Abstract

The influence of acoustic-wave diffraction on nonstationary backward stimulated Brillouin scattering (SBS) in the presence of feedback for a Stokes electromagnetic wave is numerically investigated. The cases of an acoustic-waveguide and -antiwaveguide fibers are considered. The Kerr nonlinearity is taken into account. For fibers with a small core radius (r0<3 µm), the influence of sound diffraction on the nonstationary SBS can lead to new features. The importance of the acoustic-mode structure of the fiber for the process of forming a pulse train is shown in the case of synchronous pumping in Brillouin fiber lasers. It has been found that the acoustic-antiwaveguide fibers with a small core, r0<3 µm, can be preferable for obtaining a stable train of compressed pulses. Under a constant input pump, an acoustic diffraction can essentially reduce the threshold of the modulation instability under SBS in the presence of the feedback.

© 2002 Optical Society of America

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References

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  1. D. Cotter, “Stimulated Brillouin scattering in monomode optical fiber,” J. Opt. Commun. 4, 10–19 (1983).
    [CrossRef]
  2. C. Montes, D. Bahloul, I. Bongrand, J. Botineau, G. Cheval, A. Mamhoud, E. Picholle, and A. Picozzi, “Self-pulsing and dynamic bistability in cw-pumped Brillouin fiber ring lasers,” J. Opt. Soc. Am. B 16, 932–951 (1999).
    [CrossRef]
  3. A. L. Gaeta and R. W. Boyd, “Stimulated Brillouin scattering in the presence of external feedback,” J. Nonlinear Opt. Phys. Mater. 1, 581–592 (1992).
    [CrossRef]
  4. P. J. Thomas, N. L. Rowell, H. M. Van Driel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single mode optical fibers,” Phys. Rev. B 19, 4886–4911 (1979).
    [CrossRef]
  5. A. Saffai-Jazi, C. K. Jen, and G. W. Farnell, “Analysis of weakly guiding fiber acoustic waveguides,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-32, 59–68 (1986).
    [CrossRef]
  6. C. K. Jen, J. E. B. Oliveira, N. Goto, and K. Abe, “Role of guided acoustic wave properties in single-mode optical fibre design,” Electron. Lett. 24, 1419–1420 (1988).
    [CrossRef]
  7. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).
  8. B. Ya. Zel’dovich and A. N. Pilipetskii, “Role of soundguide and antisoundguide in stimulated Brillouin scattering in a single-mode waveguide,” Sov. J. Quantum Electron. 18, 818–822 (1988).
    [CrossRef]
  9. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77 (Cambridge University, New York, 1992), p. 835.
  10. T. P. Mirtchev and N. I. Minkovski, “Extremely transient pulses from a Brillouin fiber laser,” IEEE Photon. Technol. Lett. 5, 158–161 (1993).
    [CrossRef]
  11. M. Dämming, G. Zinner, F. Mitschke, and H. Welling, “SBS in fibers with and without external feedback,” Phys. Rev. A 48, 3301–3309 (1993).
    [CrossRef]
  12. H. Li and K. Ogusu, “Instability of stimulated Brillouin scattering in a fiber ring resonator,” Opt. Rev. 7, 303–308 (2000).
    [CrossRef]
  13. H. Li and K. Ogusu, “Transient stimulated Brillouin scattering in a fiber ring resonator and its effect on optical Kerr bistability,” J. Opt. Soc. Am. B 18, 93–100 (2001).
    [CrossRef]
  14. W. T. Silfvast, “Lasers,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), Chap. 11.

2001 (1)

2000 (1)

H. Li and K. Ogusu, “Instability of stimulated Brillouin scattering in a fiber ring resonator,” Opt. Rev. 7, 303–308 (2000).
[CrossRef]

1999 (1)

1993 (2)

T. P. Mirtchev and N. I. Minkovski, “Extremely transient pulses from a Brillouin fiber laser,” IEEE Photon. Technol. Lett. 5, 158–161 (1993).
[CrossRef]

M. Dämming, G. Zinner, F. Mitschke, and H. Welling, “SBS in fibers with and without external feedback,” Phys. Rev. A 48, 3301–3309 (1993).
[CrossRef]

1992 (1)

A. L. Gaeta and R. W. Boyd, “Stimulated Brillouin scattering in the presence of external feedback,” J. Nonlinear Opt. Phys. Mater. 1, 581–592 (1992).
[CrossRef]

1988 (2)

C. K. Jen, J. E. B. Oliveira, N. Goto, and K. Abe, “Role of guided acoustic wave properties in single-mode optical fibre design,” Electron. Lett. 24, 1419–1420 (1988).
[CrossRef]

B. Ya. Zel’dovich and A. N. Pilipetskii, “Role of soundguide and antisoundguide in stimulated Brillouin scattering in a single-mode waveguide,” Sov. J. Quantum Electron. 18, 818–822 (1988).
[CrossRef]

1986 (1)

A. Saffai-Jazi, C. K. Jen, and G. W. Farnell, “Analysis of weakly guiding fiber acoustic waveguides,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-32, 59–68 (1986).
[CrossRef]

1983 (1)

D. Cotter, “Stimulated Brillouin scattering in monomode optical fiber,” J. Opt. Commun. 4, 10–19 (1983).
[CrossRef]

1979 (1)

P. J. Thomas, N. L. Rowell, H. M. Van Driel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single mode optical fibers,” Phys. Rev. B 19, 4886–4911 (1979).
[CrossRef]

Abe, K.

C. K. Jen, J. E. B. Oliveira, N. Goto, and K. Abe, “Role of guided acoustic wave properties in single-mode optical fibre design,” Electron. Lett. 24, 1419–1420 (1988).
[CrossRef]

Bahloul, D.

Bongrand, I.

Botineau, J.

Boyd, R. W.

A. L. Gaeta and R. W. Boyd, “Stimulated Brillouin scattering in the presence of external feedback,” J. Nonlinear Opt. Phys. Mater. 1, 581–592 (1992).
[CrossRef]

Cheval, G.

Cotter, D.

D. Cotter, “Stimulated Brillouin scattering in monomode optical fiber,” J. Opt. Commun. 4, 10–19 (1983).
[CrossRef]

Dämming, M.

M. Dämming, G. Zinner, F. Mitschke, and H. Welling, “SBS in fibers with and without external feedback,” Phys. Rev. A 48, 3301–3309 (1993).
[CrossRef]

Farnell, G. W.

A. Saffai-Jazi, C. K. Jen, and G. W. Farnell, “Analysis of weakly guiding fiber acoustic waveguides,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-32, 59–68 (1986).
[CrossRef]

Gaeta, A. L.

A. L. Gaeta and R. W. Boyd, “Stimulated Brillouin scattering in the presence of external feedback,” J. Nonlinear Opt. Phys. Mater. 1, 581–592 (1992).
[CrossRef]

Goto, N.

C. K. Jen, J. E. B. Oliveira, N. Goto, and K. Abe, “Role of guided acoustic wave properties in single-mode optical fibre design,” Electron. Lett. 24, 1419–1420 (1988).
[CrossRef]

Jen, C. K.

C. K. Jen, J. E. B. Oliveira, N. Goto, and K. Abe, “Role of guided acoustic wave properties in single-mode optical fibre design,” Electron. Lett. 24, 1419–1420 (1988).
[CrossRef]

A. Saffai-Jazi, C. K. Jen, and G. W. Farnell, “Analysis of weakly guiding fiber acoustic waveguides,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-32, 59–68 (1986).
[CrossRef]

Li, H.

Mamhoud, A.

Minkovski, N. I.

T. P. Mirtchev and N. I. Minkovski, “Extremely transient pulses from a Brillouin fiber laser,” IEEE Photon. Technol. Lett. 5, 158–161 (1993).
[CrossRef]

Mirtchev, T. P.

T. P. Mirtchev and N. I. Minkovski, “Extremely transient pulses from a Brillouin fiber laser,” IEEE Photon. Technol. Lett. 5, 158–161 (1993).
[CrossRef]

Mitschke, F.

M. Dämming, G. Zinner, F. Mitschke, and H. Welling, “SBS in fibers with and without external feedback,” Phys. Rev. A 48, 3301–3309 (1993).
[CrossRef]

Montes, C.

Ogusu, K.

Oliveira, J. E. B.

C. K. Jen, J. E. B. Oliveira, N. Goto, and K. Abe, “Role of guided acoustic wave properties in single-mode optical fibre design,” Electron. Lett. 24, 1419–1420 (1988).
[CrossRef]

Picholle, E.

Picozzi, A.

Pilipetskii, A. N.

B. Ya. Zel’dovich and A. N. Pilipetskii, “Role of soundguide and antisoundguide in stimulated Brillouin scattering in a single-mode waveguide,” Sov. J. Quantum Electron. 18, 818–822 (1988).
[CrossRef]

Rowell, N. L.

P. J. Thomas, N. L. Rowell, H. M. Van Driel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single mode optical fibers,” Phys. Rev. B 19, 4886–4911 (1979).
[CrossRef]

Saffai-Jazi, A.

A. Saffai-Jazi, C. K. Jen, and G. W. Farnell, “Analysis of weakly guiding fiber acoustic waveguides,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-32, 59–68 (1986).
[CrossRef]

Stegeman, G. I.

P. J. Thomas, N. L. Rowell, H. M. Van Driel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single mode optical fibers,” Phys. Rev. B 19, 4886–4911 (1979).
[CrossRef]

Thomas, P. J.

P. J. Thomas, N. L. Rowell, H. M. Van Driel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single mode optical fibers,” Phys. Rev. B 19, 4886–4911 (1979).
[CrossRef]

Van Driel, H. M.

P. J. Thomas, N. L. Rowell, H. M. Van Driel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single mode optical fibers,” Phys. Rev. B 19, 4886–4911 (1979).
[CrossRef]

Welling, H.

M. Dämming, G. Zinner, F. Mitschke, and H. Welling, “SBS in fibers with and without external feedback,” Phys. Rev. A 48, 3301–3309 (1993).
[CrossRef]

Zel’dovich, B. Ya.

B. Ya. Zel’dovich and A. N. Pilipetskii, “Role of soundguide and antisoundguide in stimulated Brillouin scattering in a single-mode waveguide,” Sov. J. Quantum Electron. 18, 818–822 (1988).
[CrossRef]

Zinner, G.

M. Dämming, G. Zinner, F. Mitschke, and H. Welling, “SBS in fibers with and without external feedback,” Phys. Rev. A 48, 3301–3309 (1993).
[CrossRef]

Electron. Lett. (1)

C. K. Jen, J. E. B. Oliveira, N. Goto, and K. Abe, “Role of guided acoustic wave properties in single-mode optical fibre design,” Electron. Lett. 24, 1419–1420 (1988).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

T. P. Mirtchev and N. I. Minkovski, “Extremely transient pulses from a Brillouin fiber laser,” IEEE Photon. Technol. Lett. 5, 158–161 (1993).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

A. Saffai-Jazi, C. K. Jen, and G. W. Farnell, “Analysis of weakly guiding fiber acoustic waveguides,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-32, 59–68 (1986).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (1)

A. L. Gaeta and R. W. Boyd, “Stimulated Brillouin scattering in the presence of external feedback,” J. Nonlinear Opt. Phys. Mater. 1, 581–592 (1992).
[CrossRef]

J. Opt. Commun. (1)

D. Cotter, “Stimulated Brillouin scattering in monomode optical fiber,” J. Opt. Commun. 4, 10–19 (1983).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Rev. (1)

H. Li and K. Ogusu, “Instability of stimulated Brillouin scattering in a fiber ring resonator,” Opt. Rev. 7, 303–308 (2000).
[CrossRef]

Phys. Rev. A (1)

M. Dämming, G. Zinner, F. Mitschke, and H. Welling, “SBS in fibers with and without external feedback,” Phys. Rev. A 48, 3301–3309 (1993).
[CrossRef]

Phys. Rev. B (1)

P. J. Thomas, N. L. Rowell, H. M. Van Driel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single mode optical fibers,” Phys. Rev. B 19, 4886–4911 (1979).
[CrossRef]

Sov. J. Quantum Electron. (1)

B. Ya. Zel’dovich and A. N. Pilipetskii, “Role of soundguide and antisoundguide in stimulated Brillouin scattering in a single-mode waveguide,” Sov. J. Quantum Electron. 18, 818–822 (1988).
[CrossRef]

Other (3)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77 (Cambridge University, New York, 1992), p. 835.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).

W. T. Silfvast, “Lasers,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), Chap. 11.

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Figures (7)

Fig. 1
Fig. 1

Spatial-temporal dependence of the Stokes wave |E2(z, t)|2 for the case of the acoustic-waveguide fiber with a core radius r0=1.5 µm under a short feedback loop (Ls=2.5Lf).

Fig. 2
Fig. 2

Spatial-temporal dependence of the Stokes wave |E2(z, t)|2 for the case of the acoustic-waveguide fiber with a core radius r0=1.5 µm under a long feedback loop (Ls=6Lf) and a great value of the Kerr-nonlinearity constant.

Fig. 3
Fig. 3

Spatial-temporal dependence of the Stokes wave |E2(z, t)|2 for the case of the acoustic-waveguide fiber with a core radius r0=1.5 µm under a long feedback loop (Ls=6Lf) and a small value of the Kerr-nonlinearity constant.

Fig. 4
Fig. 4

Spatial-temporal dependence of the Stokes wave |E2(z, t)|2 for the case of the acoustic-antiwaveguide fiber with a core radius r0=1.5 µm under a short feedback loop (Ls=2.5Lf) and a great value of the Kerr-nonlinearity constant.

Fig. 5
Fig. 5

Spatial-temporal dependence of the Stokes wave |E2(z, t)|2 for the case of the acoustic-antiwaveguide fiber with a core radius r0=1.5 µm under a short feedback loop (Ls=2.5Lf) and a small value of the Kerr-nonlinearity constant.

Fig. 6
Fig. 6

Dynamic regime of SBS in the case of an acoustic-antiwaveguide fiber with a core radius r0=1.5 µm in the case of constant pumping.

Fig. 7
Fig. 7

Evolution to steady state of SBS in the case of an acoustic-waveguide fiber.

Equations (12)

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

z+1vtE1+ΓeE1+iβ(|E1|2+2|E2|2)E1
=-α1E2U×f2(ρ),
-z+1vtE2+ΓeE2+iβ(2|E1|2+|E2|2)E2
=α1E1U*×f2(ρ),
t+Γs0+i2Ω[s2(ρ)K2-Ω2]+i2Ωs2(ρ)ΔU
=α3f2(ρ)×E1E2*,
z+1vtE1+ΓeE1+iβ(|E1|2+2|E2|2)E1
=-α1nE2AnSn,
-z+1vtE2+ΓeE2+iβ(2|E1|2+|E2|2)E2
=α1nE1An*Sn,
t+Γs0+ig0[(Knr0)2-(Kr0)2]An=α3E1E2*Sn,
U(z, ρ, t)=nAn(z, t)φn(ρ).

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