Abstract

Numerical and experimental investigations of stimulated Brillouin scattering signal amplification in standard single-mode fibers under pump depletion show that while gains are reduced, the same orthogonal input states of polarization that provide maximum and minimum gain in the undepleted case practically continue to do so in the depleted regime. Using a scaled Brillouin gain coefficient, the power distribution of these max/min polarizations along the fiber can be deduced from a scalar formulation.

© 2013 Optical Society of America

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References

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  1. X. Bao and L. Chen, Sensors 11, 4152 (2011).
    [CrossRef]
  2. L. Thévenaz, Advanced Fiber Optics (EPFL, 2011).
  3. A. Zadok, A. Eyal, and M. Tur, J. Lightwave Technol. 25, 2168 (2007).
    [CrossRef]
  4. Z. Zhu, D. J. Gauthier, and R. W. Boyd, Science 318, 1748 (2007).
    [CrossRef]
  5. A. Zadok, A. Eyal, and M. Tur, Appl. Opt. 50, E38 (2011).
    [CrossRef]
  6. M. O. van Deventer and A. J. Boot, J. Lightwave Technol. 12, 585 (1994).
    [CrossRef]
  7. A. Zadok, E. Zilka, A. Eyal, L. Thévenaz, and M. Tur, Opt. Express 16, 21692 (2008).
    [CrossRef]
  8. L. Chen and X. Bao, Opt. Commun. 152, 65 (1998).
    [CrossRef]
  9. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).
  10. R. B. Jenkins, R. M. Sova, and R. I. Joseph, J. Lightwave Technol. 25, 763 (2007).
    [CrossRef]
  11. M. Wuilpart, “Distributed measurement of polarization properties in single-mode optical fibres using a reflectometry technique,” Ph.D. thesis (Faculte Polytechnique de Mons, 2003).

2011 (2)

2008 (1)

2007 (3)

1998 (1)

L. Chen and X. Bao, Opt. Commun. 152, 65 (1998).
[CrossRef]

1994 (1)

M. O. van Deventer and A. J. Boot, J. Lightwave Technol. 12, 585 (1994).
[CrossRef]

Bao, X.

X. Bao and L. Chen, Sensors 11, 4152 (2011).
[CrossRef]

L. Chen and X. Bao, Opt. Commun. 152, 65 (1998).
[CrossRef]

Boot, A. J.

M. O. van Deventer and A. J. Boot, J. Lightwave Technol. 12, 585 (1994).
[CrossRef]

Boyd, R. W.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, Science 318, 1748 (2007).
[CrossRef]

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

Chen, L.

X. Bao and L. Chen, Sensors 11, 4152 (2011).
[CrossRef]

L. Chen and X. Bao, Opt. Commun. 152, 65 (1998).
[CrossRef]

Eyal, A.

Gauthier, D. J.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, Science 318, 1748 (2007).
[CrossRef]

Jenkins, R. B.

Joseph, R. I.

Sova, R. M.

Thévenaz, L.

Tur, M.

van Deventer, M. O.

M. O. van Deventer and A. J. Boot, J. Lightwave Technol. 12, 585 (1994).
[CrossRef]

Wuilpart, M.

M. Wuilpart, “Distributed measurement of polarization properties in single-mode optical fibres using a reflectometry technique,” Ph.D. thesis (Faculte Polytechnique de Mons, 2003).

Zadok, A.

Zhu, Z.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, Science 318, 1748 (2007).
[CrossRef]

Zilka, E.

Appl. Opt. (1)

J. Lightwave Technol. (3)

Opt. Commun. (1)

L. Chen and X. Bao, Opt. Commun. 152, 65 (1998).
[CrossRef]

Opt. Express (1)

Science (1)

Z. Zhu, D. J. Gauthier, and R. W. Boyd, Science 318, 1748 (2007).
[CrossRef]

Sensors (1)

X. Bao and L. Chen, Sensors 11, 4152 (2011).
[CrossRef]

Other (3)

L. Thévenaz, Advanced Fiber Optics (EPFL, 2011).

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

M. Wuilpart, “Distributed measurement of polarization properties in single-mode optical fibres using a reflectometry technique,” Ph.D. thesis (Faculte Polytechnique de Mons, 2003).

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Figures (3)

Fig. 1.
Fig. 1.

Simulation (solid/dashed) and experimental (Δ) results for the obtainable max/min (over SOPsigin_max) signal (logarithmic) gains versus the input signal power for a pump power of 13 dBm. Bottom squares (right y axis): the measured high parallelism between s^sigout_max and s^pumpin_conj, evaluated by the deviation of their scalar product from unity ([s^1,s^2,s^3]pumpin_conj=[s^1,s^2,s^3]pumpin).

Fig. 2.
Fig. 2.

Calculated distance distributions of pump and signal powers along the fiber using the scalar intensity Eqs. (5) for SOPsigin_max (solid lines) and SOPsigin_min (dashed lines). Here, pump and signal input powers are 20 and 0.32 mW, respectively. The superimposed x’s are the results of our numerical solution of the vector Eqs. (1), which was insensitive to the particular choice of the birefringence beat and correlation lengths, as long as they were much shorter than the distance scale of pump depletion.

Fig. 3.
Fig. 3.

Experimental setup [7]. VOA, variable optical attenuator; FBG, fiber Bragg grating; PC, polarization controller; EDFA, erbium-doped fiber amplifier; EOM, electro-optic modulator; OSA, optical spectrum analyzer; BPF, band pass filter.

Equations (5)

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dE⃗sig(z)dz=[dT(z)dzT(z)+γ02E⃗pump(z)E⃗pump(z)α2]E⃗sig(z)dE⃗pump(z)dz=[dT*(z)dzTT(z)+γ02E⃗sig(z)E⃗sig(z)+α2]E⃗pump(z)
Psigout=Psiginexp[γ020LPpump(z)(1+s^pump(z)·s^sig(z))dz].
PsigoutPsiginexp[γ02(1+s^pump(z)·s^sig(z))0LPpump(z)dz].
Psigout(L){Psiginexp[(23γ0)0LPpump(z)dz]SOPsigin_maxPsiginexp[(13γ0)0LPpump(z)dz]SOPsigin_min.
dPsig(z)/dz=γPsig(z)Ppump(z)αPsig(z)dPpump(z)/dz=γPsig(z)Ppump(z)+αPpump(z),

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