Abstract

The interaction of two initially parallel spatial optical solitons is analyzed numerically, with consideration of the nonlinear polarization coupling in a planar slab waveguide. The phase difference of the soliton pair associated with the TE and the TM fundamental modes is either 0 or π, and the orthogonal polarization is excited by a weak field of the same or an opposite transverse symmetry. Polarization coupling is shown to occur if the transverse spatial symmetries in both modes are different, although the linear birefringence is completely neglected. With this effect the nonlinear polarization instability in a weakly birefringent waveguide can be influenced by the choice of the initial transverse symmetries. The application of this interaction between even and odd fields for modulation or switching is discussed. The influence of the initial polarization errors of the strong field is shown to be reducible if the strong field and the modulating weak field have opposite transverse symmetries.

© 1995 Optical Society of America

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  1. R. Y. Chiao, E. Garmire, and C. H. Towns, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
    [CrossRef]
  2. V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972).
  3. A. Hasegava and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. 1. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
    [CrossRef]
  4. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
    [CrossRef]
  5. P. L. Kelly, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005–1008 (1965).
    [CrossRef]
  6. S. Maneuf, R. Desailly, and C. Froehly, “Stable self-trapping of laser beams: observation in a nonlinear planar waveguide,” Opt. Commun. 65, 193–198 (1988).
    [CrossRef]
  7. S. Maneuf and F. Reynaud, “Quasi-steady self-trapping of first, second and third order subnanosecond soliton beams,” Opt. Commun. 66, 325–328 (1988).
    [CrossRef]
  8. J. S. Aitchinson, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. E. Smith, “Observation of spatial optical solitons in a nonlinear glass waveguide,” Opt. Lett. 15, 471–473 (1990).
    [CrossRef]
  9. J. S. Aitchinson, A. M. Weiner, Y. Silberberg, D. E. Leaird, M. K. Oliver, J. L. Jackel, and P. W. E. Smith, “Experimental observation of spatial soliton interactions,” Opt. Lett. 16, 15–17 (1991).
    [CrossRef]
  10. J. S. Aitchinson, Y. Silberberg, A. M. Weiner, D. E. Leaird, M. K. Oliver, J. L. Jackel, E. M. Vogel, and P. W. E. Smith, “Spatial optical solitons in planar glass waveguides,” J. Opt. Soc. Am. B 8, 1290–1297 (1991).
    [CrossRef]
  11. M. Shalaby and A. Barthelemy, “Experimental spatial soliton trapping and switching,” Opt. Lett. 16, 1472–1474 (1991).
    [CrossRef] [PubMed]
  12. M. Shalaby, F. Reynaud, and A. Barthelemy, “Experimental observation of spatial soliton interaction with a π/2 relative phase difference,” Opt. Lett. 17, 778–780 (1992).
    [CrossRef] [PubMed]
  13. J. S. Aitchinson, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, “Observation of spatial solitons in AlGaAs waveguides,” Electron. Lett. 28, 1879–1880 (1992).
    [CrossRef]
  14. G. Khitrowa, H. M. Gibbs, Y. Kawamura, H. Iwamura, and T. Ikegami, “Spatial solitons in a self-focusing semiconductor gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
    [CrossRef]
  15. V. E. Zakharov and A. B. Shabat, “Interaction between solitons in a stable medium,” Sov. Phys. JETP 37, 823–828 (1973).
  16. V. I. Karpman and V. V. Solovèv, “A perturbational approach to the two soliton systems,” Physica 3D, 487–502 (1981).
  17. K. J. Blow and N. J. Doran, “Bandwidth limits of nonlinear (soliton) optical communication systems,” Electron. Lett. 19, 429–430 (1983).
    [CrossRef]
  18. J. P. Gordon, “Interaction forces among solitons in optical fibers,” Opt. Lett. 8, 596–598 (1983).
    [CrossRef] [PubMed]
  19. C. Desem and P. L. Chu, “Soliton propagation in the presence of source chirping and mutual interaction in single-mode optical fibers,” Electron. Lett. 23, 260–262 (1987).
    [CrossRef]
  20. C. Desem and P. L. Chu, “Soliton interaction in the presence of loss and periodic amplification in optical fibers,” Opt. Lett. 12, 349–351 (1987).
    [CrossRef] [PubMed]
  21. C. Desem and P. L. Chu, “Reducing soliton interaction in single-mode optical fibers,” Proc. Inst. Electr. Eng. Part J 134, 145–151 (1987).
  22. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).
  23. C. R. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron. QE-23, 174–176 (1987).
    [CrossRef]
  24. K. J. Blow, N. J. Doran, and D. Wood, “Polarization instabilities for solitons in birefringent fibers,” Opt. Lett. 12, 202–204 (1987).
    [CrossRef] [PubMed]
  25. D. N. Christodoulides and R. I. Joseph, “Vector solitons in nonlinear dispersive media,” Opt. Lett. 13, 53–55 (1988).
    [CrossRef] [PubMed]
  26. H. G. Winful, “Self-induced polarization changes in birefringent optical fibers,” Appl. Phys. Lett. 47, 213–215 (1985).
    [CrossRef]
  27. H. G. Winful, “Polarization instabilities in birefringent nonlinear media: application to fiber-optic devices,” Opt. Lett. 11, 33–35 (1986).
    [CrossRef] [PubMed]
  28. B. Daino, G. Gregori, and S. Wabnitz, “New all-optical devices based on third-order nonlinearity of birefringent fibers,” Opt. Lett. 11, 42–44 (1986).
    [CrossRef] [PubMed]
  29. B. Daino, G. Gregori, and S. Wabnitz, “New exact solutions and bifurcations in the spatial distribution of polarization in third-order nonlinear optical interactions,” Phys. Rev. Lett. 56, 600–603 (1986).
    [CrossRef]
  30. Y. Chen, “Nonlinear power coupling in the birefringent fiber form birefringent effect,” J. Appl. Phys. 66, 43–46 (1989).
    [CrossRef]
  31. Y. Chen and A. W. Snyder, “Stochastic instability in nonlinear anisotropic fiber couplers,” J. Lightwave Technol. 8, 802–810 (1990).
    [CrossRef]
  32. C. M. de Sterke and J. E. Sipe, “Polarization instability in a waveguide geometry,” Opt. Lett. 16, 202–204 (1991).
    [CrossRef] [PubMed]
  33. K. Hayata, A. Misawa, and M. Koshiba, “Spatial polarization instabilities due to transverse effects in nonlinear guided-wave systems,” J. Opt. Soc. Am. B 7, 1268–1280 (1990).
    [CrossRef]
  34. P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
    [CrossRef]
  35. D. Marcuse, Theory of Dielectric Waveguides (Academic, San Diego, Calif., 1974).
  36. L. Thylen and D. Yevick, “Beam propagation method in anisotropic media,” Appl. Opt. 21, 2751–2754 (1982).
    [CrossRef] [PubMed]
  37. U. Hempelmann and L. Bersiner, “Wave propagation in integrated acoustooptical anisotropic waveguides,” Proc. Inst. Electr. Eng. Part J 140, 193–200 (1993).
  38. J. A. Fleck, J. R. Morris, and E. S. Bliss, “Small-scale self-focusing effects in a high power glass laser amplifier,” IEEE J. Quantum Electron. QE-14, 353–363 (1978).
    [CrossRef]

1993 (2)

G. Khitrowa, H. M. Gibbs, Y. Kawamura, H. Iwamura, and T. Ikegami, “Spatial solitons in a self-focusing semiconductor gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef]

U. Hempelmann and L. Bersiner, “Wave propagation in integrated acoustooptical anisotropic waveguides,” Proc. Inst. Electr. Eng. Part J 140, 193–200 (1993).

1992 (2)

M. Shalaby, F. Reynaud, and A. Barthelemy, “Experimental observation of spatial soliton interaction with a π/2 relative phase difference,” Opt. Lett. 17, 778–780 (1992).
[CrossRef] [PubMed]

J. S. Aitchinson, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, “Observation of spatial solitons in AlGaAs waveguides,” Electron. Lett. 28, 1879–1880 (1992).
[CrossRef]

1991 (4)

1990 (3)

1989 (1)

Y. Chen, “Nonlinear power coupling in the birefringent fiber form birefringent effect,” J. Appl. Phys. 66, 43–46 (1989).
[CrossRef]

1988 (3)

D. N. Christodoulides and R. I. Joseph, “Vector solitons in nonlinear dispersive media,” Opt. Lett. 13, 53–55 (1988).
[CrossRef] [PubMed]

S. Maneuf, R. Desailly, and C. Froehly, “Stable self-trapping of laser beams: observation in a nonlinear planar waveguide,” Opt. Commun. 65, 193–198 (1988).
[CrossRef]

S. Maneuf and F. Reynaud, “Quasi-steady self-trapping of first, second and third order subnanosecond soliton beams,” Opt. Commun. 66, 325–328 (1988).
[CrossRef]

1987 (5)

C. Desem and P. L. Chu, “Soliton propagation in the presence of source chirping and mutual interaction in single-mode optical fibers,” Electron. Lett. 23, 260–262 (1987).
[CrossRef]

C. Desem and P. L. Chu, “Soliton interaction in the presence of loss and periodic amplification in optical fibers,” Opt. Lett. 12, 349–351 (1987).
[CrossRef] [PubMed]

C. Desem and P. L. Chu, “Reducing soliton interaction in single-mode optical fibers,” Proc. Inst. Electr. Eng. Part J 134, 145–151 (1987).

C. R. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron. QE-23, 174–176 (1987).
[CrossRef]

K. J. Blow, N. J. Doran, and D. Wood, “Polarization instabilities for solitons in birefringent fibers,” Opt. Lett. 12, 202–204 (1987).
[CrossRef] [PubMed]

1986 (3)

1985 (1)

H. G. Winful, “Self-induced polarization changes in birefringent optical fibers,” Appl. Phys. Lett. 47, 213–215 (1985).
[CrossRef]

1983 (2)

K. J. Blow and N. J. Doran, “Bandwidth limits of nonlinear (soliton) optical communication systems,” Electron. Lett. 19, 429–430 (1983).
[CrossRef]

J. P. Gordon, “Interaction forces among solitons in optical fibers,” Opt. Lett. 8, 596–598 (1983).
[CrossRef] [PubMed]

1982 (1)

1981 (1)

V. I. Karpman and V. V. Solovèv, “A perturbational approach to the two soliton systems,” Physica 3D, 487–502 (1981).

1980 (1)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

1978 (1)

J. A. Fleck, J. R. Morris, and E. S. Bliss, “Small-scale self-focusing effects in a high power glass laser amplifier,” IEEE J. Quantum Electron. QE-14, 353–363 (1978).
[CrossRef]

1973 (2)

A. Hasegava and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. 1. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

V. E. Zakharov and A. B. Shabat, “Interaction between solitons in a stable medium,” Sov. Phys. JETP 37, 823–828 (1973).

1972 (1)

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972).

1965 (1)

P. L. Kelly, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005–1008 (1965).
[CrossRef]

1964 (2)

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

P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

Aitchinson, J. S.

Al-Hemyari, K.

J. S. Aitchinson, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, “Observation of spatial solitons in AlGaAs waveguides,” Electron. Lett. 28, 1879–1880 (1992).
[CrossRef]

Barthelemy, A.

Bersiner, L.

U. Hempelmann and L. Bersiner, “Wave propagation in integrated acoustooptical anisotropic waveguides,” Proc. Inst. Electr. Eng. Part J 140, 193–200 (1993).

Bliss, E. S.

J. A. Fleck, J. R. Morris, and E. S. Bliss, “Small-scale self-focusing effects in a high power glass laser amplifier,” IEEE J. Quantum Electron. QE-14, 353–363 (1978).
[CrossRef]

Blow, K. J.

K. J. Blow, N. J. Doran, and D. Wood, “Polarization instabilities for solitons in birefringent fibers,” Opt. Lett. 12, 202–204 (1987).
[CrossRef] [PubMed]

K. J. Blow and N. J. Doran, “Bandwidth limits of nonlinear (soliton) optical communication systems,” Electron. Lett. 19, 429–430 (1983).
[CrossRef]

Chen, Y.

Y. Chen and A. W. Snyder, “Stochastic instability in nonlinear anisotropic fiber couplers,” J. Lightwave Technol. 8, 802–810 (1990).
[CrossRef]

Y. Chen, “Nonlinear power coupling in the birefringent fiber form birefringent effect,” J. Appl. Phys. 66, 43–46 (1989).
[CrossRef]

Chiao, R. Y.

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

Christodoulides, D. N.

Chu, P. L.

C. Desem and P. L. Chu, “Soliton interaction in the presence of loss and periodic amplification in optical fibers,” Opt. Lett. 12, 349–351 (1987).
[CrossRef] [PubMed]

C. Desem and P. L. Chu, “Reducing soliton interaction in single-mode optical fibers,” Proc. Inst. Electr. Eng. Part J 134, 145–151 (1987).

C. Desem and P. L. Chu, “Soliton propagation in the presence of source chirping and mutual interaction in single-mode optical fibers,” Electron. Lett. 23, 260–262 (1987).
[CrossRef]

Daino, B.

B. Daino, G. Gregori, and S. Wabnitz, “New exact solutions and bifurcations in the spatial distribution of polarization in third-order nonlinear optical interactions,” Phys. Rev. Lett. 56, 600–603 (1986).
[CrossRef]

B. Daino, G. Gregori, and S. Wabnitz, “New all-optical devices based on third-order nonlinearity of birefringent fibers,” Opt. Lett. 11, 42–44 (1986).
[CrossRef] [PubMed]

de Sterke, C. M.

Desailly, R.

S. Maneuf, R. Desailly, and C. Froehly, “Stable self-trapping of laser beams: observation in a nonlinear planar waveguide,” Opt. Commun. 65, 193–198 (1988).
[CrossRef]

Desem, C.

C. Desem and P. L. Chu, “Reducing soliton interaction in single-mode optical fibers,” Proc. Inst. Electr. Eng. Part J 134, 145–151 (1987).

C. Desem and P. L. Chu, “Soliton propagation in the presence of source chirping and mutual interaction in single-mode optical fibers,” Electron. Lett. 23, 260–262 (1987).
[CrossRef]

C. Desem and P. L. Chu, “Soliton interaction in the presence of loss and periodic amplification in optical fibers,” Opt. Lett. 12, 349–351 (1987).
[CrossRef] [PubMed]

Doran, N. J.

K. J. Blow, N. J. Doran, and D. Wood, “Polarization instabilities for solitons in birefringent fibers,” Opt. Lett. 12, 202–204 (1987).
[CrossRef] [PubMed]

K. J. Blow and N. J. Doran, “Bandwidth limits of nonlinear (soliton) optical communication systems,” Electron. Lett. 19, 429–430 (1983).
[CrossRef]

Fleck, J. A.

J. A. Fleck, J. R. Morris, and E. S. Bliss, “Small-scale self-focusing effects in a high power glass laser amplifier,” IEEE J. Quantum Electron. QE-14, 353–363 (1978).
[CrossRef]

Froehly, C.

S. Maneuf, R. Desailly, and C. Froehly, “Stable self-trapping of laser beams: observation in a nonlinear planar waveguide,” Opt. Commun. 65, 193–198 (1988).
[CrossRef]

Garmire, E.

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

Gibbs, H. M.

G. Khitrowa, H. M. Gibbs, Y. Kawamura, H. Iwamura, and T. Ikegami, “Spatial solitons in a self-focusing semiconductor gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef]

Gordon, J. P.

J. P. Gordon, “Interaction forces among solitons in optical fibers,” Opt. Lett. 8, 596–598 (1983).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Grant, R. S.

J. S. Aitchinson, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, “Observation of spatial solitons in AlGaAs waveguides,” Electron. Lett. 28, 1879–1880 (1992).
[CrossRef]

Gregori, G.

B. Daino, G. Gregori, and S. Wabnitz, “New all-optical devices based on third-order nonlinearity of birefringent fibers,” Opt. Lett. 11, 42–44 (1986).
[CrossRef] [PubMed]

B. Daino, G. Gregori, and S. Wabnitz, “New exact solutions and bifurcations in the spatial distribution of polarization in third-order nonlinear optical interactions,” Phys. Rev. Lett. 56, 600–603 (1986).
[CrossRef]

Hasegava, A.

A. Hasegava and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. 1. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Hayata, K.

Hempelmann, U.

U. Hempelmann and L. Bersiner, “Wave propagation in integrated acoustooptical anisotropic waveguides,” Proc. Inst. Electr. Eng. Part J 140, 193–200 (1993).

Ikegami, T.

G. Khitrowa, H. M. Gibbs, Y. Kawamura, H. Iwamura, and T. Ikegami, “Spatial solitons in a self-focusing semiconductor gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef]

Ironside, C. N.

J. S. Aitchinson, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, “Observation of spatial solitons in AlGaAs waveguides,” Electron. Lett. 28, 1879–1880 (1992).
[CrossRef]

Iwamura, H.

G. Khitrowa, H. M. Gibbs, Y. Kawamura, H. Iwamura, and T. Ikegami, “Spatial solitons in a self-focusing semiconductor gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef]

Jackel, J. L.

Joseph, R. I.

Karpman, V. I.

V. I. Karpman and V. V. Solovèv, “A perturbational approach to the two soliton systems,” Physica 3D, 487–502 (1981).

Kawamura, Y.

G. Khitrowa, H. M. Gibbs, Y. Kawamura, H. Iwamura, and T. Ikegami, “Spatial solitons in a self-focusing semiconductor gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef]

Kelly, P. L.

P. L. Kelly, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005–1008 (1965).
[CrossRef]

Khitrowa, G.

G. Khitrowa, H. M. Gibbs, Y. Kawamura, H. Iwamura, and T. Ikegami, “Spatial solitons in a self-focusing semiconductor gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef]

Koshiba, M.

Leaird, D. E.

Maker, P. D.

P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
[CrossRef]

Maneuf, S.

S. Maneuf, R. Desailly, and C. Froehly, “Stable self-trapping of laser beams: observation in a nonlinear planar waveguide,” Opt. Commun. 65, 193–198 (1988).
[CrossRef]

S. Maneuf and F. Reynaud, “Quasi-steady self-trapping of first, second and third order subnanosecond soliton beams,” Opt. Commun. 66, 325–328 (1988).
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Waveguides (Academic, San Diego, Calif., 1974).

Menyuk, C. R.

C. R. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron. QE-23, 174–176 (1987).
[CrossRef]

Misawa, A.

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Morris, J. R.

J. A. Fleck, J. R. Morris, and E. S. Bliss, “Small-scale self-focusing effects in a high power glass laser amplifier,” IEEE J. Quantum Electron. QE-14, 353–363 (1978).
[CrossRef]

Oliver, M. K.

Reynaud, F.

M. Shalaby, F. Reynaud, and A. Barthelemy, “Experimental observation of spatial soliton interaction with a π/2 relative phase difference,” Opt. Lett. 17, 778–780 (1992).
[CrossRef] [PubMed]

S. Maneuf and F. Reynaud, “Quasi-steady self-trapping of first, second and third order subnanosecond soliton beams,” Opt. Commun. 66, 325–328 (1988).
[CrossRef]

Savage, C. M.

P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
[CrossRef]

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, “Interaction between solitons in a stable medium,” Sov. Phys. JETP 37, 823–828 (1973).

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972).

Shalaby, M.

Sibbett, W.

J. S. Aitchinson, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, “Observation of spatial solitons in AlGaAs waveguides,” Electron. Lett. 28, 1879–1880 (1992).
[CrossRef]

Silberberg, Y.

Sipe, J. E.

Smith, P. W. E.

Snyder, A. W.

Y. Chen and A. W. Snyder, “Stochastic instability in nonlinear anisotropic fiber couplers,” J. Lightwave Technol. 8, 802–810 (1990).
[CrossRef]

Solovèv, V. V.

V. I. Karpman and V. V. Solovèv, “A perturbational approach to the two soliton systems,” Physica 3D, 487–502 (1981).

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Tappert, F.

A. Hasegava and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. 1. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Terhune, R. W.

P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
[CrossRef]

Thylen, L.

Towns, C. H.

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

Vogel, E. M.

Wabnitz, S.

B. Daino, G. Gregori, and S. Wabnitz, “New all-optical devices based on third-order nonlinearity of birefringent fibers,” Opt. Lett. 11, 42–44 (1986).
[CrossRef] [PubMed]

B. Daino, G. Gregori, and S. Wabnitz, “New exact solutions and bifurcations in the spatial distribution of polarization in third-order nonlinear optical interactions,” Phys. Rev. Lett. 56, 600–603 (1986).
[CrossRef]

Weiner, A. M.

Winful, H. G.

H. G. Winful, “Polarization instabilities in birefringent nonlinear media: application to fiber-optic devices,” Opt. Lett. 11, 33–35 (1986).
[CrossRef] [PubMed]

H. G. Winful, “Self-induced polarization changes in birefringent optical fibers,” Appl. Phys. Lett. 47, 213–215 (1985).
[CrossRef]

Wood, D.

Yevick, D.

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, “Interaction between solitons in a stable medium,” Sov. Phys. JETP 37, 823–828 (1973).

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972).

Appl. Opt. (1)

Appl. Phys. Lett. (2)

H. G. Winful, “Self-induced polarization changes in birefringent optical fibers,” Appl. Phys. Lett. 47, 213–215 (1985).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Nonlinear slab waveguide.

Fig. 2
Fig. 2

Polarization coupling between a soliton pair (Cf = 1) and a weak field with opposite symmetry and amplitude Cs = 0.1 when the birefringence is completely neglected. The initial separation is 2q0/w = 3. (A)Δϕs = 0, Δϕf = π; (B) Δϕs = π, Δϕf = 0.

Fig. 3
Fig. 3

Coupling length versus the initial separation for a soliton pair when the birefringence is completely neglected. Cf and phase differences are as in Fig. 2(A). Curves a, Cs = 0.05; b, Cs = 0.1; c, Cs = 0.2.

Fig. 4
Fig. 4

Relative power in the slow mode versus propagation distance when a single soliton (Cf = 1) is initially in the fast mode. The normalized effective-index difference is κ = 2 × 10−4 (dashed curves) and κ = 5 × 10−3 (solid curves). (A) Cs = 0.1, (B) Cs = 0.2.

Fig. 5
Fig. 5

Coupling length and relative coupled fraction of power for a single soliton (Cf = 1) versus normalized effective-index difference. Curves a, Cs = 0.05; b, Cs = 0.1; c, Cs = 0.2. The dashed curves show the coupled fraction of power and the coupling lengths obtained from coupled-mode theory.

Fig. 6
Fig. 6

Coupling length for a soliton pair (Cf = 1) that is initially in the fast mode of a birefringent waveguide with κ = 2.6 × 10−4 versus the initial separation for different initial symmetry combinations. The amplitude Cs is kept fixed at Cs = 0.1. Curves a, Δϕs = Δϕf = 0; b, Δϕs = Δϕf = π; c, Δϕs = 0, Δϕf = π.

Fig. 7
Fig. 7

Field evolution for the case in which both fields are even (curve a of Fig. 6 at 2q0/w = 3).

Fig. 8
Fig. 8

Coupling length for a soliton pair (Cf = 1) versus the respective amplitude of the weak field for 2q0/w = 1.5 and κ = 2.6 × 10−4. Curves a, ζc = ζc(Cspe), Csc = 0; b, ζc = ζc(Csc), Cspe = 0.

Fig. 9
Fig. 9

Output power in the slow mode at ζ = L versus the amplitude of the weak field for κ = 2.6 × 10−4 and 2q0/w = 1.5. Curves a, Cspe = 0, Cf = 1, and 0.01 ≤ Csc ≤ 0.2; b, Csc = 0, Cf = 1, and 0.01 ≤ Cspe ≤ 0.2; c, Csc = 0, (Cf)2 + (Cspe)2 = 1, and 0.01 ≤ Cspe ≤ 0.2; d, asymmetric case with polarization error fixed at Cspe = 0.05, Cf = 1, and 0.01 ≤ Csc ≤ 0.2; e, polarization coupling of a single soliton, Cf = 1.

Fig. 10
Fig. 10

Polarization coupling of a soliton pair (Cf = 1) for consideration of a polarization error of Csps = 0.05, corresponding to curve d of Fig. 9. The amplitudes of the even control field are (A) Csc = 0.01, (B) Csc = 0.05, and (C) Csc = 0.1.

Tables (1)

Tables Icon

Table 1 Waveguide Parameters as Given in Ref. 8

Equations (11)

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D = 0 n 2 + 2 0 n n 2 [ | | 2 + ( ) 2 * ] ,
t ( x , y , z ) = x A e ( x , z ) f e ( y ) P e exp ( j β 0 n e z ) + y A h ( x , z ) f h ( y ) P h exp ( j β 0 n h z ) ,
j A e z = 1 2 β 0 n e 2 A e x 2 + β 0 n 2 I { Q e | A e | 2 A e + Q e h [ 2 3 | A h | 2 A e + 1 3 A h 2 A e * exp ( + 2 j β 0 Δ n e h z ) ] } j A h z = 1 2 β 0 n h 2 A h x 2 + β 0 n 2 I { Q h | A h | 2 A h + Q h e [ 2 3 | A e | 2 A h + 1 3 A e 2 A h * exp ( 2 j β 0 Δ n e h z ) ] } .
d eff = n 2 I n ¯ 2 [ | f ( y ) | 2 d y ] 2 0 d n 2 I n 2 | f ( y ) | 4 d y .
ξ = 2 h x , ζ = 4 λ n ¯ h 2 z , κ = h 2 n ¯ 4 λ 2 Δ n s f , Ψ s , f = π h λ ( n ¯ n 2 I d eff ) 1 / 2 A s , f
4 π j Ψ s ζ = 2 Ψ s ξ 2 + 2 [ | Ψ s | 2 Ψ s + 2 3 | Ψ f | 2 Ψ s + 1 3 Ψ f 2 Ψ s * exp ( + 4 π j κ ζ ) ] , 4 π j Ψ f ζ = 2 Ψ f ξ 2 + 2 [ | Ψ f | 2 Ψ f + 2 3 | Ψ s | 2 Ψ f + 1 3 Ψ s 2 Ψ f * exp ( 4 π j κ ζ ) ] .
Ψ s ( ξ , 0 ) = [ C s l u ( ξ + q 0 ) exp ( j Δ ϕ s / 2 ) + C s r u ( ξ q 0 ) exp ( j Δ ϕ s / 2 ) ] exp ( j ϕ s 0 ) , Ψ f ( ξ , 0 ) = [ C f l u ( ξ + q 0 ) exp ( j Δ ϕ f / 2 ) + C f r u ( ξ q 0 ) exp ( j Δ ϕ f / 2 ) ] exp ( j ϕ f 0 ) ,
P P c = 1 6 π 2 κ P w eff ,
P 0 P c = C s 2 + C f 2 9 π 2 κ .
P P c ( ζ ) = P 0 P c ( ζ ) = P ¯ 0 ( q 0 ) w eff [ q ( ζ ) ] ,
Ψ s ( ξ , 0 ) = ( C s c + C s pe ) u ( ξ + q 0 ) + ( C s c C s pe ) u ( ξ q 0 ) , Ψ f ( ξ , 0 ) = C f u ( ξ + q 0 ) C f u ( ξ q 0 ) ,

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