## Low-frequency transmitted intensity noise induced by stimulated Brillouin scattering in optical fibers |

Optics Express, Vol. 19, Issue 12, pp. 11792-11803 (2011)

http://dx.doi.org/10.1364/OE.19.011792

Acrobat PDF (1707 KB)

### 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.

© 2011 OSA

## 1. Introduction

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]

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

4. 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]

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

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]

10. 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]

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

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

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]

9. Y. Takushima and K. Kikuchi, “Spectral gain hole burning and modulation instability in a Brillouin fiber amplifier,” Opt. Lett. **20**, 34–36 (1995). [CrossRef] [PubMed]

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]

10. 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]

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]

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]

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]

## 2. Theoretical model

**42**, 5514–5521 (1990). [CrossRef] [PubMed]

6. 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]

*e*(

*z,t*) =

*e*(

_{L}*z,t*) +

*e*(

_{S}*z,t*), where

*e*(

_{L}*z,t*) = 1/2{

*E*(

_{L}*z,t*) exp(

*k*) + c.c.} is the field of the forward propagating pump wave,

_{L}z – iω_{L}t*e*(

_{S}*z,t*) = 1/2{

*E*(

_{S}*z,t*) exp(−

*k*) + c.c.} is the field of the backward propagating Brillouin wave,

_{S}z – iω_{S}t*z*is the location along the fiber,

*t*is the time,

*E*(

_{L}*z,t*) and

*E*(

_{S}*z,t*) are the complex envelopes of the forward propagating pump wave and the backward propagating Brillouin wave, respectively,

*ω*and

_{L}*k*are the carrier frequency and the wavenumber of the pump wave, and

_{L}*ω*and

_{S}*k*are the carrier frequency and the wavenumber of the Brillouin wave. The propagation equations equal [5

_{S}**42**, 5514–5521 (1990). [CrossRef] [PubMed]

*ρ*(

*z,t*) is the complex envelope of the density variation,

*c*is the light velocity in vacuum,

*n*is the refractive index,

*α*is the absorption coefficient of the fiber,

*κ*and Λ are the Brillouin coupling coefficients, Γ is the phonon decay rate, and

*f*(

*z,t*) represents the thermal fluctuations of the medium density that initiates the spontaneous Brillouin scattering. We assume that

*f*(

*z,t*) is a white Gaussian noise with zero mean and with no correlation in both time and space such that <

*f*(

*z,t*)

*f*(

^{*}*z′*,

*t′*) >=

*Qδ*(

*z – z′*)

*δ*(

*t – t′*), where

*δ*is Dirac delta function,

*k*is Boltzmann constant,

_{B}*T*is the temperature,

*V*is the velocity of sound in the fiber,

_{A}*ρ*

_{0}is the average density, and

*A*

_{eff}is the effective area of the fiber. Polarization effect reduces the effective Brillouin coefficient [17

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]

*I*(

*z,t*) =

*ε*

_{0}

*cn*|

*E*(

*z,t*)|

^{2}/2, where

*ε*

_{0}is the vacuum permittivity. To calculate the transmitted RF power spectrum we assume that the output voltage equals

*v*(

*t*) =

*ηI*(

*z*=

*L,t*)

*A*

_{eff}

*R*where

*R*=50 Ω is the load impedance,

*L*is the fiber length,

*η*is the responsivity of the photodetector, and

*A*

_{eff}is the effective area of the fiber. The power spectral density of the noise is calculated by: where

*τ*is the duration of the simulated signal and

*f*is the RF frequency. The spectrum in Eq. (2) was multiplied by a factor of two since we calculate the one-sided spectrum. We note that since

*τ*is finite we actually calculate the periodogram and not the power spectral density. The periodogram is only an estimation of the power spectral density and it contains additional small fluctuations. Similar fluctuations are also obtained in experiments due to the finite duration of the measurement [18

18. 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]

*λ*= 1.55

*μ*m. Therefore, we used in our simulations the parameters for that fiber that were measured in previous works. We assume

*A*

_{eff}= 80

*μ*m

^{2}and

*n*= 1.45. The measured attenuation in our fiber equals

*α*= 0.25 dB/km. The Brillouin parameter Λ was calculated by using the equation Λ =

*γq*

^{2}

*ε*

_{0}/4Ω, where

*q*is the acoustic wave number,

*q*≃ 2

*ωn/c*, Ω is the acoustic frequency, and

*γ*= 0.902 is the elctrostrictive constant [19

19. A. Melloni, M. Frasca, A. Garavaglia, A. Tonini, and M. Martinelli, “Direct measurement of electrostriction in optical fibers,” Opt. Lett. **23**, 691–693 (1998). [CrossRef]

*κ*was calculated from the Brillouin gain coefficient

*g*[5

_{B}**42**, 5514–5521 (1990). [CrossRef] [PubMed]

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]

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]

*g*= 1.3 · 10

_{B}^{−11}m/W [21

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]

*g*= 2.6 · 10

_{B}^{−11}m/W [22

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]

*g*= 1.68 · 10

_{B}^{−11}m/W was measured in Ref. [23

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]

*g*= (1.68 · 10

_{B}^{−11}/

*M*) m/W. We also assumed

*ρ*

_{0}= 2210 kg/m

^{3}and

*V*= 5800 m/s [24

_{a}24. P. D. Dragic, “Simplified model for effect of Ge doping on silica fibre acoustic properties,” Electron. Lett. **45**, 256–257 (2009). [CrossRef]

*Q*. The phonon decay rate was set to Γ/(2

*π*) = 30 MHz as in [24

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

*η*= 1 A/W and the load impedance to

*R*= 50Ω.

*z*= 1 m and a temporal step size Δ

*t*= Δ

*zn/c*. In each step, the pump and the backward Brillouin wave were propagated in opposite directions. We used the following boundary conditions:

*E*(

_{S}*z*=

*L,t*) = 0, where

*P*

_{0}is the input optical power of the pump wave. At the beginning of the simulation we assumed that

*E*(

_{S}*z,t*< 0) = 0. The spectrum calculation was performed on the calculated data that was obtained after a duration that corresponds to 10 roundtrips in the fiber in order to ensure that initial conditions do not significantly affect the results. High accuracy of the simulation requires a sufficient small step size. We checked that by taking smaller step sizes than Δ

*z*= 1 m, we did not obtain a significant change in the calculated spectrum. The results of the simulation were also in good agreement with the steady state solution for the spatial dependence of the pump and the Brillouin wave intensities [20

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]

*f*= 30 Hz.

*z*= 0 as a function of the input power for a fiber with a 25 km length and for a fiber with a 6 km length. The results were calculated by solving numerically Eq. (1) and performing a time average of the optical powers for a period of 34 ms. To verify the results we measured the power of the transmitted pump and the backward propagating Brillouin wave for the 25-km long fiber by using our experimental setup that is described in the next session. The experimental results (green-dashed line) are in a very good agreement with the simulation results (blue-solid line). We define the SBS threshold as the input optical pump power

*P*

_{th}that gives a Brillouin wave with a power of 1%

*P*

_{th}at the input of the fiber (

*z*= 0). The threshold for the 25-km and the 6-km fibers was 4.2 mW (6.2 dBm) and 11.5 mW (10.6 dBm), respectively. The results shown in Fig. 1 are also in a very good quantitative agreement with the steady state solution given in Ref. [20

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]

*F*(

*f*) =

*F*

_{0}/[1 + (

*f / f*

_{0})]

^{2}, where the parameters

*F*

_{0}and

*f*

_{0}were extracted to obtain the best fit to the calculated spectra. The comparison shows that above a certain frequency, on the order of few tens of kHz, the power spectrum can be approximated by a Lorentzian function. The bandwidth

*f*

_{0}of the fitted Lorentzian equals

*f*

_{0}=10, 20.5, and 29 kHz for input optical powers of 6.6, 16.6, and 26.3 mW, respectively. Therefore, the bandwidth of the power spectrum becomes wider as the input power increases. The power spectrum of the transmitted wave is also significantly narrower than that of the back-reflected Brillouin wave. Figure 3 shows the transmitted RF spectra for different input optical powers for a fiber with a length of 6 km and for a fiber with a length of 25 km. We note that higher frequency noise components in the frequency region on the order of hundreds of MHz are also obtained due to double scattering process that is based on both stimulated and thermally excited phonons [10

10. 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]

*G*=

*g*

_{B}P_{0}

*L*

_{eff}

*/A*

_{eff}= 31.2, where

*L*

_{eff}= [1 − exp(−

*αL*)]

*/α*is the effective fiber length. The ratio between the time-averaged Brillouin power at z=0 and the input power was equal 0.45 ± 0.01 for all the fiber lengths. The figure shows that the bandwidth of the transmitted spectrum is inversely proportional to the fiber length. When the fiber length is about 18 km, the Lorentzian bandwidth decreases to 42 kHz compared to 90 kHz for a fiber with a length of 6 km. The decrease is obtained since in long fibers the pump depletion occurs over longer distances.

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]

**65**, 053812 (2002). [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]

**65**, 053812 (2002). [CrossRef]

*L*≳ 1 km), the hole in the transmitted wave power spectrum is narrower than that obtained in the spectrum of the Brillouin wave as shown in Fig. 2. We note that the hole can be observed at an input power that is close to the Brillouin threshold. For example, for the 6-km fiber, a 5-dB hole can be clearly observed in Fig. 3 for an input power of 15 mW. At this input power the ratio between the reflected Brillouin power and the input power equals only 6 %. The spectral hole in both the reflected and the transmitted waves was obtained by solving Eqs. (1). These equations do not contain inhomogeneous spectral broadening, as suggested in [27

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]

*c/*2

*nL*, of 17.1 kHz for the 6-km fiber and 4.1 kHz for the 25-km fiber as was also previously obtained for the backward Brillouin wave [8

**65**, 053812 (2002). [CrossRef]

9. Y. Takushima and K. Kikuchi, “Spectral gain hole burning and modulation instability in a Brillouin fiber amplifier,” Opt. Lett. **20**, 34–36 (1995). [CrossRef] [PubMed]

*S*

_{SN}= 2

*i*

_{av}

*q*, where

_{e}R*i*

_{av}is the average photodetector current,

*R*= 50Ω is the load resistance, and

*q*is the electron charge. The figure shows that the noise induced by Brillouin effect is stronger than the shot noise even when the input optical power is significantly lower than the 1% optical threshold power for the 6-km fiber,

_{e}*P*

_{th}= 11.5 mW. However, at such low input power, noise sources that are not included in Eq. (1) such as Rayleigh scattering or noise generated by the laser can be the dominant sources of noise in the system. Due to the spectral hole in the noise spectrum the noise induced by SBS in lower frequencies might be smaller than the noise in higher frequencies. For example, the noise power spectral density at 1 kHz equals −83 dBm/HZ while the noise power spectral density at 10 kHz equals −77 dBm/Hz for an optical pump power of 20 mW. At 17.5 kHz, the ripple in the spectrum significantly increases the noise at sufficient power (≳ 17 mW).

**42**, 5514–5521 (1990). [CrossRef] [PubMed]

*I*(

*z*) =

*I*(

*z*= 0) exp(−

*z/L*) where

_{B}*L*is defined as the buildup length of the Brillouin wave. Figure 6(b) shows the buildup length of the Brillouin wave that was extracted from the numerical simulation as a function of the input optical power. At lower powers (

_{B}*P*< 12 dBm) the buildup length approximately equals to the result obtained under the undepleted pump approximation,

*A*

_{eff}

*/g*

_{B}P_{0}[5

**42**, 5514–5521 (1990). [CrossRef] [PubMed]

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]

*L*. Note that a factor of two was added since the pump and the Brillouin wave propagate at opposite directions. Hence, at frequencies where the hole and the ripples do not affect the spectrum, the transmitted noise spectrum is approximately Lorentzian with a bandwidth of

_{B}n/c*BW*=

*c/*4

*πnL*. Figure 6(a) compares the relation

_{B}*BW*=

*c/*4

*πnL*to the bandwidth of the Lorentzian function that was extracted from the results of the numerical simulations. The figure shows that the relation is valid for input power of about 7–60 mW. At higher input optical powers the pump depletion becomes significant and the assumptions that yield the approximate mathematical relation become inaccurate.

_{B}*g*

_{B}I_{L}L_{eff}≫ 1, (b) pump depletion can be neglected, (c) the power of the transmitted noise is very small in compare with the average pump power, (d) the bandwidth of the Brillouin wave is significantly broader than the bandwidth of the transmitted noise, (e) the hole and the ripples in the spectrum can be neglected, and (f) the loss in the fiber is small such that

**42**, 5514–5521 (1990). [CrossRef] [PubMed]

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]

*P*is the Brillouin wave power at the fiber entrance (

_{S}*z*= 0). We note that since the pump and Brillouin wave propagate at opposite directions, noise with a frequency

*f*in the Brillouin wave causes a depletion at a frequency

*f*/2 in the pump wave. A detailed description of the model will be given elsewhere. A comparison between the reduced model and the results of the numerical simulation shows that for the 6-km fiber at power above 15 mW the RF spectrum is strongly affected by the hole and the reduced model becomes inaccurate at low frequencies. For example, at an input power of 15 mW the ratio between

*P*

_{s}/P_{0}= 6 % and the hole reduces the spectrum power density by about 5-dB. At low input power, below 9 mW, the assumption of an exponential buildup of the Brillouin wave becomes inaccurate. Therefore, the reduced model is accurate at the power region of 9 to 15 mW. At higher frequencies (

*f*≳ 50 kHz) that are not around the ripples in the spectrum, a very good agreement between the reduced model and the numerical results is obtained over a broader power region of 9–25 mW. In this frequency region the hole does not affect the spectrum.

## 3. Experimental results

*μ*m, was injected into a 25-km of standard fiber (Corning SMF-28). The laser power was controlled by using an optical attenuator and not by changing the laser current in order not to change the laser characteristics as a function of the power. The transmitted wave was measured by an RF spectrum analyzer that was connected to a photodetector. When the spectrum of the transmitted wave was measured, optical isolators were fused to both ends of the fiber to prevent back-reflections. Such back-reflections may increase the amplitude of the ripples in the spectrum [8

**65**, 053812 (2002). [CrossRef]

## 4. Conclusions

## Acknowledgments

## References and links

1. | R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, “Stimulated Brillouin Scattering and Coherent Generation of Intense Hypersonic Waves,” Phys. Rev. Lett. |

2. | E. P. Ippen and R. H. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. |

3. | R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and Brillouin scattering,” Appl. Opt. |

4. | R. W. Tkach, A. R. Chraplyvy, and R. M. Derosier, “Spontaneous Brillouin scattering for single-mode optical-fibre characterisation,” Electron. Lett. |

5. | R. W. Boyd, K. Rzaz̧ewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A |

6. | A. L. Gaeta and R. W. Boyd, “Stochastic dynamics of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. A |

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. |

8. | L. Stépien, S. Randoux, and J. Zemmouri, “Origin of spectral hole burning in Brillouin fiber amplifiers and generators,” Phys. Rev. A |

9. | Y. Takushima and K. Kikuchi, “Spectral gain hole burning and modulation instability in a Brillouin fiber amplifier,” Opt. Lett. |

10. | 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. |

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. |

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 |

13. | X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B |

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. |

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. |

17. | M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” IEEE J. Lightwave Technol. |

18. | E. Levy, M. Horowitz, and C. R. Menyuk, “Noise distribution in the radio-frequency spectrum of opto-electronic oscillators,” Opt. Lett. |

19. | A. Melloni, M. Frasca, A. Garavaglia, A. Tonini, and M. Martinelli, “Direct measurement of electrostriction in optical fibers,” Opt. Lett. |

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. |

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. |

22. | M. Nikles, L. Thevenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” IEEE J. Lightwave Technol. |

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. |

24. | P. D. Dragic, “Simplified model for effect of Ge doping on silica fibre acoustic properties,” Electron. Lett. |

25. | J. H. Mathews and K. D. Fink, |

26. | M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A |

27. | V. I. Kovalev and R. G. Harrison, “Observation of inhomogeneous spectral broadening of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. Lett. |

**OCIS Codes**

(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

(270.2500) Quantum optics : Fluctuations, relaxations, and noise

(290.5900) Scattering : Scattering, stimulated Brillouin

(350.5500) Other areas of optics : Propagation

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: March 16, 2011

Revised Manuscript: May 12, 2011

Manuscript Accepted: May 12, 2011

Published: June 2, 2011

**Citation**

Asaf David and Moshe Horowitz, "Low-frequency transmitted intensity noise induced by stimulated Brillouin scattering in optical fibers," Opt. Express **19**, 11792-11803 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-12-11792

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### References

- 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]
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