Abstract

Pulse propagation in optical fibers may electrostrictively excite acoustic waves as a result of cladding Brillouin scattering, transversally propagating with respect to the fiber axis in the fiber’s cladding, and mechanical coating. We show, for the first time to our knowledge, experimentally and theoretically that these transverse resonances within finite frequency ranges may cooperatively couple with the acoustic longitudinal modes of a fiber resonator, giving rise to stable trains of either spread or compressed three-wave Brillouin solitons and propose a first stability map for the rich four-wave dissipative dynamics.

© 2001 Optical Society of America

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  1. E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, Phys. Rev. Lett. 66, 1454 (1991).
    [CrossRef] [PubMed]
  2. C. Montes, A. Mamhoud, and E. Picholle, Phys. Rev. A 49, 1344 (1994).
    [CrossRef] [PubMed]
  3. C. Montes, D. Bahloul, I. Bongrand, J. Botineau, G. Cheval, A. Mamhoud, E. Picholle, and A. Picozzi, J. Opt. Soc. Am. 16, 932 (1999).
    [CrossRef]
  4. E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. N. Starodumov, Sov. Lightwave Commun. 1, 37 (1991).
  5. Y. Jaouën and L. du Mouza, Opt. Fibre Tech. 7, 141 (2001).
    [CrossRef]
  6. I. Bongrand, A. Picozzi, and E. Picholle, Electron. Lett. 34, 1769 (1998).
    [CrossRef]
  7. A. B. Grudinin, D. J. Richardson, and D. N. Payne, Electron. Lett. 29, 60 (1993).
    [CrossRef]
  8. C. Montes, A. Picozzi, and D. Bahloul, Phys. Rev. E 55, 1092 (1997).
    [CrossRef]
  9. E. Picholle and A. Picozzi, Opt. Commun. 135, 327 (1997).
    [CrossRef]
  10. R. W. Boyd, K. Rzazewsky, and P. Narum, Phys. Rev. A 42, 5514 (1990).
    [CrossRef] [PubMed]
  11. R. G. Harrison, P. M. Ripley, and W. Lu, Phys. Rev. A 49, R24 (1994).
    [CrossRef]
  12. A. Fellegara, A. Melloni, and M. Martinelli, Opt. Lett. 22, 1615 (1997).
    [CrossRef]

2001

Y. Jaouën and L. du Mouza, Opt. Fibre Tech. 7, 141 (2001).
[CrossRef]

1999

C. Montes, D. Bahloul, I. Bongrand, J. Botineau, G. Cheval, A. Mamhoud, E. Picholle, and A. Picozzi, J. Opt. Soc. Am. 16, 932 (1999).
[CrossRef]

1998

I. Bongrand, A. Picozzi, and E. Picholle, Electron. Lett. 34, 1769 (1998).
[CrossRef]

1997

C. Montes, A. Picozzi, and D. Bahloul, Phys. Rev. E 55, 1092 (1997).
[CrossRef]

E. Picholle and A. Picozzi, Opt. Commun. 135, 327 (1997).
[CrossRef]

A. Fellegara, A. Melloni, and M. Martinelli, Opt. Lett. 22, 1615 (1997).
[CrossRef]

1994

R. G. Harrison, P. M. Ripley, and W. Lu, Phys. Rev. A 49, R24 (1994).
[CrossRef]

C. Montes, A. Mamhoud, and E. Picholle, Phys. Rev. A 49, 1344 (1994).
[CrossRef] [PubMed]

1993

A. B. Grudinin, D. J. Richardson, and D. N. Payne, Electron. Lett. 29, 60 (1993).
[CrossRef]

1991

E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, Phys. Rev. Lett. 66, 1454 (1991).
[CrossRef] [PubMed]

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. N. Starodumov, Sov. Lightwave Commun. 1, 37 (1991).

1990

R. W. Boyd, K. Rzazewsky, and P. Narum, Phys. Rev. A 42, 5514 (1990).
[CrossRef] [PubMed]

Bahloul, D.

C. Montes, D. Bahloul, I. Bongrand, J. Botineau, G. Cheval, A. Mamhoud, E. Picholle, and A. Picozzi, J. Opt. Soc. Am. 16, 932 (1999).
[CrossRef]

C. Montes, A. Picozzi, and D. Bahloul, Phys. Rev. E 55, 1092 (1997).
[CrossRef]

Bongrand, I.

C. Montes, D. Bahloul, I. Bongrand, J. Botineau, G. Cheval, A. Mamhoud, E. Picholle, and A. Picozzi, J. Opt. Soc. Am. 16, 932 (1999).
[CrossRef]

I. Bongrand, A. Picozzi, and E. Picholle, Electron. Lett. 34, 1769 (1998).
[CrossRef]

Botineau, J.

C. Montes, D. Bahloul, I. Bongrand, J. Botineau, G. Cheval, A. Mamhoud, E. Picholle, and A. Picozzi, J. Opt. Soc. Am. 16, 932 (1999).
[CrossRef]

E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, Phys. Rev. Lett. 66, 1454 (1991).
[CrossRef] [PubMed]

Boyd, R. W.

R. W. Boyd, K. Rzazewsky, and P. Narum, Phys. Rev. A 42, 5514 (1990).
[CrossRef] [PubMed]

Cheval, G.

C. Montes, D. Bahloul, I. Bongrand, J. Botineau, G. Cheval, A. Mamhoud, E. Picholle, and A. Picozzi, J. Opt. Soc. Am. 16, 932 (1999).
[CrossRef]

Dianov, E. M.

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. N. Starodumov, Sov. Lightwave Commun. 1, 37 (1991).

du Mouza, L.

Y. Jaouën and L. du Mouza, Opt. Fibre Tech. 7, 141 (2001).
[CrossRef]

Fellegara, A.

Grudinin, A. B.

A. B. Grudinin, D. J. Richardson, and D. N. Payne, Electron. Lett. 29, 60 (1993).
[CrossRef]

Harrison, R. G.

R. G. Harrison, P. M. Ripley, and W. Lu, Phys. Rev. A 49, R24 (1994).
[CrossRef]

Jaouën, Y.

Y. Jaouën and L. du Mouza, Opt. Fibre Tech. 7, 141 (2001).
[CrossRef]

Legrand, O.

E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, Phys. Rev. Lett. 66, 1454 (1991).
[CrossRef] [PubMed]

Leycuras, C.

E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, Phys. Rev. Lett. 66, 1454 (1991).
[CrossRef] [PubMed]

Lu, W.

R. G. Harrison, P. M. Ripley, and W. Lu, Phys. Rev. A 49, R24 (1994).
[CrossRef]

Luchnikov, A. V.

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. N. Starodumov, Sov. Lightwave Commun. 1, 37 (1991).

Mamhoud, A.

C. Montes, D. Bahloul, I. Bongrand, J. Botineau, G. Cheval, A. Mamhoud, E. Picholle, and A. Picozzi, J. Opt. Soc. Am. 16, 932 (1999).
[CrossRef]

C. Montes, A. Mamhoud, and E. Picholle, Phys. Rev. A 49, 1344 (1994).
[CrossRef] [PubMed]

Martinelli, M.

Melloni, A.

Montes, C.

C. Montes, D. Bahloul, I. Bongrand, J. Botineau, G. Cheval, A. Mamhoud, E. Picholle, and A. Picozzi, J. Opt. Soc. Am. 16, 932 (1999).
[CrossRef]

C. Montes, A. Picozzi, and D. Bahloul, Phys. Rev. E 55, 1092 (1997).
[CrossRef]

C. Montes, A. Mamhoud, and E. Picholle, Phys. Rev. A 49, 1344 (1994).
[CrossRef] [PubMed]

E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, Phys. Rev. Lett. 66, 1454 (1991).
[CrossRef] [PubMed]

Narum, P.

R. W. Boyd, K. Rzazewsky, and P. Narum, Phys. Rev. A 42, 5514 (1990).
[CrossRef] [PubMed]

Payne, D. N.

A. B. Grudinin, D. J. Richardson, and D. N. Payne, Electron. Lett. 29, 60 (1993).
[CrossRef]

Picholle, E.

C. Montes, D. Bahloul, I. Bongrand, J. Botineau, G. Cheval, A. Mamhoud, E. Picholle, and A. Picozzi, J. Opt. Soc. Am. 16, 932 (1999).
[CrossRef]

I. Bongrand, A. Picozzi, and E. Picholle, Electron. Lett. 34, 1769 (1998).
[CrossRef]

E. Picholle and A. Picozzi, Opt. Commun. 135, 327 (1997).
[CrossRef]

C. Montes, A. Mamhoud, and E. Picholle, Phys. Rev. A 49, 1344 (1994).
[CrossRef] [PubMed]

E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, Phys. Rev. Lett. 66, 1454 (1991).
[CrossRef] [PubMed]

Picozzi, A.

C. Montes, D. Bahloul, I. Bongrand, J. Botineau, G. Cheval, A. Mamhoud, E. Picholle, and A. Picozzi, J. Opt. Soc. Am. 16, 932 (1999).
[CrossRef]

I. Bongrand, A. Picozzi, and E. Picholle, Electron. Lett. 34, 1769 (1998).
[CrossRef]

E. Picholle and A. Picozzi, Opt. Commun. 135, 327 (1997).
[CrossRef]

C. Montes, A. Picozzi, and D. Bahloul, Phys. Rev. E 55, 1092 (1997).
[CrossRef]

Pilipetskii, A. N.

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. N. Starodumov, Sov. Lightwave Commun. 1, 37 (1991).

Richardson, D. J.

A. B. Grudinin, D. J. Richardson, and D. N. Payne, Electron. Lett. 29, 60 (1993).
[CrossRef]

Ripley, P. M.

R. G. Harrison, P. M. Ripley, and W. Lu, Phys. Rev. A 49, R24 (1994).
[CrossRef]

Rzazewsky, K.

R. W. Boyd, K. Rzazewsky, and P. Narum, Phys. Rev. A 42, 5514 (1990).
[CrossRef] [PubMed]

Starodumov, A. N.

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. N. Starodumov, Sov. Lightwave Commun. 1, 37 (1991).

Electron. Lett.

I. Bongrand, A. Picozzi, and E. Picholle, Electron. Lett. 34, 1769 (1998).
[CrossRef]

A. B. Grudinin, D. J. Richardson, and D. N. Payne, Electron. Lett. 29, 60 (1993).
[CrossRef]

J. Opt. Soc. Am.

C. Montes, D. Bahloul, I. Bongrand, J. Botineau, G. Cheval, A. Mamhoud, E. Picholle, and A. Picozzi, J. Opt. Soc. Am. 16, 932 (1999).
[CrossRef]

Opt. Commun.

E. Picholle and A. Picozzi, Opt. Commun. 135, 327 (1997).
[CrossRef]

Opt. Fibre Tech.

Y. Jaouën and L. du Mouza, Opt. Fibre Tech. 7, 141 (2001).
[CrossRef]

Opt. Lett.

Phys. Rev. A

R. W. Boyd, K. Rzazewsky, and P. Narum, Phys. Rev. A 42, 5514 (1990).
[CrossRef] [PubMed]

R. G. Harrison, P. M. Ripley, and W. Lu, Phys. Rev. A 49, R24 (1994).
[CrossRef]

C. Montes, A. Mamhoud, and E. Picholle, Phys. Rev. A 49, 1344 (1994).
[CrossRef] [PubMed]

Phys. Rev. E

C. Montes, A. Picozzi, and D. Bahloul, Phys. Rev. E 55, 1092 (1997).
[CrossRef]

Phys. Rev. Lett.

E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, Phys. Rev. Lett. 66, 1454 (1991).
[CrossRef] [PubMed]

Sov. Lightwave Commun.

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. N. Starodumov, Sov. Lightwave Commun. 1, 37 (1991).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup for the double-cavity L,2d fiber resonator.

Fig. 2
Fig. 2

Trains of Brillouin pulses (experimental, left; numerical, right): (a) compression regime, (b) dilated regime, (c) unstable regime.

Fig. 3
Fig. 3

Stability map in the ωn,κCBS plane [from the numerical model, Eqs.  (1)–(4)]. Stable compression regions (c) are delimited by solid curves and dotted–dashed curves; stable dilated regions (d) are delimited by the dashed curves. Both families of stable soliton regimes coexist in intermediate bistable regions (b), and outside these regions the dynamics is unstable (i).

Equations (4)

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

t+c/nx+γeEp=-KSBSEBEa+iKKerrEp2+2EB2Ep+iKCBSQnEp,
t-c/nx+γeEB=KSBSEpEa*+iKKerr2Ep2+EB2EB+iKCBSQnEB,
t+γaEa=KSBSEpEB*+fa,
tt+2γnt+ωn2Qn=Ep2+EB2+fn,

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