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,” (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 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)

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]

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

1996 (5)

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]

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]

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]

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]

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 (2)

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]

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 13, 706–718 (1996).
[Crossref] [PubMed]

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]

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]

Coskun, T.

Crosignani, B.

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 13, 706–718 (1996).
[Crossref] [PubMed]

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]

DiPorto, P.

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 13, 706–718 (1996).
[Crossref] [PubMed]

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]

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]

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 13, 706–718 (1996).
[Crossref] [PubMed]

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

Shih, 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]

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.

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]

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]

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]

Valley, G. C.

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 13, 706–718 (1996).
[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]

Yariv, A.

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 13, 706–718 (1996).
[Crossref] [PubMed]

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]

Zhou, D.

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

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)

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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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