Abstract

Evidence of Bloch domain walls in nonlinear optical systems is given. These walls are found in the transverse fields of optical parametric oscillators when the polarization degree of freedom, the cavity birefringence, and (or) dichroism are taken into account. These domain walls arise spontaneously and exhibit defects where Bloch walls of different chirality join together. Two dynamic regimes are found: In the first one the vector field approaches a final homogeneous state, and in the other the walls are continually generated and annihilated. This dynamic behavior is caused by the fact that walls of opposite chirality move spontaneously with opposite velocity.

© 2000 Optical Society of America

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  1. G. De Valcárcel, E. Roldan, and R. Vilaseca, J. Opt. B. 1, 19–197 (1999).
    [CrossRef]
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    [CrossRef]
  3. G.-L. Oppo, M. Brambilla, and L. A. Lugiato, Phys. Rev. A 49, 2028 (1994).
    [CrossRef] [PubMed]
  4. S. Trillo, M. Haelterman, and A. Sheppard, Opt. Lett. 22, 970 (1997) ; S. Longhi, Phys. Scr. 56, 611 (1997); N. Kutz, T. Ernaux, S. Trillo, and M. Haelterman, J. Opt. Soc. Am. B 16, 1936 (1999).
    [CrossRef] [PubMed]
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    [CrossRef]
  6. K. Staliunas and V. Sánchez-Morcillo, Phys. Rev. A 57, 1454 (1998); G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B 1, 133 (1999); B. M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, J. Opt. BJOBPDE 1, 153 (1999).
    [CrossRef]
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    [CrossRef]
  8. U. Peschel, D. Michaelis, C. Etrich, and F. Lederer, Phys. Rev. E 58, R2745 (1998).
    [CrossRef]
  9. R. Gallego, M. San Miguel, and R. Toral, Phys. Rev. E 61, 2241 (2000).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  16. I. P. Arjona, F. Silva, V. Sanchez-Morcillo, E. Roldan, and S. G. Valcárcel, Departament d'Òptica, Universitat de València, València, Spain.
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    [CrossRef]
  18. C. Fabre, E. Mason, and N. Wong, Opt. Commun. 170, 299 (1999), and references therein.
    [CrossRef]
  19. H. Tutu, Phys. Rev. E 56, 5036 (1997).
    [CrossRef]

2000

R. Gallego, M. San Miguel, and R. Toral, Phys. Rev. E 61, 2241 (2000).
[CrossRef]

1999

M. Vaupel, A. Matre, and C. Fabre, Phys. Rev. Lett. 83, 5278 (1999).
[CrossRef]

G. De Valcárcel, E. Roldan, and R. Vilaseca, J. Opt. B. 1, 19–197 (1999).
[CrossRef]

C. Fabre, E. Mason, and N. Wong, Opt. Commun. 170, 299 (1999), and references therein.
[CrossRef]

G. Izús, M. Santagiustina, M. San Miguel, and P. Colet, J. Opt. Soc. Am. B 16, 1592 (1999).
[CrossRef]

1998

M. Santagiustina, P. Colet, M. San Miguel, and D. Walgaef, Opt. Lett. 23, 1167 (1998).
[CrossRef]

K. Staliunas and V. Sánchez-Morcillo, Phys. Rev. A 57, 1454 (1998); G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B 1, 133 (1999); B. M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, J. Opt. BJOBPDE 1, 153 (1999).
[CrossRef]

U. Peschel, D. Michaelis, C. Etrich, and F. Lederer, Phys. Rev. E 58, R2745 (1998).
[CrossRef]

V. Taranenko, K. Staliunas, and C. Weiss, Phys. Rev. Lett. 81, 2236 (1998).
[CrossRef]

1997

1994

G.-L. Oppo, M. Brambilla, and L. A. Lugiato, Phys. Rev. A 49, 2028 (1994).
[CrossRef] [PubMed]

T. Frisch, S. Rica, P. Coullet, and J. M. Gilli, Phys. Rev. Lett. 72, 1471 (1994).
[CrossRef] [PubMed]

1993

M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
[CrossRef]

1990

P. Coullet, J. Lega, B. Houchmanzadeh, and J. Lajzerowicz, Phys. Rev. Lett. 56, 1352 (1990).
[CrossRef]

Arjona, I. P.

I. P. Arjona, F. Silva, V. Sanchez-Morcillo, E. Roldan, and S. G. Valcárcel, Departament d'Òptica, Universitat de València, València, Spain.

Brambilla, M.

G.-L. Oppo, M. Brambilla, and L. A. Lugiato, Phys. Rev. A 49, 2028 (1994).
[CrossRef] [PubMed]

Colet, P.

Coullet, P.

T. Frisch, S. Rica, P. Coullet, and J. M. Gilli, Phys. Rev. Lett. 72, 1471 (1994).
[CrossRef] [PubMed]

P. Coullet, J. Lega, B. Houchmanzadeh, and J. Lajzerowicz, Phys. Rev. Lett. 56, 1352 (1990).
[CrossRef]

Cross, M. C.

M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
[CrossRef]

Ernaux, T.

Etrich, C.

U. Peschel, D. Michaelis, C. Etrich, and F. Lederer, Phys. Rev. E 58, R2745 (1998).
[CrossRef]

Fabre, C.

C. Fabre, E. Mason, and N. Wong, Opt. Commun. 170, 299 (1999), and references therein.
[CrossRef]

M. Vaupel, A. Matre, and C. Fabre, Phys. Rev. Lett. 83, 5278 (1999).
[CrossRef]

Firth, W. J.

K. Staliunas and V. Sánchez-Morcillo, Phys. Rev. A 57, 1454 (1998); G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B 1, 133 (1999); B. M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, J. Opt. BJOBPDE 1, 153 (1999).
[CrossRef]

G.-L. Oppo, A. J. Scroggie, and W. J. Firth, in European Quantum Electronic Conference (Institute of Electrical and Electronics Engineers, New York, 1998), p. 245.

Frisch, T.

T. Frisch, S. Rica, P. Coullet, and J. M. Gilli, Phys. Rev. Lett. 72, 1471 (1994).
[CrossRef] [PubMed]

Gallego, R.

R. Gallego, M. San Miguel, and R. Toral, Phys. Rev. E 61, 2241 (2000).
[CrossRef]

Gilli, J. M.

T. Frisch, S. Rica, P. Coullet, and J. M. Gilli, Phys. Rev. Lett. 72, 1471 (1994).
[CrossRef] [PubMed]

Haelterman, M.

Hohenberg, P. C.

M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
[CrossRef]

Houchmanzadeh, B.

P. Coullet, J. Lega, B. Houchmanzadeh, and J. Lajzerowicz, Phys. Rev. Lett. 56, 1352 (1990).
[CrossRef]

Izús, G.

Kutz, N.

Lajzerowicz, J.

P. Coullet, J. Lega, B. Houchmanzadeh, and J. Lajzerowicz, Phys. Rev. Lett. 56, 1352 (1990).
[CrossRef]

Le Berre, B.M.

K. Staliunas and V. Sánchez-Morcillo, Phys. Rev. A 57, 1454 (1998); G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B 1, 133 (1999); B. M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, J. Opt. BJOBPDE 1, 153 (1999).
[CrossRef]

Lederer, F.

U. Peschel, D. Michaelis, C. Etrich, and F. Lederer, Phys. Rev. E 58, R2745 (1998).
[CrossRef]

Leduc, D.

K. Staliunas and V. Sánchez-Morcillo, Phys. Rev. A 57, 1454 (1998); G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B 1, 133 (1999); B. M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, J. Opt. BJOBPDE 1, 153 (1999).
[CrossRef]

Lega, J.

P. Coullet, J. Lega, B. Houchmanzadeh, and J. Lajzerowicz, Phys. Rev. Lett. 56, 1352 (1990).
[CrossRef]

Longhi, S.

Lugiato, L. A.

G.-L. Oppo, M. Brambilla, and L. A. Lugiato, Phys. Rev. A 49, 2028 (1994).
[CrossRef] [PubMed]

Mason, E.

C. Fabre, E. Mason, and N. Wong, Opt. Commun. 170, 299 (1999), and references therein.
[CrossRef]

Matre, A.

M. Vaupel, A. Matre, and C. Fabre, Phys. Rev. Lett. 83, 5278 (1999).
[CrossRef]

Michaelis, D.

U. Peschel, D. Michaelis, C. Etrich, and F. Lederer, Phys. Rev. E 58, R2745 (1998).
[CrossRef]

Oppo, G. L.

K. Staliunas and V. Sánchez-Morcillo, Phys. Rev. A 57, 1454 (1998); G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B 1, 133 (1999); B. M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, J. Opt. BJOBPDE 1, 153 (1999).
[CrossRef]

Oppo, G.-L.

G.-L. Oppo, M. Brambilla, and L. A. Lugiato, Phys. Rev. A 49, 2028 (1994).
[CrossRef] [PubMed]

G.-L. Oppo, A. J. Scroggie, and W. J. Firth, in European Quantum Electronic Conference (Institute of Electrical and Electronics Engineers, New York, 1998), p. 245.

Peschel, U.

U. Peschel, D. Michaelis, C. Etrich, and F. Lederer, Phys. Rev. E 58, R2745 (1998).
[CrossRef]

Ressayre, E.

K. Staliunas and V. Sánchez-Morcillo, Phys. Rev. A 57, 1454 (1998); G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B 1, 133 (1999); B. M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, J. Opt. BJOBPDE 1, 153 (1999).
[CrossRef]

Rica, S.

T. Frisch, S. Rica, P. Coullet, and J. M. Gilli, Phys. Rev. Lett. 72, 1471 (1994).
[CrossRef] [PubMed]

Roldan, E.

I. P. Arjona, F. Silva, V. Sanchez-Morcillo, E. Roldan, and S. G. Valcárcel, Departament d'Òptica, Universitat de València, València, Spain.

Rozanov, N. N.

N. N. Rozanov, in Progress in Optics, E. Wolf, ed. (Pergamon, London, 1996), Vol. 35, p. 1.
[CrossRef]

San Miguel, M.

Sanchez-Morcillo, V.

I. P. Arjona, F. Silva, V. Sanchez-Morcillo, E. Roldan, and S. G. Valcárcel, Departament d'Òptica, Universitat de València, València, Spain.

Sánchez-Morcillo, V.

K. Staliunas and V. Sánchez-Morcillo, Phys. Rev. A 57, 1454 (1998); G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B 1, 133 (1999); B. M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, J. Opt. BJOBPDE 1, 153 (1999).
[CrossRef]

Santagiustina, M.

Scroggie, A. J.

K. Staliunas and V. Sánchez-Morcillo, Phys. Rev. A 57, 1454 (1998); G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B 1, 133 (1999); B. M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, J. Opt. BJOBPDE 1, 153 (1999).
[CrossRef]

G.-L. Oppo, A. J. Scroggie, and W. J. Firth, in European Quantum Electronic Conference (Institute of Electrical and Electronics Engineers, New York, 1998), p. 245.

Sheppard, A.

Silva, F.

I. P. Arjona, F. Silva, V. Sanchez-Morcillo, E. Roldan, and S. G. Valcárcel, Departament d'Òptica, Universitat de València, València, Spain.

Staliunas, K.

K. Staliunas and V. Sánchez-Morcillo, Phys. Rev. A 57, 1454 (1998); G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B 1, 133 (1999); B. M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, J. Opt. BJOBPDE 1, 153 (1999).
[CrossRef]

V. Taranenko, K. Staliunas, and C. Weiss, Phys. Rev. Lett. 81, 2236 (1998).
[CrossRef]

Tallet, A.

K. Staliunas and V. Sánchez-Morcillo, Phys. Rev. A 57, 1454 (1998); G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B 1, 133 (1999); B. M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, J. Opt. BJOBPDE 1, 153 (1999).
[CrossRef]

Taranenko, V.

V. Taranenko, K. Staliunas, and C. Weiss, Phys. Rev. Lett. 81, 2236 (1998).
[CrossRef]

Toral, R.

R. Gallego, M. San Miguel, and R. Toral, Phys. Rev. E 61, 2241 (2000).
[CrossRef]

Trillo, S.

Tutu, H.

H. Tutu, Phys. Rev. E 56, 5036 (1997).
[CrossRef]

Valcárcel, S. G.

I. P. Arjona, F. Silva, V. Sanchez-Morcillo, E. Roldan, and S. G. Valcárcel, Departament d'Òptica, Universitat de València, València, Spain.

Vaupel, M.

M. Vaupel, A. Matre, and C. Fabre, Phys. Rev. Lett. 83, 5278 (1999).
[CrossRef]

Walgaef, D.

Weiss, C.

V. Taranenko, K. Staliunas, and C. Weiss, Phys. Rev. Lett. 81, 2236 (1998).
[CrossRef]

Wong, N.

C. Fabre, E. Mason, and N. Wong, Opt. Commun. 170, 299 (1999), and references therein.
[CrossRef]

Europhys. Lett.

S. Longhi, Europhys. Lett. 37, 257 (1997).
[CrossRef]

J. Opt. B.

G. De Valcárcel, E. Roldan, and R. Vilaseca, J. Opt. B. 1, 19–197 (1999).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

C. Fabre, E. Mason, and N. Wong, Opt. Commun. 170, 299 (1999), and references therein.
[CrossRef]

Opt. Lett.

Phys. Rev. A

K. Staliunas and V. Sánchez-Morcillo, Phys. Rev. A 57, 1454 (1998); G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B 1, 133 (1999); B. M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, J. Opt. BJOBPDE 1, 153 (1999).
[CrossRef]

G.-L. Oppo, M. Brambilla, and L. A. Lugiato, Phys. Rev. A 49, 2028 (1994).
[CrossRef] [PubMed]

Phys. Rev. E

U. Peschel, D. Michaelis, C. Etrich, and F. Lederer, Phys. Rev. E 58, R2745 (1998).
[CrossRef]

R. Gallego, M. San Miguel, and R. Toral, Phys. Rev. E 61, 2241 (2000).
[CrossRef]

H. Tutu, Phys. Rev. E 56, 5036 (1997).
[CrossRef]

Phys. Rev. Lett.

V. Taranenko, K. Staliunas, and C. Weiss, Phys. Rev. Lett. 81, 2236 (1998).
[CrossRef]

M. Vaupel, A. Matre, and C. Fabre, Phys. Rev. Lett. 83, 5278 (1999).
[CrossRef]

P. Coullet, J. Lega, B. Houchmanzadeh, and J. Lajzerowicz, Phys. Rev. Lett. 56, 1352 (1990).
[CrossRef]

T. Frisch, S. Rica, P. Coullet, and J. M. Gilli, Phys. Rev. Lett. 72, 1471 (1994).
[CrossRef] [PubMed]

Rev. Mod. Phys.

M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
[CrossRef]

Other

I. P. Arjona, F. Silva, V. Sanchez-Morcillo, E. Roldan, and S. G. Valcárcel, Departament d'Òptica, Universitat de València, València, Spain.

N. N. Rozanov, in Progress in Optics, E. Wolf, ed. (Pergamon, London, 1996), Vol. 35, p. 1.
[CrossRef]

G.-L. Oppo, A. J. Scroggie, and W. J. Firth, in European Quantum Electronic Conference (Institute of Electrical and Electronics Engineers, New York, 1998), p. 245.

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Figures (3)

Fig. 1
Fig. 1

Numerical solution of Eq. (1) in one spatial dimension, showing a Bloch wall. The solid (dashed) curve, the real (imaginary) part of Ax. The parameters are γx=γx=1, γy=γy=1.002, Δx=Δy=0, Δx=0.01, Δy=0.03, ax=ay=0.125, ax=ay=0.25, K0=1, E0=1.25, cx,y=0.0251-i/2, and cx,y=0.02i. Ax± indicate the two possible homogeneous stable states.

Fig. 2
Fig. 2

Snapshot at time t=1600 of the field Axx,y,t: (a) real part, (b) intensity, (c) phase. The parameters are the same as in Fig. 1, except that cx,y=0.0251+i/2 and cx,y=0.021+i. In (a) homogeneous stable states Ax± and fronts B±, which correspond to Bloch walls with positive–negative chirality, are labeled.

Fig. 3
Fig. 3

Time evolution of Bloch walls; the intensity (real part) of Ax is shown above (below) for (a) t=0, (b) t=1000, (c) t=1150, (d) t=1550. The parameters are the same as in Fig. 1, except that cx,y=0.01 and cx,y=0.025.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

tBx=γx-1+iΔxBx+iax2Bx+cxBy+2iK0AxAy+E0,
tBy=γy-1+iΔyBy+iay2By+cyBx,
tAx=γx-1+iΔxAx+iax2Ax+iK0Ay*Bx+cxAy,
tAy=γy-1+iΔyAy+iay2Ay+iK0Ax*Bx+cyAx.
cx,y=p+iδT±p cos2ϕsin2ϕ,cx,y=p+iδT±p cos2ϕsin2ϕ,

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