Abstract

Spontaneous Brillouin backscattering, which accompanies the operation of Brillouin dynamic gratings (BDGs) setups, is investigated both theoretically and experimentally. It is shown that this noisy emission, which cannot be separated from the signal of interest, contains not only the probe spontaneous Brillouin backscattering but also a significant contribution from the spontaneous/stimulated acoustic field, originating from the high-frequency writing pump. In the absence of the low-frequency writing pump and for a strong enough high-frequency writing pump, the observed Stokes noise can exhibit an average backscattered power much higher than that from the probe alone.

© 2013 Optical Society of America

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References

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  1. W. Zou, Z. He, and K. Hotate, IEEE Photon. Technol. Lett. 22, 52 (2010).
  2. S. Chin, N. Primerov, and L. Thévenaz, IEEE Sens. J. 12, 189 (2012).
    [CrossRef]
  3. Y. Antman, N. Primerov, J. Sancho, L. Thevenaz, and A. Zadok, Opt. Express 20, 7807 (2012).
    [CrossRef]
  4. Y. Dong, L. Chen, and X. Bao, Opt. Lett. 35, 193 (2010).
    [CrossRef]
  5. K. Y. Song, K. Lee, and S. B. Lee, Opt. Express 17, 10344 (2009).
    [CrossRef]
  6. N. Primerov, S. Chin, K. Y. Song, and L. Thévenaz, Optical Fiber Communication Conference (Optical Society of America, 2010), paper OWF6.
  7. S. H. Chin, N. Primerov, K. Y. Song, L. Thévenaz, M. Santagiustina, and L. Ursini, Proceedings of Nonlinear Photonics (Optical Society of America, 2010), paper NThA6.
  8. N. Primerov, S. Chin, L. Thévenaz, L. Ursini, and M. Santagiustina, Proceedings of the Slow and Fast Light 2011 Topical Meeting (Optical Society of America, 2011), paper SLMA3.
  9. J. Sancho, N. Primerov, S. Chin, Y. Antman, A. Zadok, S. Sales, and L. Thévenaz, Opt. Express 20, 6157 (2012).
    [CrossRef]
  10. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).
  11. K. Y. Song, W. Zou, Z. He, and K. Hotate, Opt. Lett. 33, 926 (2008).
    [CrossRef]
  12. D. P. Zhou, Y. Dong, L. Chen, and X. Bao, Opt. Express 19, 20785 (2011).
    [CrossRef]
  13. R. W. Boyd, K. Rzazewski, and P. Narum, Phys. Rev. A 42, 5514 (1990).
    [CrossRef]
  14. A. L. Gaeta and R. W. Boyd, Phys. Rev. A 44, 3205 (1991).
    [CrossRef]
  15. R. B. Jenkins, R. M. Sova, and R. I. Joseph, IEEE J. Lightwave Technol. 25, 763 (2007).
    [CrossRef]
  16. L. Yaron, Y. Peled, T. Langer, and M. Tur, Proc. SPIE 8421, 84211L (2012).
    [CrossRef]

2012 (4)

2011 (1)

2010 (2)

Y. Dong, L. Chen, and X. Bao, Opt. Lett. 35, 193 (2010).
[CrossRef]

W. Zou, Z. He, and K. Hotate, IEEE Photon. Technol. Lett. 22, 52 (2010).

2009 (1)

2008 (1)

2007 (1)

R. B. Jenkins, R. M. Sova, and R. I. Joseph, IEEE J. Lightwave Technol. 25, 763 (2007).
[CrossRef]

1991 (1)

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

1990 (1)

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

Antman, Y.

Bao, X.

Boyd, R. W.

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

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

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

Chen, L.

Chin, S.

S. Chin, N. Primerov, and L. Thévenaz, IEEE Sens. J. 12, 189 (2012).
[CrossRef]

J. Sancho, N. Primerov, S. Chin, Y. Antman, A. Zadok, S. Sales, and L. Thévenaz, Opt. Express 20, 6157 (2012).
[CrossRef]

N. Primerov, S. Chin, K. Y. Song, and L. Thévenaz, Optical Fiber Communication Conference (Optical Society of America, 2010), paper OWF6.

N. Primerov, S. Chin, L. Thévenaz, L. Ursini, and M. Santagiustina, Proceedings of the Slow and Fast Light 2011 Topical Meeting (Optical Society of America, 2011), paper SLMA3.

Chin, S. H.

S. H. Chin, N. Primerov, K. Y. Song, L. Thévenaz, M. Santagiustina, and L. Ursini, Proceedings of Nonlinear Photonics (Optical Society of America, 2010), paper NThA6.

Dong, Y.

Gaeta, A. L.

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

He, Z.

W. Zou, Z. He, and K. Hotate, IEEE Photon. Technol. Lett. 22, 52 (2010).

K. Y. Song, W. Zou, Z. He, and K. Hotate, Opt. Lett. 33, 926 (2008).
[CrossRef]

Hotate, K.

W. Zou, Z. He, and K. Hotate, IEEE Photon. Technol. Lett. 22, 52 (2010).

K. Y. Song, W. Zou, Z. He, and K. Hotate, Opt. Lett. 33, 926 (2008).
[CrossRef]

Jenkins, R. B.

R. B. Jenkins, R. M. Sova, and R. I. Joseph, IEEE J. Lightwave Technol. 25, 763 (2007).
[CrossRef]

Joseph, R. I.

R. B. Jenkins, R. M. Sova, and R. I. Joseph, IEEE J. Lightwave Technol. 25, 763 (2007).
[CrossRef]

Langer, T.

L. Yaron, Y. Peled, T. Langer, and M. Tur, Proc. SPIE 8421, 84211L (2012).
[CrossRef]

Lee, K.

Lee, S. B.

Narum, P.

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

Peled, Y.

L. Yaron, Y. Peled, T. Langer, and M. Tur, Proc. SPIE 8421, 84211L (2012).
[CrossRef]

Primerov, N.

S. Chin, N. Primerov, and L. Thévenaz, IEEE Sens. J. 12, 189 (2012).
[CrossRef]

Y. Antman, N. Primerov, J. Sancho, L. Thevenaz, and A. Zadok, Opt. Express 20, 7807 (2012).
[CrossRef]

J. Sancho, N. Primerov, S. Chin, Y. Antman, A. Zadok, S. Sales, and L. Thévenaz, Opt. Express 20, 6157 (2012).
[CrossRef]

S. H. Chin, N. Primerov, K. Y. Song, L. Thévenaz, M. Santagiustina, and L. Ursini, Proceedings of Nonlinear Photonics (Optical Society of America, 2010), paper NThA6.

N. Primerov, S. Chin, L. Thévenaz, L. Ursini, and M. Santagiustina, Proceedings of the Slow and Fast Light 2011 Topical Meeting (Optical Society of America, 2011), paper SLMA3.

N. Primerov, S. Chin, K. Y. Song, and L. Thévenaz, Optical Fiber Communication Conference (Optical Society of America, 2010), paper OWF6.

Rzazewski, K.

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

Sales, S.

Sancho, J.

Santagiustina, M.

S. H. Chin, N. Primerov, K. Y. Song, L. Thévenaz, M. Santagiustina, and L. Ursini, Proceedings of Nonlinear Photonics (Optical Society of America, 2010), paper NThA6.

N. Primerov, S. Chin, L. Thévenaz, L. Ursini, and M. Santagiustina, Proceedings of the Slow and Fast Light 2011 Topical Meeting (Optical Society of America, 2011), paper SLMA3.

Song, K. Y.

K. Y. Song, K. Lee, and S. B. Lee, Opt. Express 17, 10344 (2009).
[CrossRef]

K. Y. Song, W. Zou, Z. He, and K. Hotate, Opt. Lett. 33, 926 (2008).
[CrossRef]

N. Primerov, S. Chin, K. Y. Song, and L. Thévenaz, Optical Fiber Communication Conference (Optical Society of America, 2010), paper OWF6.

S. H. Chin, N. Primerov, K. Y. Song, L. Thévenaz, M. Santagiustina, and L. Ursini, Proceedings of Nonlinear Photonics (Optical Society of America, 2010), paper NThA6.

Sova, R. M.

R. B. Jenkins, R. M. Sova, and R. I. Joseph, IEEE J. Lightwave Technol. 25, 763 (2007).
[CrossRef]

Thevenaz, L.

Thévenaz, L.

J. Sancho, N. Primerov, S. Chin, Y. Antman, A. Zadok, S. Sales, and L. Thévenaz, Opt. Express 20, 6157 (2012).
[CrossRef]

S. Chin, N. Primerov, and L. Thévenaz, IEEE Sens. J. 12, 189 (2012).
[CrossRef]

S. H. Chin, N. Primerov, K. Y. Song, L. Thévenaz, M. Santagiustina, and L. Ursini, Proceedings of Nonlinear Photonics (Optical Society of America, 2010), paper NThA6.

N. Primerov, S. Chin, K. Y. Song, and L. Thévenaz, Optical Fiber Communication Conference (Optical Society of America, 2010), paper OWF6.

N. Primerov, S. Chin, L. Thévenaz, L. Ursini, and M. Santagiustina, Proceedings of the Slow and Fast Light 2011 Topical Meeting (Optical Society of America, 2011), paper SLMA3.

Tur, M.

L. Yaron, Y. Peled, T. Langer, and M. Tur, Proc. SPIE 8421, 84211L (2012).
[CrossRef]

Ursini, L.

S. H. Chin, N. Primerov, K. Y. Song, L. Thévenaz, M. Santagiustina, and L. Ursini, Proceedings of Nonlinear Photonics (Optical Society of America, 2010), paper NThA6.

N. Primerov, S. Chin, L. Thévenaz, L. Ursini, and M. Santagiustina, Proceedings of the Slow and Fast Light 2011 Topical Meeting (Optical Society of America, 2011), paper SLMA3.

Yaron, L.

L. Yaron, Y. Peled, T. Langer, and M. Tur, Proc. SPIE 8421, 84211L (2012).
[CrossRef]

Zadok, A.

Zhou, D. P.

Zou, W.

W. Zou, Z. He, and K. Hotate, IEEE Photon. Technol. Lett. 22, 52 (2010).

K. Y. Song, W. Zou, Z. He, and K. Hotate, Opt. Lett. 33, 926 (2008).
[CrossRef]

IEEE J. Lightwave Technol. (1)

R. B. Jenkins, R. M. Sova, and R. I. Joseph, IEEE J. Lightwave Technol. 25, 763 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

W. Zou, Z. He, and K. Hotate, IEEE Photon. Technol. Lett. 22, 52 (2010).

IEEE Sens. J. (1)

S. Chin, N. Primerov, and L. Thévenaz, IEEE Sens. J. 12, 189 (2012).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. A (2)

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

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

Proc. SPIE (1)

L. Yaron, Y. Peled, T. Langer, and M. Tur, Proc. SPIE 8421, 84211L (2012).
[CrossRef]

Other (4)

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

N. Primerov, S. Chin, K. Y. Song, and L. Thévenaz, Optical Fiber Communication Conference (Optical Society of America, 2010), paper OWF6.

S. H. Chin, N. Primerov, K. Y. Song, L. Thévenaz, M. Santagiustina, and L. Ursini, Proceedings of Nonlinear Photonics (Optical Society of America, 2010), paper NThA6.

N. Primerov, S. Chin, L. Thévenaz, L. Ursini, and M. Santagiustina, Proceedings of the Slow and Fast Light 2011 Topical Meeting (Optical Society of America, 2011), paper SLMA3.

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Figures (5)

Fig. 1.
Fig. 1.

Generation of a BDG by two counterpropagating vertically polarized pumps, PumpH and PumpL, with νPumpH>νPumpL. The resulting longitudinal acoustic wave acts as a refractive index grating for the horizontally polarized Probe, reflecting it into a horizontally polarized ProbeR, which also contains spontaneous Brillouin backscattered light that contributes to the system noise.

Fig. 2.
Fig. 2.

Instead of just an illustration of the processes under discussion, here are actually measured optical spectra of the backscattered light from the fast axis of a 180 m of PM fiber, taken by the setup of Fig. 4 under the following conditions: (a) Only the horizontally polarized Probe (24 dBm at 1549.744 nm) is on. (b) Both the Probe and the vertically polarized PumpH (27.4 dBm at 1550.129 nm) are turned on. Note the significant increase in the power of the stochastic ProbeR. (c) The full BDG scenario: Probe, PumpH, and the also vertically polarized PumpL (10dBm at 1550.216) are turned on, resulting in a further, this time intentional, increase of ProbeR. The backward propagating PumpL is amplified to a level of 20dBm. The 7dBm value shown in (c) represents its leakage from the vertical to the horizontal polarization.

Fig. 3.
Fig. 3.

Dependence of the mean spontaneously initiated Probe reflectivity, RProbe, on the Probe power for different levels of PumpH. Solid lines: analytical approximation (7); markers: numerical solution of Eq. (2).

Fig. 4.
Fig. 4.

Experimental BDG setup. The two upper branches are the optical routes of the writing pumps and the lower branch is the Probe route. All backpropagating waves (only ProbeR is shown) are collected in a polarization-sensitive way, via an optical circulator and measured by an optical spectrum analyzer (OSA). PBS, polarization beam splitter; SSB, single sideband modulator to downshift PumpL frequency with respect to PumpH; Pol, polarizer; EDFA, erbium-doped fiber amplifier; Att, attenuator. Polarization components had extinction ratio (>20dB).

Fig. 5.
Fig. 5.

(a) Probe reflectivity RProbe (dB) as a function of the Probe input power for different levels of PumpH input power; (b) the PumpH reflectivity RPumpH as a function of PumpH input power for different Probe levels. In both (a) and (b) the self-reflectivities (blue circles) show good agreement with the simulation results (smooth blue lines) while the other curves fall below the simulation predictions, Fig. 3, see text. (c) Equal reflectivity contours for RProbe (solid lines, bottom and left axes) and RPumpH (dashed lines, top and left axes).

Equations (8)

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

ΔνBDGSνProbeνPumpH=νPumpH(nslownfast)/nfast.
EPumpHz+1VgEPumpHt=12ig2EPumpLρα2EPumpH,EPumpLz1VgEPumpLt=12ig2EPumpHρ*+α2EPumpL,EProbez+1VgEProbet=12ig2EProbeRρα2EProbe,EProbeRz1VgEProbeRt=12ig2EProbeρ*+α2EProbeR,ρt+12ΓBρ=ig1EPumpHEPumpL*+ig1EProbeEProbeR*+f.
EPumpLz=12ig2EPumpHρ*EPoberRz=12ig2EProbeρ*ρ*τ+12ΓBρ*=ig1(EPumpH*EPumpL+EProbe*EProbeR)+f*.
E˜PumpL=0.5s1ig2EPumpHρ˜*;E˜ProbeR=0.5s1ig2EProbeρ˜*ρ˜*τ=[12ΓB+s12g1g2(|EPumpH|2+|EProbe|2)]ρ˜*+f˜*.
ρ˜*=0τdτf˜*e[ΓB2+s12g1g2(|EPumpH|2+|EProbe|2)](ττ).
EProbeR=12ig2EProbe0τdτe[ΓB2](ττ)zLdzf*I0(GΓBL(ττ)(zz)).
RProbeP¯ProbeRP¯Probe=|EProbeR(z=0)|2¯|EProbe|2τg22Q40dτ˜eΓBτ˜0LdzI02(GΓBzτ˜L)=RtheG/2[I0(G2)I1(G2)](I1is first order modified bessel function).
RProbe={RthforG1RthπeGG3/2forG1;G=gB(IProbe+IPumpH)L.

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