Abstract

Equations of motion are derived for the nonlinear refractive coupling between two coherent optical beams in an anisotropic cubic medium, allowing for a phase mismatch between the beams. These equations contain orientation-dependent self-phase-modulation, cross-phase-modulation, and four-wave-mixing, terms plus additional anisotropic terms that, for example, can generate an orthogonal polarization component. Stationary solutions (eigenpolarizations) are identified in which the polarization state does not change, and these can be classified as stable or unstable. It is shown that TE and TM modes in the common semiconductor waveguide orientation for frequencies at the half band gap or below become unstable if the magnitude of the birefringence is sufficiently small. Diffraction is included, and the polarization-state evolution is obtained for mixed-mode (vector) spatial solitons. The polarization evolution dynamics of vector spatial solitons broadly follows the equivalent plane-wave examples.

© 1997 Optical Society of America

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  1. D. C. Hutchings and B. S. Wherrett, “Theory of the dispersion of ultrafast nonlinear refraction in zinc-blende semiconductors below the band edge,” Phys. Rev. B 50, 4622–4630 (1994).
    [CrossRef]
  2. J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. (to be published).
  3. D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zinc-blende semiconductors,” Phys. Rev. B 52, 8150–8159 (1995).
    [CrossRef]
  4. D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B 49, 2418–2426 (1994).
    [CrossRef]
  5. A. I. Kovrighin, D. V. Yakovlev, B. V. Zhdanov, and N. I. Zheludev, “Self-induced optical activity in crystals,” Opt. Commun. 35, 92–95 (1980).
    [CrossRef]
  6. M. G. Dubenskaya, R. S. Zadoyan, and N. I. Zheludev, “Nonlinear-polarization spectroscopy in GaAs crystals: one- and two-photon resonances, excitonic effects, and the saturation of nonlinear susceptibilities,” J. Opt. Soc. Am. B 2, 1174–1178 (1985).
    [CrossRef]
  7. W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Intrinsic and induced anisotropy of nonlinear absorption and refraction in zinc blende semiconductors,” J. Opt. Soc. Am. B 12, 401–415 (1995).
    [CrossRef]
  8. D. C. Hutchings, “Nonlinear-optical activity owing to anisotropy of ultrafast nonlinear refraction in cubic materials,” Opt. Lett. 20, 1607–1609 (1995).
    [CrossRef] [PubMed]
  9. N. I. Zheludev, “Polarization instability and multistability in nonlinear optics,” Sov. Phys. Usp. 32, 357–375 (1989) [Usp. Fiz. Nauk. 157, 683–717 (1989)].
    [CrossRef]
  10. J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, “Observation of spatial solitons in AlGaAs waveguides,” Electron. Lett. 20, 1879–1880 (1992).
    [CrossRef]
  11. D. N. Christodoulides and R. I. Joseph, “Vector solitons in birefringent nonlinear dispersive media,” Opt. Lett. 13, 53–55 (1988).
    [CrossRef] [PubMed]
  12. C. Martijn de Sterke and J. E. Sipe, “Polarization instability in a waveguide geometry,” Opt. Lett. 16, 202–204 (1991).
    [CrossRef]
  13. A. D. Boardman, K. Xie, and A. A. Zharov, “Polarization interaction of spatial solitons in optical planar waveguides,” Phys. Rev. A 51, 692–705 (1995).
    [CrossRef] [PubMed]
  14. J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, E. A. Ostrovskaya, and N. N. Akhmediev, “Vector spatial soliton,” in Nonlinear Guided Waves and their Applications, Vol. 15 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper SuD3.
  15. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics, P. L. Knight and W. J. Firth, eds., Vol. 9 of Cambridge Studies in Nonlinear Optics (Cambridge U. Press, Cambridge, UK, 1990).
  16. D. C. Hutchings, J. S. Aitchison, B. S. Wherrett, G. T. Kennedy, and W. Sibbett, “Polarization dependence of ultrafast nonlinear refraction in an AlGaAs waveguide at the half-band gap,” Opt. Lett. 20, 991–993 (1995).
    [CrossRef] [PubMed]
  17. J. S. Aitchison, J. U. Kang, and G. I. Stegeman, “Signal gain due to a polarization coupling in an AlGaAs channel waveguide,” Appl. Phys. Lett. 67, 2456–2458 (1995) (note that the cross-phase-modulation and four-wave-mixing terms appear incorrectly in this reference).
    [CrossRef]
  18. G. P. Agrawal, “Nonlinear fiber optics,” in Quantum Electronics: Principles and Applications, P. F. Liao and P. L. Kelly, eds. (Academic, San Diego, Calif., 1989).
  19. 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. 65, 505–516 (1973)].
  20. 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, 3699–3671 (1996).
    [CrossRef] [PubMed]
  21. P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137, A801–A818 (1965).
    [CrossRef]
  22. R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39, 3337–3350 (1989).
    [CrossRef]
  23. M. D. Johnson and K. R. Subbaswamy, “Anisotropic hyperpolarizabilities in alkali halide crystals,” Phys. Rev. B 39, 10275–10280 (1989).
    [CrossRef]
  24. M. I. Dykman and G. G. Tarasov, “Self-induced change in the polarization of electro-magnetic waves in cubic crystals,” Sov. Phys. Solid State 24, 1361–1364 (1982) [Fiz. Tverd. Tela 24, 2396–2402) (1982)].
  25. J. Yumoto and K. Otsuka, “Frustrated optical instability: self-induced periodic and chaotic spatial distribution of polarization in nonlinear optical media,” Phys. Rev. Lett. 54, 1806–1809 (1985).
    [CrossRef] [PubMed]
  26. 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] [PubMed]
  27. M. V. Tratnik and J. E. Sipe, “Nonlinear polarization dynamics. I: The single-pulse equations,” Phys. Rev. A 35, 2965–2975 (1987).
    [CrossRef] [PubMed]
  28. Y. Silberberg and Y. Barad, “Rotating vector solitary waves in isotropic fibers,” Opt. Lett. 20, 246–248 (1995).
    [CrossRef] [PubMed]
  29. N. N. Akhmediev, A. V. Buryak, and J. M. Soto-Crespo, “Elliptically polarized solitons in birefringent optical fibers,” Opt. Commun. 112, 278–282 (1994).
    [CrossRef]
  30. N. N. Akhmediev, A. V. Buryak, J. M. Soto-Crespo, and D. R. Andersen, “Phase-locked stationary soliton states in birefringent nonlinear optical fibers,” J. Opt. Soc. Am. B 12, 434–439 (1995).
    [CrossRef]
  31. N. N. Akhmediev and J. M. Soto-Crespo, “Dynamics of solitonlike pulse propagation in birefringent optical fibers,” Phys. Rev. E 49, 5742–5754 (1994).
    [CrossRef]
  32. J. P. van der Ziel and A. C. Gossard, “Absorption, refractive index, and birefringence of AlAs-GaAs monolayers,” J. Appl. Phys. 48, 3018–3023 (1977).
    [CrossRef]
  33. M. Dabbicco, A. M. Fox, G. von Plessen, and J. F. Ryan, “Role of χ(3) anisotropy in the generation of squeezed light in semiconductors,” Phys. Rev. B 53, 4479–4487 (1996).
    [CrossRef]

1996 (2)

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, 3699–3671 (1996).
[CrossRef] [PubMed]

M. Dabbicco, A. M. Fox, G. von Plessen, and J. F. Ryan, “Role of χ(3) anisotropy in the generation of squeezed light in semiconductors,” Phys. Rev. B 53, 4479–4487 (1996).
[CrossRef]

1995 (8)

Y. Silberberg and Y. Barad, “Rotating vector solitary waves in isotropic fibers,” Opt. Lett. 20, 246–248 (1995).
[CrossRef] [PubMed]

N. N. Akhmediev, A. V. Buryak, J. M. Soto-Crespo, and D. R. Andersen, “Phase-locked stationary soliton states in birefringent nonlinear optical fibers,” J. Opt. Soc. Am. B 12, 434–439 (1995).
[CrossRef]

A. D. Boardman, K. Xie, and A. A. Zharov, “Polarization interaction of spatial solitons in optical planar waveguides,” Phys. Rev. A 51, 692–705 (1995).
[CrossRef] [PubMed]

D. C. Hutchings, J. S. Aitchison, B. S. Wherrett, G. T. Kennedy, and W. Sibbett, “Polarization dependence of ultrafast nonlinear refraction in an AlGaAs waveguide at the half-band gap,” Opt. Lett. 20, 991–993 (1995).
[CrossRef] [PubMed]

J. S. Aitchison, J. U. Kang, and G. I. Stegeman, “Signal gain due to a polarization coupling in an AlGaAs channel waveguide,” Appl. Phys. Lett. 67, 2456–2458 (1995) (note that the cross-phase-modulation and four-wave-mixing terms appear incorrectly in this reference).
[CrossRef]

D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zinc-blende semiconductors,” Phys. Rev. B 52, 8150–8159 (1995).
[CrossRef]

W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Intrinsic and induced anisotropy of nonlinear absorption and refraction in zinc blende semiconductors,” J. Opt. Soc. Am. B 12, 401–415 (1995).
[CrossRef]

D. C. Hutchings, “Nonlinear-optical activity owing to anisotropy of ultrafast nonlinear refraction in cubic materials,” Opt. Lett. 20, 1607–1609 (1995).
[CrossRef] [PubMed]

1994 (4)

D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B 49, 2418–2426 (1994).
[CrossRef]

D. C. Hutchings and B. S. Wherrett, “Theory of the dispersion of ultrafast nonlinear refraction in zinc-blende semiconductors below the band edge,” Phys. Rev. B 50, 4622–4630 (1994).
[CrossRef]

N. N. Akhmediev and J. M. Soto-Crespo, “Dynamics of solitonlike pulse propagation in birefringent optical fibers,” Phys. Rev. E 49, 5742–5754 (1994).
[CrossRef]

N. N. Akhmediev, A. V. Buryak, and J. M. Soto-Crespo, “Elliptically polarized solitons in birefringent optical fibers,” Opt. Commun. 112, 278–282 (1994).
[CrossRef]

1992 (1)

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, “Observation of spatial solitons in AlGaAs waveguides,” Electron. Lett. 20, 1879–1880 (1992).
[CrossRef]

1991 (1)

1989 (3)

N. I. Zheludev, “Polarization instability and multistability in nonlinear optics,” Sov. Phys. Usp. 32, 357–375 (1989) [Usp. Fiz. Nauk. 157, 683–717 (1989)].
[CrossRef]

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39, 3337–3350 (1989).
[CrossRef]

M. D. Johnson and K. R. Subbaswamy, “Anisotropic hyperpolarizabilities in alkali halide crystals,” Phys. Rev. B 39, 10275–10280 (1989).
[CrossRef]

1988 (1)

1987 (1)

M. V. Tratnik and J. E. Sipe, “Nonlinear polarization dynamics. I: The single-pulse equations,” Phys. Rev. A 35, 2965–2975 (1987).
[CrossRef] [PubMed]

1986 (1)

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] [PubMed]

1985 (2)

J. Yumoto and K. Otsuka, “Frustrated optical instability: self-induced periodic and chaotic spatial distribution of polarization in nonlinear optical media,” Phys. Rev. Lett. 54, 1806–1809 (1985).
[CrossRef] [PubMed]

M. G. Dubenskaya, R. S. Zadoyan, and N. I. Zheludev, “Nonlinear-polarization spectroscopy in GaAs crystals: one- and two-photon resonances, excitonic effects, and the saturation of nonlinear susceptibilities,” J. Opt. Soc. Am. B 2, 1174–1178 (1985).
[CrossRef]

1982 (1)

M. I. Dykman and G. G. Tarasov, “Self-induced change in the polarization of electro-magnetic waves in cubic crystals,” Sov. Phys. Solid State 24, 1361–1364 (1982) [Fiz. Tverd. Tela 24, 2396–2402) (1982)].

1980 (1)

A. I. Kovrighin, D. V. Yakovlev, B. V. Zhdanov, and N. I. Zheludev, “Self-induced optical activity in crystals,” Opt. Commun. 35, 92–95 (1980).
[CrossRef]

1977 (1)

J. P. van der Ziel and A. C. Gossard, “Absorption, refractive index, and birefringence of AlAs-GaAs monolayers,” J. Appl. Phys. 48, 3018–3023 (1977).
[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. 65, 505–516 (1973)].

1965 (1)

P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137, A801–A818 (1965).
[CrossRef]

Adair, R.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39, 3337–3350 (1989).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, “Nonlinear fiber optics,” in Quantum Electronics: Principles and Applications, P. F. Liao and P. L. Kelly, eds. (Academic, San Diego, Calif., 1989).

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, 3699–3671 (1996).
[CrossRef] [PubMed]

J. S. Aitchison, J. U. Kang, and G. I. Stegeman, “Signal gain due to a polarization coupling in an AlGaAs channel waveguide,” Appl. Phys. Lett. 67, 2456–2458 (1995) (note that the cross-phase-modulation and four-wave-mixing terms appear incorrectly in this reference).
[CrossRef]

D. C. Hutchings, J. S. Aitchison, B. S. Wherrett, G. T. Kennedy, and W. Sibbett, “Polarization dependence of ultrafast nonlinear refraction in an AlGaAs waveguide at the half-band gap,” Opt. Lett. 20, 991–993 (1995).
[CrossRef] [PubMed]

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, “Observation of spatial solitons in AlGaAs waveguides,” Electron. Lett. 20, 1879–1880 (1992).
[CrossRef]

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. (to be published).

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, E. A. Ostrovskaya, and N. N. Akhmediev, “Vector spatial soliton,” in Nonlinear Guided Waves and their Applications, Vol. 15 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper SuD3.

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, 3699–3671 (1996).
[CrossRef] [PubMed]

Akhmediev, N. N.

N. N. Akhmediev, A. V. Buryak, J. M. Soto-Crespo, and D. R. Andersen, “Phase-locked stationary soliton states in birefringent nonlinear optical fibers,” J. Opt. Soc. Am. B 12, 434–439 (1995).
[CrossRef]

N. N. Akhmediev and J. M. Soto-Crespo, “Dynamics of solitonlike pulse propagation in birefringent optical fibers,” Phys. Rev. E 49, 5742–5754 (1994).
[CrossRef]

N. N. Akhmediev, A. V. Buryak, and J. M. Soto-Crespo, “Elliptically polarized solitons in birefringent optical fibers,” Opt. Commun. 112, 278–282 (1994).
[CrossRef]

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, E. A. Ostrovskaya, and N. N. Akhmediev, “Vector spatial soliton,” in Nonlinear Guided Waves and their Applications, Vol. 15 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper SuD3.

Al-Hemyari, K.

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, “Observation of spatial solitons in AlGaAs waveguides,” Electron. Lett. 20, 1879–1880 (1992).
[CrossRef]

Andersen, D. R.

Barad, Y.

Boardman, A. D.

A. D. Boardman, K. Xie, and A. A. Zharov, “Polarization interaction of spatial solitons in optical planar waveguides,” Phys. Rev. A 51, 692–705 (1995).
[CrossRef] [PubMed]

Buryak, A. V.

N. N. Akhmediev, A. V. Buryak, J. M. Soto-Crespo, and D. R. Andersen, “Phase-locked stationary soliton states in birefringent nonlinear optical fibers,” J. Opt. Soc. Am. B 12, 434–439 (1995).
[CrossRef]

N. N. Akhmediev, A. V. Buryak, and J. M. Soto-Crespo, “Elliptically polarized solitons in birefringent optical fibers,” Opt. Commun. 112, 278–282 (1994).
[CrossRef]

Butcher, P. N.

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics, P. L. Knight and W. J. Firth, eds., Vol. 9 of Cambridge Studies in Nonlinear Optics (Cambridge U. Press, Cambridge, UK, 1990).

Chase, L. L.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39, 3337–3350 (1989).
[CrossRef]

Christodoulides, D. N.

Cotter, D.

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics, P. L. Knight and W. J. Firth, eds., Vol. 9 of Cambridge Studies in Nonlinear Optics (Cambridge U. Press, Cambridge, UK, 1990).

Dabbicco, M.

M. Dabbicco, A. M. Fox, G. von Plessen, and J. F. Ryan, “Role of χ(3) anisotropy in the generation of squeezed light in semiconductors,” Phys. Rev. B 53, 4479–4487 (1996).
[CrossRef]

Dubenskaya, M. G.

Dvorak, M. D.

Dykman, M. I.

M. I. Dykman and G. G. Tarasov, “Self-induced change in the polarization of electro-magnetic waves in cubic crystals,” Sov. Phys. Solid State 24, 1361–1364 (1982) [Fiz. Tverd. Tela 24, 2396–2402) (1982)].

Fox, A. M.

M. Dabbicco, A. M. Fox, G. von Plessen, and J. F. Ryan, “Role of χ(3) anisotropy in the generation of squeezed light in semiconductors,” Phys. Rev. B 53, 4479–4487 (1996).
[CrossRef]

Gossard, A. C.

J. P. van der Ziel and A. C. Gossard, “Absorption, refractive index, and birefringence of AlAs-GaAs monolayers,” J. Appl. Phys. 48, 3018–3023 (1977).
[CrossRef]

Grant, R. S.

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, “Observation of spatial solitons in AlGaAs waveguides,” Electron. Lett. 20, 1879–1880 (1992).
[CrossRef]

Gregori, G.

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] [PubMed]

Harken, D. R.

Hutchings, D. C.

D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zinc-blende semiconductors,” Phys. Rev. B 52, 8150–8159 (1995).
[CrossRef]

D. C. Hutchings, “Nonlinear-optical activity owing to anisotropy of ultrafast nonlinear refraction in cubic materials,” Opt. Lett. 20, 1607–1609 (1995).
[CrossRef] [PubMed]

D. C. Hutchings, J. S. Aitchison, B. S. Wherrett, G. T. Kennedy, and W. Sibbett, “Polarization dependence of ultrafast nonlinear refraction in an AlGaAs waveguide at the half-band gap,” Opt. Lett. 20, 991–993 (1995).
[CrossRef] [PubMed]

D. C. Hutchings and B. S. Wherrett, “Theory of the dispersion of ultrafast nonlinear refraction in zinc-blende semiconductors below the band edge,” Phys. Rev. B 50, 4622–4630 (1994).
[CrossRef]

D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B 49, 2418–2426 (1994).
[CrossRef]

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. (to be published).

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, E. A. Ostrovskaya, and N. N. Akhmediev, “Vector spatial soliton,” in Nonlinear Guided Waves and their Applications, Vol. 15 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper SuD3.

Ironside, C. N.

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, “Observation of spatial solitons in AlGaAs waveguides,” Electron. Lett. 20, 1879–1880 (1992).
[CrossRef]

Johnson, M. D.

M. D. Johnson and K. R. Subbaswamy, “Anisotropic hyperpolarizabilities in alkali halide crystals,” Phys. Rev. B 39, 10275–10280 (1989).
[CrossRef]

Joseph, R. I.

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, 3699–3671 (1996).
[CrossRef] [PubMed]

J. S. Aitchison, J. U. Kang, and G. I. Stegeman, “Signal gain due to a polarization coupling in an AlGaAs channel waveguide,” Appl. Phys. Lett. 67, 2456–2458 (1995) (note that the cross-phase-modulation and four-wave-mixing terms appear incorrectly in this reference).
[CrossRef]

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, E. A. Ostrovskaya, and N. N. Akhmediev, “Vector spatial soliton,” in Nonlinear Guided Waves and their Applications, Vol. 15 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper SuD3.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. (to be published).

Kennedy, G. T.

Kovrighin, A. I.

A. I. Kovrighin, D. V. Yakovlev, B. V. Zhdanov, and N. I. Zheludev, “Self-induced optical activity in crystals,” Opt. Commun. 35, 92–95 (1980).
[CrossRef]

Maker, P. D.

P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137, A801–A818 (1965).
[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. 65, 505–516 (1973)].

Martijn de Sterke, C.

McCallum, D. S.

Ostrovskaya, E. A.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, E. A. Ostrovskaya, and N. N. Akhmediev, “Vector spatial soliton,” in Nonlinear Guided Waves and their Applications, Vol. 15 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper SuD3.

Otsuka, K.

J. Yumoto and K. Otsuka, “Frustrated optical instability: self-induced periodic and chaotic spatial distribution of polarization in nonlinear optical media,” Phys. Rev. Lett. 54, 1806–1809 (1985).
[CrossRef] [PubMed]

Payne, S. A.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39, 3337–3350 (1989).
[CrossRef]

Ryan, J. F.

M. Dabbicco, A. M. Fox, G. von Plessen, and J. F. Ryan, “Role of χ(3) anisotropy in the generation of squeezed light in semiconductors,” Phys. Rev. B 53, 4479–4487 (1996).
[CrossRef]

Schroeder, W. A.

Sibbett, W.

D. C. Hutchings, J. S. Aitchison, B. S. Wherrett, G. T. Kennedy, and W. Sibbett, “Polarization dependence of ultrafast nonlinear refraction in an AlGaAs waveguide at the half-band gap,” Opt. Lett. 20, 991–993 (1995).
[CrossRef] [PubMed]

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, “Observation of spatial solitons in AlGaAs waveguides,” Electron. Lett. 20, 1879–1880 (1992).
[CrossRef]

Silberberg, Y.

Sipe, J. E.

C. Martijn de Sterke and J. E. Sipe, “Polarization instability in a waveguide geometry,” Opt. Lett. 16, 202–204 (1991).
[CrossRef]

M. V. Tratnik and J. E. Sipe, “Nonlinear polarization dynamics. I: The single-pulse equations,” Phys. Rev. A 35, 2965–2975 (1987).
[CrossRef] [PubMed]

Smirl, A. L.

Soto-Crespo, J. M.

N. N. Akhmediev, A. V. Buryak, J. M. Soto-Crespo, and D. R. Andersen, “Phase-locked stationary soliton states in birefringent nonlinear optical fibers,” J. Opt. Soc. Am. B 12, 434–439 (1995).
[CrossRef]

N. N. Akhmediev and J. M. Soto-Crespo, “Dynamics of solitonlike pulse propagation in birefringent optical fibers,” Phys. Rev. E 49, 5742–5754 (1994).
[CrossRef]

N. N. Akhmediev, A. V. Buryak, and J. M. Soto-Crespo, “Elliptically polarized solitons in birefringent optical fibers,” Opt. Commun. 112, 278–282 (1994).
[CrossRef]

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, 3699–3671 (1996).
[CrossRef] [PubMed]

J. S. Aitchison, J. U. Kang, and G. I. Stegeman, “Signal gain due to a polarization coupling in an AlGaAs channel waveguide,” Appl. Phys. Lett. 67, 2456–2458 (1995) (note that the cross-phase-modulation and four-wave-mixing terms appear incorrectly in this reference).
[CrossRef]

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, E. A. Ostrovskaya, and N. N. Akhmediev, “Vector spatial soliton,” in Nonlinear Guided Waves and their Applications, Vol. 15 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper SuD3.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. (to be published).

Subbaswamy, K. R.

M. D. Johnson and K. R. Subbaswamy, “Anisotropic hyperpolarizabilities in alkali halide crystals,” Phys. Rev. B 39, 10275–10280 (1989).
[CrossRef]

Tarasov, G. G.

M. I. Dykman and G. G. Tarasov, “Self-induced change in the polarization of electro-magnetic waves in cubic crystals,” Sov. Phys. Solid State 24, 1361–1364 (1982) [Fiz. Tverd. Tela 24, 2396–2402) (1982)].

Terhune, R. W.

P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137, A801–A818 (1965).
[CrossRef]

Tratnik, M. V.

M. V. Tratnik and J. E. Sipe, “Nonlinear polarization dynamics. I: The single-pulse equations,” Phys. Rev. A 35, 2965–2975 (1987).
[CrossRef] [PubMed]

van der Ziel, J. P.

J. P. van der Ziel and A. C. Gossard, “Absorption, refractive index, and birefringence of AlAs-GaAs monolayers,” J. Appl. Phys. 48, 3018–3023 (1977).
[CrossRef]

Villeneuve, A.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. (to be published).

von Plessen, G.

M. Dabbicco, A. M. Fox, G. von Plessen, and J. F. Ryan, “Role of χ(3) anisotropy in the generation of squeezed light in semiconductors,” Phys. Rev. B 53, 4479–4487 (1996).
[CrossRef]

Wabnitz, S.

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] [PubMed]

Wherrett, B. S.

D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zinc-blende semiconductors,” Phys. Rev. B 52, 8150–8159 (1995).
[CrossRef]

W. A. Schroeder, D. S. McCallum, D. R. Harken, M. D. Dvorak, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Intrinsic and induced anisotropy of nonlinear absorption and refraction in zinc blende semiconductors,” J. Opt. Soc. Am. B 12, 401–415 (1995).
[CrossRef]

D. C. Hutchings, J. S. Aitchison, B. S. Wherrett, G. T. Kennedy, and W. Sibbett, “Polarization dependence of ultrafast nonlinear refraction in an AlGaAs waveguide at the half-band gap,” Opt. Lett. 20, 991–993 (1995).
[CrossRef] [PubMed]

D. C. Hutchings and B. S. Wherrett, “Theory of the dispersion of ultrafast nonlinear refraction in zinc-blende semiconductors below the band edge,” Phys. Rev. B 50, 4622–4630 (1994).
[CrossRef]

D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B 49, 2418–2426 (1994).
[CrossRef]

Xie, K.

A. D. Boardman, K. Xie, and A. A. Zharov, “Polarization interaction of spatial solitons in optical planar waveguides,” Phys. Rev. A 51, 692–705 (1995).
[CrossRef] [PubMed]

Yakovlev, D. V.

A. I. Kovrighin, D. V. Yakovlev, B. V. Zhdanov, and N. I. Zheludev, “Self-induced optical activity in crystals,” Opt. Commun. 35, 92–95 (1980).
[CrossRef]

Yumoto, J.

J. Yumoto and K. Otsuka, “Frustrated optical instability: self-induced periodic and chaotic spatial distribution of polarization in nonlinear optical media,” Phys. Rev. Lett. 54, 1806–1809 (1985).
[CrossRef] [PubMed]

Zadoyan, R. S.

Zharov, A. A.

A. D. Boardman, K. Xie, and A. A. Zharov, “Polarization interaction of spatial solitons in optical planar waveguides,” Phys. Rev. A 51, 692–705 (1995).
[CrossRef] [PubMed]

Zhdanov, B. V.

A. I. Kovrighin, D. V. Yakovlev, B. V. Zhdanov, and N. I. Zheludev, “Self-induced optical activity in crystals,” Opt. Commun. 35, 92–95 (1980).
[CrossRef]

Zheludev, N. I.

N. I. Zheludev, “Polarization instability and multistability in nonlinear optics,” Sov. Phys. Usp. 32, 357–375 (1989) [Usp. Fiz. Nauk. 157, 683–717 (1989)].
[CrossRef]

M. G. Dubenskaya, R. S. Zadoyan, and N. I. Zheludev, “Nonlinear-polarization spectroscopy in GaAs crystals: one- and two-photon resonances, excitonic effects, and the saturation of nonlinear susceptibilities,” J. Opt. Soc. Am. B 2, 1174–1178 (1985).
[CrossRef]

A. I. Kovrighin, D. V. Yakovlev, B. V. Zhdanov, and N. I. Zheludev, “Self-induced optical activity in crystals,” Opt. Commun. 35, 92–95 (1980).
[CrossRef]

Appl. Phys. Lett. (1)

J. S. Aitchison, J. U. Kang, and G. I. Stegeman, “Signal gain due to a polarization coupling in an AlGaAs channel waveguide,” Appl. Phys. Lett. 67, 2456–2458 (1995) (note that the cross-phase-modulation and four-wave-mixing terms appear incorrectly in this reference).
[CrossRef]

Electron. Lett. (1)

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, “Observation of spatial solitons in AlGaAs waveguides,” Electron. Lett. 20, 1879–1880 (1992).
[CrossRef]

J. Appl. Phys. (1)

J. P. van der Ziel and A. C. Gossard, “Absorption, refractive index, and birefringence of AlAs-GaAs monolayers,” J. Appl. Phys. 48, 3018–3023 (1977).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (2)

A. I. Kovrighin, D. V. Yakovlev, B. V. Zhdanov, and N. I. Zheludev, “Self-induced optical activity in crystals,” Opt. Commun. 35, 92–95 (1980).
[CrossRef]

N. N. Akhmediev, A. V. Buryak, and J. M. Soto-Crespo, “Elliptically polarized solitons in birefringent optical fibers,” Opt. Commun. 112, 278–282 (1994).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. (1)

P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137, A801–A818 (1965).
[CrossRef]

Phys. Rev. A (2)

M. V. Tratnik and J. E. Sipe, “Nonlinear polarization dynamics. I: The single-pulse equations,” Phys. Rev. A 35, 2965–2975 (1987).
[CrossRef] [PubMed]

A. D. Boardman, K. Xie, and A. A. Zharov, “Polarization interaction of spatial solitons in optical planar waveguides,” Phys. Rev. A 51, 692–705 (1995).
[CrossRef] [PubMed]

Phys. Rev. B (6)

D. C. Hutchings and B. S. Wherrett, “Theory of the dispersion of ultrafast nonlinear refraction in zinc-blende semiconductors below the band edge,” Phys. Rev. B 50, 4622–4630 (1994).
[CrossRef]

D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zinc-blende semiconductors,” Phys. Rev. B 52, 8150–8159 (1995).
[CrossRef]

D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B 49, 2418–2426 (1994).
[CrossRef]

M. Dabbicco, A. M. Fox, G. von Plessen, and J. F. Ryan, “Role of χ(3) anisotropy in the generation of squeezed light in semiconductors,” Phys. Rev. B 53, 4479–4487 (1996).
[CrossRef]

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39, 3337–3350 (1989).
[CrossRef]

M. D. Johnson and K. R. Subbaswamy, “Anisotropic hyperpolarizabilities in alkali halide crystals,” Phys. Rev. B 39, 10275–10280 (1989).
[CrossRef]

Phys. Rev. E (1)

N. N. Akhmediev and J. M. Soto-Crespo, “Dynamics of solitonlike pulse propagation in birefringent optical fibers,” Phys. Rev. E 49, 5742–5754 (1994).
[CrossRef]

Phys. Rev. Lett. (3)

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, 3699–3671 (1996).
[CrossRef] [PubMed]

J. Yumoto and K. Otsuka, “Frustrated optical instability: self-induced periodic and chaotic spatial distribution of polarization in nonlinear optical media,” Phys. Rev. Lett. 54, 1806–1809 (1985).
[CrossRef] [PubMed]

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] [PubMed]

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. 65, 505–516 (1973)].

Sov. Phys. Solid State (1)

M. I. Dykman and G. G. Tarasov, “Self-induced change in the polarization of electro-magnetic waves in cubic crystals,” Sov. Phys. Solid State 24, 1361–1364 (1982) [Fiz. Tverd. Tela 24, 2396–2402) (1982)].

Sov. Phys. Usp. (1)

N. I. Zheludev, “Polarization instability and multistability in nonlinear optics,” Sov. Phys. Usp. 32, 357–375 (1989) [Usp. Fiz. Nauk. 157, 683–717 (1989)].
[CrossRef]

Other (4)

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The nonlinear optical properties of AlGaAs at the half band gap,” IEEE J. Quantum Electron. (to be published).

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, E. A. Ostrovskaya, and N. N. Akhmediev, “Vector spatial soliton,” in Nonlinear Guided Waves and their Applications, Vol. 15 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), paper SuD3.

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics, P. L. Knight and W. J. Firth, eds., Vol. 9 of Cambridge Studies in Nonlinear Optics (Cambridge U. Press, Cambridge, UK, 1990).

G. P. Agrawal, “Nonlinear fiber optics,” in Quantum Electronics: Principles and Applications, P. F. Liao and P. L. Kelly, eds. (Academic, San Diego, Calif., 1989).

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Figures (10)

Fig. 1
Fig. 1

Calculated polarization evolution for a nonbirefringent cubic medium with propagation in the [1̅10] direction and a linearly polarized input at 45° to the [001] and [110] directions: (a) the power fractions along each of these directions and (b) their relative phase. This example shows oscillation around the stable eigenpolarization of [111].

Fig. 2
Fig. 2

Calculated polarization evolution for a nonbirefringent cubic medium with propagation in the [1̅10] direction and a linearly polarized input at 2° to the [110] direction: (a) the power fractions along each of these directions and (b) their relative phase. This demonstrates the unstable nature of the [110] eigenpolarization.

Fig. 3
Fig. 3

Calculated polarization evolution for a nonbirefringent cubic medium with propagation in the [1̅10] direction and a linearly polarized input parallel to the [112̅] direction (TE mode for a [111]-grown sample): (a) the power fractions along each of these directions and (b) their relative phase. The initial conditions here result in an asymptotic approach to the unstable [110] eigenpolarization.

Fig. 4
Fig. 4

Contour plots of the Hamiltonian as a function of polarization major-axis angle (with respect to [001]) and ellipticity (ratio of minor to major axes) for propagation in the [100] direction for the following ratios of birefringence to nonlinear phase shift (k˜TM-kTE)/kNL: (a) -0.6, (b) -0.3, (c) 0, (d) 0.3, (e) 0.6, and (f) 0.9.

Fig. 5
Fig. 5

Contours plot of the Hamiltonian as a function of polarization major-axis angle (with respect to [110]) and ellipticity (ratio of minor to major axes) for propagation in the [1̅10] direction for the following ratios of birefringence to nonlinear phase shift (kTM-kTE)/kNL: (a) -0.6, (b) -0.3, (c) 0, (d) 0.3, (e) 0.6, and (f) 0.9.

Fig. 6
Fig. 6

Calculated evolution of a spatial soliton for a nonbirefringent cubic medium with propagation in the [1̅10] direction and a linearly polarized input at 45° to the [001] (TM) and [110] (TE) directions. The transverse units are in micrometers and the longitudinal units are in millimeters. As in the plane-wave case (Fig. 5), this example shows oscillation around the stable eigenpolarization direction of [111].

Fig. 7
Fig. 7

As in Fig. 6 but with a birefringence (kTM-kTE)=2 cm-1.

Fig. 8
Fig. 8

As in Fig. 6 but with a birefringence (kTM-kTE)=-2 cm-1.

Fig. 9
Fig. 9

Calculated evolution of a spatial soliton for a nonbirefringent cubic medium with propagation in the [1̅10] direction and a linearly polarized input at 2° to the [110] direction. As in the plane-wave case (Fig. 2), this demonstrates the unstable nature of the [110] eigenpolarization.

Fig. 10
Fig. 10

Calculated evolution of a spatial soliton for a nonbirefringent cubic medium with propagation in the [1̅10] direction and a linearly polarized input parallel to the [112̅] direction (TE mode for a [111]-grown sample). This result differs from the plane-wave result of an asymptotic approach to the unstable [110] eigenpolarization (Fig. 3).

Tables (1)

Tables Icon

Table 1 Eigenpolarizations for Half-Band Gap and Below

Equations (19)

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Pa(3)(ω)=0-dω1-dω2-dω3ijklai*bjckdl×χijkl(3)(ω1, ω2, ω3)Eb(ω1)Ec(ω2)Ed(ω3)×δ(ω-ω1-ω2-ω3),
E(ω)=(1/2)[pˆEpδ(ω-ωp)+pˆ*Ep*δ(ω+ωp)]+(1/2)[qˆEqδ(ω-ωq)+qˆ*Eq*δ(ω+ωq)].
Pp(3)(ω)|ωq=(3/8)0Eqδ(ω-ωq)×[|Eq|2χeff(p; q*, q, q)+2|Ep|2χeff(p; p*, p, q)],
Pp(3)(ω)|2ωq-ωp=(3/8)0Eq2Ep*δ(ω-2ωq+ωp)×χeff(p; p*, q, q),
Pp(3)(ω)|2ωp-ωq=(3/8)0Ep2Eq*δ(ω-2ωp+ωq)×χeff(p; q*, p, p),
Pp(3)(ω)|ωp=(3/8)0Epδ(ω-ωp)×[2|Eq|2χeff(p; q*, q, p)+|Ep|2χeff(p; p*, p, p)],
Re χeff(a;b, c, d)=(aˆ*·bˆ)(cˆ·dˆ)χxxyy+(aˆ*·cˆ)×(bˆ·dˆ)χxyxy+(aˆ*·dˆ)(bˆ·cˆ)×χxyyx+σχxxxxsai*bicidi.
σ=χxxxx-χxxyy-χxyxy-χxyyxχxxxx.
ξpz=-iΔk2ξp+iωn2L[001]cσipi*qi|qi|2|ξq|2ξq+2σipi*qi|pi|2|ξp|2ξq+δ+σi(pi*)2qi2-12ξq2ξp*+σiqi*pi|pi|2ξp2ξq*+1-δ+σ2i|pi|2|qi|2-12|ξq|2ξp+1+σi|pi|4-1|ξp|2ξp, ξqz=iΔk2ξq+iωn2L[001]cσiqi*pi|pi|2|ξp|2ξp+2σiqi*pi|qi|2|ξq|2ξp+δ+σi(qi*)2pi2-12ξp2ξq*+σipi*qi|qi|2ξq2ξp*+1-δ+σ2i|qi|2|pi|2-12|ξp|2ξq+1+σi|qi|4-1|ξq|2ξq.
δ=χxxxx+χxxyy-2χxyxy2χxxxx.
cos2 θ=131-2ΔkσkNL,
Ω2=Δk+kNLδ+σi|qi|4-2i|qi|2|pi|2-122-kNL2δ+σiqi2(pi*)2-122.
Ω2=Δk+kNLσiqi4-3iqi2pi2×Δk+kNLδ+σiqi4-iqi2pi2-1.
-2δ<Δk/kNL<-σ,TMpolarization,
σ/2<Δk/kNL<(2δ-σ/2),TEpolarization,
ξiz=-iξi*H(ξp, ξp*, ξq, ξq*).
H=Δk2(|ξp|2-|ξq|2)-ωn2L[001]c×σipi*qi|qi|2|ξq|2ξp*ξq+σipi*qi|pi|2|ξp|2ξp*ξq+σipiqi*|qi|2|ξq|2ξpξq*+σipiqi*|pi|2|ξp|2ξpξq*+12δ+σi(pi*)2qi2-12(ξp*)2ξq2+12δ+σipi2(qi*)2-12ξp2(ξq*)2×1-δ+σ2i|pi|2|qi|2-12|ξp|2|ξq|2+121+σi|pi|4-1|ξp|4+121+σi|qi|4-1|ξq|4.
HI21-δ-σ2+|eˆ·eˆ|2×δ-σ2+σi|ei|4.
ξiz=ic2ωni2ξix2+ξizNLR,

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