Abstract

We study the dynamics of the formation of circular domain walls, which are large-intensity structures, in a degenerate optical parametric oscillator. We show that the mean-field and the propagation models predict the same increase in the domain size proportional to t1/3.

© 2000 Optical Society of America

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References

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  1. K. Staliunas and V. J. Sanchez-Morcillo, Phys. Lett. A 241, 28 (1998).
    [CrossRef]
  2. G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B Quantum Semiclass. Opt. 1, 133 (1999).
    [CrossRef]
  3. M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, J. Opt. B Quantum Semiclass. Opt. 1, 153 (1999).
    [CrossRef]
  4. S. Trillo, M. Haelterman, and A. Sheppard, Opt. Lett. 22, 970 (1997).
    [CrossRef] [PubMed]
  5. M. Tlidi, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, “High intensity localized structures in the degenerate optical parametric oscillator: comparison between the propagation and the mean-field models,” Phys. Rev. A (to be published).
  6. M. Tlidi, P. Mandel, and R. Lefever, Phys. Rev. Lett. 81, 979 (1998).
    [CrossRef]
  7. M. Tlidi and P. Mandel, Europhys. Lett. 44, 449 (1998).
    [CrossRef]
  8. J. W. Cahn, Trans. Metall. Soc. AIME 242, 166 (1968); J. E. Hilliard, in Phase Transformations, H. I. Aronson, ed. (American Society for Metals, Materials Park, Ohio, 1970); W. I. Goldburg and J. S. Huang, in Fluctuations, Instabilities, and Phase Transitions, T. Riste, ed. (Plenum, New York, 1975).
  9. I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961); C. Z. Wagner, Z. Electrochem. 65, 581 (1961).
  10. E. D. Siggia, Phys. Rev. A 20, 595 (1979).
    [CrossRef]
  11. G. L. Oppo, M. Brambilla, and L. A. Lugiato, Phys. Rev. A 49, 2028 (1994).
    [CrossRef] [PubMed]
  12. J. D. Gunton, M. San Miguel, and P. S. Sahni, in Phase Transitions and Critical Phenomena, C. Domb and J. L. Lebowitz, eds. (Academic, New York, 1983), Vol. 8, p. 267.
  13. M. San Miguel, M. Grant, and J. D. Gunton, Phys. Rev. A 31, 1001 (1985).
    [CrossRef] [PubMed]
  14. C. Yeung, T. Rogers, A. Hernandez-Machado, and D. Jasnow, J. Stat. Phys. 66, 1071 (1992).
    [CrossRef]
  15. S. C. Glotzer, E. A. Di Marzio, and M. Muthukumar, Phys. Rev. A 11, 2034 (1995).

1999 (2)

G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B Quantum Semiclass. Opt. 1, 133 (1999).
[CrossRef]

M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, J. Opt. B Quantum Semiclass. Opt. 1, 153 (1999).
[CrossRef]

1998 (3)

K. Staliunas and V. J. Sanchez-Morcillo, Phys. Lett. A 241, 28 (1998).
[CrossRef]

M. Tlidi, P. Mandel, and R. Lefever, Phys. Rev. Lett. 81, 979 (1998).
[CrossRef]

M. Tlidi and P. Mandel, Europhys. Lett. 44, 449 (1998).
[CrossRef]

1997 (1)

1995 (1)

S. C. Glotzer, E. A. Di Marzio, and M. Muthukumar, Phys. Rev. A 11, 2034 (1995).

1994 (1)

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

1992 (1)

C. Yeung, T. Rogers, A. Hernandez-Machado, and D. Jasnow, J. Stat. Phys. 66, 1071 (1992).
[CrossRef]

1985 (1)

M. San Miguel, M. Grant, and J. D. Gunton, Phys. Rev. A 31, 1001 (1985).
[CrossRef] [PubMed]

1979 (1)

E. D. Siggia, Phys. Rev. A 20, 595 (1979).
[CrossRef]

1968 (1)

J. W. Cahn, Trans. Metall. Soc. AIME 242, 166 (1968); J. E. Hilliard, in Phase Transformations, H. I. Aronson, ed. (American Society for Metals, Materials Park, Ohio, 1970); W. I. Goldburg and J. S. Huang, in Fluctuations, Instabilities, and Phase Transitions, T. Riste, ed. (Plenum, New York, 1975).

1961 (1)

I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961); C. Z. Wagner, Z. Electrochem. 65, 581 (1961).

Brambilla, M.

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

Cahn, J. W.

J. W. Cahn, Trans. Metall. Soc. AIME 242, 166 (1968); J. E. Hilliard, in Phase Transformations, H. I. Aronson, ed. (American Society for Metals, Materials Park, Ohio, 1970); W. I. Goldburg and J. S. Huang, in Fluctuations, Instabilities, and Phase Transitions, T. Riste, ed. (Plenum, New York, 1975).

Di Marzio, E. A.

S. C. Glotzer, E. A. Di Marzio, and M. Muthukumar, Phys. Rev. A 11, 2034 (1995).

Di Menza, L.

M. Tlidi, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, “High intensity localized structures in the degenerate optical parametric oscillator: comparison between the propagation and the mean-field models,” Phys. Rev. A (to be published).

Firth, W. J.

G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B Quantum Semiclass. Opt. 1, 133 (1999).
[CrossRef]

Glotzer, S. C.

S. C. Glotzer, E. A. Di Marzio, and M. Muthukumar, Phys. Rev. A 11, 2034 (1995).

Grant, M.

M. San Miguel, M. Grant, and J. D. Gunton, Phys. Rev. A 31, 1001 (1985).
[CrossRef] [PubMed]

Gunton, J. D.

M. San Miguel, M. Grant, and J. D. Gunton, Phys. Rev. A 31, 1001 (1985).
[CrossRef] [PubMed]

J. D. Gunton, M. San Miguel, and P. S. Sahni, in Phase Transitions and Critical Phenomena, C. Domb and J. L. Lebowitz, eds. (Academic, New York, 1983), Vol. 8, p. 267.

Haelterman, M.

Hernandez-Machado, A.

C. Yeung, T. Rogers, A. Hernandez-Machado, and D. Jasnow, J. Stat. Phys. 66, 1071 (1992).
[CrossRef]

Jasnow, D.

C. Yeung, T. Rogers, A. Hernandez-Machado, and D. Jasnow, J. Stat. Phys. 66, 1071 (1992).
[CrossRef]

Le Berre, M.

M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, J. Opt. B Quantum Semiclass. Opt. 1, 153 (1999).
[CrossRef]

M. Tlidi, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, “High intensity localized structures in the degenerate optical parametric oscillator: comparison between the propagation and the mean-field models,” Phys. Rev. A (to be published).

Leduc, D.

M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, J. Opt. B Quantum Semiclass. Opt. 1, 153 (1999).
[CrossRef]

Lefever, R.

M. Tlidi, P. Mandel, and R. Lefever, Phys. Rev. Lett. 81, 979 (1998).
[CrossRef]

Lifshitz, I. M.

I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961); C. Z. Wagner, Z. Electrochem. 65, 581 (1961).

Lugiato, L. A.

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

Mandel, P.

M. Tlidi, P. Mandel, and R. Lefever, Phys. Rev. Lett. 81, 979 (1998).
[CrossRef]

M. Tlidi and P. Mandel, Europhys. Lett. 44, 449 (1998).
[CrossRef]

Muthukumar, M.

S. C. Glotzer, E. A. Di Marzio, and M. Muthukumar, Phys. Rev. A 11, 2034 (1995).

Oppo, G. L.

G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B Quantum Semiclass. Opt. 1, 133 (1999).
[CrossRef]

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

Ressayre, E.

M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, J. Opt. B Quantum Semiclass. Opt. 1, 153 (1999).
[CrossRef]

M. Tlidi, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, “High intensity localized structures in the degenerate optical parametric oscillator: comparison between the propagation and the mean-field models,” Phys. Rev. A (to be published).

Rogers, T.

C. Yeung, T. Rogers, A. Hernandez-Machado, and D. Jasnow, J. Stat. Phys. 66, 1071 (1992).
[CrossRef]

Sahni, P. S.

J. D. Gunton, M. San Miguel, and P. S. Sahni, in Phase Transitions and Critical Phenomena, C. Domb and J. L. Lebowitz, eds. (Academic, New York, 1983), Vol. 8, p. 267.

San Miguel, M.

M. San Miguel, M. Grant, and J. D. Gunton, Phys. Rev. A 31, 1001 (1985).
[CrossRef] [PubMed]

J. D. Gunton, M. San Miguel, and P. S. Sahni, in Phase Transitions and Critical Phenomena, C. Domb and J. L. Lebowitz, eds. (Academic, New York, 1983), Vol. 8, p. 267.

Sanchez-Morcillo, V. J.

K. Staliunas and V. J. Sanchez-Morcillo, Phys. Lett. A 241, 28 (1998).
[CrossRef]

Scroggie, A. J.

G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B Quantum Semiclass. Opt. 1, 133 (1999).
[CrossRef]

Sheppard, A.

Siggia, E. D.

E. D. Siggia, Phys. Rev. A 20, 595 (1979).
[CrossRef]

Slyozov, V. V.

I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961); C. Z. Wagner, Z. Electrochem. 65, 581 (1961).

Staliunas, K.

K. Staliunas and V. J. Sanchez-Morcillo, Phys. Lett. A 241, 28 (1998).
[CrossRef]

Tallet, A.

M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, J. Opt. B Quantum Semiclass. Opt. 1, 153 (1999).
[CrossRef]

M. Tlidi, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, “High intensity localized structures in the degenerate optical parametric oscillator: comparison between the propagation and the mean-field models,” Phys. Rev. A (to be published).

Tlidi, M.

M. Tlidi and P. Mandel, Europhys. Lett. 44, 449 (1998).
[CrossRef]

M. Tlidi, P. Mandel, and R. Lefever, Phys. Rev. Lett. 81, 979 (1998).
[CrossRef]

M. Tlidi, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, “High intensity localized structures in the degenerate optical parametric oscillator: comparison between the propagation and the mean-field models,” Phys. Rev. A (to be published).

Trillo, S.

Yeung, C.

C. Yeung, T. Rogers, A. Hernandez-Machado, and D. Jasnow, J. Stat. Phys. 66, 1071 (1992).
[CrossRef]

Europhys. Lett. (1)

M. Tlidi and P. Mandel, Europhys. Lett. 44, 449 (1998).
[CrossRef]

J. Opt. B Quantum Semiclass. Opt. (2)

G. L. Oppo, A. J. Scroggie, and W. J. Firth, J. Opt. B Quantum Semiclass. Opt. 1, 133 (1999).
[CrossRef]

M. Le Berre, D. Leduc, E. Ressayre, and A. Tallet, J. Opt. B Quantum Semiclass. Opt. 1, 153 (1999).
[CrossRef]

J. Phys. Chem. Solids (1)

I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961); C. Z. Wagner, Z. Electrochem. 65, 581 (1961).

J. Stat. Phys. (1)

C. Yeung, T. Rogers, A. Hernandez-Machado, and D. Jasnow, J. Stat. Phys. 66, 1071 (1992).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (1)

K. Staliunas and V. J. Sanchez-Morcillo, Phys. Lett. A 241, 28 (1998).
[CrossRef]

Phys. Rev. A (4)

S. C. Glotzer, E. A. Di Marzio, and M. Muthukumar, Phys. Rev. A 11, 2034 (1995).

M. San Miguel, M. Grant, and J. D. Gunton, Phys. Rev. A 31, 1001 (1985).
[CrossRef] [PubMed]

E. D. Siggia, Phys. Rev. A 20, 595 (1979).
[CrossRef]

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

Phys. Rev. Lett. (1)

M. Tlidi, P. Mandel, and R. Lefever, Phys. Rev. Lett. 81, 979 (1998).
[CrossRef]

Trans. Metall. Soc. AIME (1)

J. W. Cahn, Trans. Metall. Soc. AIME 242, 166 (1968); J. E. Hilliard, in Phase Transformations, H. I. Aronson, ed. (American Society for Metals, Materials Park, Ohio, 1970); W. I. Goldburg and J. S. Huang, in Fluctuations, Instabilities, and Phase Transitions, T. Riste, ed. (Plenum, New York, 1975).

Other (2)

M. Tlidi, M. Le Berre, E. Ressayre, A. Tallet, and L. Di Menza, “High intensity localized structures in the degenerate optical parametric oscillator: comparison between the propagation and the mean-field models,” Phys. Rev. A (to be published).

J. D. Gunton, M. San Miguel, and P. S. Sahni, in Phase Transitions and Critical Phenomena, C. Domb and J. L. Lebowitz, eds. (Academic, New York, 1983), Vol. 8, p. 267.

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Figures (2)

Fig. 1
Fig. 1

Plot of log10 R versus log10 t. The solid line and the filled circles are obtained from the mean-field model. The dotted line and the open circles correspond to the propagation model. The propagation parameters are θ0=θ1=0, α0in=0.03, R0,1=0.9, and β=10. The corresponding mean-field parameters are Δ0=Δ1=0 and E=3. The grid step size is 0.06.

Fig. 2
Fig. 2

Time evolution of the real part of the signal amplitude with the propagation model. (a) t=10, (b) t=30, (c) t=100, (d) t=250, (e) t=800, (f) t=1200. The parameters are the same as in Fig. 1.

Equations (3)

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

tA0=E-γ+iΔ0A0+i22A0-A12,tA1=-1+iΔ1A1+i2A1+A0A1*,
zα0=i22α0+iα12 expizΔk,zα1=i2α1+iα0α1* exp-izΔk,
α00,x,y,t=α0in+R0 expiθ0α0l,x,y,t-τ,α10,x,y,t=R1 expiθ1α1l,x,y,t-τ.

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