Abstract

Polarization-decoupled four-wave mixing (FWM) based on stimulated Brillouin scattering (SBS) in a polarization-maintaining fiber is studied both theoretically and experimentally. We show the difference between Brillouin-enhanced FWM, which was studied a long time ago, and the Brillouin dynamic grating that was proposed in recent years. Under undepleted pump approximation, an analytical solution is given for the coupled equations, showing that a net phase-matching condition is dependent on pump power and frequency detuning from the Brillouin frequency. Experimental investigation of this net phase-matching condition provides a method to measure the spectral change in the refractive index that is responsible for the slow light effect based on SBS. Small refractive index changes (on the order of 108) versus frequency detuning can be determined experimentally.

© 2013 Optical Society of America

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  1. Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318, 1748–1750 (2007).
    [CrossRef]
  2. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
    [CrossRef]
  3. K. Y. Song, M. G. Herráez, and L. Thévenaz, “Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering,” Opt. Express 13, 82–88 (2005).
    [CrossRef]
  4. L. Thévenaz, “Slow and fast light in optical fibres,” Nat. Photonics 2, 474–481 (2008).
    [CrossRef]
  5. X. Bao and L. Chen, “Recent progress in Brillouin scattering based fiber sensors,” Sensors 11, 4152–4187 (2011).
    [CrossRef]
  6. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).
  7. A. M. Scott, “Efficient phase conjugation by Brillouin enhanced four wave mixing,” Opt. Commun. 45, 127–132 (1983).
    [CrossRef]
  8. A. M. Scott and M. S. Hazell, “High-efficiency scattering in transient Brillouin-enhanced four-wave mixing,” IEEE J. Quantum Electron. 22, 1248–1257 (1986).
    [CrossRef]
  9. M. D. Skeldon, P. Narum, and R. W. Boyd, “Non-frequency-shifted, high-fidelity phase conjugation with aberrated pump waves by Brillouin-enhanced four-wave mixing,” Opt. Lett. 12, 343–345 (1987).
    [CrossRef]
  10. A. M. Scott and K. D. Ridley, “A review of Brillouin-enhanced four-wave mixing,” IEEE J. Quantum Electron. 25, 438–459 (1989).
    [CrossRef]
  11. W. A. Schroeder, M. J. Damzen, and M. H. R. Hutchinson, “Polarization-decoupled Brillouin-enhanced four-wave mixing,” IEEE J. Quantum Electron. 25, 460–469 (1989).
    [CrossRef]
  12. K. Y. Song, W. Zou, Z. He, and K. Hotate, “All-optical dynamic grating generation based on Brillouin scattering in polarization-maintaining fiber,” Opt. Lett. 33, 926–928 (2008).
    [CrossRef]
  13. Y. Dong, X. Bao, and L. Chen, “Distributed temperature sensing based on birefringence effect on transient Brillouin grating in a polarization-maintaining photonic crystal fiber,” Opt. Lett. 34, 2590–2592 (2009).
    [CrossRef]
  14. K. Y. Song and H. J. Yoon, “High-resolution Brillouin optical time domain analysis based on Brillouin dynamic grating,” Opt. Lett. 35, 52–54 (2010).
    [CrossRef]
  15. K. Y. Song, S. Chin, N. Primerov, and L. Thévenaz, “Time-domain distributed fiber sensor with 1 cm spatial resolution based on Brillouin dynamic grating,” J. Lightwave Technol. 28, 2062–2067 (2010).
    [CrossRef]
  16. S. Chin, N. Primerov, and L. Thévenaz, “Sub-centimetre spatial resolution in distributed fibre sensing, based on dynamic Brillouin grating in optical fibers,” IEEE Sens. J. 12, 189–194 (2012).
    [CrossRef]
  17. W. Zou, Z. He, and K. Hotate, “Complete discrimination of strain and temperature using Brillouin frequency shift and birefringence in a polarization-maintaining fiber,” Opt. Express 17, 1248–1255 (2009).
    [CrossRef]
  18. W. Zou, Z. He, and K. Hotate, “Demonstration of Brillouin distributed discrimination of strain and temperature using a polarization-maintaining optical fiber,” IEEE Photon. Technol. Lett. 22, 526–528 (2010).
    [CrossRef]
  19. Y. Dong, L. Chen, and X. Bao, “High-spatial-resolution time-domain simultaneous strain and temperature sensor using Brillouin scattering and birefringence in a polarization-maintaining fiber,” IEEE Photon. Technol. Lett. 22, 1364–1366 (2010).
    [CrossRef]
  20. W. Zou, Z. He, and K. Hotate, “One-laser-based generation/detection of Brillouin dynamic grating and its application to distributed discrimination of strain and temperature,” Opt. Express 19, 2363–2370 (2011).
    [CrossRef]
  21. K. Y. Song, K. Lee, and S. B. Lee, “Tunable optical delays based on Brillouin dynamic grating in optical fibers,” Opt. Express 17, 10344–10349 (2009).
    [CrossRef]
  22. Y. Dong, L. Chen, and X. Bao, “Truly distributed birefringence measurement of polarization-maintaining fibers based on transient Brillouin grating,” Opt. Lett. 35, 193–195 (2010).
    [CrossRef]
  23. D. P. Zhou, Y. Dong, L. Chen, and X. Bao, “Four-wave mixing analysis of Brillouin dynamic grating in a polarization-maintaining fiber: theory and experiment,” Opt. Express 19, 20785–20798 (2011).
    [CrossRef]
  24. A. Loayssa, D. Benito, and M. J. Garde, “Narrow-bandwidth technique for stimulated Brillouin scattering spectral characterization,” Electron. Lett. 37, 367–368 (2001).
    [CrossRef]
  25. A. Loayssa, R. Hernández, D. Benito, and S. Galech, “Characterization of stimulated Brillouin scattering spectra by use of optical single-sideband modulation,” Opt. Lett. 29, 638–640 (2004).
    [CrossRef]
  26. R. W. Boyd, Nonlinear Optics (Academic, 2008).
  27. A. Kobyakov, S. Kumar, D. Q. Chowdhury, A. B. Ruffin, M. Sauer, S. R. Bickham, and R. Mishra, “Design concept for optical fibers with enhanced SBS threshold,” Opt. Express 13, 5338–5346 (2005).
    [CrossRef]
  28. A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photon. 2, 1–59(2010).
    [CrossRef]
  29. Y. Dong, L. Chen, and X. Bao, “High-spatial-resolution time-domain simultaneous strain and temperature sensor using Brillouin scattering and birefringence in a polarization-maintaining fiber,” IEEE Photon. Technol. Lett. 22, 1364–1366 (2010).
    [CrossRef]

2012 (1)

S. Chin, N. Primerov, and L. Thévenaz, “Sub-centimetre spatial resolution in distributed fibre sensing, based on dynamic Brillouin grating in optical fibers,” IEEE Sens. J. 12, 189–194 (2012).
[CrossRef]

2011 (3)

2010 (7)

A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photon. 2, 1–59(2010).
[CrossRef]

K. Y. Song and H. J. Yoon, “High-resolution Brillouin optical time domain analysis based on Brillouin dynamic grating,” Opt. Lett. 35, 52–54 (2010).
[CrossRef]

Y. Dong, L. Chen, and X. Bao, “Truly distributed birefringence measurement of polarization-maintaining fibers based on transient Brillouin grating,” Opt. Lett. 35, 193–195 (2010).
[CrossRef]

K. Y. Song, S. Chin, N. Primerov, and L. Thévenaz, “Time-domain distributed fiber sensor with 1 cm spatial resolution based on Brillouin dynamic grating,” J. Lightwave Technol. 28, 2062–2067 (2010).
[CrossRef]

W. Zou, Z. He, and K. Hotate, “Demonstration of Brillouin distributed discrimination of strain and temperature using a polarization-maintaining optical fiber,” IEEE Photon. Technol. Lett. 22, 526–528 (2010).
[CrossRef]

Y. Dong, L. Chen, and X. Bao, “High-spatial-resolution time-domain simultaneous strain and temperature sensor using Brillouin scattering and birefringence in a polarization-maintaining fiber,” IEEE Photon. Technol. Lett. 22, 1364–1366 (2010).
[CrossRef]

Y. Dong, L. Chen, and X. Bao, “High-spatial-resolution time-domain simultaneous strain and temperature sensor using Brillouin scattering and birefringence in a polarization-maintaining fiber,” IEEE Photon. Technol. Lett. 22, 1364–1366 (2010).
[CrossRef]

2009 (3)

2008 (2)

2007 (1)

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318, 1748–1750 (2007).
[CrossRef]

2005 (3)

2004 (1)

2001 (1)

A. Loayssa, D. Benito, and M. J. Garde, “Narrow-bandwidth technique for stimulated Brillouin scattering spectral characterization,” Electron. Lett. 37, 367–368 (2001).
[CrossRef]

1989 (2)

A. M. Scott and K. D. Ridley, “A review of Brillouin-enhanced four-wave mixing,” IEEE J. Quantum Electron. 25, 438–459 (1989).
[CrossRef]

W. A. Schroeder, M. J. Damzen, and M. H. R. Hutchinson, “Polarization-decoupled Brillouin-enhanced four-wave mixing,” IEEE J. Quantum Electron. 25, 460–469 (1989).
[CrossRef]

1987 (1)

1986 (1)

A. M. Scott and M. S. Hazell, “High-efficiency scattering in transient Brillouin-enhanced four-wave mixing,” IEEE J. Quantum Electron. 22, 1248–1257 (1986).
[CrossRef]

1983 (1)

A. M. Scott, “Efficient phase conjugation by Brillouin enhanced four wave mixing,” Opt. Commun. 45, 127–132 (1983).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

Bao, X.

X. Bao and L. Chen, “Recent progress in Brillouin scattering based fiber sensors,” Sensors 11, 4152–4187 (2011).
[CrossRef]

D. P. Zhou, Y. Dong, L. Chen, and X. Bao, “Four-wave mixing analysis of Brillouin dynamic grating in a polarization-maintaining fiber: theory and experiment,” Opt. Express 19, 20785–20798 (2011).
[CrossRef]

Y. Dong, L. Chen, and X. Bao, “Truly distributed birefringence measurement of polarization-maintaining fibers based on transient Brillouin grating,” Opt. Lett. 35, 193–195 (2010).
[CrossRef]

Y. Dong, L. Chen, and X. Bao, “High-spatial-resolution time-domain simultaneous strain and temperature sensor using Brillouin scattering and birefringence in a polarization-maintaining fiber,” IEEE Photon. Technol. Lett. 22, 1364–1366 (2010).
[CrossRef]

Y. Dong, L. Chen, and X. Bao, “High-spatial-resolution time-domain simultaneous strain and temperature sensor using Brillouin scattering and birefringence in a polarization-maintaining fiber,” IEEE Photon. Technol. Lett. 22, 1364–1366 (2010).
[CrossRef]

Y. Dong, X. Bao, and L. Chen, “Distributed temperature sensing based on birefringence effect on transient Brillouin grating in a polarization-maintaining photonic crystal fiber,” Opt. Lett. 34, 2590–2592 (2009).
[CrossRef]

Benito, D.

A. Loayssa, R. Hernández, D. Benito, and S. Galech, “Characterization of stimulated Brillouin scattering spectra by use of optical single-sideband modulation,” Opt. Lett. 29, 638–640 (2004).
[CrossRef]

A. Loayssa, D. Benito, and M. J. Garde, “Narrow-bandwidth technique for stimulated Brillouin scattering spectral characterization,” Electron. Lett. 37, 367–368 (2001).
[CrossRef]

Bickham, S. R.

Bigelow, M. S.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef]

Boyd, R. W.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318, 1748–1750 (2007).
[CrossRef]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef]

M. D. Skeldon, P. Narum, and R. W. Boyd, “Non-frequency-shifted, high-fidelity phase conjugation with aberrated pump waves by Brillouin-enhanced four-wave mixing,” Opt. Lett. 12, 343–345 (1987).
[CrossRef]

R. W. Boyd, Nonlinear Optics (Academic, 2008).

Chen, L.

X. Bao and L. Chen, “Recent progress in Brillouin scattering based fiber sensors,” Sensors 11, 4152–4187 (2011).
[CrossRef]

D. P. Zhou, Y. Dong, L. Chen, and X. Bao, “Four-wave mixing analysis of Brillouin dynamic grating in a polarization-maintaining fiber: theory and experiment,” Opt. Express 19, 20785–20798 (2011).
[CrossRef]

Y. Dong, L. Chen, and X. Bao, “Truly distributed birefringence measurement of polarization-maintaining fibers based on transient Brillouin grating,” Opt. Lett. 35, 193–195 (2010).
[CrossRef]

Y. Dong, L. Chen, and X. Bao, “High-spatial-resolution time-domain simultaneous strain and temperature sensor using Brillouin scattering and birefringence in a polarization-maintaining fiber,” IEEE Photon. Technol. Lett. 22, 1364–1366 (2010).
[CrossRef]

Y. Dong, L. Chen, and X. Bao, “High-spatial-resolution time-domain simultaneous strain and temperature sensor using Brillouin scattering and birefringence in a polarization-maintaining fiber,” IEEE Photon. Technol. Lett. 22, 1364–1366 (2010).
[CrossRef]

Y. Dong, X. Bao, and L. Chen, “Distributed temperature sensing based on birefringence effect on transient Brillouin grating in a polarization-maintaining photonic crystal fiber,” Opt. Lett. 34, 2590–2592 (2009).
[CrossRef]

Chin, S.

S. Chin, N. Primerov, and L. Thévenaz, “Sub-centimetre spatial resolution in distributed fibre sensing, based on dynamic Brillouin grating in optical fibers,” IEEE Sens. J. 12, 189–194 (2012).
[CrossRef]

K. Y. Song, S. Chin, N. Primerov, and L. Thévenaz, “Time-domain distributed fiber sensor with 1 cm spatial resolution based on Brillouin dynamic grating,” J. Lightwave Technol. 28, 2062–2067 (2010).
[CrossRef]

Chowdhury, D.

Chowdhury, D. Q.

Damzen, M. J.

W. A. Schroeder, M. J. Damzen, and M. H. R. Hutchinson, “Polarization-decoupled Brillouin-enhanced four-wave mixing,” IEEE J. Quantum Electron. 25, 460–469 (1989).
[CrossRef]

Dong, Y.

D. P. Zhou, Y. Dong, L. Chen, and X. Bao, “Four-wave mixing analysis of Brillouin dynamic grating in a polarization-maintaining fiber: theory and experiment,” Opt. Express 19, 20785–20798 (2011).
[CrossRef]

Y. Dong, L. Chen, and X. Bao, “Truly distributed birefringence measurement of polarization-maintaining fibers based on transient Brillouin grating,” Opt. Lett. 35, 193–195 (2010).
[CrossRef]

Y. Dong, L. Chen, and X. Bao, “High-spatial-resolution time-domain simultaneous strain and temperature sensor using Brillouin scattering and birefringence in a polarization-maintaining fiber,” IEEE Photon. Technol. Lett. 22, 1364–1366 (2010).
[CrossRef]

Y. Dong, L. Chen, and X. Bao, “High-spatial-resolution time-domain simultaneous strain and temperature sensor using Brillouin scattering and birefringence in a polarization-maintaining fiber,” IEEE Photon. Technol. Lett. 22, 1364–1366 (2010).
[CrossRef]

Y. Dong, X. Bao, and L. Chen, “Distributed temperature sensing based on birefringence effect on transient Brillouin grating in a polarization-maintaining photonic crystal fiber,” Opt. Lett. 34, 2590–2592 (2009).
[CrossRef]

Gaeta, A. L.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef]

Galech, S.

Garde, M. J.

A. Loayssa, D. Benito, and M. J. Garde, “Narrow-bandwidth technique for stimulated Brillouin scattering spectral characterization,” Electron. Lett. 37, 367–368 (2001).
[CrossRef]

Gauthier, D. J.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318, 1748–1750 (2007).
[CrossRef]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef]

Hazell, M. S.

A. M. Scott and M. S. Hazell, “High-efficiency scattering in transient Brillouin-enhanced four-wave mixing,” IEEE J. Quantum Electron. 22, 1248–1257 (1986).
[CrossRef]

He, Z.

Hernández, R.

Herráez, M. G.

Hotate, K.

Hutchinson, M. H. R.

W. A. Schroeder, M. J. Damzen, and M. H. R. Hutchinson, “Polarization-decoupled Brillouin-enhanced four-wave mixing,” IEEE J. Quantum Electron. 25, 460–469 (1989).
[CrossRef]

Kobyakov, A.

Kumar, S.

Lee, K.

Lee, S. B.

Loayssa, A.

A. Loayssa, R. Hernández, D. Benito, and S. Galech, “Characterization of stimulated Brillouin scattering spectra by use of optical single-sideband modulation,” Opt. Lett. 29, 638–640 (2004).
[CrossRef]

A. Loayssa, D. Benito, and M. J. Garde, “Narrow-bandwidth technique for stimulated Brillouin scattering spectral characterization,” Electron. Lett. 37, 367–368 (2001).
[CrossRef]

Mishra, R.

Narum, P.

Okawachi, Y.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef]

Primerov, N.

S. Chin, N. Primerov, and L. Thévenaz, “Sub-centimetre spatial resolution in distributed fibre sensing, based on dynamic Brillouin grating in optical fibers,” IEEE Sens. J. 12, 189–194 (2012).
[CrossRef]

K. Y. Song, S. Chin, N. Primerov, and L. Thévenaz, “Time-domain distributed fiber sensor with 1 cm spatial resolution based on Brillouin dynamic grating,” J. Lightwave Technol. 28, 2062–2067 (2010).
[CrossRef]

Ridley, K. D.

A. M. Scott and K. D. Ridley, “A review of Brillouin-enhanced four-wave mixing,” IEEE J. Quantum Electron. 25, 438–459 (1989).
[CrossRef]

Ruffin, A. B.

Sauer, M.

Schroeder, W. A.

W. A. Schroeder, M. J. Damzen, and M. H. R. Hutchinson, “Polarization-decoupled Brillouin-enhanced four-wave mixing,” IEEE J. Quantum Electron. 25, 460–469 (1989).
[CrossRef]

Schweinsberg, A.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef]

Scott, A. M.

A. M. Scott and K. D. Ridley, “A review of Brillouin-enhanced four-wave mixing,” IEEE J. Quantum Electron. 25, 438–459 (1989).
[CrossRef]

A. M. Scott and M. S. Hazell, “High-efficiency scattering in transient Brillouin-enhanced four-wave mixing,” IEEE J. Quantum Electron. 22, 1248–1257 (1986).
[CrossRef]

A. M. Scott, “Efficient phase conjugation by Brillouin enhanced four wave mixing,” Opt. Commun. 45, 127–132 (1983).
[CrossRef]

Sharping, J. E.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef]

Skeldon, M. D.

Song, K. Y.

Thévenaz, L.

S. Chin, N. Primerov, and L. Thévenaz, “Sub-centimetre spatial resolution in distributed fibre sensing, based on dynamic Brillouin grating in optical fibers,” IEEE Sens. J. 12, 189–194 (2012).
[CrossRef]

K. Y. Song, S. Chin, N. Primerov, and L. Thévenaz, “Time-domain distributed fiber sensor with 1 cm spatial resolution based on Brillouin dynamic grating,” J. Lightwave Technol. 28, 2062–2067 (2010).
[CrossRef]

L. Thévenaz, “Slow and fast light in optical fibres,” Nat. Photonics 2, 474–481 (2008).
[CrossRef]

K. Y. Song, M. G. Herráez, and L. Thévenaz, “Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering,” Opt. Express 13, 82–88 (2005).
[CrossRef]

Yoon, H. J.

Zhou, D. P.

Zhu, Z.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318, 1748–1750 (2007).
[CrossRef]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef]

Zou, W.

Adv. Opt. Photon. (1)

Electron. Lett. (1)

A. Loayssa, D. Benito, and M. J. Garde, “Narrow-bandwidth technique for stimulated Brillouin scattering spectral characterization,” Electron. Lett. 37, 367–368 (2001).
[CrossRef]

IEEE J. Quantum Electron. (3)

A. M. Scott and M. S. Hazell, “High-efficiency scattering in transient Brillouin-enhanced four-wave mixing,” IEEE J. Quantum Electron. 22, 1248–1257 (1986).
[CrossRef]

A. M. Scott and K. D. Ridley, “A review of Brillouin-enhanced four-wave mixing,” IEEE J. Quantum Electron. 25, 438–459 (1989).
[CrossRef]

W. A. Schroeder, M. J. Damzen, and M. H. R. Hutchinson, “Polarization-decoupled Brillouin-enhanced four-wave mixing,” IEEE J. Quantum Electron. 25, 460–469 (1989).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

W. Zou, Z. He, and K. Hotate, “Demonstration of Brillouin distributed discrimination of strain and temperature using a polarization-maintaining optical fiber,” IEEE Photon. Technol. Lett. 22, 526–528 (2010).
[CrossRef]

Y. Dong, L. Chen, and X. Bao, “High-spatial-resolution time-domain simultaneous strain and temperature sensor using Brillouin scattering and birefringence in a polarization-maintaining fiber,” IEEE Photon. Technol. Lett. 22, 1364–1366 (2010).
[CrossRef]

Y. Dong, L. Chen, and X. Bao, “High-spatial-resolution time-domain simultaneous strain and temperature sensor using Brillouin scattering and birefringence in a polarization-maintaining fiber,” IEEE Photon. Technol. Lett. 22, 1364–1366 (2010).
[CrossRef]

IEEE Sens. J. (1)

S. Chin, N. Primerov, and L. Thévenaz, “Sub-centimetre spatial resolution in distributed fibre sensing, based on dynamic Brillouin grating in optical fibers,” IEEE Sens. J. 12, 189–194 (2012).
[CrossRef]

J. Lightwave Technol. (1)

Nat. Photonics (1)

L. Thévenaz, “Slow and fast light in optical fibres,” Nat. Photonics 2, 474–481 (2008).
[CrossRef]

Opt. Commun. (1)

A. M. Scott, “Efficient phase conjugation by Brillouin enhanced four wave mixing,” Opt. Commun. 45, 127–132 (1983).
[CrossRef]

Opt. Express (6)

Opt. Lett. (6)

Phys. Rev. Lett. (1)

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef]

Science (1)

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318, 1748–1750 (2007).
[CrossRef]

Sensors (1)

X. Bao and L. Chen, “Recent progress in Brillouin scattering based fiber sensors,” Sensors 11, 4152–4187 (2011).
[CrossRef]

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

R. W. Boyd, Nonlinear Optics (Academic, 2008).

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Figures (6)

Fig. 1.
Fig. 1.

Diagram of the theoretical model. A pump wave and a Stokes wave whose frequency difference is near Brillouin frequency polarized along the fast axis counterpropagate in a PMF; a probe beam polarized along the slow axis is diffracted strongly by the acoustic wave when the phase-matching condition is satisfied: pol, polarized; PMF, polarization-maintaining fiber. Inset shows the frequency relations among the four optical waves.

Fig. 2.
Fig. 2.

Diffracted wave reflectivity with respect to the phase mismatch Δk for the detuning parameter δ=±1.

Fig. 3.
Fig. 3.

(a) SBS-induced frequency variation ΔνSBS and refractive index change ΔnSBS versus normalized detuning parameter δ with pump power of 1 W. (b) Absolute value of maximum frequency change |ΔνSBSmax| and refractive index change |ΔnSBSmax| as a function of pump power |Ap|2.

Fig. 4.
Fig. 4.

Experimental setup. OC, optical coupler; EDFA, erbium-doped fiber amplifier; PD, photodetector; PC, polarization controller; CIR, circulator; PBC, polarization beam combiner; EOM, electro-optic modulator; TF, tunable filter; PM, power meter; PMF, polarization-maintaining fiber; DAQ, data acquisition. Dashed line, electrical cable; solid line, optical fiber.

Fig. 5.
Fig. 5.

Measured normalized diffracted wave reflectivity with respect to frequency difference Δν of pump and probe waves at two different locking frequencies between pump and Stokes waves with the power levels of 1 W for the pump wave, 8 mW for the Stokes wave, and 10 mW for the probe wave, respectively. Red dashed curves are Gaussian fitting of the spectra. a.u. represents arbitrary unit.

Fig. 6.
Fig. 6.

(a) Measured normalized Brillouin gain of the fast axis of the PMF and the peak frequency of the diffracted spectrum versus locking frequency. Red dashed curve is the Lorentzian fitting of the Brillouin gain. The red dot–dashed curve is the fitting by Eq. (9) of the experimental data (open circles) with pump power of 1 W, Stokes power of 8 mW, and probe power of 10 mW. (b) Absolute value of maximum peak frequency change (maximum refractive index change) versus pump power with Stokes and probe power levels of 8 and 10 mW, respectively. Red dashed line is the linear fitting of the experimental data (solid circles). a.u. represents arbitrary unit.

Equations (38)

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2ρ˜t2ΓA2ρ˜tvA22ρ˜=12ε0γe2E˜tot2,
E˜x=12x^[F(x,y)A˜p(z,t)ei(kpzωpt)+F(x,y)A˜s(z,t)ei(kszωst)]+c.c.,
E˜y=12y^[F(x,y)A˜pr(z,t)ei(kprzωprt)+F(x,y)A˜d(z,t)ei(kdzωdt)]+c.c.,
Apz=iη(Ap|As|2+AsAprAd*eiΔkz),
Asz=iη*(|Ap|2As+ApApr*AdeiΔkz),
Aprz=iη(Apr|Ad|2+ApAs*AdeiΔkz),
Adz=iη*(|Apr|2Ad+Ap*AsApreiΔkz),
η=π2γe2ρ0cλp2nxvA(ΩBΩiΓB/2)Aeffao=κ1(δ)+iκ2(δ),
κ1(δ)=gp2Aeffaoδδ2+1,κ2(δ)=gp2Aeffao1δ2+1,
gp=4π2γe2ρ0cλp2nxvAΓB,
Aeffao=[F2(x,y)F2(x,y)FA(x,y)]2FA2(x,y),
Apz=iη(Ap|As|2+AsAprAd*eiΔkz),
Adz=iη*(|Apr|2Ad+Ap*AsApreiΔkz),
Asz=iη*(|Ap|2As+ApApr*AdeiΔkz),
Adz=iη*(|Apr|2Ad+Ap*AsApreiΔkz).
Asz=iη*|Ap|2As,
Aprz=iηApAs*AdeiΔkz,
Adz=iη*Ap*AsApreiΔkz,
Ad(z)Apr(0)=ζ*|ζ|e12(κ2|Ap|2iθ)zIf(γ)Kf(γeκ2|Ap|2(Lz))If(γeκ2|Ap|2(Lz))Kf(γ)If1(γeκ2|Ap|2L)Kf(γ)+If(γ)Kf1(γeκ2|Ap|2L),
θ=Δk+κ1(δ)|Ap|2,
R=|Ad(0)Apr(0)|2=|If(γ)Kf(γeκ2|Ap|2L)If(γeκ2|Ap|2L)Kf(γ)If1(γeκ2|Ap|2L)Kf(γ)+If(γ)Kf1(γeκ2|Ap|2L)|2.
Δνp(δ,|Ap|2)=B(2ωpΩB)4πny+ΔνSBS(δ,|Ap|2),
ΔνSBS(δ,|Ap|2)=cκ1(δ)|Ap|24πny.
ΔnSBS(δ,|Ap|2)=ckSBSωs=4πnyΔνSBS(δ,|Ap|2)ωs.
As|z=L=As(L),
Apr|z=0=Apr(0)=1ζ*Adz|z=0,
Ad|z=L=Ad(L)=0,
As(z)=As(L)eiη*|Ap|2(Lz),
Aprz=ζAde[κ2(δ)|Ap|2+iθ]z,
Adz=ζ*Apre[κ2(δ)|Ap|2iθ]z,
θ=Δk+κ1(δ)|Ap|2,
2Adz2+(κ2|Ap|2iθ)Adz|ζ|2Ade2κ2|Ap|2z=0.
x22yx2+xyx(x2+f2)y=0,
y=Ad(z)e12(κ2|Ap|2iθ)z,x=γeκ2|Ap|2(Lz),f=12iθ2κ2|Ap|2,
Ad(z)=e12(κ2|Ap|2iθ)z[C1If(γeκ2|Ap|2(Lz))+C2Kf(γeκ2|Ap|2(Lz))].
If(x)+fxIf(x)=If1(x),Kf(x)+fxKf(x)=Kf1(x),
C1=ζ*|ζ|Apr(0)Kf(γ)Kf(γ)If1(γeκ2|Ap|2L)+Kf1(γeκ2|Ap|2L)If(γ),
C2=ζ*|ζ|Apr(0)If(γ)Kf(γ)If1(γeκ2|Ap|2L)+Kf1(γeκ2|Ap|2L)If(γ).

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