Abstract

We propose a new scheme for self-trapping of (2+1)-dimensional optical beams: parametric interaction between self-guided waves of optical and microwave (or terahertz) frequencies, which relies on the combination of optical rectification and the electro-optic effect in a bulk noncentrosymmetric medium. We show that, in spite of strong domination of quasi-cubic terms, quadratic nonlinearity provides an effective stabilization mechanism to prevent collapse in a large range of parameters where three-wave solitons exist.

© 2000 Optical Society of America

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  1. G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
    [CrossRef]
  2. O. Bang, Yu. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, “Two-dimensional solitary waves in media with quadratic and cubic nonlinearity,” Phys. Rev. E 58, 5057–5069 (1998).
    [CrossRef]
  3. D. Zhou and M. Segev, “Solitons via optical rectification cascading,” Final Project Rep. ELE 553 (Princeton University, Princeton, N.J., 1997).
  4. The authors are preparing a manuscript to be called “Solitons via optical rectification cascading.”
  5. C. Bosshard, R. Spreiter, M. Zgonik, and P. Gunter, “Kerr nonlinearity via cascaded optical rectification and the linear electro-optic effect,” Phys. Rev. Lett. 74, 2816–2819 (1995).
    [CrossRef] [PubMed]
  6. L. A. Ostrovskii, “Self-action of light in crystals,” JETP Lett. 5, 272–275 (1967) [Pis'ma Zh. Eksp. Teor. Fiz. 5, 331–334 (1967)].
  7. J. J. Rasmussen and K. Rypdal, “Blow-up in nonlinear Schroedinger equations. I. A general review,” Phys. Scr. 33, 481–497 (1986).
    [CrossRef]
  8. A. V. Buryak, Yu. S. Kivshar, and S. Trillo, “Parametric spatial solitary waves due to type-II second harmonic generation,” J. Opt. Soc. Am. B 14, 3110–3118 (1997).
    [CrossRef]
  9. S. J. Hewlett and F. Ladouceur, “Fourier decomposition method applied to mapped infinite domains: scalar analysis of dielectric waveguides down to modal cut-off,” J. Lightwave Technol. 13, 375–383 (1995).
    [CrossRef]
  10. N. N. Akhmediev and A. V. Buryak, “Soliton states and bi-furcation phenomena in three-core nonlinear fiber couplers,” J. Opt. Soc. Am. B 11, 804–809 (1994).
    [CrossRef]
  11. J. Yang, “Classification of the solitary waves in coupled nonlinear Schrödinger equations,” Physica D 108, 92–102 (1997).
    [CrossRef]
  12. A. V. Buryak, Yu. S. Kivshar, and S. Trillo, “Stability of three-wave parametric solitons in diffractive quadratic media,” Phys. Rev. Lett. 77, 5210–5213 (1996).
    [CrossRef] [PubMed]
  13. S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974) [Zh. Eksp. Teor. Fiz. Pis'ma Red. 65, 505–516 (1973)].
  14. J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76, 3699–3072 (1996).
    [CrossRef] [PubMed]
  15. Z. Chen, M. Segev, T. Coskun, and D. N. Christodoulides, “Observation of incoherently coupled photorefractive spatial soliton pairs,” Opt. Lett. 21, 1436–1439 (1996).
    [CrossRef] [PubMed]
  16. C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, “Energy-exchange interactions between colliding vector solitons,” Phys. Rev. Lett. 83, 2332–2335 (1999).
    [CrossRef]
  17. D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
    [CrossRef]
  18. M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994); D. N. Christodoulides and M. I. Carvalho, “Bright, dark, and gray-spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12, 1628–1633 (1995); M. Segev, M. Shih, and G. C. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B JOBPDE 13, 706–718 (1996).
    [CrossRef] [PubMed]
  19. S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Optical solitary waves induced by cross-phase modulation,” Opt. Lett. 13, 871–873 (1988).
    [CrossRef] [PubMed]
  20. M. Mitchell, M. Segev, and D. N. Christodoulides, “Observation of multihump multimode solitons,” Phys. Rev. Lett. 80, 4657–4660 (1998).
    [CrossRef]
  21. A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, “Induced coherence and stable soliton spiraling,” Phys. Rev. Lett. 82, 81–84 (1999).
    [CrossRef]

1999 (2)

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, “Energy-exchange interactions between colliding vector solitons,” Phys. Rev. Lett. 83, 2332–2335 (1999).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, “Induced coherence and stable soliton spiraling,” Phys. Rev. Lett. 82, 81–84 (1999).
[CrossRef]

1998 (2)

M. Mitchell, M. Segev, and D. N. Christodoulides, “Observation of multihump multimode solitons,” Phys. Rev. Lett. 80, 4657–4660 (1998).
[CrossRef]

O. Bang, Yu. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, “Two-dimensional solitary waves in media with quadratic and cubic nonlinearity,” Phys. Rev. E 58, 5057–5069 (1998).
[CrossRef]

1997 (2)

1996 (5)

Z. Chen, M. Segev, T. Coskun, and D. N. Christodoulides, “Observation of incoherently coupled photorefractive spatial soliton pairs,” Opt. Lett. 21, 1436–1439 (1996).
[CrossRef] [PubMed]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, “Stability of three-wave parametric solitons in diffractive quadratic media,” Phys. Rev. Lett. 77, 5210–5213 (1996).
[CrossRef] [PubMed]

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76, 3699–3072 (1996).
[CrossRef] [PubMed]

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

1995 (2)

C. Bosshard, R. Spreiter, M. Zgonik, and P. Gunter, “Kerr nonlinearity via cascaded optical rectification and the linear electro-optic effect,” Phys. Rev. Lett. 74, 2816–2819 (1995).
[CrossRef] [PubMed]

S. J. Hewlett and F. Ladouceur, “Fourier decomposition method applied to mapped infinite domains: scalar analysis of dielectric waveguides down to modal cut-off,” J. Lightwave Technol. 13, 375–383 (1995).
[CrossRef]

1994 (1)

1988 (1)

1986 (1)

J. J. Rasmussen and K. Rypdal, “Blow-up in nonlinear Schroedinger equations. I. A general review,” Phys. Scr. 33, 481–497 (1986).
[CrossRef]

1974 (1)

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974) [Zh. Eksp. Teor. Fiz. Pis'ma Red. 65, 505–516 (1973)].

1967 (1)

L. A. Ostrovskii, “Self-action of light in crystals,” JETP Lett. 5, 272–275 (1967) [Pis'ma Zh. Eksp. Teor. Fiz. 5, 331–334 (1967)].

Aitchison, J. S.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76, 3699–3072 (1996).
[CrossRef] [PubMed]

Akhmediev, N.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76, 3699–3072 (1996).
[CrossRef] [PubMed]

Akhmediev, N. N.

Anastassiou, C.

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, “Energy-exchange interactions between colliding vector solitons,” Phys. Rev. Lett. 83, 2332–2335 (1999).
[CrossRef]

Bang, O.

O. Bang, Yu. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, “Two-dimensional solitary waves in media with quadratic and cubic nonlinearity,” Phys. Rev. E 58, 5057–5069 (1998).
[CrossRef]

Bosshard, C.

C. Bosshard, R. Spreiter, M. Zgonik, and P. Gunter, “Kerr nonlinearity via cascaded optical rectification and the linear electro-optic effect,” Phys. Rev. Lett. 74, 2816–2819 (1995).
[CrossRef] [PubMed]

Buryak, A. V.

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, “Induced coherence and stable soliton spiraling,” Phys. Rev. Lett. 82, 81–84 (1999).
[CrossRef]

O. Bang, Yu. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, “Two-dimensional solitary waves in media with quadratic and cubic nonlinearity,” Phys. Rev. E 58, 5057–5069 (1998).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, “Parametric spatial solitary waves due to type-II second harmonic generation,” J. Opt. Soc. Am. B 14, 3110–3118 (1997).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, “Stability of three-wave parametric solitons in diffractive quadratic media,” Phys. Rev. Lett. 77, 5210–5213 (1996).
[CrossRef] [PubMed]

N. N. Akhmediev and A. V. Buryak, “Soliton states and bi-furcation phenomena in three-core nonlinear fiber couplers,” J. Opt. Soc. Am. B 11, 804–809 (1994).
[CrossRef]

Carvalho, M. I.

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

Chen, Z.

Christodoulides, D. N.

M. Mitchell, M. Segev, and D. N. Christodoulides, “Observation of multihump multimode solitons,” Phys. Rev. Lett. 80, 4657–4660 (1998).
[CrossRef]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

Z. Chen, M. Segev, T. Coskun, and D. N. Christodoulides, “Observation of incoherently coupled photorefractive spatial soliton pairs,” Opt. Lett. 21, 1436–1439 (1996).
[CrossRef] [PubMed]

Coskun, T.

De Rossi, A.

O. Bang, Yu. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, “Two-dimensional solitary waves in media with quadratic and cubic nonlinearity,” Phys. Rev. E 58, 5057–5069 (1998).
[CrossRef]

Giordmaine, J. A.

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, “Energy-exchange interactions between colliding vector solitons,” Phys. Rev. Lett. 83, 2332–2335 (1999).
[CrossRef]

Gunter, P.

C. Bosshard, R. Spreiter, M. Zgonik, and P. Gunter, “Kerr nonlinearity via cascaded optical rectification and the linear electro-optic effect,” Phys. Rev. Lett. 74, 2816–2819 (1995).
[CrossRef] [PubMed]

Hagan, D. J.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Hewlett, S. J.

S. J. Hewlett and F. Ladouceur, “Fourier decomposition method applied to mapped infinite domains: scalar analysis of dielectric waveguides down to modal cut-off,” J. Lightwave Technol. 13, 375–383 (1995).
[CrossRef]

Kang, J. U.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76, 3699–3072 (1996).
[CrossRef] [PubMed]

Kivshar, Yu. S.

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, “Induced coherence and stable soliton spiraling,” Phys. Rev. Lett. 82, 81–84 (1999).
[CrossRef]

O. Bang, Yu. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, “Two-dimensional solitary waves in media with quadratic and cubic nonlinearity,” Phys. Rev. E 58, 5057–5069 (1998).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, “Parametric spatial solitary waves due to type-II second harmonic generation,” J. Opt. Soc. Am. B 14, 3110–3118 (1997).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, “Stability of three-wave parametric solitons in diffractive quadratic media,” Phys. Rev. Lett. 77, 5210–5213 (1996).
[CrossRef] [PubMed]

Ladouceur, F.

S. J. Hewlett and F. Ladouceur, “Fourier decomposition method applied to mapped infinite domains: scalar analysis of dielectric waveguides down to modal cut-off,” J. Lightwave Technol. 13, 375–383 (1995).
[CrossRef]

Lan, S.

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, “Energy-exchange interactions between colliding vector solitons,” Phys. Rev. Lett. 83, 2332–2335 (1999).
[CrossRef]

Manakov, S. V.

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974) [Zh. Eksp. Teor. Fiz. Pis'ma Red. 65, 505–516 (1973)].

Martin, J.

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, “Energy-exchange interactions between colliding vector solitons,” Phys. Rev. Lett. 83, 2332–2335 (1999).
[CrossRef]

Mitchell, M.

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, “Energy-exchange interactions between colliding vector solitons,” Phys. Rev. Lett. 83, 2332–2335 (1999).
[CrossRef]

M. Mitchell, M. Segev, and D. N. Christodoulides, “Observation of multihump multimode solitons,” Phys. Rev. Lett. 80, 4657–4660 (1998).
[CrossRef]

Ostrovskii, L. A.

L. A. Ostrovskii, “Self-action of light in crystals,” JETP Lett. 5, 272–275 (1967) [Pis'ma Zh. Eksp. Teor. Fiz. 5, 331–334 (1967)].

Rasmussen, J. J.

J. J. Rasmussen and K. Rypdal, “Blow-up in nonlinear Schroedinger equations. I. A general review,” Phys. Scr. 33, 481–497 (1986).
[CrossRef]

Rypdal, K.

J. J. Rasmussen and K. Rypdal, “Blow-up in nonlinear Schroedinger equations. I. A general review,” Phys. Scr. 33, 481–497 (1986).
[CrossRef]

Segev, M.

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, “Energy-exchange interactions between colliding vector solitons,” Phys. Rev. Lett. 83, 2332–2335 (1999).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, “Induced coherence and stable soliton spiraling,” Phys. Rev. Lett. 82, 81–84 (1999).
[CrossRef]

M. Mitchell, M. Segev, and D. N. Christodoulides, “Observation of multihump multimode solitons,” Phys. Rev. Lett. 80, 4657–4660 (1998).
[CrossRef]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

Z. Chen, M. Segev, T. Coskun, and D. N. Christodoulides, “Observation of incoherently coupled photorefractive spatial soliton pairs,” Opt. Lett. 21, 1436–1439 (1996).
[CrossRef] [PubMed]

Shih, M.

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, “Induced coherence and stable soliton spiraling,” Phys. Rev. Lett. 82, 81–84 (1999).
[CrossRef]

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, “Energy-exchange interactions between colliding vector solitons,” Phys. Rev. Lett. 83, 2332–2335 (1999).
[CrossRef]

Singh, S. R.

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

Spreiter, R.

C. Bosshard, R. Spreiter, M. Zgonik, and P. Gunter, “Kerr nonlinearity via cascaded optical rectification and the linear electro-optic effect,” Phys. Rev. Lett. 74, 2816–2819 (1995).
[CrossRef] [PubMed]

Stegeman, G. I.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76, 3699–3072 (1996).
[CrossRef] [PubMed]

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Optical solitary waves induced by cross-phase modulation,” Opt. Lett. 13, 871–873 (1988).
[CrossRef] [PubMed]

Steiglitz, K.

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, “Energy-exchange interactions between colliding vector solitons,” Phys. Rev. Lett. 83, 2332–2335 (1999).
[CrossRef]

Torner, L.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Trillo, S.

O. Bang, Yu. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, “Two-dimensional solitary waves in media with quadratic and cubic nonlinearity,” Phys. Rev. E 58, 5057–5069 (1998).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, “Parametric spatial solitary waves due to type-II second harmonic generation,” J. Opt. Soc. Am. B 14, 3110–3118 (1997).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, “Stability of three-wave parametric solitons in diffractive quadratic media,” Phys. Rev. Lett. 77, 5210–5213 (1996).
[CrossRef] [PubMed]

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Optical solitary waves induced by cross-phase modulation,” Opt. Lett. 13, 871–873 (1988).
[CrossRef] [PubMed]

Wabnitz, S.

Wright, E. M.

Yang, J.

J. Yang, “Classification of the solitary waves in coupled nonlinear Schrödinger equations,” Physica D 108, 92–102 (1997).
[CrossRef]

Zgonik, M.

C. Bosshard, R. Spreiter, M. Zgonik, and P. Gunter, “Kerr nonlinearity via cascaded optical rectification and the linear electro-optic effect,” Phys. Rev. Lett. 74, 2816–2819 (1995).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

J. Lightwave Technol. (1)

S. J. Hewlett and F. Ladouceur, “Fourier decomposition method applied to mapped infinite domains: scalar analysis of dielectric waveguides down to modal cut-off,” J. Lightwave Technol. 13, 375–383 (1995).
[CrossRef]

J. Opt. Soc. Am. B (2)

JETP Lett. (1)

L. A. Ostrovskii, “Self-action of light in crystals,” JETP Lett. 5, 272–275 (1967) [Pis'ma Zh. Eksp. Teor. Fiz. 5, 331–334 (1967)].

Opt. Lett. (2)

Opt. Quantum Electron. (1)

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Phys. Rev. E (1)

O. Bang, Yu. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, “Two-dimensional solitary waves in media with quadratic and cubic nonlinearity,” Phys. Rev. E 58, 5057–5069 (1998).
[CrossRef]

Phys. Rev. Lett. (6)

C. Bosshard, R. Spreiter, M. Zgonik, and P. Gunter, “Kerr nonlinearity via cascaded optical rectification and the linear electro-optic effect,” Phys. Rev. Lett. 74, 2816–2819 (1995).
[CrossRef] [PubMed]

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, “Energy-exchange interactions between colliding vector solitons,” Phys. Rev. Lett. 83, 2332–2335 (1999).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, “Stability of three-wave parametric solitons in diffractive quadratic media,” Phys. Rev. Lett. 77, 5210–5213 (1996).
[CrossRef] [PubMed]

M. Mitchell, M. Segev, and D. N. Christodoulides, “Observation of multihump multimode solitons,” Phys. Rev. Lett. 80, 4657–4660 (1998).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, “Induced coherence and stable soliton spiraling,” Phys. Rev. Lett. 82, 81–84 (1999).
[CrossRef]

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76, 3699–3072 (1996).
[CrossRef] [PubMed]

Phys. Scr. (1)

J. J. Rasmussen and K. Rypdal, “Blow-up in nonlinear Schroedinger equations. I. A general review,” Phys. Scr. 33, 481–497 (1986).
[CrossRef]

Physica D (1)

J. Yang, “Classification of the solitary waves in coupled nonlinear Schrödinger equations,” Physica D 108, 92–102 (1997).
[CrossRef]

Sov. Phys. JETP (1)

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974) [Zh. Eksp. Teor. Fiz. Pis'ma Red. 65, 505–516 (1973)].

Other (3)

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994); D. N. Christodoulides and M. I. Carvalho, “Bright, dark, and gray-spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12, 1628–1633 (1995); M. Segev, M. Shih, and G. C. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B JOBPDE 13, 706–718 (1996).
[CrossRef] [PubMed]

D. Zhou and M. Segev, “Solitons via optical rectification cascading,” Final Project Rep. ELE 553 (Princeton University, Princeton, N.J., 1997).

The authors are preparing a manuscript to be called “Solitons via optical rectification cascading.”

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Figures (3)

Fig. 1
Fig. 1

Existence diagram for three-wave solitons of Eqs. (3) with Δ=0, K=10, σ=10. Solid curve, existence domain boundary found numerically; dashed curve, analytical result [Eq. (5)].

Fig. 2
Fig. 2

Soliton examples in transformed (left) and physical (right) coordinates for four sets of parameters on the plane (βu, βv). A, B, C, and D correspond to points A, B, C, and D, respectively, in Fig. 1.

Fig. 3
Fig. 3

Example of three-wave soliton formation from two optical Gaussian beams, W=0.856 exp(-r2/3.662) and V=1.404 exp(-r2/2.311). The simulation parameters are Δ=0, K=10, and σ=10. The final state corresponds to a three-wave soliton with βu0.05 and βv0.20.

Equations (21)

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2ik1E1z+2E1+χ1E3*E2 exp(-iΔkz)
+ρ1(|E1|2+|E2|2+|E3|2)E1=0,
2ik2E2z+2E2+χ2E3E1 exp(iΔkz)
+ρ2(|E1|2+|E2|2+|E3|2)E2=0,
2ik3E3z+2E3+χ3E1*E2 exp(-iΔkz)
+ρ3(|E1|2+|E2|2+|E3|2)E3=0,
iσ1B1z+2B1+B3*B2 exp(-iΔz)+(K1|B1|2
+L1|B2|2+S1|B3|2)B1=0,
iσ2B2z+2B2+B3B1 exp(iΔz)+(K2|B1|2
+L2|B2|2+S2|B3|2)B2=0,
iB3z+2B3+B1*B2 exp(-iΔz)+(K3|B1|2
+L3|B2|2+S3|B3|2)B3=0
iσVz+2V+WU*K exp(-iΔz)+FV=0,
iσWz+2W+UVK exp(iΔz)+FW=0,
iσUz+2U+WV*K exp(-iΔz)=0,
d2vdr2+1rdvdr-σβvv+wuK+(v2+w2)v=0,
d2wdr2+1rdwdr-σBww+uvK+(w2+v2)w=0,
d2udr2+1rdudr-βuσu+wvK=0,
βv=βuσ{8/[Kσ(βu+Δ)]3-1}3,
βv=4βuσ{1+8/[Kσ(βu+Δ)]-1}2,
QvβvQuβu-QvβuQuβv=0,

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