Abstract

We study theoretically and experimentally the spectral properties of low-frequency transmitted intensity noise induced by stimulated Brillouin scattering in optical fibers. In fibers with a length of 25 km the Brillouin scattering induces transmitted intensity noise with a bandwidth on the order of tens of kHz. The power spectral density of the noise can be stronger than the shot noise in the photo-detector even when the optical power is significantly lower than the Brillouin threshold. The low-frequency transmitted intensity noise is caused due to depletion of the pump wave by the stochastic Brillouin wave. Since pump depletion occurs over a long distance, noise with a narrow bandwidth is generated in the transmitted wave. When the pump power is high enough, the spectrum of the induced noise contains features such as hole at low frequencies and ripples. Good quantitative agreement between theory and experiments is obtained. Low-frequency intensity noise induced by Brillouin scattering may limit the generation of ultra-low noise signals in optoelectronic oscillators and may limit the transfer of ultra-low noise signals in fibers.

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    [CrossRef]
  3. R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and Brillouin scattering,” Appl. Opt. 11, 2489–2494 (1972).
    [CrossRef] [PubMed]
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    [CrossRef]
  5. R. W. Boyd, K. Rzaz̧ewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521 (1990).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. A. A. Fotiadi, R. Kiyan, O. Deparis, P. Mégret, and M. Blondel, “Statistical properties of stimulated Brillouin scattering in single-mode optical fibers above threshold,” Opt. Lett. 27, 83–85 (2002).
    [CrossRef]
  8. L. Stépien, S. Randoux, and J. Zemmouri, “Origin of spectral hole burning in Brillouin fiber amplifiers and generators,” Phys. Rev. A 65, 053812 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  11. X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, and R. M. Derosier, “Stimulated Brillouin threshold dependence on fiber type and uniformity,” IEEE Photon. Technol. Lett. 4, 66–69 (1992).
    [CrossRef]
  12. P. A. Williams, W. C. Swann, and N. R. Newbury, “High-stability transfer of an optical frequency over long fiber-optic links,” J. Opt. Soc. Am. B 25, 1284–1293 (2008).
    [CrossRef]
  13. X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13, 1725–1735 (1996).
    [CrossRef]
  14. C. W. Nelson, A. Hati, D. A. Howe, and W. Zhou, “Microwave optoelectronic oscillator with optical gain,” in Proc. IEEE Frequency Control Symp., pp. 1014–1019 (May2007).
  15. C. W. Nelson, A. Hati, and D. A. Howe, “Relative intensity noise suppression for RF photonic links,” IEEE Photon. Technol. Lett. 20, 1542–1544 (2008).
    [CrossRef]
  16. D. Eliyahu, D. Seidel, and L. Maleki, “RF amplitude and phase-noise reduction of an optical link and an opto-electronic oscillator,” IEEE Trans. Microwave Theory Tech. 56, 449–456 (2008).
    [CrossRef]
  17. M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” IEEE J. Lightwave Technol. 12, 585–590 (1994).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  20. R. B. Jenkins, R. M. Sova, and R. I. Joseph, “Steady-state noise analysis of spontaneous and stimulated Brillouin scattering in optical fibers,” IEEE J. Lightwave Technol. 25, 763–770 (2007).
    [CrossRef]
  21. C. J. Misas, P. Petropoulos, and D. J. Richardson, “Slowing of pulses to c/10 with subwatt power levels and low latency using Brillouin amplification in a bismuth-oxide optical fiber,” IEEE J. Lightwave Technol. 25, 216–221 (2007).
    [CrossRef]
  22. M. Nikles, L. Thevenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” IEEE J. Lightwave Technol. 15, 1842–1851 (1997).
    [CrossRef]
  23. V. Lanticq, S. Jiang, R. Gabet, Y. Jaouën, F. Taillade, G. Moreau, and G. P. Agrawal, “Self-referenced and single-ended method to measure Brillouin gain in monomode optical fibers,” Opt. Lett. 34, 1018–1020 (2009).
    [CrossRef] [PubMed]
  24. P. D. Dragic, “Simplified model for effect of Ge doping on silica fibre acoustic properties,” Electron. Lett. 45, 256–257 (2009).
    [CrossRef]
  25. J. H. Mathews and K. D. Fink, Numerical Methods Using MATLAB, 3rd ed., (Prentice Hall, 1999), Chap. 9.
  26. M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).
    [CrossRef]
  27. V. I. Kovalev and R. G. Harrison, “Observation of inhomogeneous spectral broadening of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. Lett. 85, 1879–1882 (2000).
    [CrossRef] [PubMed]

2009 (2)

2008 (4)

P. A. Williams, W. C. Swann, and N. R. Newbury, “High-stability transfer of an optical frequency over long fiber-optic links,” J. Opt. Soc. Am. B 25, 1284–1293 (2008).
[CrossRef]

C. W. Nelson, A. Hati, and D. A. Howe, “Relative intensity noise suppression for RF photonic links,” IEEE Photon. Technol. Lett. 20, 1542–1544 (2008).
[CrossRef]

D. Eliyahu, D. Seidel, and L. Maleki, “RF amplitude and phase-noise reduction of an optical link and an opto-electronic oscillator,” IEEE Trans. Microwave Theory Tech. 56, 449–456 (2008).
[CrossRef]

E. Levy, M. Horowitz, and C. R. Menyuk, “Noise distribution in the radio-frequency spectrum of opto-electronic oscillators,” Opt. Lett. 33, 2883–2885 (2008).
[CrossRef] [PubMed]

2007 (2)

R. B. Jenkins, R. M. Sova, and R. I. Joseph, “Steady-state noise analysis of spontaneous and stimulated Brillouin scattering in optical fibers,” IEEE J. Lightwave Technol. 25, 763–770 (2007).
[CrossRef]

C. J. Misas, P. Petropoulos, and D. J. Richardson, “Slowing of pulses to c/10 with subwatt power levels and low latency using Brillouin amplification in a bismuth-oxide optical fiber,” IEEE J. Lightwave Technol. 25, 216–221 (2007).
[CrossRef]

2002 (2)

A. A. Fotiadi, R. Kiyan, O. Deparis, P. Mégret, and M. Blondel, “Statistical properties of stimulated Brillouin scattering in single-mode optical fibers above threshold,” Opt. Lett. 27, 83–85 (2002).
[CrossRef]

L. Stépien, S. Randoux, and J. Zemmouri, “Origin of spectral hole burning in Brillouin fiber amplifiers and generators,” Phys. Rev. A 65, 053812 (2002).
[CrossRef]

2000 (1)

V. I. Kovalev and R. G. Harrison, “Observation of inhomogeneous spectral broadening of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. Lett. 85, 1879–1882 (2000).
[CrossRef] [PubMed]

1998 (1)

1997 (2)

M. Horowitz, A. R. Chraplyvy, R. W. Tkach, and J. L. Zyskind, “Broad-band transmitted intensity noise induced by Stokes and anti-Stokes Brillouin scattering in single-mode fibers,” IEEE Photon. Technol. Lett. 9, 124–126 (1997).
[CrossRef]

M. Nikles, L. Thevenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” IEEE J. Lightwave Technol. 15, 1842–1851 (1997).
[CrossRef]

1996 (1)

1995 (1)

1994 (1)

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” IEEE J. Lightwave Technol. 12, 585–590 (1994).
[CrossRef]

1992 (1)

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, and R. M. Derosier, “Stimulated Brillouin threshold dependence on fiber type and uniformity,” IEEE Photon. Technol. Lett. 4, 66–69 (1992).
[CrossRef]

1991 (1)

A. L. Gaeta and R. W. Boyd, “Stochastic dynamics of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. A 44, 3205–3209 (1991).
[CrossRef] [PubMed]

1990 (1)

R. W. Boyd, K. Rzaz̧ewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521 (1990).
[CrossRef] [PubMed]

1986 (1)

R. W. Tkach, A. R. Chraplyvy, and R. M. Derosier, “Spontaneous Brillouin scattering for single-mode optical-fibre characterisation,” Electron. Lett. 22, 1011–1013 (1986).
[CrossRef]

1981 (1)

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).
[CrossRef]

1972 (2)

1964 (1)

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, “Stimulated Brillouin Scattering and Coherent Generation of Intense Hypersonic Waves,” Phys. Rev. Lett. 12, 592–595 (1964).
[CrossRef]

Agrawal, G. P.

Blondel, M.

Boot, A. J.

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” IEEE J. Lightwave Technol. 12, 585–590 (1994).
[CrossRef]

Boyd, R. W.

A. L. Gaeta and R. W. Boyd, “Stochastic dynamics of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. A 44, 3205–3209 (1991).
[CrossRef] [PubMed]

R. W. Boyd, K. Rzaz̧ewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521 (1990).
[CrossRef] [PubMed]

Chiao, R. Y.

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, “Stimulated Brillouin Scattering and Coherent Generation of Intense Hypersonic Waves,” Phys. Rev. Lett. 12, 592–595 (1964).
[CrossRef]

Chraplyvy, A. R.

M. Horowitz, A. R. Chraplyvy, R. W. Tkach, and J. L. Zyskind, “Broad-band transmitted intensity noise induced by Stokes and anti-Stokes Brillouin scattering in single-mode fibers,” IEEE Photon. Technol. Lett. 9, 124–126 (1997).
[CrossRef]

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, and R. M. Derosier, “Stimulated Brillouin threshold dependence on fiber type and uniformity,” IEEE Photon. Technol. Lett. 4, 66–69 (1992).
[CrossRef]

R. W. Tkach, A. R. Chraplyvy, and R. M. Derosier, “Spontaneous Brillouin scattering for single-mode optical-fibre characterisation,” Electron. Lett. 22, 1011–1013 (1986).
[CrossRef]

Deparis, O.

Derosier, R. M.

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, and R. M. Derosier, “Stimulated Brillouin threshold dependence on fiber type and uniformity,” IEEE Photon. Technol. Lett. 4, 66–69 (1992).
[CrossRef]

R. W. Tkach, A. R. Chraplyvy, and R. M. Derosier, “Spontaneous Brillouin scattering for single-mode optical-fibre characterisation,” Electron. Lett. 22, 1011–1013 (1986).
[CrossRef]

Dragic, P. D.

P. D. Dragic, “Simplified model for effect of Ge doping on silica fibre acoustic properties,” Electron. Lett. 45, 256–257 (2009).
[CrossRef]

Eliyahu, D.

D. Eliyahu, D. Seidel, and L. Maleki, “RF amplitude and phase-noise reduction of an optical link and an opto-electronic oscillator,” IEEE Trans. Microwave Theory Tech. 56, 449–456 (2008).
[CrossRef]

Fink, K. D.

J. H. Mathews and K. D. Fink, Numerical Methods Using MATLAB, 3rd ed., (Prentice Hall, 1999), Chap. 9.

Fotiadi, A. A.

Frasca, M.

Gabet, R.

Gaeta, A. L.

A. L. Gaeta and R. W. Boyd, “Stochastic dynamics of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. A 44, 3205–3209 (1991).
[CrossRef] [PubMed]

Garavaglia, A.

Harrison, R. G.

V. I. Kovalev and R. G. Harrison, “Observation of inhomogeneous spectral broadening of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. Lett. 85, 1879–1882 (2000).
[CrossRef] [PubMed]

Hati, A.

C. W. Nelson, A. Hati, and D. A. Howe, “Relative intensity noise suppression for RF photonic links,” IEEE Photon. Technol. Lett. 20, 1542–1544 (2008).
[CrossRef]

C. W. Nelson, A. Hati, D. A. Howe, and W. Zhou, “Microwave optoelectronic oscillator with optical gain,” in Proc. IEEE Frequency Control Symp., pp. 1014–1019 (May2007).

Horowitz, M.

E. Levy, M. Horowitz, and C. R. Menyuk, “Noise distribution in the radio-frequency spectrum of opto-electronic oscillators,” Opt. Lett. 33, 2883–2885 (2008).
[CrossRef] [PubMed]

M. Horowitz, A. R. Chraplyvy, R. W. Tkach, and J. L. Zyskind, “Broad-band transmitted intensity noise induced by Stokes and anti-Stokes Brillouin scattering in single-mode fibers,” IEEE Photon. Technol. Lett. 9, 124–126 (1997).
[CrossRef]

Howe, D. A.

C. W. Nelson, A. Hati, and D. A. Howe, “Relative intensity noise suppression for RF photonic links,” IEEE Photon. Technol. Lett. 20, 1542–1544 (2008).
[CrossRef]

C. W. Nelson, A. Hati, D. A. Howe, and W. Zhou, “Microwave optoelectronic oscillator with optical gain,” in Proc. IEEE Frequency Control Symp., pp. 1014–1019 (May2007).

Ippen, E. P.

E. P. Ippen and R. H. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21, 539–541 (1972).
[CrossRef]

Jaouën, Y.

Jenkins, R. B.

R. B. Jenkins, R. M. Sova, and R. I. Joseph, “Steady-state noise analysis of spontaneous and stimulated Brillouin scattering in optical fibers,” IEEE J. Lightwave Technol. 25, 763–770 (2007).
[CrossRef]

Jiang, S.

Jopson, R. M.

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, and R. M. Derosier, “Stimulated Brillouin threshold dependence on fiber type and uniformity,” IEEE Photon. Technol. Lett. 4, 66–69 (1992).
[CrossRef]

Joseph, R. I.

R. B. Jenkins, R. M. Sova, and R. I. Joseph, “Steady-state noise analysis of spontaneous and stimulated Brillouin scattering in optical fibers,” IEEE J. Lightwave Technol. 25, 763–770 (2007).
[CrossRef]

Kikuchi, K.

Kiyan, R.

Kovalev, V. I.

V. I. Kovalev and R. G. Harrison, “Observation of inhomogeneous spectral broadening of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. Lett. 85, 1879–1882 (2000).
[CrossRef] [PubMed]

Lanticq, V.

Levy, E.

Maleki, L.

D. Eliyahu, D. Seidel, and L. Maleki, “RF amplitude and phase-noise reduction of an optical link and an opto-electronic oscillator,” IEEE Trans. Microwave Theory Tech. 56, 449–456 (2008).
[CrossRef]

X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13, 1725–1735 (1996).
[CrossRef]

Mao, X. P.

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, and R. M. Derosier, “Stimulated Brillouin threshold dependence on fiber type and uniformity,” IEEE Photon. Technol. Lett. 4, 66–69 (1992).
[CrossRef]

Martinelli, M.

Mathews, J. H.

J. H. Mathews and K. D. Fink, Numerical Methods Using MATLAB, 3rd ed., (Prentice Hall, 1999), Chap. 9.

Mégret, P.

Melloni, A.

Menyuk, C. R.

Misas, C. J.

C. J. Misas, P. Petropoulos, and D. J. Richardson, “Slowing of pulses to c/10 with subwatt power levels and low latency using Brillouin amplification in a bismuth-oxide optical fiber,” IEEE J. Lightwave Technol. 25, 216–221 (2007).
[CrossRef]

Moreau, G.

Mostowski, J.

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).
[CrossRef]

Narum, P.

R. W. Boyd, K. Rzaz̧ewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521 (1990).
[CrossRef] [PubMed]

Nelson, C. W.

C. W. Nelson, A. Hati, and D. A. Howe, “Relative intensity noise suppression for RF photonic links,” IEEE Photon. Technol. Lett. 20, 1542–1544 (2008).
[CrossRef]

C. W. Nelson, A. Hati, D. A. Howe, and W. Zhou, “Microwave optoelectronic oscillator with optical gain,” in Proc. IEEE Frequency Control Symp., pp. 1014–1019 (May2007).

Newbury, N. R.

Nikles, M.

M. Nikles, L. Thevenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” IEEE J. Lightwave Technol. 15, 1842–1851 (1997).
[CrossRef]

Petropoulos, P.

C. J. Misas, P. Petropoulos, and D. J. Richardson, “Slowing of pulses to c/10 with subwatt power levels and low latency using Brillouin amplification in a bismuth-oxide optical fiber,” IEEE J. Lightwave Technol. 25, 216–221 (2007).
[CrossRef]

Randoux, S.

L. Stépien, S. Randoux, and J. Zemmouri, “Origin of spectral hole burning in Brillouin fiber amplifiers and generators,” Phys. Rev. A 65, 053812 (2002).
[CrossRef]

Raymer, M. G.

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).
[CrossRef]

Richardson, D. J.

C. J. Misas, P. Petropoulos, and D. J. Richardson, “Slowing of pulses to c/10 with subwatt power levels and low latency using Brillouin amplification in a bismuth-oxide optical fiber,” IEEE J. Lightwave Technol. 25, 216–221 (2007).
[CrossRef]

Robert, P. A.

M. Nikles, L. Thevenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” IEEE J. Lightwave Technol. 15, 1842–1851 (1997).
[CrossRef]

Rzaz¸ewski, K.

R. W. Boyd, K. Rzaz̧ewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521 (1990).
[CrossRef] [PubMed]

Seidel, D.

D. Eliyahu, D. Seidel, and L. Maleki, “RF amplitude and phase-noise reduction of an optical link and an opto-electronic oscillator,” IEEE Trans. Microwave Theory Tech. 56, 449–456 (2008).
[CrossRef]

Smith, R. G.

Sova, R. M.

R. B. Jenkins, R. M. Sova, and R. I. Joseph, “Steady-state noise analysis of spontaneous and stimulated Brillouin scattering in optical fibers,” IEEE J. Lightwave Technol. 25, 763–770 (2007).
[CrossRef]

Stépien, L.

L. Stépien, S. Randoux, and J. Zemmouri, “Origin of spectral hole burning in Brillouin fiber amplifiers and generators,” Phys. Rev. A 65, 053812 (2002).
[CrossRef]

Stoicheff, B. P.

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, “Stimulated Brillouin Scattering and Coherent Generation of Intense Hypersonic Waves,” Phys. Rev. Lett. 12, 592–595 (1964).
[CrossRef]

Stolen, R. H.

E. P. Ippen and R. H. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21, 539–541 (1972).
[CrossRef]

Swann, W. C.

Taillade, F.

Takushima, Y.

Thevenaz, L.

M. Nikles, L. Thevenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” IEEE J. Lightwave Technol. 15, 1842–1851 (1997).
[CrossRef]

Tkach, R. W.

M. Horowitz, A. R. Chraplyvy, R. W. Tkach, and J. L. Zyskind, “Broad-band transmitted intensity noise induced by Stokes and anti-Stokes Brillouin scattering in single-mode fibers,” IEEE Photon. Technol. Lett. 9, 124–126 (1997).
[CrossRef]

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, and R. M. Derosier, “Stimulated Brillouin threshold dependence on fiber type and uniformity,” IEEE Photon. Technol. Lett. 4, 66–69 (1992).
[CrossRef]

R. W. Tkach, A. R. Chraplyvy, and R. M. Derosier, “Spontaneous Brillouin scattering for single-mode optical-fibre characterisation,” Electron. Lett. 22, 1011–1013 (1986).
[CrossRef]

Tonini, A.

Townes, C. H.

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, “Stimulated Brillouin Scattering and Coherent Generation of Intense Hypersonic Waves,” Phys. Rev. Lett. 12, 592–595 (1964).
[CrossRef]

van Deventer, M. O.

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” IEEE J. Lightwave Technol. 12, 585–590 (1994).
[CrossRef]

Williams, P. A.

Yao, X. S.

Zemmouri, J.

L. Stépien, S. Randoux, and J. Zemmouri, “Origin of spectral hole burning in Brillouin fiber amplifiers and generators,” Phys. Rev. A 65, 053812 (2002).
[CrossRef]

Zhou, W.

C. W. Nelson, A. Hati, D. A. Howe, and W. Zhou, “Microwave optoelectronic oscillator with optical gain,” in Proc. IEEE Frequency Control Symp., pp. 1014–1019 (May2007).

Zyskind, J. L.

M. Horowitz, A. R. Chraplyvy, R. W. Tkach, and J. L. Zyskind, “Broad-band transmitted intensity noise induced by Stokes and anti-Stokes Brillouin scattering in single-mode fibers,” IEEE Photon. Technol. Lett. 9, 124–126 (1997).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

E. P. Ippen and R. H. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21, 539–541 (1972).
[CrossRef]

Electron. Lett. (2)

R. W. Tkach, A. R. Chraplyvy, and R. M. Derosier, “Spontaneous Brillouin scattering for single-mode optical-fibre characterisation,” Electron. Lett. 22, 1011–1013 (1986).
[CrossRef]

P. D. Dragic, “Simplified model for effect of Ge doping on silica fibre acoustic properties,” Electron. Lett. 45, 256–257 (2009).
[CrossRef]

IEEE J. Lightwave Technol. (4)

R. B. Jenkins, R. M. Sova, and R. I. Joseph, “Steady-state noise analysis of spontaneous and stimulated Brillouin scattering in optical fibers,” IEEE J. Lightwave Technol. 25, 763–770 (2007).
[CrossRef]

C. J. Misas, P. Petropoulos, and D. J. Richardson, “Slowing of pulses to c/10 with subwatt power levels and low latency using Brillouin amplification in a bismuth-oxide optical fiber,” IEEE J. Lightwave Technol. 25, 216–221 (2007).
[CrossRef]

M. Nikles, L. Thevenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” IEEE J. Lightwave Technol. 15, 1842–1851 (1997).
[CrossRef]

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” IEEE J. Lightwave Technol. 12, 585–590 (1994).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

C. W. Nelson, A. Hati, and D. A. Howe, “Relative intensity noise suppression for RF photonic links,” IEEE Photon. Technol. Lett. 20, 1542–1544 (2008).
[CrossRef]

M. Horowitz, A. R. Chraplyvy, R. W. Tkach, and J. L. Zyskind, “Broad-band transmitted intensity noise induced by Stokes and anti-Stokes Brillouin scattering in single-mode fibers,” IEEE Photon. Technol. Lett. 9, 124–126 (1997).
[CrossRef]

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, and R. M. Derosier, “Stimulated Brillouin threshold dependence on fiber type and uniformity,” IEEE Photon. Technol. Lett. 4, 66–69 (1992).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

D. Eliyahu, D. Seidel, and L. Maleki, “RF amplitude and phase-noise reduction of an optical link and an opto-electronic oscillator,” IEEE Trans. Microwave Theory Tech. 56, 449–456 (2008).
[CrossRef]

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

Opt. Lett. (5)

Phys. Rev. A (4)

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).
[CrossRef]

L. Stépien, S. Randoux, and J. Zemmouri, “Origin of spectral hole burning in Brillouin fiber amplifiers and generators,” Phys. Rev. A 65, 053812 (2002).
[CrossRef]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

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[CrossRef]

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[CrossRef] [PubMed]

Other (2)

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Figures (9)

Fig. 1
Fig. 1

Calculated average optical power of the transmitted pump wave and the backward propagating Brillouin wave at z = 0 as a function of the incident optical pump power for (a,b) a 25-km long fiber and for (c,d) a 6-km long fiber. The results for the 25-km fiber are compared to experimental results (green-dashed line).

Fig. 2
Fig. 2

RF power spectrum of the transmitted wave (left column) and of the back-reflected Brillouin wave (right column) calculated for a 25-km fiber for different input optical powers: (a) P 0 = 6.6 mW, (b) P 0 = 16.6 mW, and (c) P 0 = 26.3 mW. A fit of a Lorentzian function to the transmitted wave power spectrum is added (black dashed-lines). The Lorentzian bandwidths equal (a) 10 kHz, (b) 20.5 kHz, and (c) 29 kHz.

Fig. 3
Fig. 3

RF power spectrum of the transmitted wave calculated for (a) a fiber with a length of 6 km and input optical powers of 15 mW (red), 20 mW (light blue), 30 mW (black), and 60 mW (green) and (b) calculated for a fiber with a length of 25 km and input optical powers of 6.6 mW (red), 10.5 mW (light blue), 16.6 mW (black), and 26.3 mW (green).

Fig. 4
Fig. 4

Bandwidth of the fitted Lorentzian function (blue dots) as a function of the fiber length. The same small signal Brillouin gain was used for all the fiber lengths: G = gBP 0 L eff/A eff = 31.2 and the ratio between the time-averaged Brillouin power and the input power was equal 0.45 ± 0.01. A linear fit (dashed-red line) shows that the bandwidth is inversely proportional to the fiber length.

Fig. 5
Fig. 5

RF Power spectrum (blue-dashed-line) of the transmitted wave as a function of the input optical power calculated for a 6-km fiber at frequencies (a) 1 kHz, (b) 10 kHz, (c) 17.5 kHz, and (d) 100 kHz. The calculated power spectral density is compared to the shot noise power spectral density (red-solid-line) at the output of the photodetector.

Fig. 6
Fig. 6

(a) Bandwidth of the Lorentzian function that is fitted to the RF power spectrum of the transmitted pump wave (blue line) as a function of the input optical power. The Lorentzian bandwidth is also compared to the relation c/4πnLB (dashed-red line). (b) Buildup length of the backward propagating Brillouin wave, LB , as a function of the input optical power P 0. The fiber length equals 6 km.

Fig. 7
Fig. 7

Experimental setup used for measuring the RF power spectrum of the transmitted pump wave.

Fig. 8
Fig. 8

Comparison between theoretical (blue line) and measured (green line) RF power spectra of the transmitted pump wave in the frequency region of 1 kHz–1 MHz for two input optical powers: (a) P 0 = 16.6 mW, and (b) P 0 = 26.3 mW. The fiber length equals 25 km. The hole in the theoretical spectrum is in a good quantitative agreement with experimental results.

Fig. 9
Fig. 9

Comparison between theoretical (blue line) and measured (green line) RF spectra of the transmitted pump wave in the frequency region of 800 Hz–30 kHz for four input optical powers: (a) P 0 = 10.5 mW, (b) P 0 = 16.6 mW, (c) P 0 = 20.8 mW, and (d) P 0 = 26.3 mW. The fiber length equals 25 km. The ripples in the theoretical power spectrum are in a good agreement with experimental results.

Equations (6)

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E L ( z , t ) z + n c E L ( z , t ) t = α 2 E L ( z , t ) + i κ E S ( z , t ) ρ ( z , t )
E S ( z , t ) z n c E S ( z , t ) t = α 2 E S ( z , t ) i κ E L ( z , t ) ρ * ( z , t )
ρ ( z , t ) t + Γ 2 ρ ( z , t ) = i Λ E L ( z , t ) E S * ( z , t ) + f ( z , t ) ,
S R F = 2 R τ | 0 τ v ( t ) exp ( 2 π i f t ) d t | 2 ,
g B = 8 κ Λ ε 0 cn Γ = γ 2 ω 2 n V A c 3 ρ 0 Γ .
S RF ( f ) R η 2 P S 2 1 + ( 4 π n f A e f f / P 0 g B c ) 2 ,

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