Abstract

With the variational method we analytically study rotating vector soliton bound states in Kerr media. A standard linear stability analysis reveals that, in the presence of nonlinear birefringence, these soliton bound states exhibit a symmetry-breaking instability. In the absence of nonlinear birefringence, that is, in the Manakov system, the bound states are shown to be neutrally stable and not robust against soliton collisions. We show that these stability properties are not influenced by saturation of the nonlinearity, a result that is relevant to recent experimental observations of soliton bound states in photorefractive media.

© 1999 Optical Society of America

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  1. N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, and L. P. Shil’nikov, “Steady-state pulses in a birefringent nonlinear optical fiber: soliton multiplication processes,” Sov. Tech. Phys. Lett. 15(8), 587–588 (1989).
  2. D. N. Christodoulides and R. I. Joseph, “Vector solitons in birefringent nonlinear dispersive media,” Opt. Lett. 13, 53–55 (1988).
    [CrossRef] [PubMed]
  3. M. V. Tratnik and J. E. Sipe, “Bound solitary waves in birefringent optical fiber,” Phys. Rev. A 38, 2011–2017 (1988).
    [CrossRef] [PubMed]
  4. R. J. Dowling, “Stability of solitary waves in a nonlinear birefringent optical fiber,” Phys. Rev. A 42, 5553–5560 (1990).
    [CrossRef] [PubMed]
  5. M. Haelterman and A. P. Sheppard, “Bifurcation phenomena and multiple soliton-bound states in isotropic Kerr media,” Phys. Rev. E 49, 3376–3381 (1994).
    [CrossRef]
  6. M. Haelterman and A. P. Sheppard, “Cancelling soliton interaction in singlemode optical fibres,” Electron. Lett. 29, 1176–1177 (1993).
    [CrossRef]
  7. M. Haelterman, A. P. Sheppard, and A. W. Snyder, “Bound vector solitary waves in isotropic nonlinear dispersive media,” Opt. Lett. 18, 1406–1408 (1993).
    [CrossRef] [PubMed]
  8. D. N. Christodoulides, “Black and white vector solitons in weakly birefringent optical fibers,” Phys. Lett. A 132, 451–452 (1988).
    [CrossRef]
  9. S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Optical solitary waves induced by cross-phase modulation,” Opt. Lett. 13, 871–873 (1988).
    [CrossRef] [PubMed]
  10. Y. S. Kivshar and S. K. Turitsyn, “Vector dark solitons,” Opt. Lett. 18, 337–339 (1993).
    [CrossRef] [PubMed]
  11. M. Haelterman and A. P. Sheppard, “Polarization domain walls in diffractive or dispersive Kerr media,” Opt. Lett. 19, 96–98 (1994).
    [CrossRef] [PubMed]
  12. V. V. Afanasyev, Y. S. Kivshar, V. V. Konotop, and V. N. Serkin, “Dynamics of coupled dark and bright optical solitons,” Opt. Lett. 14, 805–807 (1989).
    [CrossRef] [PubMed]
  13. Y. S. Kivshar, “Soliton stability in birefringent optical fibers: analytical approach,” J. Opt. Soc. Am. B 7, 2204–2209 (1990).
    [CrossRef]
  14. B. A. Malomed, “Polarization dynamics and interactions of solitons in a birefringent optical fiber,” Phys. Rev. A 43, 410–423 (1991).
    [CrossRef] [PubMed]
  15. C. Paré, “Accurate variational approach for vector solitary waves,” Phys. Rev. E 54, 846–851 (1996).
    [CrossRef]
  16. M. Haelterman and A. P. Sheppard, “The elliptically polarized fundamental vector soliton of isotropic Kerr media,” Phys. Lett. A 194, 191–196 (1994).
    [CrossRef]
  17. Y. Silberberg and Y. Barad, “Rotating vector solitary waves in isotropic fibers,” Opt. Lett. 20, 246–248 (1995).
    [CrossRef] [PubMed]
  18. M. Mitchell, M. Segev, and D. N. Christodoulides, “Observation of multihump multimode solitons,” Phys. Rev. Lett. 80, 4657–4660 (1998).
    [CrossRef]
  19. D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in Biased photorefractive media,” Phys. Rev. Lett. 78, 646–649 (1997).
    [CrossRef]
  20. M. Mitchell, M. Segev, T. H. Cosun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).
    [CrossRef]
  21. 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]
  22. P. D. Maker and R. W. Terhune, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507–509 (1964).
    [CrossRef]
  23. D. Anderson and M. Lisak, “Bandwidth limits due to incoherent soliton interaction in optical-fiber communication systems,” Phys. Rev. A 32, 2270–2274 (1985).
    [CrossRef] [PubMed]
  24. S. Wabnitz, Y. Kodama, and A. B. Aceves, “Control of optical soliton interactions,” Opt. Fiber Technol.: Mater., Devices Syst. 1, 187–217 (1995).
    [CrossRef]
  25. B. Daino, G. Gregori, and S. Wabnitz, “Stability analysis of nonlinear coherent coupling,” J. Appl. Phys. 58, 4512–4514 (1985).
    [CrossRef]
  26. Y. Silberberg and G. I. Stegeman, “Nonlinear coupling of waveguide modes,” Appl. Phys. Lett. 50, 801–803 (1987).
    [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. Y. Barad and Y. Silberberg, “Polarization evolution and polarization instability of solitons in a birefringent optical fiber,” Phys. Rev. Lett. 78, 3290–3293 (1997).
    [CrossRef]
  30. S. F. Feldman, D. A. Weinberger, and H. G. Winful, “Polarization instability in a twisted birefringent optical fiber,” J. Opt. Soc. Am. B 10, 1191–1201 (1993).
    [CrossRef]
  31. M. Haelterman and S. Trillo, “Multiple soliton bound states and symmetry breaking in quadratic media,” Opt. Lett. 22, 84–86 (1997).
    [CrossRef] [PubMed]
  32. S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974).
  33. C. De Angelis and S. Wabnitz, “Interactions of orthogonally polarized solitons in optical fibers,” Opt. Commun. 125, 186–196 (1996).
    [CrossRef]
  34. S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10(1), 28–35 (1992).
    [CrossRef]
  35. M. Segev, M. Shih, and G. C. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B 13, 706–718 (1996).
    [CrossRef]

1998

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

1997

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in Biased photorefractive media,” Phys. Rev. Lett. 78, 646–649 (1997).
[CrossRef]

M. Mitchell, M. Segev, T. H. Cosun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).
[CrossRef]

Y. Barad and Y. Silberberg, “Polarization evolution and polarization instability of solitons in a birefringent optical fiber,” Phys. Rev. Lett. 78, 3290–3293 (1997).
[CrossRef]

M. Haelterman and S. Trillo, “Multiple soliton bound states and symmetry breaking in quadratic media,” Opt. Lett. 22, 84–86 (1997).
[CrossRef] [PubMed]

1996

C. De Angelis and S. Wabnitz, “Interactions of orthogonally polarized solitons in optical fibers,” Opt. Commun. 125, 186–196 (1996).
[CrossRef]

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

C. Paré, “Accurate variational approach for vector solitary waves,” Phys. Rev. E 54, 846–851 (1996).
[CrossRef]

1995

1994

M. Haelterman and A. P. Sheppard, “Polarization domain walls in diffractive or dispersive Kerr media,” Opt. Lett. 19, 96–98 (1994).
[CrossRef] [PubMed]

M. Haelterman and A. P. Sheppard, “The elliptically polarized fundamental vector soliton of isotropic Kerr media,” Phys. Lett. A 194, 191–196 (1994).
[CrossRef]

M. Haelterman and A. P. Sheppard, “Bifurcation phenomena and multiple soliton-bound states in isotropic Kerr media,” Phys. Rev. E 49, 3376–3381 (1994).
[CrossRef]

1993

1992

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10(1), 28–35 (1992).
[CrossRef]

1991

B. A. Malomed, “Polarization dynamics and interactions of solitons in a birefringent optical fiber,” Phys. Rev. A 43, 410–423 (1991).
[CrossRef] [PubMed]

1990

R. J. Dowling, “Stability of solitary waves in a nonlinear birefringent optical fiber,” Phys. Rev. A 42, 5553–5560 (1990).
[CrossRef] [PubMed]

Y. S. Kivshar, “Soliton stability in birefringent optical fibers: analytical approach,” J. Opt. Soc. Am. B 7, 2204–2209 (1990).
[CrossRef]

1989

V. V. Afanasyev, Y. S. Kivshar, V. V. Konotop, and V. N. Serkin, “Dynamics of coupled dark and bright optical solitons,” Opt. Lett. 14, 805–807 (1989).
[CrossRef] [PubMed]

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, and L. P. Shil’nikov, “Steady-state pulses in a birefringent nonlinear optical fiber: soliton multiplication processes,” Sov. Tech. Phys. Lett. 15(8), 587–588 (1989).

1988

M. V. Tratnik and J. E. Sipe, “Bound solitary waves in birefringent optical fiber,” Phys. Rev. A 38, 2011–2017 (1988).
[CrossRef] [PubMed]

D. N. Christodoulides, “Black and white vector solitons in weakly birefringent optical fibers,” Phys. Lett. A 132, 451–452 (1988).
[CrossRef]

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

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

1987

Y. Silberberg and G. I. Stegeman, “Nonlinear coupling of waveguide modes,” Appl. Phys. Lett. 50, 801–803 (1987).
[CrossRef]

1986

1985

D. Anderson and M. Lisak, “Bandwidth limits due to incoherent soliton interaction in optical-fiber communication systems,” Phys. Rev. A 32, 2270–2274 (1985).
[CrossRef] [PubMed]

B. Daino, G. Gregori, and S. Wabnitz, “Stability analysis of nonlinear coherent coupling,” J. Appl. Phys. 58, 4512–4514 (1985).
[CrossRef]

1974

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974).

1964

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

Aceves, A. B.

S. Wabnitz, Y. Kodama, and A. B. Aceves, “Control of optical soliton interactions,” Opt. Fiber Technol.: Mater., Devices Syst. 1, 187–217 (1995).
[CrossRef]

Afanasyev, V. V.

Akhmediev, N. N.

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, and L. P. Shil’nikov, “Steady-state pulses in a birefringent nonlinear optical fiber: soliton multiplication processes,” Sov. Tech. Phys. Lett. 15(8), 587–588 (1989).

Anderson, D.

D. Anderson and M. Lisak, “Bandwidth limits due to incoherent soliton interaction in optical-fiber communication systems,” Phys. Rev. A 32, 2270–2274 (1985).
[CrossRef] [PubMed]

Barad, Y.

Y. Barad and Y. Silberberg, “Polarization evolution and polarization instability of solitons in a birefringent optical fiber,” Phys. Rev. Lett. 78, 3290–3293 (1997).
[CrossRef]

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

Bergano, N. S.

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10(1), 28–35 (1992).
[CrossRef]

Carvalho, M. I.

Christodoulides, D. N.

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

M. Mitchell, M. Segev, T. H. Cosun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in Biased photorefractive media,” Phys. Rev. Lett. 78, 646–649 (1997).
[CrossRef]

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]

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

D. N. Christodoulides, “Black and white vector solitons in weakly birefringent optical fibers,” Phys. Lett. A 132, 451–452 (1988).
[CrossRef]

Coskun, T. H.

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in Biased photorefractive media,” Phys. Rev. Lett. 78, 646–649 (1997).
[CrossRef]

Cosun, T. H.

M. Mitchell, M. Segev, T. H. Cosun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).
[CrossRef]

Daino, B.

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, “Stability analysis of nonlinear coherent coupling,” J. Appl. Phys. 58, 4512–4514 (1985).
[CrossRef]

De Angelis, C.

C. De Angelis and S. Wabnitz, “Interactions of orthogonally polarized solitons in optical fibers,” Opt. Commun. 125, 186–196 (1996).
[CrossRef]

Dowling, R. J.

R. J. Dowling, “Stability of solitary waves in a nonlinear birefringent optical fiber,” Phys. Rev. A 42, 5553–5560 (1990).
[CrossRef] [PubMed]

Eleonskii, V. M.

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, and L. P. Shil’nikov, “Steady-state pulses in a birefringent nonlinear optical fiber: soliton multiplication processes,” Sov. Tech. Phys. Lett. 15(8), 587–588 (1989).

Evangelides, S. G.

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10(1), 28–35 (1992).
[CrossRef]

Feldman, S. F.

Gordon, J. P.

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10(1), 28–35 (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, “Stability analysis of nonlinear coherent coupling,” J. Appl. Phys. 58, 4512–4514 (1985).
[CrossRef]

Haelterman, M.

M. Haelterman and S. Trillo, “Multiple soliton bound states and symmetry breaking in quadratic media,” Opt. Lett. 22, 84–86 (1997).
[CrossRef] [PubMed]

M. Haelterman and A. P. Sheppard, “The elliptically polarized fundamental vector soliton of isotropic Kerr media,” Phys. Lett. A 194, 191–196 (1994).
[CrossRef]

M. Haelterman and A. P. Sheppard, “Polarization domain walls in diffractive or dispersive Kerr media,” Opt. Lett. 19, 96–98 (1994).
[CrossRef] [PubMed]

M. Haelterman and A. P. Sheppard, “Bifurcation phenomena and multiple soliton-bound states in isotropic Kerr media,” Phys. Rev. E 49, 3376–3381 (1994).
[CrossRef]

M. Haelterman and A. P. Sheppard, “Cancelling soliton interaction in singlemode optical fibres,” Electron. Lett. 29, 1176–1177 (1993).
[CrossRef]

M. Haelterman, A. P. Sheppard, and A. W. Snyder, “Bound vector solitary waves in isotropic nonlinear dispersive media,” Opt. Lett. 18, 1406–1408 (1993).
[CrossRef] [PubMed]

Joseph, R. I.

Kivshar, Y. S.

Kodama, Y.

S. Wabnitz, Y. Kodama, and A. B. Aceves, “Control of optical soliton interactions,” Opt. Fiber Technol.: Mater., Devices Syst. 1, 187–217 (1995).
[CrossRef]

Konotop, V. V.

Kulagin, N. E.

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, and L. P. Shil’nikov, “Steady-state pulses in a birefringent nonlinear optical fiber: soliton multiplication processes,” Sov. Tech. Phys. Lett. 15(8), 587–588 (1989).

Lisak, M.

D. Anderson and M. Lisak, “Bandwidth limits due to incoherent soliton interaction in optical-fiber communication systems,” Phys. Rev. A 32, 2270–2274 (1985).
[CrossRef] [PubMed]

Maker, P. D.

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

Malomed, B. A.

B. A. Malomed, “Polarization dynamics and interactions of solitons in a birefringent optical fiber,” Phys. Rev. A 43, 410–423 (1991).
[CrossRef] [PubMed]

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).

Mitchell, M.

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

M. Mitchell, M. Segev, T. H. Cosun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in Biased photorefractive media,” Phys. Rev. Lett. 78, 646–649 (1997).
[CrossRef]

Mollenauer, L. F.

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10(1), 28–35 (1992).
[CrossRef]

Paré, C.

C. Paré, “Accurate variational approach for vector solitary waves,” Phys. Rev. E 54, 846–851 (1996).
[CrossRef]

Segev, M.

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

M. Mitchell, M. Segev, T. H. Cosun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of incoherent self-focusing in Biased photorefractive media,” Phys. Rev. Lett. 78, 646–649 (1997).
[CrossRef]

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

Serkin, V. N.

Sheppard, A. P.

M. Haelterman and A. P. Sheppard, “Bifurcation phenomena and multiple soliton-bound states in isotropic Kerr media,” Phys. Rev. E 49, 3376–3381 (1994).
[CrossRef]

M. Haelterman and A. P. Sheppard, “The elliptically polarized fundamental vector soliton of isotropic Kerr media,” Phys. Lett. A 194, 191–196 (1994).
[CrossRef]

M. Haelterman and A. P. Sheppard, “Polarization domain walls in diffractive or dispersive Kerr media,” Opt. Lett. 19, 96–98 (1994).
[CrossRef] [PubMed]

M. Haelterman, A. P. Sheppard, and A. W. Snyder, “Bound vector solitary waves in isotropic nonlinear dispersive media,” Opt. Lett. 18, 1406–1408 (1993).
[CrossRef] [PubMed]

M. Haelterman and A. P. Sheppard, “Cancelling soliton interaction in singlemode optical fibres,” Electron. Lett. 29, 1176–1177 (1993).
[CrossRef]

Shih, M.

Shil’nikov, L. P.

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, and L. P. Shil’nikov, “Steady-state pulses in a birefringent nonlinear optical fiber: soliton multiplication processes,” Sov. Tech. Phys. Lett. 15(8), 587–588 (1989).

Silberberg, Y.

Y. Barad and Y. Silberberg, “Polarization evolution and polarization instability of solitons in a birefringent optical fiber,” Phys. Rev. Lett. 78, 3290–3293 (1997).
[CrossRef]

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

Y. Silberberg and G. I. Stegeman, “Nonlinear coupling of waveguide modes,” Appl. Phys. Lett. 50, 801–803 (1987).
[CrossRef]

Sipe, J. E.

M. V. Tratnik and J. E. Sipe, “Bound solitary waves in birefringent optical fiber,” Phys. Rev. A 38, 2011–2017 (1988).
[CrossRef] [PubMed]

Snyder, A. W.

Stegeman, G. I.

Terhune, R. W.

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

Tratnik, M. V.

M. V. Tratnik and J. E. Sipe, “Bound solitary waves in birefringent optical fiber,” Phys. Rev. A 38, 2011–2017 (1988).
[CrossRef] [PubMed]

Trillo, S.

Turitsyn, S. K.

Valley, G. C.

Wabnitz, S.

C. De Angelis and S. Wabnitz, “Interactions of orthogonally polarized solitons in optical fibers,” Opt. Commun. 125, 186–196 (1996).
[CrossRef]

S. Wabnitz, Y. Kodama, and A. B. Aceves, “Control of optical soliton interactions,” Opt. Fiber Technol.: Mater., Devices Syst. 1, 187–217 (1995).
[CrossRef]

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

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, “Stability analysis of nonlinear coherent coupling,” J. Appl. Phys. 58, 4512–4514 (1985).
[CrossRef]

Weinberger, D. A.

Winful, H. G.

Wright, E. M.

Appl. Phys. Lett.

Y. Silberberg and G. I. Stegeman, “Nonlinear coupling of waveguide modes,” Appl. Phys. Lett. 50, 801–803 (1987).
[CrossRef]

Electron. Lett.

M. Haelterman and A. P. Sheppard, “Cancelling soliton interaction in singlemode optical fibres,” Electron. Lett. 29, 1176–1177 (1993).
[CrossRef]

J. Appl. Phys.

B. Daino, G. Gregori, and S. Wabnitz, “Stability analysis of nonlinear coherent coupling,” J. Appl. Phys. 58, 4512–4514 (1985).
[CrossRef]

J. Lightwave Technol.

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10(1), 28–35 (1992).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

C. De Angelis and S. Wabnitz, “Interactions of orthogonally polarized solitons in optical fibers,” Opt. Commun. 125, 186–196 (1996).
[CrossRef]

Opt. Fiber Technol.: Mater., Devices Syst.

S. Wabnitz, Y. Kodama, and A. B. Aceves, “Control of optical soliton interactions,” Opt. Fiber Technol.: Mater., Devices Syst. 1, 187–217 (1995).
[CrossRef]

Opt. Lett.

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

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]

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Figures (13)

Fig. 1
Fig. 1

Circular polarization envelopes U and V of a two-soliton bound state. The separation between the two corresponding linearly polarized solitons is 1.2 times their FWHM.

Fig. 2
Fig. 2

Linear polarization envelopes E1 and E2 of the two-soliton bound state of Fig. 1.

Fig. 3
Fig. 3

Rotation rate δ versus the soliton distance r as provided by the variational method, Eqs. (10) and (11). Each curve corresponds to a different value of the soliton amplitude α (amplitudes are indicated above each curve: α=1/4, 1/2, 1, 2).

Fig. 4
Fig. 4

Soliton width parameter η versus the soliton distance r as provided by the variational method, Eq. (11), for different soliton amplitudes (amplitude α=1/4, 1/2, 1, 2).

Fig. 5
Fig. 5

Propagation constant θ versus the soliton distance r as provided by the variational method at different fixed soliton amplitudes (amplitude α=1/4, 1/2, 1, 2).

Fig. 6
Fig. 6

Ratio δ/θ versus product ηr (inversely proportional to the soliton overlap integral) as provided by the variational method (solid curve) and by direct numerical solution of the coupled NLS equations (crosses). The value of δ/θ at the origin (○) is calculated analytically as explained in the text.

Fig. 7
Fig. 7

Real parts of the eigenvalue of the linear stability analysis versus the rotation rate δ for θ=1. Neutral stability occurs in δ=0, corresponding to infinitely separated solitons (ηr =), and in δ=0.52, corresponding to a single soliton of circular polarization (ηr=0).

Fig. 8
Fig. 8

Amplitude and phase of the eigenfunctions u(x) and v(x) associated with the unstable eigenvalue for α=1.53, r =1.56, θ=1.175, δ=0.175, and η=1.56.

Fig. 9
Fig. 9

Contour plot of the intensity distribution of a slightly perturbed soliton bound state of amplitude α=1.53 and soliton distance r=1.56. The longitudinal coordinate is in soliton lengths. The system clearly undergoes a symmetry-breaking instability.

Fig. 10
Fig. 10

Real parts of the leading eigenvalue versus the birefringence coefficient B (θ=1, and the rotation rate is fixed at δ =0.1). Neutral stability occurs in the limit of the Manakov system B=0.

Fig. 11
Fig. 11

Contour plot of the evolution of the intensity profile of a perturbed soliton bound state in the Manakov system. The bound state is determined by α=1.47 and r=2.46, and the perturbation is μ=ν=0.012. The longitudinal coordinate is in soliton lengths.

Fig. 12
Fig. 12

Contour plot of the evolution of the intensity profile of a perturbed soliton bound state in the Manakov system. The bound state is determined by α=1.47 and r=2.46, and the perturbation is μ=ν=0.025. The longitudinal coordinate is in soliton lengths.

Fig. 13
Fig. 13

Contour plot showing the two polarization components of a two-soliton bound state colliding with a third soliton. This simulation illustrates the fragility of the two-soliton bound state. The longitudinal coordinate is in soliton lengths.

Equations (18)

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iE1z+122E1x2+|E1|2E1+(1-B)|E2|2E1+BE22E1*=0,
iE2z+122E2x2+|E2|2E2+(1-B)|E1|2E2+BE12E2*=0,
iuz+122ux2+|u|2u+(1-B)|v|2u+Bv2u*=-iδv,
ivz+122vx2+|v|2v+(1-B)|u|2v+Bu2v*=iu.
L=2 Imu*uz+v*vz-2δuv*+ux2+vx2-(|u|2+|v|2)2+4B Im2(uv*).
u=α sech[η(x+r/2)]exp(iθz),
v=iα sech[η(x-r/2)]exp(iθz).
rL=ddzrzL,
δ=BrIm2(uv*)-12r|u|2|v|2rIm(uv*).
δ=α22(1-2B)3 sinh 2ηr-2ηr(2+cosh 2ηr)sinh2 ηr(sinh ηr-ηr cosh ηr).
η=α1+3(1-2B)ηr coth(ηr)-1sinh2(ηr)1/2.
θ=α221+2(1-2B)×3ηr cosh ηr-[(ηr)2+3]sinh ηrsinh2 ηr(sinh ηr-ηr cosh ηr).
za=-122bx2-23(U02+2V02-βU)b,
zb=122ax2+23(3U02+2V02-βU)a+23U0V0c,
zc=-122dx2-23(V02+2U02-βV)d,
zd=122cx2+23(3V02+2U02-βV)c+23V0U0a.
iUz+122Ux2+|U|2+|V|21+(|U|2+|V|2)/IsU=0,
iVz+122Vx2+|U|2+|V|21+(|U|2+|V|2)/IsV=0,

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