Abstract

Second-harmonic generation in a photorefractive crystal is investigated. It is shown that a fundamental wave that is not in the photorefractive regime can be locked onto a second harmonic, creating a photorefractive effect. This locked state can be manipulated by another harmonic beam to suggest some scanning and routing applications. An interesting split-field method is used to account for the soliton dynamics in a (1+1)D configuration. Numerical simulations are used to confirm analytical results for this case.

© 2002 Optical Society of America

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  1. V. L. Vinetskii, N. Kukhtarev, S. G. Odulov, and M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
    [CrossRef]
  2. 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).
    [CrossRef] [PubMed]
  3. 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).
    [CrossRef]
  4. K. Kos, H. X. Meng, G. Salamo, M. F. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–4336 (1996).
    [CrossRef]
  5. M. F. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons,” Opt. Lett. 21, 324–326 (1996).
    [CrossRef] [PubMed]
  6. A. D. Boardman, P. Bontemps, W. Ilecki, and A. Zharov, “Theoretical demonstration of beam scanning and switching using spatial solitons in a photorefractive crystal,” J. Mod. Opt. 47, 1941–1957 (2000).
    [CrossRef]
  7. M. Morin, G. Duree, G. Salamo, and M. Segev, Opt. Lett. 20, 2066–2068 (1995).
    [CrossRef] [PubMed]
  8. Y. N. Karamzin and A. P. Sukhorukov, “Nonlinear interaction of diffracted light beams in a medium with quadratic nonlinearity: mutual focusing of beams and limitation on the efficiency of optical frequency converters,” Sov. Phys. JETP Lett. 20, 339–342 (1974).
  9. R. Desalvo, D. J. Hagan, M. Sheik-Bahae, and G. Stegeman, “Self-focusing and self-defocusing by cascaded second-order effect in KTP,” Opt. Lett. 17, 28–30 (1992).
    [CrossRef] [PubMed]
  10. G. Assanto, G. Stegeman, M. Sheik-Bahae, and E. Van Stryland, “All-optical switching devices based on large nonlinear phase shifts from second harmonic generation,” Appl. Phys. Lett. 62, 1323–1325 (1993).
    [CrossRef]
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    [CrossRef] [PubMed]
  12. A. D. Boardman, K. Xie, and A. Sangarpaul, “Stability of scalar spatial solitons in cascadable nonlinear media,” Phys. Rev. A 52, 4099–4106 (1995).
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    [CrossRef]
  15. S. Lan, M. F. Shih, G. Mizell, J. A. Giordmaine, Z. Chen, C. Anastassiou, J. Martin, and M. Segev, “Second-harmonic generation in waveguides induced by photorefractive spatial solitons,” Opt. Lett. 24, 1145–1147 (1999).
    [CrossRef]
  16. S. Lan, C. Anastassiou, M. Segev, M. Shih, J. A. Giordmaine, and G. Mizell, “Tuning of second-harmonic generation in waveguides induced by photorefractive spatial solitons,” Appl. Phys. Lett. 77, 2101 (2000).
    [CrossRef]
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    [CrossRef] [PubMed]
  19. A. D. Boardman, P. Bontemps, and K. Xie, “Vector solitary optical beam control with mixed type I, type II second harmonic generation,” Opt. Quantum Electron. 30, 891–905 (1998).
    [CrossRef]
  20. S. Trillo, A. V. Buryak, and Y. S. Kivshar, “Modulational instabilities and optical solitons due to competition of χ(2) and χ(3) nonlinearities,” Opt. Commun. 122, 200–211 (1996).
    [CrossRef]
  21. M. L. Lyra and A. S. Gouveia-Neto, “Saturation effects on modulational instability in non-Kerr-like monomode optical fibers,” Opt. Commun. 108, 117–121 (1994).
    [CrossRef]
  22. J. M. Hickman, S. B. Cavalcanti, N. M. Borges, E. A. Gouveia, and A. S. Gouveia-Neto, “Modulational instability in semiconductor-doped glass fibers with saturable nonlinearity,” Opt. Commun. 18, 182–184 (1993).
  23. Y. M. Aliev, A. D. Boardman, A. I. Smirnov, K. Xie, and A. A. Zharov, “Spatial dynamics of solitonlike channels near interfaces between optically linear and nonlinear media,” Phys. Rev. E 53, 5409–5419 (1996).
    [CrossRef]
  24. R. Uzdin, M. Segev, and G. Salamo, “Theory of self-focusing and self-defocusing in photorefractive InP,” in Nonlinear Guided Waves and Their Applications, Vol. 55 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), p. 58.
  25. M. Segev, M. Shih, and G. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B 13, 706–718 (1996).
    [CrossRef]

2000

A. D. Boardman, P. Bontemps, W. Ilecki, and A. Zharov, “Theoretical demonstration of beam scanning and switching using spatial solitons in a photorefractive crystal,” J. Mod. Opt. 47, 1941–1957 (2000).
[CrossRef]

S. Lan, C. Anastassiou, M. Segev, M. Shih, J. A. Giordmaine, and G. Mizell, “Tuning of second-harmonic generation in waveguides induced by photorefractive spatial solitons,” Appl. Phys. Lett. 77, 2101 (2000).
[CrossRef]

1999

1998

A. D. Boardman, P. Bontemps, and K. Xie, “Vector solitary optical beam control with mixed type I, type II second harmonic generation,” Opt. Quantum Electron. 30, 891–905 (1998).
[CrossRef]

1997

1996

S. Trillo, A. V. Buryak, and Y. S. Kivshar, “Modulational instabilities and optical solitons due to competition of χ(2) and χ(3) nonlinearities,” Opt. Commun. 122, 200–211 (1996).
[CrossRef]

K. Kos, H. X. Meng, G. Salamo, M. F. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–4336 (1996).
[CrossRef]

M. F. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons,” Opt. Lett. 21, 324–326 (1996).
[CrossRef] [PubMed]

Y. M. Aliev, A. D. Boardman, A. I. Smirnov, K. Xie, and A. A. Zharov, “Spatial dynamics of solitonlike channels near interfaces between optically linear and nonlinear media,” Phys. Rev. E 53, 5409–5419 (1996).
[CrossRef]

M. Segev, M. Shih, and G. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B 13, 706–718 (1996).
[CrossRef]

1995

1994

A. V. Buryak and Y. S. Kivshar, “Spatial optical solitons governed by quadratic nonlinearity,” Opt. Lett. 19, 1612–1614 (1994).
[CrossRef] [PubMed]

M. L. Lyra and A. S. Gouveia-Neto, “Saturation effects on modulational instability in non-Kerr-like monomode optical fibers,” Opt. Commun. 108, 117–121 (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).
[CrossRef] [PubMed]

1993

J. M. Hickman, S. B. Cavalcanti, N. M. Borges, E. A. Gouveia, and A. S. Gouveia-Neto, “Modulational instability in semiconductor-doped glass fibers with saturable nonlinearity,” Opt. Commun. 18, 182–184 (1993).

G. Assanto, G. Stegeman, M. Sheik-Bahae, and E. Van Stryland, “All-optical switching devices based on large nonlinear phase shifts from second harmonic generation,” Appl. Phys. Lett. 62, 1323–1325 (1993).
[CrossRef]

1992

1979

V. L. Vinetskii, N. Kukhtarev, S. G. Odulov, and M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[CrossRef]

1974

Y. N. Karamzin and A. P. Sukhorukov, “Nonlinear interaction of diffracted light beams in a medium with quadratic nonlinearity: mutual focusing of beams and limitation on the efficiency of optical frequency converters,” Sov. Phys. JETP Lett. 20, 339–342 (1974).

Aliev, Y. M.

Y. M. Aliev, A. D. Boardman, A. I. Smirnov, K. Xie, and A. A. Zharov, “Spatial dynamics of solitonlike channels near interfaces between optically linear and nonlinear media,” Phys. Rev. E 53, 5409–5419 (1996).
[CrossRef]

Anastassiou, C.

S. Lan, C. Anastassiou, M. Segev, M. Shih, J. A. Giordmaine, and G. Mizell, “Tuning of second-harmonic generation in waveguides induced by photorefractive spatial solitons,” Appl. Phys. Lett. 77, 2101 (2000).
[CrossRef]

S. Lan, M. F. Shih, G. Mizell, J. A. Giordmaine, Z. Chen, C. Anastassiou, J. Martin, and M. Segev, “Second-harmonic generation in waveguides induced by photorefractive spatial solitons,” Opt. Lett. 24, 1145–1147 (1999).
[CrossRef]

Assanto, G.

G. Assanto, G. Stegeman, M. Sheik-Bahae, and E. Van Stryland, “All-optical switching devices based on large nonlinear phase shifts from second harmonic generation,” Appl. Phys. Lett. 62, 1323–1325 (1993).
[CrossRef]

Boardman, A. D.

A. D. Boardman, P. Bontemps, W. Ilecki, and A. Zharov, “Theoretical demonstration of beam scanning and switching using spatial solitons in a photorefractive crystal,” J. Mod. Opt. 47, 1941–1957 (2000).
[CrossRef]

A. D. Boardman, P. Bontemps, and K. Xie, “Vector solitary optical beam control with mixed type I, type II second harmonic generation,” Opt. Quantum Electron. 30, 891–905 (1998).
[CrossRef]

A. D. Boardman, P. Bontemps, and K. Xie, “Transverse modulation instability of vector optical beams in quadratic nonlinear media,” J. Opt. Soc. Am. B 14, 3119–3126 (1997).
[CrossRef]

Y. M. Aliev, A. D. Boardman, A. I. Smirnov, K. Xie, and A. A. Zharov, “Spatial dynamics of solitonlike channels near interfaces between optically linear and nonlinear media,” Phys. Rev. E 53, 5409–5419 (1996).
[CrossRef]

A. D. Boardman, K. Xie, and A. Sangarpaul, “Stability of scalar spatial solitons in cascadable nonlinear media,” Phys. Rev. A 52, 4099–4106 (1995).
[CrossRef] [PubMed]

Bontemps, P.

A. D. Boardman, P. Bontemps, W. Ilecki, and A. Zharov, “Theoretical demonstration of beam scanning and switching using spatial solitons in a photorefractive crystal,” J. Mod. Opt. 47, 1941–1957 (2000).
[CrossRef]

A. D. Boardman, P. Bontemps, and K. Xie, “Vector solitary optical beam control with mixed type I, type II second harmonic generation,” Opt. Quantum Electron. 30, 891–905 (1998).
[CrossRef]

A. D. Boardman, P. Bontemps, and K. Xie, “Transverse modulation instability of vector optical beams in quadratic nonlinear media,” J. Opt. Soc. Am. B 14, 3119–3126 (1997).
[CrossRef]

Borges, N. M.

J. M. Hickman, S. B. Cavalcanti, N. M. Borges, E. A. Gouveia, and A. S. Gouveia-Neto, “Modulational instability in semiconductor-doped glass fibers with saturable nonlinearity,” Opt. Commun. 18, 182–184 (1993).

Buryak, A. V.

S. Trillo, A. V. Buryak, and Y. S. Kivshar, “Modulational instabilities and optical solitons due to competition of χ(2) and χ(3) nonlinearities,” Opt. Commun. 122, 200–211 (1996).
[CrossRef]

A. V. Buryak and Y. S. Kivshar, “Spatial optical solitons governed by quadratic nonlinearity,” Opt. Lett. 19, 1612–1614 (1994).
[CrossRef] [PubMed]

Carvalho, M. I.

Cavalcanti, S. B.

J. M. Hickman, S. B. Cavalcanti, N. M. Borges, E. A. Gouveia, and A. S. Gouveia-Neto, “Modulational instability in semiconductor-doped glass fibers with saturable nonlinearity,” Opt. Commun. 18, 182–184 (1993).

Chen, Z.

Christodoulides, D. N.

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).
[CrossRef] [PubMed]

Desalvo, R.

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).
[CrossRef] [PubMed]

Duree, G.

Ferro, P.

Garrett, M. H.

Giordmaine, J. A.

S. Lan, C. Anastassiou, M. Segev, M. Shih, J. A. Giordmaine, and G. Mizell, “Tuning of second-harmonic generation in waveguides induced by photorefractive spatial solitons,” Appl. Phys. Lett. 77, 2101 (2000).
[CrossRef]

S. Lan, M. F. Shih, G. Mizell, J. A. Giordmaine, Z. Chen, C. Anastassiou, J. Martin, and M. Segev, “Second-harmonic generation in waveguides induced by photorefractive spatial solitons,” Opt. Lett. 24, 1145–1147 (1999).
[CrossRef]

Gouveia, E. A.

J. M. Hickman, S. B. Cavalcanti, N. M. Borges, E. A. Gouveia, and A. S. Gouveia-Neto, “Modulational instability in semiconductor-doped glass fibers with saturable nonlinearity,” Opt. Commun. 18, 182–184 (1993).

Gouveia-Neto, A. S.

M. L. Lyra and A. S. Gouveia-Neto, “Saturation effects on modulational instability in non-Kerr-like monomode optical fibers,” Opt. Commun. 108, 117–121 (1994).
[CrossRef]

J. M. Hickman, S. B. Cavalcanti, N. M. Borges, E. A. Gouveia, and A. S. Gouveia-Neto, “Modulational instability in semiconductor-doped glass fibers with saturable nonlinearity,” Opt. Commun. 18, 182–184 (1993).

Hagan, D. J.

Hickman, J. M.

J. M. Hickman, S. B. Cavalcanti, N. M. Borges, E. A. Gouveia, and A. S. Gouveia-Neto, “Modulational instability in semiconductor-doped glass fibers with saturable nonlinearity,” Opt. Commun. 18, 182–184 (1993).

Ilecki, W.

A. D. Boardman, P. Bontemps, W. Ilecki, and A. Zharov, “Theoretical demonstration of beam scanning and switching using spatial solitons in a photorefractive crystal,” J. Mod. Opt. 47, 1941–1957 (2000).
[CrossRef]

Karamzin, Y. N.

Y. N. Karamzin and A. P. Sukhorukov, “Nonlinear interaction of diffracted light beams in a medium with quadratic nonlinearity: mutual focusing of beams and limitation on the efficiency of optical frequency converters,” Sov. Phys. JETP Lett. 20, 339–342 (1974).

Kivshar, Y. S.

S. Trillo, A. V. Buryak, and Y. S. Kivshar, “Modulational instabilities and optical solitons due to competition of χ(2) and χ(3) nonlinearities,” Opt. Commun. 122, 200–211 (1996).
[CrossRef]

A. V. Buryak and Y. S. Kivshar, “Spatial optical solitons governed by quadratic nonlinearity,” Opt. Lett. 19, 1612–1614 (1994).
[CrossRef] [PubMed]

Kos, K.

K. Kos, H. X. Meng, G. Salamo, M. F. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–4336 (1996).
[CrossRef]

Kukhtarev, N.

V. L. Vinetskii, N. Kukhtarev, S. G. Odulov, and M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[CrossRef]

Lan, S.

S. Lan, C. Anastassiou, M. Segev, M. Shih, J. A. Giordmaine, and G. Mizell, “Tuning of second-harmonic generation in waveguides induced by photorefractive spatial solitons,” Appl. Phys. Lett. 77, 2101 (2000).
[CrossRef]

S. Lan, M. F. Shih, G. Mizell, J. A. Giordmaine, Z. Chen, C. Anastassiou, J. Martin, and M. Segev, “Second-harmonic generation in waveguides induced by photorefractive spatial solitons,” Opt. Lett. 24, 1145–1147 (1999).
[CrossRef]

Leach, P.

Lyra, M. L.

M. L. Lyra and A. S. Gouveia-Neto, “Saturation effects on modulational instability in non-Kerr-like monomode optical fibers,” Opt. Commun. 108, 117–121 (1994).
[CrossRef]

Martin, J.

Meng, H. X.

K. Kos, H. X. Meng, G. Salamo, M. F. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–4336 (1996).
[CrossRef]

Mizell, G.

S. Lan, C. Anastassiou, M. Segev, M. Shih, J. A. Giordmaine, and G. Mizell, “Tuning of second-harmonic generation in waveguides induced by photorefractive spatial solitons,” Appl. Phys. Lett. 77, 2101 (2000).
[CrossRef]

S. Lan, M. F. Shih, G. Mizell, J. A. Giordmaine, Z. Chen, C. Anastassiou, J. Martin, and M. Segev, “Second-harmonic generation in waveguides induced by photorefractive spatial solitons,” Opt. Lett. 24, 1145–1147 (1999).
[CrossRef]

Morin, M.

Odulov, S. G.

V. L. Vinetskii, N. Kukhtarev, S. G. Odulov, and M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[CrossRef]

Salamo, G.

Sangarpaul, A.

A. D. Boardman, K. Xie, and A. Sangarpaul, “Stability of scalar spatial solitons in cascadable nonlinear media,” Phys. Rev. A 52, 4099–4106 (1995).
[CrossRef] [PubMed]

Segev, M.

S. Lan, C. Anastassiou, M. Segev, M. Shih, J. A. Giordmaine, and G. Mizell, “Tuning of second-harmonic generation in waveguides induced by photorefractive spatial solitons,” Appl. Phys. Lett. 77, 2101 (2000).
[CrossRef]

S. Lan, M. F. Shih, G. Mizell, J. A. Giordmaine, Z. Chen, C. Anastassiou, J. Martin, and M. Segev, “Second-harmonic generation in waveguides induced by photorefractive spatial solitons,” Opt. Lett. 24, 1145–1147 (1999).
[CrossRef]

M. F. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons,” Opt. Lett. 21, 324–326 (1996).
[CrossRef] [PubMed]

K. Kos, H. X. Meng, G. Salamo, M. F. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–4336 (1996).
[CrossRef]

M. Segev, M. Shih, and G. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B 13, 706–718 (1996).
[CrossRef]

M. Morin, G. Duree, G. Salamo, and M. Segev, Opt. Lett. 20, 2066–2068 (1995).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

Sheik-Bahae, M.

G. Assanto, G. Stegeman, M. Sheik-Bahae, and E. Van Stryland, “All-optical switching devices based on large nonlinear phase shifts from second harmonic generation,” Appl. Phys. Lett. 62, 1323–1325 (1993).
[CrossRef]

R. Desalvo, D. J. Hagan, M. Sheik-Bahae, and G. Stegeman, “Self-focusing and self-defocusing by cascaded second-order effect in KTP,” Opt. Lett. 17, 28–30 (1992).
[CrossRef] [PubMed]

Shih, M.

S. Lan, C. Anastassiou, M. Segev, M. Shih, J. A. Giordmaine, and G. Mizell, “Tuning of second-harmonic generation in waveguides induced by photorefractive spatial solitons,” Appl. Phys. Lett. 77, 2101 (2000).
[CrossRef]

M. Segev, M. Shih, and G. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B 13, 706–718 (1996).
[CrossRef]

Shih, M. F.

Smirnov, A. I.

Y. M. Aliev, A. D. Boardman, A. I. Smirnov, K. Xie, and A. A. Zharov, “Spatial dynamics of solitonlike channels near interfaces between optically linear and nonlinear media,” Phys. Rev. E 53, 5409–5419 (1996).
[CrossRef]

Soskin, M. S.

V. L. Vinetskii, N. Kukhtarev, S. G. Odulov, and M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[CrossRef]

Stegeman, G.

G. Assanto, G. Stegeman, M. Sheik-Bahae, and E. Van Stryland, “All-optical switching devices based on large nonlinear phase shifts from second harmonic generation,” Appl. Phys. Lett. 62, 1323–1325 (1993).
[CrossRef]

R. Desalvo, D. J. Hagan, M. Sheik-Bahae, and G. Stegeman, “Self-focusing and self-defocusing by cascaded second-order effect in KTP,” Opt. Lett. 17, 28–30 (1992).
[CrossRef] [PubMed]

Sukhorukov, A. P.

Y. N. Karamzin and A. P. Sukhorukov, “Nonlinear interaction of diffracted light beams in a medium with quadratic nonlinearity: mutual focusing of beams and limitation on the efficiency of optical frequency converters,” Sov. Phys. JETP Lett. 20, 339–342 (1974).

Trillo, S.

S. Trillo, A. V. Buryak, and Y. S. Kivshar, “Modulational instabilities and optical solitons due to competition of χ(2) and χ(3) nonlinearities,” Opt. Commun. 122, 200–211 (1996).
[CrossRef]

S. Trillo and P. Ferro, “Modulational instability in second-harmonic generation,” Opt. Lett. 20, 438–440 (1995).
[CrossRef] [PubMed]

Valley, G.

Valley, G. C.

M. F. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons,” Opt. Lett. 21, 324–326 (1996).
[CrossRef] [PubMed]

K. Kos, H. X. Meng, G. Salamo, M. F. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–4336 (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).
[CrossRef] [PubMed]

Van Stryland, E.

G. Assanto, G. Stegeman, M. Sheik-Bahae, and E. Van Stryland, “All-optical switching devices based on large nonlinear phase shifts from second harmonic generation,” Appl. Phys. Lett. 62, 1323–1325 (1993).
[CrossRef]

Vinetskii, V. L.

V. L. Vinetskii, N. Kukhtarev, S. G. Odulov, and M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[CrossRef]

Xie, K.

A. D. Boardman, P. Bontemps, and K. Xie, “Vector solitary optical beam control with mixed type I, type II second harmonic generation,” Opt. Quantum Electron. 30, 891–905 (1998).
[CrossRef]

A. D. Boardman, P. Bontemps, and K. Xie, “Transverse modulation instability of vector optical beams in quadratic nonlinear media,” J. Opt. Soc. Am. B 14, 3119–3126 (1997).
[CrossRef]

Y. M. Aliev, A. D. Boardman, A. I. Smirnov, K. Xie, and A. A. Zharov, “Spatial dynamics of solitonlike channels near interfaces between optically linear and nonlinear media,” Phys. Rev. E 53, 5409–5419 (1996).
[CrossRef]

A. D. Boardman, K. Xie, and A. Sangarpaul, “Stability of scalar spatial solitons in cascadable nonlinear media,” Phys. Rev. A 52, 4099–4106 (1995).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

Zharov, A.

A. D. Boardman, P. Bontemps, W. Ilecki, and A. Zharov, “Theoretical demonstration of beam scanning and switching using spatial solitons in a photorefractive crystal,” J. Mod. Opt. 47, 1941–1957 (2000).
[CrossRef]

Zharov, A. A.

Y. M. Aliev, A. D. Boardman, A. I. Smirnov, K. Xie, and A. A. Zharov, “Spatial dynamics of solitonlike channels near interfaces between optically linear and nonlinear media,” Phys. Rev. E 53, 5409–5419 (1996).
[CrossRef]

Appl. Phys. Lett.

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[CrossRef]

S. Lan, C. Anastassiou, M. Segev, M. Shih, J. A. Giordmaine, and G. Mizell, “Tuning of second-harmonic generation in waveguides induced by photorefractive spatial solitons,” Appl. Phys. Lett. 77, 2101 (2000).
[CrossRef]

J. Mod. Opt.

A. D. Boardman, P. Bontemps, W. Ilecki, and A. Zharov, “Theoretical demonstration of beam scanning and switching using spatial solitons in a photorefractive crystal,” J. Mod. Opt. 47, 1941–1957 (2000).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

S. Trillo, A. V. Buryak, and Y. S. Kivshar, “Modulational instabilities and optical solitons due to competition of χ(2) and χ(3) nonlinearities,” Opt. Commun. 122, 200–211 (1996).
[CrossRef]

M. L. Lyra and A. S. Gouveia-Neto, “Saturation effects on modulational instability in non-Kerr-like monomode optical fibers,” Opt. Commun. 108, 117–121 (1994).
[CrossRef]

J. M. Hickman, S. B. Cavalcanti, N. M. Borges, E. A. Gouveia, and A. S. Gouveia-Neto, “Modulational instability in semiconductor-doped glass fibers with saturable nonlinearity,” Opt. Commun. 18, 182–184 (1993).

Opt. Lett.

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A. D. Boardman, P. Bontemps, and K. Xie, “Vector solitary optical beam control with mixed type I, type II second harmonic generation,” Opt. Quantum Electron. 30, 891–905 (1998).
[CrossRef]

Phys. Rev. A

A. D. Boardman, K. Xie, and A. Sangarpaul, “Stability of scalar spatial solitons in cascadable nonlinear media,” Phys. Rev. A 52, 4099–4106 (1995).
[CrossRef] [PubMed]

Phys. Rev. E

K. Kos, H. X. Meng, G. Salamo, M. F. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–4336 (1996).
[CrossRef]

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[CrossRef]

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R. Uzdin, M. Segev, and G. Salamo, “Theory of self-focusing and self-defocusing in photorefractive InP,” in Nonlinear Guided Waves and Their Applications, Vol. 55 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), p. 58.

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Figures (11)

Fig. 1
Fig. 1

(a) Gain versus frequency and applied electric field E0. (b) Gain versus frequency for two values of E0.

Fig. 2
Fig. 2

Maximum gain versus intensity of a FF.

Fig. 3
Fig. 3

Numerically found amplitudes of a FF and a SH for K=4×10-4 and B=12.5.

Fig. 4
Fig. 4

Process of creation of the balance state between a FF and a SH; intensity of a FF and a SH.

Fig. 5
Fig. 5

Split field for interaction of two identical localized states of a FF and a SH.

Fig. 6
Fig. 6

(a) Comparison of numerically and analytically calculated trajectories (dashed curves) for E0=10.08×104 V/m. (b) Fusion distance versus applied electric field calculated both numerically and analytically.

Fig. 7
Fig. 7

Interaction of two in-phase bound states of copropagating FF and SH at E0=5×104 V/m. Initial separation, s0=2; inclination angle, arctan(α)=0.4.

Fig. 8
Fig. 8

Interaction of a two-component bound state with a photorefractive soliton. SH and FF fields are shown separately; (a) Δφ=1.57, (b) Δφ=2.09, (c) Δφ=2.62, (d) Δφ=3.14.

Fig. 9
Fig. 9

Output position of FF versus phase difference Δφ.

Fig. 10
Fig. 10

Four output channels of the multiplexer.

Fig. 11
Fig. 11

Output energy in channel 2 versus Δφ.

Equations (59)

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i2kω E1Z+2E1X2+ωc2κE1*E2 exp(iΔkZ)
-ωc2Δn1(|E2|2)E1=0,
i2K2ω E2Z+2E2X2+12 2ωc2κE12exp(-iΔkZ)
-2ωc2Δn2(|E2|2)E2=0,
Δn1(|E2|2)=nω4r13Esc,
Δn2(|E2|2)=n2ω4r33Esc,
Esc=E0Idn2ω2η0|E2|2+Id,
X=x0x,Z=kωx02z,
E1=w2η0Idn2ω1/2 exp(iβωZ),
E2=v2η0Idn2ω1/2 exp(iβ2ωZ),
iwz+12 2wx2-L1βωw+Kw*v-ρ Bw1+|v|2=0,
iαvz+12 2vx2-L2β2ωv+2Kw2-Bv1+|v|2=0,
L1=12kωx02,L2=12K2ωx02,
K=12 ωc2κ(2)x022η0Idnω1/2,
B=12 2ωc2n2ω4r33E0x02,ρ=r134r33.
2K1+L2L1v¯4ΔkL2v¯3+2K1-C+L2L1v¯2
-2ρBL2L1-ΔkL2-Bv¯-2KC=0.
βω=-1L1 Kv¯-ρB(1+v¯2),β2ω=2βω-Δk.
w(z, x)=[w¯+a1s(z, x)exp(iΩx)+a1a(z, x)exp(-iΩx)],
v(z, x)=[v¯+a2s(z, x)exp(iΩx)+a2a(z, x)exp(-iΩx)].
da/dz=iAa,
A=-E-b1-b2b3b1-E-b3b2-b40F-b50b4b5-F,
E=12Ω2+L1βω+ρB1+v¯2,
F=Ω2/2-2L2βω-L2Δkα+Bα(1+v¯2)2,
b1=Kv¯,b2=Kw¯-ρBw¯v¯(1+v¯2),b3=ρBw¯v¯(1+v¯2)2,
b4=2Kαw¯,b5=ρBv¯22α(1+v¯2)2.
2E1+ωc2n2E1+ωc2χ(2)E1*E2
-R11+γ|E2|2E1=0,
2E2+ωc2n2E2+2ωc2χ(2)E12
-R21+γ|E2|2E2=0,
E1,2=Ψ1,2(X, h1,2)exp(-ih1,2Z),
Δk+h2-2h1=0,R1=n4r13E0,
R2=n4r33E0,γ=n2η0Id,
2Ψ1X2-h12Ψ1+ωc2n2Ψ1+ωc2χ(2)Ψ1*Ψ2
-R11+γ|Ψ2|2Ψ1=0,
2Ψ2X2-h22Ψ2+2ωc2n2Ψ2+2ωc2χ(2)Ψ12
-R21+γ|Ψ2|2Ψ2=0.
2E1(2)+ωc2n2E1(2)
+ωc2χ(2)E1(2)*E2(2)-R1E1(2)1+γ|E2(2)|2 
=-12χ(2)ωc2[E1(1)*E2(2)+E1(2)*E2(1)]
-R1γ|E2(2)|2E1(1)1+γ|E2(2)|2F1(2),
2E2(2)+ωc2n2E2(2)+2ωc2χ(2)E1(2)-R2E2(2)1+γ|E2(2)|2
=-2ωc2χ(2)E1(1)E1(2)-R2γ|E2(2)|2E2(1)1+γ|E2(2)|2F2(2),
E1(2)={Ψ1(2)[X-Xs(Z),h1]+ξ1(2)}exp-i  h1dZ-iα1[X-Xs(Z)],
E2(2)={Ψ2(2)[X-Xs(Z),h2]+ξ2(2)}exp{-i  h2dZ-iα2[X+Xs(Z)]},
α1=h1 dXsdZ,
d2ξ1(2)dX2-h12+ωnc2ξ1(2)+ωc2χ[Ψ2(2)ξ1(2)
+Ψ1(2)ξ2(2)]-Rξ1(2)1+Ψ2(2)2
=-d2Ψ1(2)dX2 dXsdZ2+dΨ1(2)dX d2XsdZ2+h12dXsdZ2Ψ1(2)-2h12 d2XsdZ2(X-Xs)Ψ1(2)-12 ωc2χ[Ψ1(1)Ψ2(2)
+Ψ1(2)Ψ2(1)]-RγΨ2(2)2Ψ2(1)1+γΨ2(2)2,
α2=h2 dXsdZ,
d2ξ2(2)dX2-k22ξ2(2)+4k02χΨ1(2)ξ1(2)-4Rξ2(2)1+Ψ2(2)2
=-d2Ψ2(2)dX2 dXsdZ2+dΨ2dX d2XsdZ2+h22dXsdZ2Ψ2(2)+2h22 d2XsdZ2(X-Xs)Ψ2(2)-2k02χΨ1(1)Ψ1(2)
-4γRΨ2(2)2Ψ2(1)1+γΨ2(2)2.
-2 dΨ1dX Re{S1}+dΨ2dX Re{S2}dX=0,
-[2Ψ1 Im{S1}+Ψ2 Im{S2}]dX=0.
M1 2XsZ2=T1(Xs),
M1=-2h12Ψ1(2)2-2dΨ1(2)dX2+h22Ψ2(2)2-dΨ2(2)dX2dX,
T1(Xs)=--k02χ[Ψ1(1)Ψ2(2)+Ψ1(2)Ψ2(1)] Ψ1(2)X-2γRΨ2(2)2Ψ1(1)1+γΨ2(2)2 Ψ1(2)X-2k02χΨ1(1)Ψ1(2) Ψ2(2)X-4γRΨ2(2)2Ψ2(1)1+γΨ2(2)2 Ψ2(2)X dX.

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