Abstract

We performed numerical simulations to obtain statistical and spectral characteristics of stimulated Brillouin scattering (SBS) initiated by Gaussian noise in single-mode optical fibers. Recently published experimental spectra of SBS power [e.g., Phys. Rev. Lett. 85, 1879 (2000)] are explained completely by a one-dimensional SBS model. We give a clear physical insight into the problem and, for what is to our knowledge the first time, reveal how the probability function of Stokes power, the power-correlation function, and the SBS spectra evolve as key parameters of the model vary, leading to a modification of Stokes field statistics.

© 2002 Optical Society of America

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References

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  1. E. A. Kuzin, M. P. Petrov, and A. A. Fotiadi, in Optical Phase Conjugation, M. Gower and D. Proch, eds. (Springer-Verlag, Berlin, 1994), pp. 74–96.
  2. R. W. Boyd, K. Rzazewski, and P. Narum, Phys. Rev. A 42, 5514–5521 (1990).
    [CrossRef] [PubMed]
  3. A. L. Gaeta and R. W. Boyd, Phys. Rev. A 44, 3205–3209 (1991).
    [CrossRef] [PubMed]
  4. A. A. Fotiadi and R. V. Kiyan, Opt. Lett. 23, 1805–1807 (1998).
    [CrossRef]
  5. R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, Phys. Rev. Lett. 65, 167–170 (1990).
    [CrossRef] [PubMed]
  6. V. I. Kovalev and R. G. Harrison, Phys. Rev. Lett. 85, 1879–1882 (2000).
    [CrossRef] [PubMed]
  7. A. A. Fotiadi and E. A. Kuzin, in Quantum Electronics and Laser Science Conference, Vol. 16 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 128–129.
  8. E. M. Dianov, A. Ya. Karasik, A. V. Luchnikov, and A. K. Senatorov, Sov. J. Quantum Electron. 19, 508–512 (1989).
    [CrossRef]
  9. E. M. Dianov, A. Ya. Karasik, A. V. Luchnikov, and A. N. Pilipetskii, Opt. Quantum Electron. 21, 381–395 (1989).
    [CrossRef]
  10. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, Boston, Mass., 1995).
  11. A. A. Fotiadi, E. A. Kuzin, M. P. Petrov, and A. A. Ganichev, Sov. Techn. Phys. Lett. 15, 434–436 (1989).
  12. Y. Takushima and K. Kikuchi, Opt. Lett. 20, 34–36 (1995).
    [CrossRef] [PubMed]
  13. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
    [CrossRef]

2000

V. I. Kovalev and R. G. Harrison, Phys. Rev. Lett. 85, 1879–1882 (2000).
[CrossRef] [PubMed]

1998

1995

1991

A. L. Gaeta and R. W. Boyd, Phys. Rev. A 44, 3205–3209 (1991).
[CrossRef] [PubMed]

1990

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, Phys. Rev. Lett. 65, 167–170 (1990).
[CrossRef] [PubMed]

R. W. Boyd, K. Rzazewski, and P. Narum, Phys. Rev. A 42, 5514–5521 (1990).
[CrossRef] [PubMed]

1989

E. M. Dianov, A. Ya. Karasik, A. V. Luchnikov, and A. K. Senatorov, Sov. J. Quantum Electron. 19, 508–512 (1989).
[CrossRef]

E. M. Dianov, A. Ya. Karasik, A. V. Luchnikov, and A. N. Pilipetskii, Opt. Quantum Electron. 21, 381–395 (1989).
[CrossRef]

A. A. Fotiadi, E. A. Kuzin, M. P. Petrov, and A. A. Ganichev, Sov. Techn. Phys. Lett. 15, 434–436 (1989).

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, Boston, Mass., 1995).

Boyd, R. W.

A. L. Gaeta and R. W. Boyd, Phys. Rev. A 44, 3205–3209 (1991).
[CrossRef] [PubMed]

R. W. Boyd, K. Rzazewski, and P. Narum, Phys. Rev. A 42, 5514–5521 (1990).
[CrossRef] [PubMed]

Dianov, E. M.

E. M. Dianov, A. Ya. Karasik, A. V. Luchnikov, and A. K. Senatorov, Sov. J. Quantum Electron. 19, 508–512 (1989).
[CrossRef]

E. M. Dianov, A. Ya. Karasik, A. V. Luchnikov, and A. N. Pilipetskii, Opt. Quantum Electron. 21, 381–395 (1989).
[CrossRef]

Fotiadi, A. A.

A. A. Fotiadi and R. V. Kiyan, Opt. Lett. 23, 1805–1807 (1998).
[CrossRef]

A. A. Fotiadi, E. A. Kuzin, M. P. Petrov, and A. A. Ganichev, Sov. Techn. Phys. Lett. 15, 434–436 (1989).

E. A. Kuzin, M. P. Petrov, and A. A. Fotiadi, in Optical Phase Conjugation, M. Gower and D. Proch, eds. (Springer-Verlag, Berlin, 1994), pp. 74–96.

A. A. Fotiadi and E. A. Kuzin, in Quantum Electronics and Laser Science Conference, Vol. 16 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 128–129.

Gaeta, A. L.

A. L. Gaeta and R. W. Boyd, Phys. Rev. A 44, 3205–3209 (1991).
[CrossRef] [PubMed]

Ganichev, A. A.

A. A. Fotiadi, E. A. Kuzin, M. P. Petrov, and A. A. Ganichev, Sov. Techn. Phys. Lett. 15, 434–436 (1989).

Harrison, R. G.

V. I. Kovalev and R. G. Harrison, Phys. Rev. Lett. 85, 1879–1882 (2000).
[CrossRef] [PubMed]

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, Phys. Rev. Lett. 65, 167–170 (1990).
[CrossRef] [PubMed]

Johnstone, A.

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, Phys. Rev. Lett. 65, 167–170 (1990).
[CrossRef] [PubMed]

Karasik, A. Ya.

E. M. Dianov, A. Ya. Karasik, A. V. Luchnikov, and A. N. Pilipetskii, Opt. Quantum Electron. 21, 381–395 (1989).
[CrossRef]

E. M. Dianov, A. Ya. Karasik, A. V. Luchnikov, and A. K. Senatorov, Sov. J. Quantum Electron. 19, 508–512 (1989).
[CrossRef]

Kikuchi, K.

Kiyan, R. V.

Kovalev, V. I.

V. I. Kovalev and R. G. Harrison, Phys. Rev. Lett. 85, 1879–1882 (2000).
[CrossRef] [PubMed]

Kuzin, E. A.

A. A. Fotiadi, E. A. Kuzin, M. P. Petrov, and A. A. Ganichev, Sov. Techn. Phys. Lett. 15, 434–436 (1989).

E. A. Kuzin, M. P. Petrov, and A. A. Fotiadi, in Optical Phase Conjugation, M. Gower and D. Proch, eds. (Springer-Verlag, Berlin, 1994), pp. 74–96.

A. A. Fotiadi and E. A. Kuzin, in Quantum Electronics and Laser Science Conference, Vol. 16 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 128–129.

Luchnikov, A. V.

E. M. Dianov, A. Ya. Karasik, A. V. Luchnikov, and A. K. Senatorov, Sov. J. Quantum Electron. 19, 508–512 (1989).
[CrossRef]

E. M. Dianov, A. Ya. Karasik, A. V. Luchnikov, and A. N. Pilipetskii, Opt. Quantum Electron. 21, 381–395 (1989).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

Moloney, J. V.

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, Phys. Rev. Lett. 65, 167–170 (1990).
[CrossRef] [PubMed]

Narum, P.

R. W. Boyd, K. Rzazewski, and P. Narum, Phys. Rev. A 42, 5514–5521 (1990).
[CrossRef] [PubMed]

Petrov, M. P.

A. A. Fotiadi, E. A. Kuzin, M. P. Petrov, and A. A. Ganichev, Sov. Techn. Phys. Lett. 15, 434–436 (1989).

E. A. Kuzin, M. P. Petrov, and A. A. Fotiadi, in Optical Phase Conjugation, M. Gower and D. Proch, eds. (Springer-Verlag, Berlin, 1994), pp. 74–96.

Pilipetskii, A. N.

E. M. Dianov, A. Ya. Karasik, A. V. Luchnikov, and A. N. Pilipetskii, Opt. Quantum Electron. 21, 381–395 (1989).
[CrossRef]

Rzazewski, K.

R. W. Boyd, K. Rzazewski, and P. Narum, Phys. Rev. A 42, 5514–5521 (1990).
[CrossRef] [PubMed]

Senatorov, A. K.

E. M. Dianov, A. Ya. Karasik, A. V. Luchnikov, and A. K. Senatorov, Sov. J. Quantum Electron. 19, 508–512 (1989).
[CrossRef]

Takushima, Y.

Uppal, J. S.

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, Phys. Rev. Lett. 65, 167–170 (1990).
[CrossRef] [PubMed]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

1995 OSA Technical Digest Series

A. A. Fotiadi and E. A. Kuzin, in Quantum Electronics and Laser Science Conference, Vol. 16 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 128–129.

Opt. Lett.

Opt. Quantum Electron.

E. M. Dianov, A. Ya. Karasik, A. V. Luchnikov, and A. N. Pilipetskii, Opt. Quantum Electron. 21, 381–395 (1989).
[CrossRef]

Phys. Rev. A

R. W. Boyd, K. Rzazewski, and P. Narum, Phys. Rev. A 42, 5514–5521 (1990).
[CrossRef] [PubMed]

A. L. Gaeta and R. W. Boyd, Phys. Rev. A 44, 3205–3209 (1991).
[CrossRef] [PubMed]

Phys. Rev. Lett.

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, Phys. Rev. Lett. 65, 167–170 (1990).
[CrossRef] [PubMed]

V. I. Kovalev and R. G. Harrison, Phys. Rev. Lett. 85, 1879–1882 (2000).
[CrossRef] [PubMed]

Sov. J. Quantum Electron.

E. M. Dianov, A. Ya. Karasik, A. V. Luchnikov, and A. K. Senatorov, Sov. J. Quantum Electron. 19, 508–512 (1989).
[CrossRef]

Sov. Techn. Phys. Lett.

A. A. Fotiadi, E. A. Kuzin, M. P. Petrov, and A. A. Ganichev, Sov. Techn. Phys. Lett. 15, 434–436 (1989).

Other

E. A. Kuzin, M. P. Petrov, and A. A. Fotiadi, in Optical Phase Conjugation, M. Gower and D. Proch, eds. (Springer-Verlag, Berlin, 1994), pp. 74–96.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, Boston, Mass., 1995).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Pump–Stokes conversion efficiency χ and (b) Stokes power deviation Δ as functions of N for (curves 1–4) γ=10,1,0.1,0.01. Typical temporal behaviors of the Stokes power, PS0,t/P0, are also shown for two limit cases at N=10: (c) γ=10, (d) γ=0.01.

Fig. 2
Fig. 2

Probability functions of the Stokes power for (a) γ=10, (b) γ=1, (c) γ=0.1, and (d) γ=0.01. Curves 1–8: N=1.25,2.5,5,7.5,10,100,1.9,1.5.

Fig. 3
Fig. 3

Spectra of the Stokes power (normalized to average power) for (a) γ=10, (b) γ=1, (c) γ=0.1, and (d) γ=0.01. Curves 1–5: N=1.25,2.5,5,7.5,10.

Fig. 4
Fig. 4

Spectra SPν and correlation functions Cτ/C0 for (a), (c) γ=10 and (b), (d) 0.01 and N=10. Solid curves, calculated from Eqs. (1); dashed curves, evaluated for Gaussian stochastic processes with the same field spectra Sν as those of the processes under consideration; gray curve, SPνKνSPthν, from a linearized SBS model.1

Fig. 5
Fig. 5

Spectra of the Stokes power calculated for comparison with those from Ref. 6. The fiber length is L=250 m. Curves 1–4: N=1.1,1.5,5.4,10; γ=nL/10cT2N12.5/N. Curve 0, difference between the spectra at N=1.5 and N=10.

Equations (1)

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ncELt+ELz=-g2SρES,  ncESt-ESz=g2Sρ*EL,  T2ρt+ρ=ELES*+fz,t,

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