Abstract

It is shown that a Kerr cavity with different losses for the two polarization components of the field can support both dark and bright cavity solitons (CS’s). A parametrically driven Ginzburg–Landau equation is shown to describe the system for large-cavity anisotropy. In one transverse dimension the nonlinear dynamics of the bright CS’s is numerically investigated.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. J. Sánchez-Morcillo, G. J. de Valcárcel, and E. Roldán, Opt. Comun. 173, 381 (2000).
    [CrossRef]
  2. J. B. Geddes, J. V. Moloney, E. M. Wright, and W. J. Firth, Opt. Commun. 111, 623 (1994).
    [CrossRef]
  3. L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
    [CrossRef] [PubMed]
  4. M. Hoyuelos, P. Colet, M. San Miguel, and D. Walgraef, Phys. Rev. E 58, 2992 (1998).
    [CrossRef]
  5. J. W. Miles, J. Fluid Mech. 148, 451 (1984).
    [CrossRef]
  6. S. Fauve and O. Thual, Phys. Rev. Lett. 64, 282 (1990).
    [CrossRef] [PubMed]
  7. R. Gallego, M. San Miguel, and R. Toral, Phys. Rev. E 61, 2241 (2000).
    [CrossRef]
  8. M. Bondila, I. V. Barashenkov, and M. M. Bogdan, Physica D 87, 314 (1995).
    [CrossRef]
  9. S. Longhi, G. Steinmeyer, and W. S. Wong, J. Opt. Soc. Am. B 14, 2167 (1997).
    [CrossRef]

2000

V. J. Sánchez-Morcillo, G. J. de Valcárcel, and E. Roldán, Opt. Comun. 173, 381 (2000).
[CrossRef]

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

1998

M. Hoyuelos, P. Colet, M. San Miguel, and D. Walgraef, Phys. Rev. E 58, 2992 (1998).
[CrossRef]

1997

S. Longhi, G. Steinmeyer, and W. S. Wong, J. Opt. Soc. Am. B 14, 2167 (1997).
[CrossRef]

1995

M. Bondila, I. V. Barashenkov, and M. M. Bogdan, Physica D 87, 314 (1995).
[CrossRef]

1994

J. B. Geddes, J. V. Moloney, E. M. Wright, and W. J. Firth, Opt. Commun. 111, 623 (1994).
[CrossRef]

1990

S. Fauve and O. Thual, Phys. Rev. Lett. 64, 282 (1990).
[CrossRef] [PubMed]

1987

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[CrossRef] [PubMed]

1984

J. W. Miles, J. Fluid Mech. 148, 451 (1984).
[CrossRef]

Barashenkov, I. V.

M. Bondila, I. V. Barashenkov, and M. M. Bogdan, Physica D 87, 314 (1995).
[CrossRef]

Bogdan, M. M.

M. Bondila, I. V. Barashenkov, and M. M. Bogdan, Physica D 87, 314 (1995).
[CrossRef]

Bondila, M.

M. Bondila, I. V. Barashenkov, and M. M. Bogdan, Physica D 87, 314 (1995).
[CrossRef]

Colet, P.

M. Hoyuelos, P. Colet, M. San Miguel, and D. Walgraef, Phys. Rev. E 58, 2992 (1998).
[CrossRef]

de Valcárcel, G. J.

V. J. Sánchez-Morcillo, G. J. de Valcárcel, and E. Roldán, Opt. Comun. 173, 381 (2000).
[CrossRef]

Fauve, S.

S. Fauve and O. Thual, Phys. Rev. Lett. 64, 282 (1990).
[CrossRef] [PubMed]

Firth, W. J.

J. B. Geddes, J. V. Moloney, E. M. Wright, and W. J. Firth, Opt. Commun. 111, 623 (1994).
[CrossRef]

Gallego, R.

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

Geddes, J. B.

J. B. Geddes, J. V. Moloney, E. M. Wright, and W. J. Firth, Opt. Commun. 111, 623 (1994).
[CrossRef]

Hoyuelos, M.

M. Hoyuelos, P. Colet, M. San Miguel, and D. Walgraef, Phys. Rev. E 58, 2992 (1998).
[CrossRef]

Lefever, R.

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[CrossRef] [PubMed]

Longhi, S.

S. Longhi, G. Steinmeyer, and W. S. Wong, J. Opt. Soc. Am. B 14, 2167 (1997).
[CrossRef]

Lugiato, L. A.

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[CrossRef] [PubMed]

Miles, J. W.

J. W. Miles, J. Fluid Mech. 148, 451 (1984).
[CrossRef]

Moloney, J. V.

J. B. Geddes, J. V. Moloney, E. M. Wright, and W. J. Firth, Opt. Commun. 111, 623 (1994).
[CrossRef]

Roldán, E.

V. J. Sánchez-Morcillo, G. J. de Valcárcel, and E. Roldán, Opt. Comun. 173, 381 (2000).
[CrossRef]

San Miguel, M.

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

M. Hoyuelos, P. Colet, M. San Miguel, and D. Walgraef, Phys. Rev. E 58, 2992 (1998).
[CrossRef]

Sánchez-Morcillo, V. J.

V. J. Sánchez-Morcillo, G. J. de Valcárcel, and E. Roldán, Opt. Comun. 173, 381 (2000).
[CrossRef]

Steinmeyer, G.

S. Longhi, G. Steinmeyer, and W. S. Wong, J. Opt. Soc. Am. B 14, 2167 (1997).
[CrossRef]

Thual, O.

S. Fauve and O. Thual, Phys. Rev. Lett. 64, 282 (1990).
[CrossRef] [PubMed]

Toral, R.

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

Walgraef, D.

M. Hoyuelos, P. Colet, M. San Miguel, and D. Walgraef, Phys. Rev. E 58, 2992 (1998).
[CrossRef]

Wong, W. S.

S. Longhi, G. Steinmeyer, and W. S. Wong, J. Opt. Soc. Am. B 14, 2167 (1997).
[CrossRef]

Wright, E. M.

J. B. Geddes, J. V. Moloney, E. M. Wright, and W. J. Firth, Opt. Commun. 111, 623 (1994).
[CrossRef]

J. Fluid Mech.

J. W. Miles, J. Fluid Mech. 148, 451 (1984).
[CrossRef]

J. Opt. Soc. Am. B

S. Longhi, G. Steinmeyer, and W. S. Wong, J. Opt. Soc. Am. B 14, 2167 (1997).
[CrossRef]

Opt. Commun.

J. B. Geddes, J. V. Moloney, E. M. Wright, and W. J. Firth, Opt. Commun. 111, 623 (1994).
[CrossRef]

Opt. Comun.

V. J. Sánchez-Morcillo, G. J. de Valcárcel, and E. Roldán, Opt. Comun. 173, 381 (2000).
[CrossRef]

Phys. Rev. E

M. Hoyuelos, P. Colet, M. San Miguel, and D. Walgraef, Phys. Rev. E 58, 2992 (1998).
[CrossRef]

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

Phys. Rev. Lett.

S. Fauve and O. Thual, Phys. Rev. Lett. 64, 282 (1990).
[CrossRef] [PubMed]

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[CrossRef] [PubMed]

Physica D

M. Bondila, I. V. Barashenkov, and M. M. Bogdan, Physica D 87, 314 (1995).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Cavity solitons for liquids. (a) Bright soliton in the self-focusing case, (b) dark soliton in the self-defocusing case. Parameters are (a) Δ=2.5, E=1.5, and γ=10, 25, 50 from bottom to top; (b) Δ=0.5, E=2, and γ=25, 50, 150 from bottom to top. Dashed curves correspond to the solutions [Eqs. (3) and (4)] of the PGLE.

Fig. 2
Fig. 2

Bifurcation diagram of the bright CS for γ=10 and η=+1 in the case of liquids. See text.

Fig. 3
Fig. 3

Field portraits corresponding to the center of the bright CS, showing a period-doubling cascade for Δ=7.25. (a) P1E=2.40, (b) P2E=2.20, (c) P4E=2.16, (d) P8E=2.144, (e) chaos E=2.14. (f) A P6E=2.12 behavior that occurs in a periodic window inside the chaotic domain.

Equations (5)

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

tAj=-λj+iηΔAj+iηAj2Aj+AAk2Aj+B/2Ak2Aj*+i2Aj+γ1-jE,
tu=-1+iηθu+μu*+iηu2u+i2u,
ubright=2β expiϕsechβx,
udark=β exp-iϕtanh1/2βx,
β2=θ±μ2-1,  2ϕ=±arccosμ-1.

Metrics