Abstract

The nonlinear interaction between two intense counterpropagating laser beams in an isotropic optical fiber may lead to spatiotemporal polarization instabilities of both waves. Experiments with various mutual polarization arrangements and different powers of the two counterpropagating input beams showed that nonlinear birefringence may lead to significant polarization cross switching of both beams. In the case of two counterrotating circular input waves, the cross-polarization interaction of the beams led to the generation of a polarization kink or domain wall soliton. This soliton is formed by a superposition of counterpropagating waves that represent switching of the state of polarization of light between two domains where both waves are circularly polarized and corotating. The experimental observations are found to be in good agreement with the theoretical predictions.

© 2001 Optical Society of America

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  31. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]

1999 (1)

P. Kockaert, M. Haelterman, S. Pitois, and G. Millot, “Isotropic polarization modulational instability and domain walls in spun fibers,” Appl. Phys. Lett. 75, 2873–2875 (1999).
[CrossRef]

1998 (1)

S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counterpropagating laser beams,” Phys. Rev. Lett. 81, 1409–1412 (1998).
[CrossRef]

1996 (1)

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

1993 (2)

A. L. Gaeta and R. W. Boyd, “Transverse instabilities in the polarizations and intensities of counterpropagating light waves,” Phys. Rev. A 48, 1610–1624 (1993).
[CrossRef] [PubMed]

S. Wabnitz and B. Daino, “Polarization domains and instabilities in nonlinear optical fibers,” Phys. Lett. A 182, 289–293 (1993).
[CrossRef]

1991 (1)

1990 (4)

W. J. Firth, A. Fitzgerald, and C. Paré, “Transverse instabilities due to counterpropagation in Kerr media,” J. Opt. Soc. Am. B 7, 1087–1097 (1990).
[CrossRef]

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. B. Boyd, “Polarization bistability of counterpropagating laser beams,” Phys. Rev. Lett. 64, 1721–1724 (1990).
[CrossRef] [PubMed]

A. V. Mikhailov and S. Wabnitz, “Polarization dynamics of counterpropagating beams in optical fibers,” Opt. Lett. 15, 1055–1057 (1990).
[CrossRef] [PubMed]

D. David, D. D. Holm, and M. V. Tratnik, “Hamiltonian chaos in nonlinear optical polarization dynamics,” Phys. Rep. 187, 281–367 (1990).
[CrossRef]

1989 (3)

D. D. Tskhakaya, “Integrability conditions for equations that describe the interaction of colliding wave packets of different polarizations in nonlinear optics,” Theor. Math. Phys. (USSR) 81, 1119–1122 (1989) [ Teor. Mat. Fiz. 81, 154–157 (1989)].
[CrossRef]

A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic optical media,” Phys. Lett. A 141, 37–42 (1989).
[CrossRef]

C. T. Law and A. E. Kaplan, “Dispersion-related multimode instabilities and self-sustained oscillations in nonlinear counterpropagating waves,” Opt. Lett. 14, 734–736 (1989).
[CrossRef] [PubMed]

1988 (2)

W. J. Firth and C. Paré, “Transverse modulational instabilities for counterpropagating beams in Kerr media,” Opt. Lett. 13, 1096–1098 (1988).
[CrossRef] [PubMed]

D. J. Gauthier, M. S. Malcuit, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams in sodium vapor,” Phys. Rev. Lett. 61, 1827–1830 (1988).
[CrossRef] [PubMed]

1987 (7)

S. Trillo and S. Wabnitz, “Intermittent spatial chaos in the polarization of counterpropagating beams in a birefringent optical fiber,” Phys. Rev. A 36, 3881–3884 (1987).
[CrossRef] [PubMed]

M. V. Tratnik and J. E. Sipe, “Nonlinear polarization dynamics. III. Spatial polarization chaos in counterpropagating beams,” Phys. Rev. A 36, 4817–4822 (1987).
[CrossRef] [PubMed]

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, “Instabilities and chaos in the polarization of counterpropagating light fields,” Phys. Rev. Lett. 58, 2432–2435 (1987).
[CrossRef] [PubMed]

M. V. Tratnik and J. E. Sipe, “Nonlinear polarization dynamics. II. Counterpropagating-beam equations: new simple solutions and the possibilities for chaos,” Phys. Rev. A 35, 2976–2988 (1987).
[CrossRef] [PubMed]

V. E. Zakharov and A. V. Mikhailov, “Polarization domains in nonlinear optics,” Pis’ma Zh. Eksp. Teor. Fiz. 45, 279–282 (1987) [ JETP Lett. 45, 349–352 (1987)].

M. V. Tratnik and J. E. Sipe, “Polarization solitons,” Phys. Rev. Lett. 58, 1104–1107 (1987).
[CrossRef] [PubMed]

W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. 58, 160–163 (1987).
[CrossRef] [PubMed]

1986 (2)

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]

S. Wabnitz and G. Gregori, “Symmetry-breaking and intrinsic polarization instability in degenerate four-wave mixing,” Opt. Commun. 59, 72–76 (1986).
[CrossRef]

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]

A. E. Kaplan and C. T. Law, “Isolas in four-wave mixing optical bistability,” IEEE J. Quantum Electron. QE-21, 1529–1537 (1985).
[CrossRef]

1984 (1)

1983 (2)

A. E. Kaplan, “Light-induced nonreciprocity, field invariants, and nonlinear eigenpolarizations,” Opt. Lett. 8, 560–562 (1983).
[CrossRef] [PubMed]

A. P. Veselov, “On integrability conditions for the Euler equations on SO(4),” Dokl. Akad. Nauk SSSR 270, 1298 (1983) [ Sov. Math. Dokl. 27, 740–742 (1983)].

1982 (1)

Y. Silberberg and I. Bar-Joseph, “Instabilities, self-oscillation, and chaos in a simple nonlinear optical interaction,” Phys. Rev. Lett. 48, 1541–1543 (1982).
[CrossRef]

1981 (2)

H. M. Gibbs, F. A. Hopf, D. L. Kaplan, and R. L. Shoemaker, “Observation of chaos in optical bistability,” Phys. Rev. Lett. 46, 474–477 (1981).
[CrossRef]

A. J. Barlow, J. J. Ramskov-Hansen, and D. N. Payne, “Birefringence and polarization mode-dispersion in spun single-mode fibers,” Appl. Opt. 20, 2962–2968 (1981).
[CrossRef] [PubMed]

1970 (1)

A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Sov. Phys. JETP 31, 486–490 (1970).

1935 (1)

L. D. Landau and E. M. Lifshitz, “On the theory of the dispersion of magnetic permeability in ferromagnetic bodies,” Phys. Z. Sowjet Union 8, 153–162 (1935).

Aceves, A. B.

A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic optical media,” Phys. Lett. A 141, 37–42 (1989).
[CrossRef]

Ackerhalt, J. R.

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, “Instabilities and chaos in the polarization of counterpropagating light fields,” Phys. Rev. Lett. 58, 2432–2435 (1987).
[CrossRef] [PubMed]

Bar-Joseph, I.

Y. Silberberg and I. Bar-Joseph, “Optical instabilities in a nonlinear Kerr medium,” J. Opt. Soc. Am. B 1, 662–670 (1984).
[CrossRef]

Y. Silberberg and I. Bar-Joseph, “Instabilities, self-oscillation, and chaos in a simple nonlinear optical interaction,” Phys. Rev. Lett. 48, 1541–1543 (1982).
[CrossRef]

Barlow, A. J.

Berkhoer, A. L.

A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Sov. Phys. JETP 31, 486–490 (1970).

Boyd, R. B.

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. B. Boyd, “Polarization bistability of counterpropagating laser beams,” Phys. Rev. Lett. 64, 1721–1724 (1990).
[CrossRef] [PubMed]

Boyd, R. W.

A. L. Gaeta and R. W. Boyd, “Transverse instabilities in the polarizations and intensities of counterpropagating light waves,” Phys. Rev. A 48, 1610–1624 (1993).
[CrossRef] [PubMed]

D. J. Gauthier, M. S. Malcuit, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams in sodium vapor,” Phys. Rev. Lett. 61, 1827–1830 (1988).
[CrossRef] [PubMed]

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, “Instabilities and chaos in the polarization of counterpropagating light fields,” Phys. Rev. Lett. 58, 2432–2435 (1987).
[CrossRef] [PubMed]

Chen, W.

W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. 58, 160–163 (1987).
[CrossRef] [PubMed]

Daino, B.

S. Wabnitz and B. Daino, “Polarization domains and instabilities in nonlinear optical fibers,” Phys. Lett. A 182, 289–293 (1993).
[CrossRef]

David, D.

D. David, D. D. Holm, and M. V. Tratnik, “Hamiltonian chaos in nonlinear optical polarization dynamics,” Phys. Rep. 187, 281–367 (1990).
[CrossRef]

de Sterke, C. M.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

Eggleton, B. J.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

Firth, W. J.

Fitzgerald, A.

Gaeta, A. L.

A. L. Gaeta and R. W. Boyd, “Transverse instabilities in the polarizations and intensities of counterpropagating light waves,” Phys. Rev. A 48, 1610–1624 (1993).
[CrossRef] [PubMed]

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. B. Boyd, “Polarization bistability of counterpropagating laser beams,” Phys. Rev. Lett. 64, 1721–1724 (1990).
[CrossRef] [PubMed]

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, “Instabilities and chaos in the polarization of counterpropagating light fields,” Phys. Rev. Lett. 58, 2432–2435 (1987).
[CrossRef] [PubMed]

Gauthier, D. J.

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. B. Boyd, “Polarization bistability of counterpropagating laser beams,” Phys. Rev. Lett. 64, 1721–1724 (1990).
[CrossRef] [PubMed]

D. J. Gauthier, M. S. Malcuit, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams in sodium vapor,” Phys. Rev. Lett. 61, 1827–1830 (1988).
[CrossRef] [PubMed]

Gibbs, H. M.

H. M. Gibbs, F. A. Hopf, D. L. Kaplan, and R. L. Shoemaker, “Observation of chaos in optical bistability,” Phys. Rev. Lett. 46, 474–477 (1981).
[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]

S. Wabnitz and G. Gregori, “Symmetry-breaking and intrinsic polarization instability in degenerate four-wave mixing,” Opt. Commun. 59, 72–76 (1986).
[CrossRef]

Haelterman, M.

P. Kockaert, M. Haelterman, S. Pitois, and G. Millot, “Isotropic polarization modulational instability and domain walls in spun fibers,” Appl. Phys. Lett. 75, 2873–2875 (1999).
[CrossRef]

Holm, D. D.

D. David, D. D. Holm, and M. V. Tratnik, “Hamiltonian chaos in nonlinear optical polarization dynamics,” Phys. Rep. 187, 281–367 (1990).
[CrossRef]

Hopf, F. A.

H. M. Gibbs, F. A. Hopf, D. L. Kaplan, and R. L. Shoemaker, “Observation of chaos in optical bistability,” Phys. Rev. Lett. 46, 474–477 (1981).
[CrossRef]

Kaplan, A. E.

Kaplan, D. L.

H. M. Gibbs, F. A. Hopf, D. L. Kaplan, and R. L. Shoemaker, “Observation of chaos in optical bistability,” Phys. Rev. Lett. 46, 474–477 (1981).
[CrossRef]

Kockaert, P.

P. Kockaert, M. Haelterman, S. Pitois, and G. Millot, “Isotropic polarization modulational instability and domain walls in spun fibers,” Appl. Phys. Lett. 75, 2873–2875 (1999).
[CrossRef]

Krug, P. A.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, “On the theory of the dispersion of magnetic permeability in ferromagnetic bodies,” Phys. Z. Sowjet Union 8, 153–162 (1935).

Law, C. T.

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, “On the theory of the dispersion of magnetic permeability in ferromagnetic bodies,” Phys. Z. Sowjet Union 8, 153–162 (1935).

Malcuit, M. S.

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. B. Boyd, “Polarization bistability of counterpropagating laser beams,” Phys. Rev. Lett. 64, 1721–1724 (1990).
[CrossRef] [PubMed]

D. J. Gauthier, M. S. Malcuit, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams in sodium vapor,” Phys. Rev. Lett. 61, 1827–1830 (1988).
[CrossRef] [PubMed]

Mikhailov, A. V.

A. V. Mikhailov and S. Wabnitz, “Polarization dynamics of counterpropagating beams in optical fibers,” Opt. Lett. 15, 1055–1057 (1990).
[CrossRef] [PubMed]

V. E. Zakharov and A. V. Mikhailov, “Polarization domains in nonlinear optics,” Pis’ma Zh. Eksp. Teor. Fiz. 45, 279–282 (1987) [ JETP Lett. 45, 349–352 (1987)].

Millot, G.

P. Kockaert, M. Haelterman, S. Pitois, and G. Millot, “Isotropic polarization modulational instability and domain walls in spun fibers,” Appl. Phys. Lett. 75, 2873–2875 (1999).
[CrossRef]

S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counterpropagating laser beams,” Phys. Rev. Lett. 81, 1409–1412 (1998).
[CrossRef]

Mills, D. L.

W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. 58, 160–163 (1987).
[CrossRef] [PubMed]

Milonni, P. W.

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, “Instabilities and chaos in the polarization of counterpropagating light fields,” Phys. Rev. Lett. 58, 2432–2435 (1987).
[CrossRef] [PubMed]

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]

Paré, C.

Payne, D. N.

Pitois, S.

P. Kockaert, M. Haelterman, S. Pitois, and G. Millot, “Isotropic polarization modulational instability and domain walls in spun fibers,” Appl. Phys. Lett. 75, 2873–2875 (1999).
[CrossRef]

S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counterpropagating laser beams,” Phys. Rev. Lett. 81, 1409–1412 (1998).
[CrossRef]

Ramskov-Hansen, J. J.

Shoemaker, R. L.

H. M. Gibbs, F. A. Hopf, D. L. Kaplan, and R. L. Shoemaker, “Observation of chaos in optical bistability,” Phys. Rev. Lett. 46, 474–477 (1981).
[CrossRef]

Silberberg, Y.

Y. Silberberg and I. Bar-Joseph, “Optical instabilities in a nonlinear Kerr medium,” J. Opt. Soc. Am. B 1, 662–670 (1984).
[CrossRef]

Y. Silberberg and I. Bar-Joseph, “Instabilities, self-oscillation, and chaos in a simple nonlinear optical interaction,” Phys. Rev. Lett. 48, 1541–1543 (1982).
[CrossRef]

Sipe, J. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

M. V. Tratnik and J. E. Sipe, “Polarization solitons,” Phys. Rev. Lett. 58, 1104–1107 (1987).
[CrossRef] [PubMed]

M. V. Tratnik and J. E. Sipe, “Nonlinear polarization dynamics. III. Spatial polarization chaos in counterpropagating beams,” Phys. Rev. A 36, 4817–4822 (1987).
[CrossRef] [PubMed]

M. V. Tratnik and J. E. Sipe, “Nonlinear polarization dynamics. II. Counterpropagating-beam equations: new simple solutions and the possibilities for chaos,” Phys. Rev. A 35, 2976–2988 (1987).
[CrossRef] [PubMed]

Slusher, R. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

Tratnik, M. V.

D. David, D. D. Holm, and M. V. Tratnik, “Hamiltonian chaos in nonlinear optical polarization dynamics,” Phys. Rep. 187, 281–367 (1990).
[CrossRef]

M. V. Tratnik and J. E. Sipe, “Nonlinear polarization dynamics. III. Spatial polarization chaos in counterpropagating beams,” Phys. Rev. A 36, 4817–4822 (1987).
[CrossRef] [PubMed]

M. V. Tratnik and J. E. Sipe, “Nonlinear polarization dynamics. II. Counterpropagating-beam equations: new simple solutions and the possibilities for chaos,” Phys. Rev. A 35, 2976–2988 (1987).
[CrossRef] [PubMed]

M. V. Tratnik and J. E. Sipe, “Polarization solitons,” Phys. Rev. Lett. 58, 1104–1107 (1987).
[CrossRef] [PubMed]

Trillo, S.

S. Trillo and S. Wabnitz, “Intermittent spatial chaos in the polarization of counterpropagating beams in a birefringent optical fiber,” Phys. Rev. A 36, 3881–3884 (1987).
[CrossRef] [PubMed]

Tskhakaya, D. D.

D. D. Tskhakaya, “Integrability conditions for equations that describe the interaction of colliding wave packets of different polarizations in nonlinear optics,” Theor. Math. Phys. (USSR) 81, 1119–1122 (1989) [ Teor. Mat. Fiz. 81, 154–157 (1989)].
[CrossRef]

Veselov, A. P.

A. P. Veselov, “On integrability conditions for the Euler equations on SO(4),” Dokl. Akad. Nauk SSSR 270, 1298 (1983) [ Sov. Math. Dokl. 27, 740–742 (1983)].

Wabnitz, S.

S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counterpropagating laser beams,” Phys. Rev. Lett. 81, 1409–1412 (1998).
[CrossRef]

S. Wabnitz and B. Daino, “Polarization domains and instabilities in nonlinear optical fibers,” Phys. Lett. A 182, 289–293 (1993).
[CrossRef]

A. V. Mikhailov and S. Wabnitz, “Polarization dynamics of counterpropagating beams in optical fibers,” Opt. Lett. 15, 1055–1057 (1990).
[CrossRef] [PubMed]

A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic optical media,” Phys. Lett. A 141, 37–42 (1989).
[CrossRef]

S. Trillo and S. Wabnitz, “Intermittent spatial chaos in the polarization of counterpropagating beams in a birefringent optical fiber,” Phys. Rev. A 36, 3881–3884 (1987).
[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]

S. Wabnitz and G. Gregori, “Symmetry-breaking and intrinsic polarization instability in degenerate four-wave mixing,” Opt. Commun. 59, 72–76 (1986).
[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]

Zakharov, V. E.

V. E. Zakharov and A. V. Mikhailov, “Polarization domains in nonlinear optics,” Pis’ma Zh. Eksp. Teor. Fiz. 45, 279–282 (1987) [ JETP Lett. 45, 349–352 (1987)].

A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Sov. Phys. JETP 31, 486–490 (1970).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

P. Kockaert, M. Haelterman, S. Pitois, and G. Millot, “Isotropic polarization modulational instability and domain walls in spun fibers,” Appl. Phys. Lett. 75, 2873–2875 (1999).
[CrossRef]

Dokl. Akad. Nauk SSSR (1)

A. P. Veselov, “On integrability conditions for the Euler equations on SO(4),” Dokl. Akad. Nauk SSSR 270, 1298 (1983) [ Sov. Math. Dokl. 27, 740–742 (1983)].

IEEE J. Quantum Electron. (1)

A. E. Kaplan and C. T. Law, “Isolas in four-wave mixing optical bistability,” IEEE J. Quantum Electron. QE-21, 1529–1537 (1985).
[CrossRef]

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

JETP Lett. (1)

V. E. Zakharov and A. V. Mikhailov, “Polarization domains in nonlinear optics,” Pis’ma Zh. Eksp. Teor. Fiz. 45, 279–282 (1987) [ JETP Lett. 45, 349–352 (1987)].

Opt. Commun. (1)

S. Wabnitz and G. Gregori, “Symmetry-breaking and intrinsic polarization instability in degenerate four-wave mixing,” Opt. Commun. 59, 72–76 (1986).
[CrossRef]

Opt. Lett. (4)

Phys. Lett. A (2)

A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic optical media,” Phys. Lett. A 141, 37–42 (1989).
[CrossRef]

S. Wabnitz and B. Daino, “Polarization domains and instabilities in nonlinear optical fibers,” Phys. Lett. A 182, 289–293 (1993).
[CrossRef]

Phys. Rep. (1)

D. David, D. D. Holm, and M. V. Tratnik, “Hamiltonian chaos in nonlinear optical polarization dynamics,” Phys. Rep. 187, 281–367 (1990).
[CrossRef]

Phys. Rev. A (4)

A. L. Gaeta and R. W. Boyd, “Transverse instabilities in the polarizations and intensities of counterpropagating light waves,” Phys. Rev. A 48, 1610–1624 (1993).
[CrossRef] [PubMed]

M. V. Tratnik and J. E. Sipe, “Nonlinear polarization dynamics. II. Counterpropagating-beam equations: new simple solutions and the possibilities for chaos,” Phys. Rev. A 35, 2976–2988 (1987).
[CrossRef] [PubMed]

S. Trillo and S. Wabnitz, “Intermittent spatial chaos in the polarization of counterpropagating beams in a birefringent optical fiber,” Phys. Rev. A 36, 3881–3884 (1987).
[CrossRef] [PubMed]

M. V. Tratnik and J. E. Sipe, “Nonlinear polarization dynamics. III. Spatial polarization chaos in counterpropagating beams,” Phys. Rev. A 36, 4817–4822 (1987).
[CrossRef] [PubMed]

Phys. Rev. Lett. (11)

D. J. Gauthier, M. S. Malcuit, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams in sodium vapor,” Phys. Rev. Lett. 61, 1827–1830 (1988).
[CrossRef] [PubMed]

H. M. Gibbs, F. A. Hopf, D. L. Kaplan, and R. L. Shoemaker, “Observation of chaos in optical bistability,” Phys. Rev. Lett. 46, 474–477 (1981).
[CrossRef]

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, “Instabilities and chaos in the polarization of counterpropagating light fields,” Phys. Rev. Lett. 58, 2432–2435 (1987).
[CrossRef] [PubMed]

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. B. Boyd, “Polarization bistability of counterpropagating laser beams,” Phys. Rev. Lett. 64, 1721–1724 (1990).
[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]

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. V. Tratnik and J. E. Sipe, “Polarization solitons,” Phys. Rev. Lett. 58, 1104–1107 (1987).
[CrossRef] [PubMed]

S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counterpropagating laser beams,” Phys. Rev. Lett. 81, 1409–1412 (1998).
[CrossRef]

W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. 58, 160–163 (1987).
[CrossRef] [PubMed]

Y. Silberberg and I. Bar-Joseph, “Instabilities, self-oscillation, and chaos in a simple nonlinear optical interaction,” Phys. Rev. Lett. 48, 1541–1543 (1982).
[CrossRef]

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

Phys. Z. Sowjet Union (1)

L. D. Landau and E. M. Lifshitz, “On the theory of the dispersion of magnetic permeability in ferromagnetic bodies,” Phys. Z. Sowjet Union 8, 153–162 (1935).

Sov. Phys. JETP (1)

A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Sov. Phys. JETP 31, 486–490 (1970).

Teor. Mat. Fiz. (1)

D. D. Tskhakaya, “Integrability conditions for equations that describe the interaction of colliding wave packets of different polarizations in nonlinear optics,” Theor. Math. Phys. (USSR) 81, 1119–1122 (1989) [ Teor. Mat. Fiz. 81, 154–157 (1989)].
[CrossRef]

Other (4)

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).

A. V. Mikhailov, “Integrable magnetic models,” in Solitons, S. E. Trullinger, V. E. Zakharov, and V. L. Pokrovsky, eds. (Elsevier, Amsterdam, 1986) Chap. 13, pp. 623–690.

A. M. Kosevich, “Dynamical and topological solitons in ferromagnets and antiferromagnets,” in Solitons, S. E. Trullinger, V. E. Zakharov, and V. L. Pokrovsky, eds. (Elsevier, Amsterdam, 1986), Chap. 11, pp. 555–603.

D. M. Pepper and A. Yariv, “Optical phase conjugation using three-wave and four-wave mixing via elastic photon scattering in transparent media,” in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), pp. 23–27.

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Figures (16)

Fig. 1
Fig. 1

Counterrotating circular polarization: Theoretical evolution of the power in the left circular component and in the right circular component of the forward and backward beams, showing the formation of a polarization domain wall. P=P¯=80 W.

Fig. 2
Fig. 2

PDW generation with counterrotating pulsed beams. Solid curves, output Stokes parameters of forward (s2) and backward (s¯2) beams; dashed curves; total intensity profiles of the pulses. P=P¯=80 W.

Fig. 3
Fig. 3

Orthogonal linear polarization: theoretical evolution of the power in the x and y components of the forward and backward beams. P=P¯=80 W.

Fig. 4
Fig. 4

Theoretical evolution with time of the polarization state of the forward beam from the input (z=0, point A) to the output (z=L, point B) of the fiber with (a) orthogonal and (b) parallel linear polarization pumping. P=P¯=80 W.

Fig. 5
Fig. 5

Parallel linear polarization: theoretical evolution of the power in the x and y components of the forward and backward beams. P=P¯=80 W.

Fig. 6
Fig. 6

Circular linear polarization: theoretical evolution of the power in the left and right circular components for the forward and backward beams. P=P¯=80 W.

Fig. 7
Fig. 7

Experimental setup. BS’s, beam splitters; P’s, polarizers; λ/2’s, half-wave plates; λ/4, quarter-wave plate; A, Analyzer; PD 1, photodiode; OSCILLO, oscilloscope; PC, computer.

Fig. 8
Fig. 8

Corotating circular polarization: measured power in the two circular polarization components of the forward beam. Solid curves, output; open circles, input. P=P¯=235 W.

Fig. 9
Fig. 9

Counterrotating circular polarization: measured power in the two circular polarization components of the forward beam. Solid curves, output; open circles, input. P=P¯=85 W.

Fig. 10
Fig. 10

Counterrotating circular polarization: theoretical power for the forward beam at the fiber output in the circular basis. P=P¯=85 W.

Fig. 11
Fig. 11

Orthogonal linear polarization: measured power in the linear polarization components of the forward beam. Solid curves, output; open circles, input. P=P¯=130 W.

Fig. 12
Fig. 12

Orthogonal linear polarization: theoretical power in the linear polarization components of the forward beam at the fiber output. P=P¯=130 W.

Fig. 13
Fig. 13

Parallel linear polarization: measured power in the linear polarization components of the forward beam. Solid curves, output; open circles, input. P=P¯=130 W.

Fig. 14
Fig. 14

Parallel linear polarization: theoretical power in the linear polarization components of the forward beam at the fiber output. P=P¯=130 W.

Fig. 15
Fig. 15

Circular linear polarization: measured power in the circular polarization components of the forward beam. Solid curves, output; open circles, input. P=P¯=130 W.

Fig. 16
Fig. 16

Circular linear polarization: theoretical power in the circular polarization components of the forward beam at the fiber output. P=P¯=130 W.

Equations (62)

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Px=(χxxyy+χxyxy+χxyyx)|Ex|2Ex+(χxxyy+χxyxy)|Ey|2Ex+χxyyxEy2Ex*,
Py=(χxxyy+χxyxy+χxyyx)|Ey|2Ey+(χxxyy+χxyxy)|Ex|2Ey+χxyyxEx2Ey*.
Px=χxxxx|Ex|2Ex+23|Ey|2Ex+13Ey2Ex*,
Py=χxxxx|Ey|2Ey+23|Ex|2Ey+13Ex2Ey*.
u=(Ax+iAy)/2,v=(Ax-iAy)/2;
u¯=(A¯x+iA¯y)/2,v¯=(A¯x-iA¯y)/2.
ut+cn uz=i 23γ [(|u|2+2|v|2)u+(2|u¯|2+2|v¯|2)u+2u¯v¯*v],
vt+cn vz=i 23γ [(|v|2+2|u|2)v+(2|u¯|2+2|v¯|2)v+2u¯*v¯u];
u¯t-cn u¯z=i 23γ [(|u¯|2+2|v¯|2)u¯+(2|u|2+2|v|2)u¯+2uv*v¯],
v¯t-cn v¯z=i 23γ [(|v¯|2+2|u¯|2)v¯+(2|u|2+2|v|2)v¯+2u*vu¯],
S1=iu*v+c.c.,S¯1=iu¯*v¯+c.c.,
S2=|u|2-|v|2,S¯2=|u¯|2-|v¯|2,
S3=u*v+c.c.S¯3=u¯*v¯+c.c.
St+cn Sz=SJS+2SJS¯,
S¯t-cn S¯z=S¯JS¯+2S¯JS,
J=γ diag(λ1, λ2, λ3).
|u|2=(S12+S22+S32)1/2+S22,
|v|2=(S12+S22+S32)1/2-S22,
|Ax|2=(S12+S22+S32)1/2+S32,
|Ay|2=(S12+S22+S32)1/2-S32.
s2(ζ)=tanh(ζ),s¯2(ζ)=-tanh(ζ),
ξ=12 t+ncz,
η=12 t-ncz.
Exξ=Ext+cn Exz,
E¯xη=E¯xt-cn E¯xz,
L=i2 ExξEx*-Ex*ξEx+i2 EyξEy*-Ey*ξEy+i2 E¯xηE¯x*-E¯x*ηE¯x+i2 E¯yηE¯y*-E¯y*ηE¯y+12(|Ex|4+|Ey|4+|E¯x|4+|E¯y|4)+2(|Ex|2|E¯x|2+|Ey|2|E¯y|2)+23(|Ex|2|Ey|2+|E¯x|2|E¯y|2+|Ex|2|E¯y|2+|E¯x|2|Ey|2)+23(EyE¯yEx*E¯x*+EyE¯y*Ex*E¯x+ExE¯xEy*E¯y*+ExE¯x*Ey*E¯y)+16(Ey2Ex*2+Ex2Ey*2+E¯y2E¯x*2+E¯x2E¯y*2).
δLδX*=ζ L(X*/ζ)-LX*=0,
H=L-i2 XXζX*-X*ζX,
H=Hs+H¯s+Hint,
Hs=γ2 23(|Ex|2+|Ey|2)2+13(|Ex|4+|Ey|4)+13(Ex2Ey*2+Ex*2Ey2),
H¯s=γ2 23(|E¯x|2+|E¯y|2)2+13(|E¯x|4+|E¯y|4)+13(E¯x2E¯y*2+E¯x*2E¯y2),
Hint=γ2(|Ex|2+|Ey|2)(|E¯x|2+|E¯y|2)-43(|Ex|2|E¯y|2+|Ey|2|E¯x|2)+γ23(ExEy*E¯xE¯y*+Ex*EyE¯x*E¯y)+23(ExEy*E¯x*E¯y+Ex*EyE¯xE¯y*).
Exξ=i δ(Hˆs+Hˆint)δEx*,
Eyξ=i δ(Hˆs+Hˆint)δEf*,
τ=r¯K¯ξ+rKη,
ξ=K¯r¯ τ,
η=Kr τ.
S˙1=-23γ K¯r¯S2S3-43γ K¯r¯S2S¯3,
S˙2=-43γ K¯r¯S¯1S3+43γ K¯r¯S1S¯3,
S˙3=+23γ K¯r¯S1S2+43γ K¯r¯S¯1S2,
S1=r sin(θ)sin(Φ),
S2=r cos(θ),
S3=r sin(θ)cos(Φ).
θ˙=-43γ K¯sin(θ¯)sin(Φ-Φ¯),
θ¯˙=+43γ K sin(θ)sin(Φ-Φ¯),
Φ˙=-23γ K¯r/r¯ cos(θ)-43γ K¯cot(θ)sin(θ¯)cos(Φ-Φ¯),
Φ¯˙=-23γ K¯r/r cos(θ¯)-43γ K cot(θ¯)sin(θ)cos(Φ-Φ¯).
FΦ0:(Φ, Φ¯)(Φ+Φ0, Φ¯+Φ0),
α=Φ-Φ¯,
β=Φ+Φ¯,
ψ=θ,
ψ˙=-43γ K¯sin(ψ)sin(α),
α˙=-83γ K¯cos(ψ)cos(α)+12,
β˙=0.
ψ˙=-43γ K¯sin(ψ) 32.
ψ=2 arctan[exp(±ξ)],
S1=P sech(ξ)sin[(β0+2π/3)/2],
S2=±P tanh(ξ)
S3=P sech(ξ)cos[(β0+2π/3)/2];
S¯1=P sech(ξ)sin[(β0-2π/3)/2],
S¯2=±P tanh(ξ),
S¯3=P sech(ξ)cos[(β0-2π/3)/2],

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