyuk, and G. I. Stegeman, “Excitation of solitons with cascaded χ(2) nonlinearities,” Opt. Lett. 19, 1615 (1994).
[Crossref] [PubMed]

See, for example, G. I. Stegeman, R. Schiek, L. Torner, W. E. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. W. Van Stryland, D. J. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

Sukhorukov, A. P.

Y. N. Karamzin and A. P. Sukhorukov, “Mutual focusing of high-power light beams in media with quadratic nonlinearity,” Sov. Phys. JETP 41, 414 (1976).

Torner, L.

L. Torner, D. Mazilu, and D. Mihalache, “Walking solitons in quadratic nonlinear media,” Phys. Rev. Lett. 77, 2455 (1996).
[Crossref] [PubMed]

L. Torner and E. M. Wright, “Soliton excitation and mutual locking of light beams in bulk quadratic nonlinear crystals,” J. Opt. Soc. Am. B 13, 864 (1996).
[Crossref]

L. Torner, J. P. Torres, and C. R. Menyuk, “Fission and self-deflection of spatial solitons by cascading,” Opt. Lett. 21, 462 (1996).

D.-M. Baboiu, G. I. Stegeman, and L. Torner, “Interaction of one-dimensional bright solitary waves in quadratic media,” Opt. Lett. 20, 2282 (1995).
[Crossref] [PubMed]

L. Torner, W. E. Torruellas, G. I. Stegeman, and C. R. Menyuk, “Beam steering by χ(2) trapping,” Opt. Lett. 20, 1952 (1995).
[Crossref] [PubMed]

L. Torner, C. R. Menyuk, W. E. Torruellas, and G. I. Stegeman, “Two-dimensional solitons with second-order nonlinearities,” Opt. Lett. 20, 13 (1995).
[Crossref] [PubMed]

W. E. Torruellas, Z. Wang, L. Torner, and G. I. Stegeman, “Observation of mutual trapping and dragging of two-dimensional spatial solitary waves in a quadratic medium,” Opt. Lett. 20, 1949 (1995).
[Crossref] [PubMed]

L. Torner, D. Mihalache, D. Mazilu, and N. N. Akhmediev, “Stability of spatial solitary waves in quadratic media,” Opt. Lett. 20, 2183 (1995).
[Crossref] [PubMed]

L. Torner, C. R. Menyuk, and G. I. Stegeman, “Bright solitons with second-order nonlinearities,” J. Opt. Soc. Am. B 12, 889 (1995).
[Crossref]

L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruellas, and G. I. Stegeman, “Stationary trapping of light beams in bulk second-order nonlinear media,” Opt. Commun. 121, 149 (1995).
[Crossref]

L. Torner, “Stationary solitary waves with second-order nonlinearities,” Opt. Commun. 114, 136 (1995).
[Crossref]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[Crossref] [PubMed]

C. R. Menyuk, R. Schiek, and L. Torner, “Solitary waves due to χ(2):χ(2) cascading,” J. Opt. Soc. Am. B 11, 234 (1994).

L. Torner, C. R. Menyuk, and G. I. Stegeman, “Excitation of solitons with cascaded χ(2) nonlinearities,” Opt. Lett. 19, 1615 (1994).
[Crossref] [PubMed]

See, for example, G. I. Stegeman, R. Schiek, L. Torner, W. E. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. W. Van Stryland, D. J. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

Torres, J. P.

Torruellas, W. E.

G. Leo, G. Assanto, and W. E. Torruellas, “Intensity controlled interactions between vectorial spatial solitary waves in quadratic nonlinear media,” Opt. Lett. 22, 7 (1997).
[Crossref] [PubMed]

R. A. Fuerst, B. L. Lawrence, W. E. Torruellas, and G. I. Stegeman, “Beam reshaping by use of spatial solitons in the quadratic nonlinear medium KTP,” Opt. Lett. 22, 19 (1997).
[Crossref] [PubMed]

G. Leo, G. Assanto, and W. E. Torruellas, “Beam pointing control with spatial solitary waves in quadratic nonlinear media,” Opt. Commun. 134, 223 (1997).
[Crossref]

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, “All-optical switching by spatial walk-off compensation and solitary-wave locking,” Appl. Phys. Lett. 68, 1449 (1996).
[Crossref]

L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruellas, and G. I. Stegeman, “Stationary trapping of light beams in bulk second-order nonlinear media,” Opt. Commun. 121, 149 (1995).
[Crossref]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[Crossref] [PubMed]

L. Torner, W. E. Torruellas, G. I. Stegeman, and C. R. Menyuk, “Beam steering by χ(2) trapping,” Opt. Lett. 20, 1952 (1995).
[Crossref] [PubMed]

W. E. Torruellas, Z. Wang, L. Torner, and G. I. Stegeman, “Observation of mutual trapping and dragging of two-dimensional spatial solitary waves in a quadratic medium,” Opt. Lett. 20, 1949 (1995).
[Crossref] [PubMed]

L. Torner, C. R. Menyuk, W. E. Torruellas, and G. I. Stegeman, “Two-dimensional solitons with second-order nonlinearities,” Opt. Lett. 20, 13 (1995).
[Crossref] [PubMed]

See, for example, G. I. Stegeman, R. Schiek, L. Torner, W. E. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. W. Van Stryland, D. J. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

Tran, H. T.

H. T. Tran, “Self-induced phase matching and three-wave bright spatial solitons in quadratic media,” Opt. Commun. 118, 581 (1995).
[Crossref]

Trillo, S.

Van Stryland, E. W.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[Crossref] [PubMed]

R. deSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, and E. W. Van Stryland, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28 (1992).
[Crossref] [PubMed]

See, for example, G. I. Stegeman, R. Schiek, L. Torner, W. E. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. W. Van Stryland, D. J. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

Wang, Z.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[Crossref] [PubMed]

W. E. Torruellas, Z. Wang, L. Torner, and G. I. Stegeman, “Observation of mutual trapping and dragging of two-dimensional spatial solitary waves in a quadratic medium,” Opt. Lett. 20, 1949 (1995).
[Crossref] [PubMed]

See, for example, G. I. Stegeman, R. Schiek, L. Torner, W. E. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. W. Van Stryland, D. J. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

Werner, M. J.

Wright, E. M.

L. Torner and E. M. Wright, “Soliton excitation and mutual locking of light beams in bulk quadratic nonlinear crystals,” J. Opt. Soc. Am. B 13, 864 (1996).
[Crossref]

L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruellas, and G. I. Stegeman, “Stationary trapping of light beams in bulk second-order nonlinear media,” Opt. Commun. 121, 149 (1995).
[Crossref]

Wyller, J.

L. Bergé, V. K. Mezentsev, J. J. Rasmussen, and J. Wyller, “Formation of stable solitons in quadratic nonlinear media,” Phys. Rev. A 52, R28 (1995).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, “All-optical switching by spatial walk-off compensation and solitary-wave locking,” Appl. Phys. Lett. 68, 1449 (1996).
[Crossref]

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

Opt. Commun. (6)

L. Torner, “Stationary solitary waves with second-order nonlinearities,” Opt. Commun. 114, 136 (1995).
[Crossref]

L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruellas, and G. I. Stegeman, “Stationary trapping of light beams in bulk second-order nonlinear media,” Opt. Commun. 121, 149 (1995).
[Crossref]

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, “Self-guided beams in a diffractive χ(2) medium: variational approach,” Opt. Commun. 118, 345 (1995).
[Crossref]

H. T. Tran, “Self-induced phase matching and three-wave bright spatial solitons in quadratic media,” Opt. Commun. 118, 581 (1995).
[Crossref]

B. A. Malomed, D. Anderson, and M. Lisak, “Three-wave interaction solitons in a dispersive medium with quadratic nonlinearity,” Opt. Commun. 126, 251 (1996).
[Crossref]

G. Leo, G. Assanto, and W. E. Torruellas, “Beam pointing control with spatial solitary waves in quadratic nonlinear media,” Opt. Commun. 134, 223 (1997).
[Crossref]

Opt. Eng. (1)

D. Mihalache, F. Lederer, D. Mazilu, and L. C. Crasovan, “Multiple-humped bright solitary waves in second-order nonlinear media,” Opt. Eng. 35, 1616 (1996).
[Crossref]

Opt. Lett. (13)

M. Haelterman, S. Trillo, and P. Ferro, “Higher-order self-guided mode solitary waves in diffractive quadratic media,” Opt. Lett. 22, 84 (1997).
[Crossref] [PubMed]

L. Torner, W. E. Torruellas, G. I. Stegeman, and C. R. Menyuk, “Beam steering by χ(2) trapping,” Opt. Lett. 20, 1952 (1995).
[Crossref] [PubMed]

L. Torner, J. P. Torres, and C. R. Menyuk, “Fission and self-deflection of spatial solitons by cascading,” Opt. Lett. 21, 462 (1996).

R. A. Fuerst, B. L. Lawrence, W. E. Torruellas, and G. I. Stegeman, “Beam reshaping by use of spatial solitons in the quadratic nonlinear medium KTP,” Opt. Lett. 22, 19 (1997).
[Crossref] [PubMed]

D.-M. Baboiu, G. I. Stegeman, and L. Torner, “Interaction of one-dimensional bright solitary waves in quadratic media,” Opt. Lett. 20, 2282 (1995).
[Crossref] [PubMed]

L. Torner, C. R. Menyuk, W. E. Torruellas, and G. I. Stegeman, “Two-dimensional solitons with second-order nonlinearities,” Opt. Lett. 20, 13 (1995).
[Crossref] [PubMed]

L. Torner, D. Mihalache, D. Mazilu, and N. N. Akhmediev, “Stability of spatial solitary waves in quadratic media,” Opt. Lett. 20, 2183 (1995).
[Crossref] [PubMed]

A. V. Buryak and Y. S. Kivshar, “Spatial optical solitons governed by quadratic nonlinearity,” Opt. Lett. 19, 1612 (1994).
[Crossref] [PubMed]

L. Torner, C. R. Menyuk, and G. I. Stegeman, “Excitation of solitons with cascaded χ(2) nonlinearities,” Opt. Lett. 19, 1615 (1994).
[Crossref] [PubMed]

R. deSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, and E. W. Van Stryland, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28 (1992).
[Crossref] [PubMed]

G. Leo, G. Assanto, and W. E. Torruellas, “Intensity controlled interactions between vectorial spatial solitary waves in quadratic nonlinear media,” Opt. Lett. 22, 7 (1997).
[Crossref] [PubMed]

R. Mollame, S. Trillo, and G. Assanto, “Polarization controlled soliton switching in type II second-harmonic generation,” Opt. Lett. 21, 1969 (1996).
[Crossref] [PubMed]

W. E. Torruellas, Z. Wang, L. Torner, and G. I. Stegeman, “Observation of mutual trapping and dragging of two-dimensional spatial solitary waves in a quadratic medium,” Opt. Lett. 20, 1949 (1995).
[Crossref] [PubMed]

Phys. Rev. A (3)

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, “Collision of solitary waves in media with a second-order nonlinearity,” Phys. Rev. A 52, 3444 (1995).
[Crossref]

L. Bergé, V. K. Mezentsev, J. J. Rasmussen, and J. Wyller, “Formation of stable solitons in quadratic nonlinear media,” Phys. Rev. A 52, R28 (1995).
[Crossref] [PubMed]

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, “Self-trapping of light beams and parametric solitons in diffractive quadratic media,” Phys. Rev. A 52, 1670 (1995).
[Crossref] [PubMed]

Phys. Rev. E (2)

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, “Origin of the persistent oscillations of solitary waves in nonlinear quadratic media,” Phys. Rev. E 54, 4321 (1996).
[Crossref]

R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138 (1996).
[Crossref]

Phys. Rev. Lett. (6)

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005 (1965).
[Crossref]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036 (1995).
[Crossref] [PubMed]

K. Hayata and M. Koshiba, “Multidimensional solitons in quadratic nonlinear media,” Phys. Rev. Lett. 71, 3275 (1993).
[Crossref] [PubMed]

D. E. Pelinovsky, A. V. Buryak, and Y. S. Kivshar, “Instabilities of solitons governed by quadratic nonlinearities,” Phys. Rev. Lett. 75, 591 (1995).
[Crossref] [PubMed]

L. Torner, D. Mazilu, and D. Mihalache, “Walking solitons in quadratic nonlinear media,” Phys. Rev. Lett. 77, 2455 (1996).
[Crossref] [PubMed]

A. V. Buryak, Y. S. Kivshar, and S. Trillo, “Stability of three-wave parametric solitons in diffractive quadratic media,” Phys. Rev. Lett. 77, 5210 (1996).
[Crossref] [PubMed]

Sov. Phys. JETP (1)

Y. N. Karamzin and A. P. Sukhorukov, “Mutual focusing of high-power light beams in media with quadratic nonlinearity,” Sov. Phys. JETP 41, 414 (1976).

Other (2)

See, for example, G. I. Stegeman, R. Schiek, L. Torner, W. E. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. W. Van Stryland, D. J. Hagan, and G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley, New York, 1997), pp. 49–76.

G. Leo and G. Assanto, “Multiple branching of vectorial spatial solitary waves in quadratic media,” Opt. Commun. (to be published).

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Figures (19)

Fig. 1
Fig. 1

Intensity profiles of the three interacting fields along the x axis and without walk-off: SH, solid curves; o FF, dotted curves; e FF, dashed curves (a) After one interaction length (z =0.27LD) and (b) at z=0.7LD. The input beam is at normal incidence, Io=24J0, Ie=20J0, and Δk=10π m-1. The FF curves in (a) are magnified by a factor of 2, J0=1 GW/cm2, and the values are normalized to Itot=Ie+Io.

Fig. 2
Fig. 2

Phase profiles, in units of π, of the three interacting fields along the x axis and without walk-off: SH, solid curves; o FF, dotted curves; e FF, dashed curves (a) at z=0.7LD and (b) at z=5LD for the same conditions as in Fig. 1. Note the correspondence between phase and intensity profiles at a given z (Fig. 1).

Fig. 3
Fig. 3

Same as in Fig. 1, but in the presence of walk-off: SH, solid curves; o FF, dashed curves; e FF, dotted curves. Here Io=20J0 and Ie=24J0. (a) After one interaction length (z =0.31LD), (b) at z=0.7LD. The FF curves in (a) are magnified by a factor of 2.

Fig. 4
Fig. 4

Same as in Fig. 2 in the presence of walk-off: SH, solid curves; o FF, dashed curves; e FF, dotted curves. Intensities are as in Fig. 3.

Fig. 5
Fig. 5

FF intensity contour plots along x and z/LD at normal incidence for an ordinary wave with input intensity Io=20J0 and three different values of the input imbalance δ=(Ie -Io)/(Ie+Io): (a) δ=-3.9%, (b) δ=-1.2%, (c) δ =+1.2%.

Fig. 6
Fig. 6

Pictorial view of the steering action at normal incidence for Io=20J0 and several values of Ie. The values in parentheses indicate the lateral x shifts in micrometers.

Fig. 7
Fig. 7

Solitary-wave peak shift along x at the exit face versus e input intensity Ie, at normal incidence (Io=20J0), for several values of the mismatch: (a) near phase matching and (b) for Δk=±500π m-1.

Fig. 8
Fig. 8

FF integrated transmission through a 30-µm aperture centered at the natural o output position (solid curve) and the associated peak shift (dashed curve) versus the e input Ie (at normal incidence with Io=20J0 and Δk=10π m-1).

Fig. 9
Fig. 9

Output profiles along x for various cases. The solid curves correspond to an e polarization with input tilt θx=ρω and (a) Io=20J0 and Ie=20.5J0, (b) Io=20J0 and Ie =18.5J0. The short-dashed curve refers to both input components launched with no tilt and Io=20J0, Ie=21J0, showing the enhanced displacement afforded by an initial e tilt. The dotted–dashed curve is the FF input field profile.

Fig. 10
Fig. 10

Solitary-wave peak shift along x at the exit face versus input intensity Ie, for various input tilts θx in the e component, with Io=20J0 and Δk=10π m-1. Angles θx are expressed in units of ρω.

Fig. 11
Fig. 11

Same as in Fig. 10, but with tilts θx in the o component.

Fig. 12
Fig. 12

Same as in Fig. 10, but with tilts θx in both polarization components.

Fig. 13
Fig. 13

Normalized FF output peak total intensity {[Io(z) +Ie(z)]/Itot} as a function of Ie for Io=5J0 and various input tilts θx (in units of ρω) in the e component.

Fig. 14
Fig. 14

Normalized FF output intensity profile at z=5LD, y =0 versus Ie, for Io=5J0 and normal incidence.

Fig. 15
Fig. 15

Same as in Fig. 10, but with Io=5J0.

Fig. 16
Fig. 16

Integrated transmission through a 30-µm aperture centered at the natural o output position, as a function of input intensity Ie (with Io=5J0), for various tilts θx (in units of ρω) in the e component.

Fig. 17
Fig. 17

FF bidimensional contour plots of the outputs at z =10LD for Io=20J0, Ie=22J0, and various input tilts in the e component. Each spot is labeled with the pair (θx, θy) for the e input wave (in units of ρω).

Fig. 18
Fig. 18

FF bidimensional contour plots of the outputs at z =10LD for FF inputs Io=20J0 and (a) Ie=22J0, (b) Ie =16J0. The tilts in the e inputs in the xz and yz planes are θx=θy=2ρω.

Fig. 19
Fig. 19

Same as in Fig. 17, but with Ie=16J0.

Equations (7)

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Eq(r, t)=12q2cJ00nq(ω¯)1/2Eqω¯(x, y, z)exp[i(ω¯t-kqω¯z)]+c.c.(ω¯=ω, 2ω;q=e, o),
Eoωz+Δ2Eoω2ikoω-iΓEe2ω(Eeω)* exp(-iΔkz)=0,
Eeωz-ρω Eeωx+Δ2Eeω2ikeω-iΓEe2ω(Eoω)*
×exp(-iΔkz)=0,
Ee2ωz-ρ2ω Ee2ωx+Δ2Ee2ω2ike2ω-i2ΓEeωEoω
×exp(+iΔkz)=0,
Γ=ωdeffc2J0cne(q, ω)no(ω)ne(q, 2ω)01/2

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