Abstract

Stimulated Brillouin Scattering (SBS) is a typical backward traveling wave parametric interaction1 with inherent spatial feedback between the forward and backward scattered waves and may oscillate under high pump excitation. The pump excitation threshold is normally proportional to the nonlinearity of the medium and the interaction length. For long optical fibers and light guides, the high phonon loss and nonlinear interaction often changes the interacting field distribution into a special whispering mode7 with the phonon loss effectively compensated by pump depletion such that the threshold for pump excitation is nearly independent of the interaction length. In this paper, we will discuss the characteristics of this model of SBS and propose methods to characterize it.

© 2000 Optical Society of America

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References

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  1. Hsuing Hsu, Chung Yu, “Parametric amplification and oscillation in nonlinear backscatterings,” Appl. Phys. Lett., vol. 22, no. 1, pp. 41-43 and p. 613, (Jan.1973); H. Hsu: “Backward traveling-wave parametric amplifier,” in “Microwave Tubes,” ed. J. Wosik, Academic Press, New York, p. 341 (1961).
    [CrossRef]
  2. R. A. Fisher, “Optical phase conjugation,” Academic Press, New York, (1983); Y. I. Baspalov, G. A. Pasmanik, “Nonlinear optics and adaptive laser systems,” (in Russian), Nauka, (1986). (English translation, NOVA, New York, New York).
  3. Y. Aoki, K. Tajima, Jour. Opt. Soc. Am., vol. B5, p. 358, (1988).
    [CrossRef]
  4. H. Hsu, Y. Gao, Opt. and Quantum Electronics, vol. 22, pp. 33-6, (1990).
    [CrossRef]
  5. H. Hsu, Sheau-Shong Bor, IEEE Jour. Quantum Electronics, vol. 25, No. 3, pp. 430-7.
  6. H. Hsu, Tongning Li, “Numerical analysis of nonlinear interactions,” Journal of Nonlinear Optical Physics and Materials, vol. 8, No. 4, pp. 455-9, (Dec.1999).
    [CrossRef]
  7. H. Hsu, Tongning Li, “Whispering oscillations in highly dissipative stimulated Brillouin scattering,” to be published.
  8. X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, R. M. Derosie, IEEE Photonics Technology Letters, vol. 4.1, Jan., 1992, pp. 66-9.
    [CrossRef]
  9. M. S. Mangir, Nonlinear Optics ’98; Materials, Fundamentals, and Applications Topical Meeting, 1998, pp. 285-7.
    [CrossRef]

1999 (1)

H. Hsu, Tongning Li, “Numerical analysis of nonlinear interactions,” Journal of Nonlinear Optical Physics and Materials, vol. 8, No. 4, pp. 455-9, (Dec.1999).
[CrossRef]

1992 (1)

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, R. M. Derosie, IEEE Photonics Technology Letters, vol. 4.1, Jan., 1992, pp. 66-9.
[CrossRef]

1990 (1)

H. Hsu, Y. Gao, Opt. and Quantum Electronics, vol. 22, pp. 33-6, (1990).
[CrossRef]

1988 (1)

Y. Aoki, K. Tajima, Jour. Opt. Soc. Am., vol. B5, p. 358, (1988).
[CrossRef]

Aoki, Y.

Y. Aoki, K. Tajima, Jour. Opt. Soc. Am., vol. B5, p. 358, (1988).
[CrossRef]

Bor, Sheau-Shong

H. Hsu, Sheau-Shong Bor, IEEE Jour. Quantum Electronics, vol. 25, No. 3, pp. 430-7.

Chraplyvy, A. R.

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, R. M. Derosie, IEEE Photonics Technology Letters, vol. 4.1, Jan., 1992, pp. 66-9.
[CrossRef]

Derosie, R. M.

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, R. M. Derosie, IEEE Photonics Technology Letters, vol. 4.1, Jan., 1992, pp. 66-9.
[CrossRef]

Fisher, R. A.

R. A. Fisher, “Optical phase conjugation,” Academic Press, New York, (1983); Y. I. Baspalov, G. A. Pasmanik, “Nonlinear optics and adaptive laser systems,” (in Russian), Nauka, (1986). (English translation, NOVA, New York, New York).

Gao, Y.

H. Hsu, Y. Gao, Opt. and Quantum Electronics, vol. 22, pp. 33-6, (1990).
[CrossRef]

Hsu, H.

H. Hsu, Tongning Li, “Numerical analysis of nonlinear interactions,” Journal of Nonlinear Optical Physics and Materials, vol. 8, No. 4, pp. 455-9, (Dec.1999).
[CrossRef]

H. Hsu, Y. Gao, Opt. and Quantum Electronics, vol. 22, pp. 33-6, (1990).
[CrossRef]

H. Hsu, Sheau-Shong Bor, IEEE Jour. Quantum Electronics, vol. 25, No. 3, pp. 430-7.

H. Hsu, Tongning Li, “Whispering oscillations in highly dissipative stimulated Brillouin scattering,” to be published.

Hsu, Hsuing

Hsuing Hsu, Chung Yu, “Parametric amplification and oscillation in nonlinear backscatterings,” Appl. Phys. Lett., vol. 22, no. 1, pp. 41-43 and p. 613, (Jan.1973); H. Hsu: “Backward traveling-wave parametric amplifier,” in “Microwave Tubes,” ed. J. Wosik, Academic Press, New York, p. 341 (1961).
[CrossRef]

Jopson, R. M.

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, R. M. Derosie, IEEE Photonics Technology Letters, vol. 4.1, Jan., 1992, pp. 66-9.
[CrossRef]

Li, Tongning

H. Hsu, Tongning Li, “Numerical analysis of nonlinear interactions,” Journal of Nonlinear Optical Physics and Materials, vol. 8, No. 4, pp. 455-9, (Dec.1999).
[CrossRef]

H. Hsu, Tongning Li, “Whispering oscillations in highly dissipative stimulated Brillouin scattering,” to be published.

Mangir, M. S.

M. S. Mangir, Nonlinear Optics ’98; Materials, Fundamentals, and Applications Topical Meeting, 1998, pp. 285-7.
[CrossRef]

Mao, X. P.

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, R. M. Derosie, IEEE Photonics Technology Letters, vol. 4.1, Jan., 1992, pp. 66-9.
[CrossRef]

Tajima, K.

Y. Aoki, K. Tajima, Jour. Opt. Soc. Am., vol. B5, p. 358, (1988).
[CrossRef]

Tkach, R. W.

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, R. M. Derosie, IEEE Photonics Technology Letters, vol. 4.1, Jan., 1992, pp. 66-9.
[CrossRef]

Yu, Chung

Hsuing Hsu, Chung Yu, “Parametric amplification and oscillation in nonlinear backscatterings,” Appl. Phys. Lett., vol. 22, no. 1, pp. 41-43 and p. 613, (Jan.1973); H. Hsu: “Backward traveling-wave parametric amplifier,” in “Microwave Tubes,” ed. J. Wosik, Academic Press, New York, p. 341 (1961).
[CrossRef]

IEEE Jour. Quantum Electronics (1)

H. Hsu, Sheau-Shong Bor, IEEE Jour. Quantum Electronics, vol. 25, No. 3, pp. 430-7.

IEEE Photonics Technology Letters (1)

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, R. M. Derosie, IEEE Photonics Technology Letters, vol. 4.1, Jan., 1992, pp. 66-9.
[CrossRef]

Jour. Opt. Soc. Am. (1)

Y. Aoki, K. Tajima, Jour. Opt. Soc. Am., vol. B5, p. 358, (1988).
[CrossRef]

Journal of Nonlinear Optical Physics and Materials (1)

H. Hsu, Tongning Li, “Numerical analysis of nonlinear interactions,” Journal of Nonlinear Optical Physics and Materials, vol. 8, No. 4, pp. 455-9, (Dec.1999).
[CrossRef]

Opt. and Quantum Electronics (1)

H. Hsu, Y. Gao, Opt. and Quantum Electronics, vol. 22, pp. 33-6, (1990).
[CrossRef]

Other (4)

Hsuing Hsu, Chung Yu, “Parametric amplification and oscillation in nonlinear backscatterings,” Appl. Phys. Lett., vol. 22, no. 1, pp. 41-43 and p. 613, (Jan.1973); H. Hsu: “Backward traveling-wave parametric amplifier,” in “Microwave Tubes,” ed. J. Wosik, Academic Press, New York, p. 341 (1961).
[CrossRef]

R. A. Fisher, “Optical phase conjugation,” Academic Press, New York, (1983); Y. I. Baspalov, G. A. Pasmanik, “Nonlinear optics and adaptive laser systems,” (in Russian), Nauka, (1986). (English translation, NOVA, New York, New York).

H. Hsu, Tongning Li, “Whispering oscillations in highly dissipative stimulated Brillouin scattering,” to be published.

M. S. Mangir, Nonlinear Optics ’98; Materials, Fundamentals, and Applications Topical Meeting, 1998, pp. 285-7.
[CrossRef]

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Figures (5)

Figure 1
Figure 1

SBS pump at threshold Np(0)th versus α/β.

Figure 2
Figure 2

SBS threshold pump excitation Uth normalized to π/2, versus α/B showing that Uth = π/2 when α = 0 independent of β.

Figure 3
Figure 3

SBS pump at threshold Nh(0)th versus β for a lossless fiber and a fiber in whispering resonance mode.

Figure 4
Figure 4

SBS threshold pump ratio for two identical fibers of respective lengths L and 2L.

Figure 5
Figure 5

Characteristics of transmitted power versus incident power for SBS in whispering modes of α/β = 100 and 200 and also for normal SBS

Equations (7)

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

dNp/dz=-β Nbz Nfz
dNb/dz=-β Npz Nfz
dNf/dz=-α Nfz+β Npz Nbz
Uth=Np0th β L=π/2
Np0th=incident pump amplitude at threshold    =π/2 β L    L=the total length of the nonlinear medium.
Np, thL/Np, th2L=2.
Np, thL/Np, th2L=1.

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