Abstract

The polarization properties of stimulated Brillouin scattering (SBS) amplification or attenuation in standard single-mode fibers are examined through vectorial analysis, simulation and experiment. Vector propagation equations for the signal wave, incorporating SBS and birefringence, are derived and analyzed in both the Jones and Stokes spaces. The analysis shows that in the undepleted pump regime, the fiber may be regarded as a polarization-dependent gain (or loss) medium, having two orthogonal input SOPs, and corresponding two orthogonal output SOPs, for the signal, which, respectively, provide the signal with maximum and minimum SBS amplification (or attenuation). Under high Brillouin gain conditions and excluding zero-probability cases, the output SOP of arbitrarily polarized input signals, would tend to converge towards that of maximum SBS gain. In the case of high SBS attenuation the output SOP of an arbitrarily polarized signal would approach the output SOP corresponding to minimum attenuation. It is found that for a wide range of practical pump powers (≤ 100mW) and for sufficiently long fibers with typical SBS and birefringence parameters, the signal aligned for maximum SBS interaction will enter/emerge from the fiber with its electric field closely tracing the same ellipse in space as that of the pump at the corresponding side of the fiber, albeit with the opposite sense of rotation. The analytic predictions are experimentally demonstrated for both Stokes (amplification) and anti-Stokes (attenuation) signals.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. Horiguchi, T. Kurashima, and M. Tateda, "A technique to measure distributed strain in optical fibers," IEEE Photon. Technol. Lett. 2, 352-354 (1990).
    [CrossRef]
  2. M. Nikles, L. Thévenaz, and P. Robert, "Brillouin gain spectrum characterization in single-mode optical fibers," J. Lightwave Technol. 15, 1842-1851 (1997).
    [CrossRef]
  3. X. Bao, D. J. Webb, and D. A. Jackson, "32-km distributed temperature sensor using Brillouin loss in optical fiber," Opt. Lett. 18, 1561-1563 (1993).
    [CrossRef] [PubMed]
  4. J. C. Yong, L. Thévenaz, and B. Y. Kim, "Brillouin fiber laser pumped by a DFB laser diode," J. Lightwave Technol. 12, 546-554 (2003).
    [CrossRef]
  5. A. Loayssa, D. Benito, and M. J. Grade, "Optical carrier-suppression technique with a Brillouin-erbium fiber laser," Opt. Lett. 25, 197-199 (2000).
    [CrossRef]
  6. Y. Shen, X. Zhang, and K. Chen, "Optical single side-band modulation of 11 GHz RoF system using stimulated Brillouin scattering," IEEE Photon. Technol. Lett. 17, 1277-1279 (2005).
    [CrossRef]
  7. A. Zadok, A. Eyal, and M. Tur, "GHz-wide optically reconfigurable filters using stimulated Brillouin scattering," J. Lightwave Technol. 25, 2168-2174 (2007).
    [CrossRef]
  8. A. Loayssa, and F. J. Lahoz, "Broadband RF photonic phase shifter based on stimulated Brillouin scattering and single side-band modulation," IEEE Photon. Technol. Lett. 18, 208-210 (2006).
    [CrossRef]
  9. A. Loayssa, J. Capmany, M. Sagues, and J. Mora, "Demonstration of incoherent microwave photonic filters with all-optical complex coefficients," IEEE Photon. Technol. Lett. 18, 1744-1746 (2006).
    [CrossRef]
  10. 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] [PubMed]
  11. M. González-Herráez, K.-Y. Song, and L. Thévenaz, "Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering," Appl. Phys. Lett. 87, 081113 (2005).
    [CrossRef]
  12. M. D. Stenner, M. A. Neifeld, Z. Zhu, A. M. C. Dawes, and D. J. Gauthier, "Distortion management in slow-light pulse delay," Opt. Express 13, 9995-10002 (2005).
    [CrossRef] [PubMed]
  13. Z. Zhu, A. M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, "Broadband SBS slow light in an optical fiber," J. Lightwave Technol. 25, 201-206 (2007).
    [CrossRef]
  14. M. González-Herráez, K.-Y. Song, and L. Thévenaz, "Arbitrary-bandwidth Brillouin slow light in optical fibers," Opt. Express 14, 1395-1400 (2006).
    [CrossRef] [PubMed]
  15. K. Y. Song, M. Gonzalez Herraez, and L. Thévenaz, "Observation of pulse delay and advancement in optical fibers using stimulated Brillouin scattering," Opt. Express 13, 82-88 (2005).
    [CrossRef] [PubMed]
  16. A. Zadok, A. Eyal, and M. Tur, "Extended delay of broadband signals in stimulated Brillouin scattering slow light using synthesized pump chirp," Opt. Express 14, 8498-8505 (2006).
    [CrossRef] [PubMed]
  17. R. W. Boyd, Nonlinear optics, (San Diego, CA: Academic Press, 2003) Chap. 9, pp. 409-427.
    [CrossRef]
  18. A. Yariv, Optoelectronics, (Orlando FL: Saunders College Publishing, 4th Edition, 1991), Chap. 19, pp. 670-678.
  19. Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, "Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber," J. Opt. Soc. Am. B 22, 2378-2384 (2005).
    [CrossRef]
  20. T. Horiguchi, M. Tateda, M. Shibata, and Y. Azuma, "Brillouin gain variation due to a polarization-state change of the pump or Stokes field in standard single mode fibers," Opt. Lett. 14, 329-331 (1989).
    [CrossRef] [PubMed]
  21. M. O. van Deventer, and A. J. Boot, "Polarization properties of stimulated Brillouin scattering in single mode fibers," J. Lightwave Technol. 12, 585-590 (1994).
    [CrossRef]
  22. In [21], the pump and probe SOPs are defined in two different reference frames, corresponding to opposite directions of propagation. In this work, as well as in most of the literature on polarization [23,24], a single reference frame is used. Therefore, we defer the mathematical description of the conditions for maximum/minimum SBS gain to Section 2.
  23. R. C. Jones, "A new calculus for the treatment of optical system," J. Opt. Soc. Am. 37, 107-110, (1947).
    [CrossRef]
  24. E. Collett, Ed., Polarized light fundamentals and applications. (New York: Marcel Dekker, 1993).
  25. L. Thévenaz, A. Zadok, A. Eyal, and M. Tur, "All-optical polarization control through Brillouin amplification," paper OML7 in OFC/NFOEC 2008, San Diego, Ca, (2008).
  26. J. P. Gordon and H. Kogelnik, "PMD fundamentals: polarization mode dispersion in optical fibers", P. Natl. Acad. Sci. USA 97, 4541-4550, (2000).
    [CrossRef]
  27. R. H. Stolen, "Polarization effects in fiber Raman and Brillouin lasers," IEEE J. of Quantum Electron. 15, 1157-1160, (1979).
    [CrossRef]
  28. F. Corsi, A. Galtarossa, and L. Palmieri, "Analytical treatment of polarization mode dispersion in single mode fibers by means of the backscattered signal," J. Opt. Soc. Am. A 16, 574-583, (1999).
    [CrossRef]
  29. M. Brodsky, N. J. Frigo, ad M. Tur, "Polarization mode dispersion," chapter 17 in Optical Fiber Telecommunications V-A, Ed. I. P. Kaminow, T. Li and A. E. Willner, (Academic Press, 2008).
    [CrossRef]
  30. A. Loayssa, D. Benito, and M. J. Grade, "High resolution measurement of stimulated Brillouin scattering spectra in single-mode fibers," IEE Proc. Optoelectron. 148, 143-148, (2001).
    [CrossRef]
  31. A. Eyal, D. Kuperman, O. Dimenstein, and M. Tur, "Polarization dependence of the intensity modulation transfer function of an optical system with PMD and PDL," IEEE Photon. Technol. Lett. 14, 1515-1517 (2002).
    [CrossRef]
  32. S. Pitois, J. Fatome, and G. Millot, "Polarization attraction using counter-propagating waves in optical fiber at telecommunication wavelengths," Opt. Express 16, 6646-6651 (2008).
    [CrossRef] [PubMed]
  33. A. Küng, L. Thévenaz, and P. A. Robert, "Polarization analysis of Brillouin scattering in a circularly birefringent fiber ring resonator," J. Lightwave. Technol. 15, 977-982 (1997).
    [CrossRef]
  34. S. Randoux, and J. Zemmouri, "Polarization dynamics of a Brillouin fiber ring laser," Phys. Rev. A 59,1644-1653 (1999).
    [CrossRef]
  35. L. Thévenaz, S. Foaleng Mafang, and M. Nikles, "Fast measurement of local PMD with high spatial resolution using stimulated Brillouin scattering," paper 10.1.2 in ECOC 2007, Berlin, Germany, (2007).
  36. X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, "Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering," J. Lightwave Technol. 13, 1340-1348 (1995).
    [CrossRef]
  37. S. Chin, M. Gonzalez-Herraez, and L. Thévenaz, "Zero-gain slow and fast light propagation in an optical fiber," Opt. Express 14, 10684-10692 (2006).
    [CrossRef] [PubMed]
  38. D. R. Walker, M. Bashkanski, A. Gulian, F. K. Fatemi, and M. Steiner, "Stabilizing slow light delay in stimulated Brillouin scattering using a Faraday rotator mirror," to be published in J. Opt. Soc. Am. B 25, (2008).
  39. A. Galtarossa, L. Palmieri, M. Santagiustina, L. Schenato, and L. Ursini, "Polarized Brillouin amplification in randomly birefringent and unidrectionally spun fibers," IEEE Photon Technol. Lett 20, 1420-1422 (2008).
    [CrossRef]

2008 (3)

D. R. Walker, M. Bashkanski, A. Gulian, F. K. Fatemi, and M. Steiner, "Stabilizing slow light delay in stimulated Brillouin scattering using a Faraday rotator mirror," to be published in J. Opt. Soc. Am. B 25, (2008).

A. Galtarossa, L. Palmieri, M. Santagiustina, L. Schenato, and L. Ursini, "Polarized Brillouin amplification in randomly birefringent and unidrectionally spun fibers," IEEE Photon Technol. Lett 20, 1420-1422 (2008).
[CrossRef]

S. Pitois, J. Fatome, and G. Millot, "Polarization attraction using counter-propagating waves in optical fiber at telecommunication wavelengths," Opt. Express 16, 6646-6651 (2008).
[CrossRef] [PubMed]

2007 (3)

2006 (5)

A. Loayssa, and F. J. Lahoz, "Broadband RF photonic phase shifter based on stimulated Brillouin scattering and single side-band modulation," IEEE Photon. Technol. Lett. 18, 208-210 (2006).
[CrossRef]

A. Loayssa, J. Capmany, M. Sagues, and J. Mora, "Demonstration of incoherent microwave photonic filters with all-optical complex coefficients," IEEE Photon. Technol. Lett. 18, 1744-1746 (2006).
[CrossRef]

M. González-Herráez, K.-Y. Song, and L. Thévenaz, "Arbitrary-bandwidth Brillouin slow light in optical fibers," Opt. Express 14, 1395-1400 (2006).
[CrossRef] [PubMed]

A. Zadok, A. Eyal, and M. Tur, "Extended delay of broadband signals in stimulated Brillouin scattering slow light using synthesized pump chirp," Opt. Express 14, 8498-8505 (2006).
[CrossRef] [PubMed]

S. Chin, M. Gonzalez-Herraez, and L. Thévenaz, "Zero-gain slow and fast light propagation in an optical fiber," Opt. Express 14, 10684-10692 (2006).
[CrossRef] [PubMed]

2005 (5)

2003 (1)

J. C. Yong, L. Thévenaz, and B. Y. Kim, "Brillouin fiber laser pumped by a DFB laser diode," J. Lightwave Technol. 12, 546-554 (2003).
[CrossRef]

2002 (1)

A. Eyal, D. Kuperman, O. Dimenstein, and M. Tur, "Polarization dependence of the intensity modulation transfer function of an optical system with PMD and PDL," IEEE Photon. Technol. Lett. 14, 1515-1517 (2002).
[CrossRef]

2001 (1)

A. Loayssa, D. Benito, and M. J. Grade, "High resolution measurement of stimulated Brillouin scattering spectra in single-mode fibers," IEE Proc. Optoelectron. 148, 143-148, (2001).
[CrossRef]

2000 (2)

J. P. Gordon and H. Kogelnik, "PMD fundamentals: polarization mode dispersion in optical fibers", P. Natl. Acad. Sci. USA 97, 4541-4550, (2000).
[CrossRef]

A. Loayssa, D. Benito, and M. J. Grade, "Optical carrier-suppression technique with a Brillouin-erbium fiber laser," Opt. Lett. 25, 197-199 (2000).
[CrossRef]

1999 (2)

1997 (2)

A. Küng, L. Thévenaz, and P. A. Robert, "Polarization analysis of Brillouin scattering in a circularly birefringent fiber ring resonator," J. Lightwave. Technol. 15, 977-982 (1997).
[CrossRef]

M. Nikles, L. Thévenaz, and P. Robert, "Brillouin gain spectrum characterization in single-mode optical fibers," J. Lightwave Technol. 15, 1842-1851 (1997).
[CrossRef]

1995 (1)

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, "Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering," J. Lightwave Technol. 13, 1340-1348 (1995).
[CrossRef]

1994 (1)

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

1993 (1)

1990 (1)

T. Horiguchi, T. Kurashima, and M. Tateda, "A technique to measure distributed strain in optical fibers," IEEE Photon. Technol. Lett. 2, 352-354 (1990).
[CrossRef]

1989 (1)

1979 (1)

R. H. Stolen, "Polarization effects in fiber Raman and Brillouin lasers," IEEE J. of Quantum Electron. 15, 1157-1160, (1979).
[CrossRef]

1947 (1)

Azuma, Y.

Bao, X.

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, "Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering," J. Lightwave Technol. 13, 1340-1348 (1995).
[CrossRef]

X. Bao, D. J. Webb, and D. A. Jackson, "32-km distributed temperature sensor using Brillouin loss in optical fiber," Opt. Lett. 18, 1561-1563 (1993).
[CrossRef] [PubMed]

Bashkanski, M.

D. R. Walker, M. Bashkanski, A. Gulian, F. K. Fatemi, and M. Steiner, "Stabilizing slow light delay in stimulated Brillouin scattering using a Faraday rotator mirror," to be published in J. Opt. Soc. Am. B 25, (2008).

Benito, D.

A. Loayssa, D. Benito, and M. J. Grade, "High resolution measurement of stimulated Brillouin scattering spectra in single-mode fibers," IEE Proc. Optoelectron. 148, 143-148, (2001).
[CrossRef]

A. Loayssa, D. Benito, and M. J. Grade, "Optical carrier-suppression technique with a Brillouin-erbium fiber laser," Opt. Lett. 25, 197-199 (2000).
[CrossRef]

Boot, A. J.

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

Boyd, R. W.

Capmany, J.

A. Loayssa, J. Capmany, M. Sagues, and J. Mora, "Demonstration of incoherent microwave photonic filters with all-optical complex coefficients," IEEE Photon. Technol. Lett. 18, 1744-1746 (2006).
[CrossRef]

Chen, K.

Y. Shen, X. Zhang, and K. Chen, "Optical single side-band modulation of 11 GHz RoF system using stimulated Brillouin scattering," IEEE Photon. Technol. Lett. 17, 1277-1279 (2005).
[CrossRef]

Chin, S.

Corsi, F.

Dawes, A. M. C.

Dhliwayo, J.

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, "Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering," J. Lightwave Technol. 13, 1340-1348 (1995).
[CrossRef]

Dimenstein, O.

A. Eyal, D. Kuperman, O. Dimenstein, and M. Tur, "Polarization dependence of the intensity modulation transfer function of an optical system with PMD and PDL," IEEE Photon. Technol. Lett. 14, 1515-1517 (2002).
[CrossRef]

Eyal, A.

Fatemi, F. K.

D. R. Walker, M. Bashkanski, A. Gulian, F. K. Fatemi, and M. Steiner, "Stabilizing slow light delay in stimulated Brillouin scattering using a Faraday rotator mirror," to be published in J. Opt. Soc. Am. B 25, (2008).

Fatome, J.

Gaeta, A. L.

Galtarossa, A.

A. Galtarossa, L. Palmieri, M. Santagiustina, L. Schenato, and L. Ursini, "Polarized Brillouin amplification in randomly birefringent and unidrectionally spun fibers," IEEE Photon Technol. Lett 20, 1420-1422 (2008).
[CrossRef]

F. Corsi, A. Galtarossa, and L. Palmieri, "Analytical treatment of polarization mode dispersion in single mode fibers by means of the backscattered signal," J. Opt. Soc. Am. A 16, 574-583, (1999).
[CrossRef]

Gauthier, D. J.

Gonzalez Herraez, M.

Gonzalez-Herraez, M.

González-Herráez, M.

M. González-Herráez, K.-Y. Song, and L. Thévenaz, "Arbitrary-bandwidth Brillouin slow light in optical fibers," Opt. Express 14, 1395-1400 (2006).
[CrossRef] [PubMed]

M. González-Herráez, K.-Y. Song, and L. Thévenaz, "Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering," Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

Gordon, J. P.

J. P. Gordon and H. Kogelnik, "PMD fundamentals: polarization mode dispersion in optical fibers", P. Natl. Acad. Sci. USA 97, 4541-4550, (2000).
[CrossRef]

Grade, M. J.

A. Loayssa, D. Benito, and M. J. Grade, "High resolution measurement of stimulated Brillouin scattering spectra in single-mode fibers," IEE Proc. Optoelectron. 148, 143-148, (2001).
[CrossRef]

A. Loayssa, D. Benito, and M. J. Grade, "Optical carrier-suppression technique with a Brillouin-erbium fiber laser," Opt. Lett. 25, 197-199 (2000).
[CrossRef]

Gulian, A.

D. R. Walker, M. Bashkanski, A. Gulian, F. K. Fatemi, and M. Steiner, "Stabilizing slow light delay in stimulated Brillouin scattering using a Faraday rotator mirror," to be published in J. Opt. Soc. Am. B 25, (2008).

Heron, N.

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, "Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering," J. Lightwave Technol. 13, 1340-1348 (1995).
[CrossRef]

Horiguchi, T.

Jackson, D. A.

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, "Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering," J. Lightwave Technol. 13, 1340-1348 (1995).
[CrossRef]

X. Bao, D. J. Webb, and D. A. Jackson, "32-km distributed temperature sensor using Brillouin loss in optical fiber," Opt. Lett. 18, 1561-1563 (1993).
[CrossRef] [PubMed]

Jones, R. C.

Kim, B. Y.

J. C. Yong, L. Thévenaz, and B. Y. Kim, "Brillouin fiber laser pumped by a DFB laser diode," J. Lightwave Technol. 12, 546-554 (2003).
[CrossRef]

Kogelnik, H.

J. P. Gordon and H. Kogelnik, "PMD fundamentals: polarization mode dispersion in optical fibers", P. Natl. Acad. Sci. USA 97, 4541-4550, (2000).
[CrossRef]

Küng, A.

A. Küng, L. Thévenaz, and P. A. Robert, "Polarization analysis of Brillouin scattering in a circularly birefringent fiber ring resonator," J. Lightwave. Technol. 15, 977-982 (1997).
[CrossRef]

Kuperman, D.

A. Eyal, D. Kuperman, O. Dimenstein, and M. Tur, "Polarization dependence of the intensity modulation transfer function of an optical system with PMD and PDL," IEEE Photon. Technol. Lett. 14, 1515-1517 (2002).
[CrossRef]

Kurashima, T.

T. Horiguchi, T. Kurashima, and M. Tateda, "A technique to measure distributed strain in optical fibers," IEEE Photon. Technol. Lett. 2, 352-354 (1990).
[CrossRef]

Lahoz, F. J.

A. Loayssa, and F. J. Lahoz, "Broadband RF photonic phase shifter based on stimulated Brillouin scattering and single side-band modulation," IEEE Photon. Technol. Lett. 18, 208-210 (2006).
[CrossRef]

Loayssa, A.

A. Loayssa, and F. J. Lahoz, "Broadband RF photonic phase shifter based on stimulated Brillouin scattering and single side-band modulation," IEEE Photon. Technol. Lett. 18, 208-210 (2006).
[CrossRef]

A. Loayssa, J. Capmany, M. Sagues, and J. Mora, "Demonstration of incoherent microwave photonic filters with all-optical complex coefficients," IEEE Photon. Technol. Lett. 18, 1744-1746 (2006).
[CrossRef]

A. Loayssa, D. Benito, and M. J. Grade, "High resolution measurement of stimulated Brillouin scattering spectra in single-mode fibers," IEE Proc. Optoelectron. 148, 143-148, (2001).
[CrossRef]

A. Loayssa, D. Benito, and M. J. Grade, "Optical carrier-suppression technique with a Brillouin-erbium fiber laser," Opt. Lett. 25, 197-199 (2000).
[CrossRef]

Millot, G.

Mora, J.

A. Loayssa, J. Capmany, M. Sagues, and J. Mora, "Demonstration of incoherent microwave photonic filters with all-optical complex coefficients," IEEE Photon. Technol. Lett. 18, 1744-1746 (2006).
[CrossRef]

Neifeld, M. A.

Nikles, M.

M. Nikles, L. Thévenaz, and P. Robert, "Brillouin gain spectrum characterization in single-mode optical fibers," J. Lightwave Technol. 15, 1842-1851 (1997).
[CrossRef]

Okawachi, Y.

Palmieri, L.

A. Galtarossa, L. Palmieri, M. Santagiustina, L. Schenato, and L. Ursini, "Polarized Brillouin amplification in randomly birefringent and unidrectionally spun fibers," IEEE Photon Technol. Lett 20, 1420-1422 (2008).
[CrossRef]

F. Corsi, A. Galtarossa, and L. Palmieri, "Analytical treatment of polarization mode dispersion in single mode fibers by means of the backscattered signal," J. Opt. Soc. Am. A 16, 574-583, (1999).
[CrossRef]

Pitois, S.

Randoux, S.

S. Randoux, and J. Zemmouri, "Polarization dynamics of a Brillouin fiber ring laser," Phys. Rev. A 59,1644-1653 (1999).
[CrossRef]

Robert, P.

M. Nikles, L. Thévenaz, and P. Robert, "Brillouin gain spectrum characterization in single-mode optical fibers," J. Lightwave Technol. 15, 1842-1851 (1997).
[CrossRef]

Robert, P. A.

A. Küng, L. Thévenaz, and P. A. Robert, "Polarization analysis of Brillouin scattering in a circularly birefringent fiber ring resonator," J. Lightwave. Technol. 15, 977-982 (1997).
[CrossRef]

Sagues, M.

A. Loayssa, J. Capmany, M. Sagues, and J. Mora, "Demonstration of incoherent microwave photonic filters with all-optical complex coefficients," IEEE Photon. Technol. Lett. 18, 1744-1746 (2006).
[CrossRef]

Santagiustina, M.

A. Galtarossa, L. Palmieri, M. Santagiustina, L. Schenato, and L. Ursini, "Polarized Brillouin amplification in randomly birefringent and unidrectionally spun fibers," IEEE Photon Technol. Lett 20, 1420-1422 (2008).
[CrossRef]

Schenato, L.

A. Galtarossa, L. Palmieri, M. Santagiustina, L. Schenato, and L. Ursini, "Polarized Brillouin amplification in randomly birefringent and unidrectionally spun fibers," IEEE Photon Technol. Lett 20, 1420-1422 (2008).
[CrossRef]

Sharping, J. E.

Shen, Y.

Y. Shen, X. Zhang, and K. Chen, "Optical single side-band modulation of 11 GHz RoF system using stimulated Brillouin scattering," IEEE Photon. Technol. Lett. 17, 1277-1279 (2005).
[CrossRef]

Shibata, M.

Song, K. Y.

Song, K.-Y.

M. González-Herráez, K.-Y. Song, and L. Thévenaz, "Arbitrary-bandwidth Brillouin slow light in optical fibers," Opt. Express 14, 1395-1400 (2006).
[CrossRef] [PubMed]

M. González-Herráez, K.-Y. Song, and L. Thévenaz, "Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering," Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

Steiner, M.

D. R. Walker, M. Bashkanski, A. Gulian, F. K. Fatemi, and M. Steiner, "Stabilizing slow light delay in stimulated Brillouin scattering using a Faraday rotator mirror," to be published in J. Opt. Soc. Am. B 25, (2008).

Stenner, M. D.

Stolen, R. H.

R. H. Stolen, "Polarization effects in fiber Raman and Brillouin lasers," IEEE J. of Quantum Electron. 15, 1157-1160, (1979).
[CrossRef]

Tateda, M.

Thévenaz, L.

S. Chin, M. Gonzalez-Herraez, and L. Thévenaz, "Zero-gain slow and fast light propagation in an optical fiber," Opt. Express 14, 10684-10692 (2006).
[CrossRef] [PubMed]

M. González-Herráez, K.-Y. Song, and L. Thévenaz, "Arbitrary-bandwidth Brillouin slow light in optical fibers," Opt. Express 14, 1395-1400 (2006).
[CrossRef] [PubMed]

M. González-Herráez, K.-Y. Song, and L. Thévenaz, "Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering," Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

K. Y. Song, M. Gonzalez Herraez, and L. Thévenaz, "Observation of pulse delay and advancement in optical fibers using stimulated Brillouin scattering," Opt. Express 13, 82-88 (2005).
[CrossRef] [PubMed]

J. C. Yong, L. Thévenaz, and B. Y. Kim, "Brillouin fiber laser pumped by a DFB laser diode," J. Lightwave Technol. 12, 546-554 (2003).
[CrossRef]

M. Nikles, L. Thévenaz, and P. Robert, "Brillouin gain spectrum characterization in single-mode optical fibers," J. Lightwave Technol. 15, 1842-1851 (1997).
[CrossRef]

A. Küng, L. Thévenaz, and P. A. Robert, "Polarization analysis of Brillouin scattering in a circularly birefringent fiber ring resonator," J. Lightwave. Technol. 15, 977-982 (1997).
[CrossRef]

Tur, M.

Ursini, L.

A. Galtarossa, L. Palmieri, M. Santagiustina, L. Schenato, and L. Ursini, "Polarized Brillouin amplification in randomly birefringent and unidrectionally spun fibers," IEEE Photon Technol. Lett 20, 1420-1422 (2008).
[CrossRef]

van Deventer, M. O.

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

Walker, D. R.

D. R. Walker, M. Bashkanski, A. Gulian, F. K. Fatemi, and M. Steiner, "Stabilizing slow light delay in stimulated Brillouin scattering using a Faraday rotator mirror," to be published in J. Opt. Soc. Am. B 25, (2008).

Webb, D. J.

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, "Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering," J. Lightwave Technol. 13, 1340-1348 (1995).
[CrossRef]

X. Bao, D. J. Webb, and D. A. Jackson, "32-km distributed temperature sensor using Brillouin loss in optical fiber," Opt. Lett. 18, 1561-1563 (1993).
[CrossRef] [PubMed]

Willner, A. E.

Yong, J. C.

J. C. Yong, L. Thévenaz, and B. Y. Kim, "Brillouin fiber laser pumped by a DFB laser diode," J. Lightwave Technol. 12, 546-554 (2003).
[CrossRef]

Zadok, A.

Zemmouri, J.

S. Randoux, and J. Zemmouri, "Polarization dynamics of a Brillouin fiber ring laser," Phys. Rev. A 59,1644-1653 (1999).
[CrossRef]

Zhang, L.

Zhang, X.

Y. Shen, X. Zhang, and K. Chen, "Optical single side-band modulation of 11 GHz RoF system using stimulated Brillouin scattering," IEEE Photon. Technol. Lett. 17, 1277-1279 (2005).
[CrossRef]

Zhu, Z.

Appl. Phys. Lett. (1)

M. González-Herráez, K.-Y. Song, and L. Thévenaz, "Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering," Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

IEE Proc. Optoelectron. (1)

A. Loayssa, D. Benito, and M. J. Grade, "High resolution measurement of stimulated Brillouin scattering spectra in single-mode fibers," IEE Proc. Optoelectron. 148, 143-148, (2001).
[CrossRef]

IEEE J. of Quantum Electron. (1)

R. H. Stolen, "Polarization effects in fiber Raman and Brillouin lasers," IEEE J. of Quantum Electron. 15, 1157-1160, (1979).
[CrossRef]

IEEE Photon Technol. Lett (1)

A. Galtarossa, L. Palmieri, M. Santagiustina, L. Schenato, and L. Ursini, "Polarized Brillouin amplification in randomly birefringent and unidrectionally spun fibers," IEEE Photon Technol. Lett 20, 1420-1422 (2008).
[CrossRef]

IEEE Photon. Technol. Lett. (5)

A. Eyal, D. Kuperman, O. Dimenstein, and M. Tur, "Polarization dependence of the intensity modulation transfer function of an optical system with PMD and PDL," IEEE Photon. Technol. Lett. 14, 1515-1517 (2002).
[CrossRef]

Y. Shen, X. Zhang, and K. Chen, "Optical single side-band modulation of 11 GHz RoF system using stimulated Brillouin scattering," IEEE Photon. Technol. Lett. 17, 1277-1279 (2005).
[CrossRef]

T. Horiguchi, T. Kurashima, and M. Tateda, "A technique to measure distributed strain in optical fibers," IEEE Photon. Technol. Lett. 2, 352-354 (1990).
[CrossRef]

A. Loayssa, and F. J. Lahoz, "Broadband RF photonic phase shifter based on stimulated Brillouin scattering and single side-band modulation," IEEE Photon. Technol. Lett. 18, 208-210 (2006).
[CrossRef]

A. Loayssa, J. Capmany, M. Sagues, and J. Mora, "Demonstration of incoherent microwave photonic filters with all-optical complex coefficients," IEEE Photon. Technol. Lett. 18, 1744-1746 (2006).
[CrossRef]

J. Lightwave Technol. (6)

M. Nikles, L. Thévenaz, and P. Robert, "Brillouin gain spectrum characterization in single-mode optical fibers," J. Lightwave Technol. 15, 1842-1851 (1997).
[CrossRef]

J. C. Yong, L. Thévenaz, and B. Y. Kim, "Brillouin fiber laser pumped by a DFB laser diode," J. Lightwave Technol. 12, 546-554 (2003).
[CrossRef]

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, "Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering," J. Lightwave Technol. 13, 1340-1348 (1995).
[CrossRef]

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

Z. Zhu, A. M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, "Broadband SBS slow light in an optical fiber," J. Lightwave Technol. 25, 201-206 (2007).
[CrossRef]

A. Zadok, A. Eyal, and M. Tur, "GHz-wide optically reconfigurable filters using stimulated Brillouin scattering," J. Lightwave Technol. 25, 2168-2174 (2007).
[CrossRef]

J. Lightwave. Technol. (1)

A. Küng, L. Thévenaz, and P. A. Robert, "Polarization analysis of Brillouin scattering in a circularly birefringent fiber ring resonator," J. Lightwave. Technol. 15, 977-982 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

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

D. R. Walker, M. Bashkanski, A. Gulian, F. K. Fatemi, and M. Steiner, "Stabilizing slow light delay in stimulated Brillouin scattering using a Faraday rotator mirror," to be published in J. Opt. Soc. Am. B 25, (2008).

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, "Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber," J. Opt. Soc. Am. B 22, 2378-2384 (2005).
[CrossRef]

Opt. Express (6)

Opt. Lett. (3)

P. Natl. Acad. Sci. USA (1)

J. P. Gordon and H. Kogelnik, "PMD fundamentals: polarization mode dispersion in optical fibers", P. Natl. Acad. Sci. USA 97, 4541-4550, (2000).
[CrossRef]

Phys. Rev. A (1)

S. Randoux, and J. Zemmouri, "Polarization dynamics of a Brillouin fiber ring laser," Phys. Rev. A 59,1644-1653 (1999).
[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] [PubMed]

Other (7)

R. W. Boyd, Nonlinear optics, (San Diego, CA: Academic Press, 2003) Chap. 9, pp. 409-427.
[CrossRef]

A. Yariv, Optoelectronics, (Orlando FL: Saunders College Publishing, 4th Edition, 1991), Chap. 19, pp. 670-678.

E. Collett, Ed., Polarized light fundamentals and applications. (New York: Marcel Dekker, 1993).

L. Thévenaz, A. Zadok, A. Eyal, and M. Tur, "All-optical polarization control through Brillouin amplification," paper OML7 in OFC/NFOEC 2008, San Diego, Ca, (2008).

L. Thévenaz, S. Foaleng Mafang, and M. Nikles, "Fast measurement of local PMD with high spatial resolution using stimulated Brillouin scattering," paper 10.1.2 in ECOC 2007, Berlin, Germany, (2007).

In [21], the pump and probe SOPs are defined in two different reference frames, corresponding to opposite directions of propagation. In this work, as well as in most of the literature on polarization [23,24], a single reference frame is used. Therefore, we defer the mathematical description of the conditions for maximum/minimum SBS gain to Section 2.

M. Brodsky, N. J. Frigo, ad M. Tur, "Polarization mode dispersion," chapter 17 in Optical Fiber Telecommunications V-A, Ed. I. P. Kaminow, T. Li and A. E. Willner, (Academic Press, 2008).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1.

(a). The projection, ŝin_max sig·ŝpump*(z=0), of the input signal (normalized) Stokes vector for maximum SBS gain, onto the (normalized) Stokes vector corresponding to E⃗*pump(z=0), as a function of pump power, for 20 different fiber realizations. (b) The pump power dependence of max s ̂ sig ( z = 0 ) { s ̂ pump · s ̂ sig L } for the same realizations. The beat length in all realizations was 40 m.

Fig. 2.
Fig. 2.

Signal gain as a function of pump power for different SOPs of the input signal. The linear curves are calculated for an input SOP, aligned with either the pump-dependent E⃗in_max sig (blue-top line), or orthogonal to it, i.e., parallel to E⃗in_min sig (green-bottom line). The red-dashed line is for the case where the input SOP deviates from E⃗in_min sig (Ppump =50mW) pump by a π/20 rad rotation about the ŝ1 axis on the Poincare sphere

Fig. 3.
Fig. 3.

(a) and (b): Scatter plots of output amplified signal SOP on the Poincare sphere, corresponding to 100 random input signal SOPs, for a specific fiber realization. The input pump Stokes vector ŝpump was chosen as [0 1 0] T . The horizontal and vertical axes in all figures correspond to the Stokes s 1 and s 3 axes, respectively. Red closed circles indicate SOPs for which s 2 is positive, whereas open blue squares indicate a negative s 2. ‘X’ denotes the location E⃗out_max sig in Stokes space. The pump power was 5 mW (a) and 50 mW (b). (c): Stokes space projection of the signal SOP on the conjugate of the pump SOP, ŝpump*(z)·ŝsig(z), as a function of position for an input signal SOP exactly orthogonal to that of E⃗*pump(z=0). Pump power was 25 mW (red dashed), 40 mW (black dotted) and 50 mW (blue solid).

Fig. 4.
Fig. 4.

Scatter plots of attenuated output signal SOP on the Poincare sphere, corresponding to 100 random input signal SOPs, for a specific fiber realization. The input pump Stokes vector ŝpump was chosen as [0 1 0] T . The horizontal and vertical axes in all figures correspond to Stokes s 1 and s 3 axes, respectively. Red closed circles indicate SOPs for which s 2 is positive, whereas open blue squares indicate a negative s 2. X’ denotes the location E⃗out_maxsig in Stokes space. The pump power was 5 mW (left), 25 mW (center) and 50 mW (right).

Fig. 5.
Fig. 5.

Experimental setup for characterizing the polarization dependence of SBS. ATT: Optical attenuator. VOA: Variable optical attenuator. FBG: Fiber Bragg grating. DSB: Double side band modulation. SSB: single side band modulation. PC: Polarization controller. EDFA: Erbium-doped fiber amplifier. EOM: electro-optic modulator. νp denotes the optical frequency of the pump

Fig. 6.
Fig. 6.

(a). SBS gain (Stokes signal) in dB as a function of pump power, for a 2250 m long fiber. Lower curve (Green) — optimized for minimum gain, Upper curve (Blue) — optimized for maximum gain, Dashed curve (Red) — for an input SOP in the vicinity of E⃗in_minsig(Stokes) , rotated from it by 400 around the s3 (RL) axis (the black squares are explained in the text). (b) The SOPs of the emerging amplified signals for the three cases of (a): maximum (blue solid circles), minimum (green open diamonds), and red squares for the intermediate case. Open symbols denote SOPs in the back of the sphere. The size of the square is a measure of the signal power, increasing with pump power for Stokes signals. The black ‘+’ is the SOP of the spontaneous SBS. The straight line through the center of the sphere connects this SOP to its orthogonal counterpart. (c) SBS attenuation (anti-Stokes signal) in dB as a function of pump power. Lower curve (Green) — optimized for minimum output power (maximum attenuation), Upper curve (Blue)— optimized for maximum output power (minimum attenuation), Dashed curve (Red) — for an input SOP in the vicinity of E⃗in_min sig(A-Stokes), rotated from it by 400 around the s3 (RL) axis. (d) The SOPs of the emerging attenuated signals for the cases of (c): maximum (blue open circles), minimum (green solid diamonds), and red squares for the intermediate case. The straight line through the center of the sphere is that of (b), shown here for reference.

Fig. 7.
Fig. 7.

Measured output signal SOP for SBS signal gain and SBS signal loss for twenty evenly distributed input signal SOPs. (a) Stokes SOP, pump power is 5 mW. (b) Stokes SOP, pump power is 45 mW. (c) Anti-Stokes SOP, pump power is 20mW (SOP measurements in the signal attenuation scenario were difficult due to the presence of spontaneous SBS, which competed with the attenuated signal. Thus, reliable readings could not be obtained for pump powers above 25 mW.)

Equations (37)

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

E sig ( z ) = T ( z ) E sig ( 0 )
E pump ( 0 ) = T T ( z ) E pump ( z ) E pump ( z ) = T * ( z ) E pump ( 0 ) ;
d E sig ( z ) dz = [ d T ( z ) dz T ( z ) + γ 0 2 [ E pump ( z ) E pump ( z ) ] ] E sig ( z )
d E pump ( z ) dz = [ d T * ( z ) dz T T ( z ) + γ 0 2 E sig ( z ) E sig ( z ) ] E pump ( z )
E sig ( L ) = H · E sig ( 0 ) ,
H = U · S · V = U · [ G 1 0 0 G 2 ] · V ,
E sig in _ max = [ V ] 1 [ 1 0 ] = V [ 1 0 ] ; E sig in _ min = V [ 0 1 ]
E sig out _ max = U · S · V · V [ 1 0 ] = U · S [ 1 0 ] = G 1 U [ 1 0 ]
E sig out _ min = U · S · V · V [ 0 1 ] = U · S [ 0 1 ] = G 2 U [ 0 1 ]
E sig in = α 0 E sig in _ max + β 0 E sig in _ min
E sig out = α 0 G 1 U [ 1 0 ] + β 0 G 2 U [ 0 1 ]
P sig out = α 0 2 G 1 2 + β 0 2 G 2 2
d S 0 _ sig ( z ) dz = γ 0 P pump ( z ) 2 ( 1 + s ̂ pump ( z ) · s ̂ sig ( z ) ) S 0 _ sig ( z )
d s ̂ sig ( z ) dz = β ( z ) · s ̂ sig ( z ) + γ 0 P pump ( z ) 2 s ̂ sig ( z ) · ( s ̂ pump ( z ) · s ̂ sig ( z ) )
= β ( z ) · s ̂ sig ( z ) + γ 0 P pump ( z ) 2 [ s ̂ pump ( z ) ( s ̂ pump ( z ) · s ̂ sig ( z ) ) s ̂ sig ( z ) ]
β · σ 2 j d T dz T ,
d ln ( S 0 _ sig ) dz = γ 0 P pump ( z ) 2 ( 1 + s ̂ pump · s ̂ sig ) .
S 0 _ sig out = S 0 _ sig in exp [ γ 0 P pump 2 0 L ( 1 + s ̂ pump · s ̂ sig ) dz ' ]
= S 0 _ sig in exp [ γ 0 P pump 2 L ( 1 + s ̂ pump · s ̂ sig L ) ]
γ = γ 0 2 ( 1 + s ̂ pump · s ̂ sig L )
s ̂ pump · s ̂ sig L s ̂ pump ( z ) · s ̂ sig ( z ) Ensemble Average = s ̂ pump T ( 0 ) M T * T ( z ) · M T ( z ) s ̂ sig ( 0 ) Ensemble Average
= s ̂ pump T ( 0 ) M T * T · M T ( z ) Ensemble Average s ̂ sig ( 0 )
= s ̂ pump T ( 0 ) [ 1 3 1 3 1 3 ] s ̂ sig ( 0 ) .
d E sig ( z ) dz = [ d T ( z ) dz T ( z ) + γ 0 2 E pump ( z ) E pump ( z ) ] E sig ( z )
d E pump ( z ) dz = [ d T * ( z ) dz T T ( z ) + γ 0 2 E sig ( z ) E sig ( z ) ] E pump ( z )
S 0 E E ; S 0 s ̂ E σ E ; σ 1 = [ 1 0 0 1 ] , σ 2 = [ 0 1 1 0 ] and σ 3 = [ 0 j j 0 ]
β . σ 2 j d T dz T ,
E E S 0 2 ( I + s ̂ · σ ) ,
d E sig dz = [ j 2 β · σ + γ 0 S pump 0 4 ( I + s ̂ pump · σ ) ] E sig .
d S sig 0 dz = d ( E sig E sig ) dz = E sig [ j 2 β · σ + γ 0 S pump 0 4 ( I + s ̂ pump · σ ) ] E sig +
E sig [ j 2 β · σ + γ 0 S pump 0 4 ( I + s ̂ pump · σ ) ] E sig = γ 0 2 ( 1 + s ̂ pump · s ̂ sig ) S pump 0 S sig 0
d s ̂ sig dz = d dz ( E sig σ E sig E sig E sig ) = ( E sig E sig ) d ( E sig σ E sig ) dz ( E sig σ E sig ) d ( E sig E sig ) dz ( E sig E sig ) 2
= [ d ( E sig σ E sig ) dz S sig 0 s sig γ 0 S pump 0 2 ( 1 + s ̂ pump × s ̂ sig ) ] S sig 0
= 1 S sig 0 [ ( d dz E sig ) σ E sig + E sig σ ( d dz E sig ) ] γ 0 S pump 0 2 ( 1 + s ̂ pump × s ̂ sig ) s ̂ sig
= β × s ̂ sig + γ 0 S pump 0 2 [ s ̂ sig + s ̂ pump ] γ 0 S pump 0 2 ( 1 + s ̂ pump × s ̂ sig ) s ̂ sig
= β × s ̂ sig + γ 0 S pump 0 2 s ̂ pump γ 0 S pump 0 2 ( s ̂ pump × s ̂ sig ) s ̂ sig = β × s ̂ sig + γ 0 S pump 0 2 s ̂ sig × ( s ̂ pump × s ̂ sig )
d S sig 0 dz = γ 0 2 ( 1 + s ̂ pump × s ̂ pump ) S pump 0 S sig 0 d s ̂ sig dz = β × s ̂ sig + γ 0 S pump 0 2 s ̂ sig × ( s ̂ pump × s ̂ sig ) ; d S pump 0 dz = γ 0 2 ( 1 + s ̂ sig × s ̂ pump ) S sig 0 S pump 0 d s ̂ pump dz = β ˜ × s ̂ pump + γ 0 S sig 0 2 s ̂ pump × ( s ̂ sig × s ̂ pump )

Metrics