Abstract

Polarization-dependent gain (PDG) of fiber Raman amplifiers (FRAs) will degrade the performance of optical communication systems. An efficient numerical model is presented to predict PDG quantitatively by substituting the polarization-dependent polarization factor for the constant one in the coupled nonlinear equations usually adopted. The simulation is carried out by estimating the polarization length by use of the average polarization-mode dispersion of the tested fiber; the results, including the Raman gain profile and the fluctuation of the PDG, are highly accordant with the experimental data reported previously. The model can aid in the design of FRAs and in the analysis of system performance.

© 2004 Optical Society of America

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References

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  1. R. H. Stolen, “Polarization effects in fiber Raman and Brillouin lasers,” IEEE J. Quantum Electron. QE-15, 1157–1160 (1979).
    [CrossRef]
  2. M. C. Tobin, T. Baak, “Raman spectra of some low-expansion glasses,” J. Opt. Soc. Am. 58, 1459–1461 (1968).
    [CrossRef]
  3. A. Berntson, S. Popov, E. Vanin, G. Jacobsen, J. Karlsson, “Polarisation dependence and gain tilt of Raman amplifiers for WDM systems,” in Postconference Digest of the Optical Fiber Communication Conference (OFC) (Optical Society of America, Washington, D.C., 2001), paper MI2.
  4. S. Popov, E. Vanin, G. Jacobsen, “Influence of polarization mode dispersion value in dispersion-compensating fibers on the polarization dependence of Raman gain,” Opt. Lett. 27, 848–850 (2002).
    [CrossRef]
  5. D. Mahgerefteh, H. Y. Hu, D. L. Butler, J. Goldhar, D. Wang, E. Golovchenko, A. N. Pilipetskii, C. R. Menyuk, L. J. Joneckis, “Effect of randomly varying birefringence on the Raman gain in optical fibers,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 11 of OSA 1997 Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper CThW5.
  6. P. Ebrahimi, M. C. Hauer, Q. Yu, R. Khosravani, D. Gurkan, D. W. Kim, D. W. Lee, A. E. Willner, “Statistics of polarization dependent gain in Raman fiber amplifiers due to PMD,” in Postconference Digest of Conference on Lasers and Electro-optics (CLEO) (Optical Society of America, Washington, D.C., 2001), paper CTuJ.
  7. J. Zhang, V. Dominic, M. Misey, S. Sanders, D. Mehuys, “Dependence of Raman polarization dependent gain on pump degree of polarization at high gain levels,” in Optical Amplifiers and Their Applications, A. Mecozzi, M. Shimizu, J. Zyskind, eds., Vol. 44 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper OMB4.
  8. R. W. Hellwarth, “Theory of phase conjugation by stimulated scattering in a waveguide,” J. Opt. Soc. Am. 68, 1050–1056 (1978).
    [CrossRef]
  9. S. Tariq, J. C. Palais, “A computer model of non-dispersion-limited stimulated Raman scattering in optical fiber multiple-channel communications,” J. Lightwave Technol. 11, 1914–1924 (1993).
    [CrossRef]
  10. V. E. Perlin, H. G. Winful, “Optimal design of flat-gain wide-band fiber Raman amplifiers,” J. Lightwave Technol. 20, 250–254 (2002).
    [CrossRef]
  11. Y. Aoki, “Properties of fiber Raman amplifiers and their applicability to digital optical communication systems,” J. Lightwave Technol. 6, 1225–1239 (1988).
    [CrossRef]

2002 (2)

1993 (1)

S. Tariq, J. C. Palais, “A computer model of non-dispersion-limited stimulated Raman scattering in optical fiber multiple-channel communications,” J. Lightwave Technol. 11, 1914–1924 (1993).
[CrossRef]

1988 (1)

Y. Aoki, “Properties of fiber Raman amplifiers and their applicability to digital optical communication systems,” J. Lightwave Technol. 6, 1225–1239 (1988).
[CrossRef]

1979 (1)

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

1978 (1)

1968 (1)

Aoki, Y.

Y. Aoki, “Properties of fiber Raman amplifiers and their applicability to digital optical communication systems,” J. Lightwave Technol. 6, 1225–1239 (1988).
[CrossRef]

Baak, T.

Berntson, A.

A. Berntson, S. Popov, E. Vanin, G. Jacobsen, J. Karlsson, “Polarisation dependence and gain tilt of Raman amplifiers for WDM systems,” in Postconference Digest of the Optical Fiber Communication Conference (OFC) (Optical Society of America, Washington, D.C., 2001), paper MI2.

Butler, D. L.

D. Mahgerefteh, H. Y. Hu, D. L. Butler, J. Goldhar, D. Wang, E. Golovchenko, A. N. Pilipetskii, C. R. Menyuk, L. J. Joneckis, “Effect of randomly varying birefringence on the Raman gain in optical fibers,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 11 of OSA 1997 Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper CThW5.

Dominic, V.

J. Zhang, V. Dominic, M. Misey, S. Sanders, D. Mehuys, “Dependence of Raman polarization dependent gain on pump degree of polarization at high gain levels,” in Optical Amplifiers and Their Applications, A. Mecozzi, M. Shimizu, J. Zyskind, eds., Vol. 44 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper OMB4.

Ebrahimi, P.

P. Ebrahimi, M. C. Hauer, Q. Yu, R. Khosravani, D. Gurkan, D. W. Kim, D. W. Lee, A. E. Willner, “Statistics of polarization dependent gain in Raman fiber amplifiers due to PMD,” in Postconference Digest of Conference on Lasers and Electro-optics (CLEO) (Optical Society of America, Washington, D.C., 2001), paper CTuJ.

Goldhar, J.

D. Mahgerefteh, H. Y. Hu, D. L. Butler, J. Goldhar, D. Wang, E. Golovchenko, A. N. Pilipetskii, C. R. Menyuk, L. J. Joneckis, “Effect of randomly varying birefringence on the Raman gain in optical fibers,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 11 of OSA 1997 Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper CThW5.

Golovchenko, E.

D. Mahgerefteh, H. Y. Hu, D. L. Butler, J. Goldhar, D. Wang, E. Golovchenko, A. N. Pilipetskii, C. R. Menyuk, L. J. Joneckis, “Effect of randomly varying birefringence on the Raman gain in optical fibers,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 11 of OSA 1997 Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper CThW5.

Gurkan, D.

P. Ebrahimi, M. C. Hauer, Q. Yu, R. Khosravani, D. Gurkan, D. W. Kim, D. W. Lee, A. E. Willner, “Statistics of polarization dependent gain in Raman fiber amplifiers due to PMD,” in Postconference Digest of Conference on Lasers and Electro-optics (CLEO) (Optical Society of America, Washington, D.C., 2001), paper CTuJ.

Hauer, M. C.

P. Ebrahimi, M. C. Hauer, Q. Yu, R. Khosravani, D. Gurkan, D. W. Kim, D. W. Lee, A. E. Willner, “Statistics of polarization dependent gain in Raman fiber amplifiers due to PMD,” in Postconference Digest of Conference on Lasers and Electro-optics (CLEO) (Optical Society of America, Washington, D.C., 2001), paper CTuJ.

Hellwarth, R. W.

Hu, H. Y.

D. Mahgerefteh, H. Y. Hu, D. L. Butler, J. Goldhar, D. Wang, E. Golovchenko, A. N. Pilipetskii, C. R. Menyuk, L. J. Joneckis, “Effect of randomly varying birefringence on the Raman gain in optical fibers,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 11 of OSA 1997 Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper CThW5.

Jacobsen, G.

S. Popov, E. Vanin, G. Jacobsen, “Influence of polarization mode dispersion value in dispersion-compensating fibers on the polarization dependence of Raman gain,” Opt. Lett. 27, 848–850 (2002).
[CrossRef]

A. Berntson, S. Popov, E. Vanin, G. Jacobsen, J. Karlsson, “Polarisation dependence and gain tilt of Raman amplifiers for WDM systems,” in Postconference Digest of the Optical Fiber Communication Conference (OFC) (Optical Society of America, Washington, D.C., 2001), paper MI2.

Joneckis, L. J.

D. Mahgerefteh, H. Y. Hu, D. L. Butler, J. Goldhar, D. Wang, E. Golovchenko, A. N. Pilipetskii, C. R. Menyuk, L. J. Joneckis, “Effect of randomly varying birefringence on the Raman gain in optical fibers,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 11 of OSA 1997 Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper CThW5.

Karlsson, J.

A. Berntson, S. Popov, E. Vanin, G. Jacobsen, J. Karlsson, “Polarisation dependence and gain tilt of Raman amplifiers for WDM systems,” in Postconference Digest of the Optical Fiber Communication Conference (OFC) (Optical Society of America, Washington, D.C., 2001), paper MI2.

Khosravani, R.

P. Ebrahimi, M. C. Hauer, Q. Yu, R. Khosravani, D. Gurkan, D. W. Kim, D. W. Lee, A. E. Willner, “Statistics of polarization dependent gain in Raman fiber amplifiers due to PMD,” in Postconference Digest of Conference on Lasers and Electro-optics (CLEO) (Optical Society of America, Washington, D.C., 2001), paper CTuJ.

Kim, D. W.

P. Ebrahimi, M. C. Hauer, Q. Yu, R. Khosravani, D. Gurkan, D. W. Kim, D. W. Lee, A. E. Willner, “Statistics of polarization dependent gain in Raman fiber amplifiers due to PMD,” in Postconference Digest of Conference on Lasers and Electro-optics (CLEO) (Optical Society of America, Washington, D.C., 2001), paper CTuJ.

Lee, D. W.

P. Ebrahimi, M. C. Hauer, Q. Yu, R. Khosravani, D. Gurkan, D. W. Kim, D. W. Lee, A. E. Willner, “Statistics of polarization dependent gain in Raman fiber amplifiers due to PMD,” in Postconference Digest of Conference on Lasers and Electro-optics (CLEO) (Optical Society of America, Washington, D.C., 2001), paper CTuJ.

Mahgerefteh, D.

D. Mahgerefteh, H. Y. Hu, D. L. Butler, J. Goldhar, D. Wang, E. Golovchenko, A. N. Pilipetskii, C. R. Menyuk, L. J. Joneckis, “Effect of randomly varying birefringence on the Raman gain in optical fibers,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 11 of OSA 1997 Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper CThW5.

Mehuys, D.

J. Zhang, V. Dominic, M. Misey, S. Sanders, D. Mehuys, “Dependence of Raman polarization dependent gain on pump degree of polarization at high gain levels,” in Optical Amplifiers and Their Applications, A. Mecozzi, M. Shimizu, J. Zyskind, eds., Vol. 44 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper OMB4.

Menyuk, C. R.

D. Mahgerefteh, H. Y. Hu, D. L. Butler, J. Goldhar, D. Wang, E. Golovchenko, A. N. Pilipetskii, C. R. Menyuk, L. J. Joneckis, “Effect of randomly varying birefringence on the Raman gain in optical fibers,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 11 of OSA 1997 Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper CThW5.

Misey, M.

J. Zhang, V. Dominic, M. Misey, S. Sanders, D. Mehuys, “Dependence of Raman polarization dependent gain on pump degree of polarization at high gain levels,” in Optical Amplifiers and Their Applications, A. Mecozzi, M. Shimizu, J. Zyskind, eds., Vol. 44 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper OMB4.

Palais, J. C.

S. Tariq, J. C. Palais, “A computer model of non-dispersion-limited stimulated Raman scattering in optical fiber multiple-channel communications,” J. Lightwave Technol. 11, 1914–1924 (1993).
[CrossRef]

Perlin, V. E.

Pilipetskii, A. N.

D. Mahgerefteh, H. Y. Hu, D. L. Butler, J. Goldhar, D. Wang, E. Golovchenko, A. N. Pilipetskii, C. R. Menyuk, L. J. Joneckis, “Effect of randomly varying birefringence on the Raman gain in optical fibers,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 11 of OSA 1997 Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper CThW5.

Popov, S.

S. Popov, E. Vanin, G. Jacobsen, “Influence of polarization mode dispersion value in dispersion-compensating fibers on the polarization dependence of Raman gain,” Opt. Lett. 27, 848–850 (2002).
[CrossRef]

A. Berntson, S. Popov, E. Vanin, G. Jacobsen, J. Karlsson, “Polarisation dependence and gain tilt of Raman amplifiers for WDM systems,” in Postconference Digest of the Optical Fiber Communication Conference (OFC) (Optical Society of America, Washington, D.C., 2001), paper MI2.

Sanders, S.

J. Zhang, V. Dominic, M. Misey, S. Sanders, D. Mehuys, “Dependence of Raman polarization dependent gain on pump degree of polarization at high gain levels,” in Optical Amplifiers and Their Applications, A. Mecozzi, M. Shimizu, J. Zyskind, eds., Vol. 44 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper OMB4.

Stolen, R. H.

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

Tariq, S.

S. Tariq, J. C. Palais, “A computer model of non-dispersion-limited stimulated Raman scattering in optical fiber multiple-channel communications,” J. Lightwave Technol. 11, 1914–1924 (1993).
[CrossRef]

Tobin, M. C.

Vanin, E.

S. Popov, E. Vanin, G. Jacobsen, “Influence of polarization mode dispersion value in dispersion-compensating fibers on the polarization dependence of Raman gain,” Opt. Lett. 27, 848–850 (2002).
[CrossRef]

A. Berntson, S. Popov, E. Vanin, G. Jacobsen, J. Karlsson, “Polarisation dependence and gain tilt of Raman amplifiers for WDM systems,” in Postconference Digest of the Optical Fiber Communication Conference (OFC) (Optical Society of America, Washington, D.C., 2001), paper MI2.

Wang, D.

D. Mahgerefteh, H. Y. Hu, D. L. Butler, J. Goldhar, D. Wang, E. Golovchenko, A. N. Pilipetskii, C. R. Menyuk, L. J. Joneckis, “Effect of randomly varying birefringence on the Raman gain in optical fibers,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 11 of OSA 1997 Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper CThW5.

Willner, A. E.

P. Ebrahimi, M. C. Hauer, Q. Yu, R. Khosravani, D. Gurkan, D. W. Kim, D. W. Lee, A. E. Willner, “Statistics of polarization dependent gain in Raman fiber amplifiers due to PMD,” in Postconference Digest of Conference on Lasers and Electro-optics (CLEO) (Optical Society of America, Washington, D.C., 2001), paper CTuJ.

Winful, H. G.

Yu, Q.

P. Ebrahimi, M. C. Hauer, Q. Yu, R. Khosravani, D. Gurkan, D. W. Kim, D. W. Lee, A. E. Willner, “Statistics of polarization dependent gain in Raman fiber amplifiers due to PMD,” in Postconference Digest of Conference on Lasers and Electro-optics (CLEO) (Optical Society of America, Washington, D.C., 2001), paper CTuJ.

Zhang, J.

J. Zhang, V. Dominic, M. Misey, S. Sanders, D. Mehuys, “Dependence of Raman polarization dependent gain on pump degree of polarization at high gain levels,” in Optical Amplifiers and Their Applications, A. Mecozzi, M. Shimizu, J. Zyskind, eds., Vol. 44 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper OMB4.

IEEE J. Quantum Electron. (1)

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

J. Lightwave Technol. (3)

S. Tariq, J. C. Palais, “A computer model of non-dispersion-limited stimulated Raman scattering in optical fiber multiple-channel communications,” J. Lightwave Technol. 11, 1914–1924 (1993).
[CrossRef]

Y. Aoki, “Properties of fiber Raman amplifiers and their applicability to digital optical communication systems,” J. Lightwave Technol. 6, 1225–1239 (1988).
[CrossRef]

V. E. Perlin, H. G. Winful, “Optimal design of flat-gain wide-band fiber Raman amplifiers,” J. Lightwave Technol. 20, 250–254 (2002).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Lett. (1)

Other (4)

A. Berntson, S. Popov, E. Vanin, G. Jacobsen, J. Karlsson, “Polarisation dependence and gain tilt of Raman amplifiers for WDM systems,” in Postconference Digest of the Optical Fiber Communication Conference (OFC) (Optical Society of America, Washington, D.C., 2001), paper MI2.

D. Mahgerefteh, H. Y. Hu, D. L. Butler, J. Goldhar, D. Wang, E. Golovchenko, A. N. Pilipetskii, C. R. Menyuk, L. J. Joneckis, “Effect of randomly varying birefringence on the Raman gain in optical fibers,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 11 of OSA 1997 Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper CThW5.

P. Ebrahimi, M. C. Hauer, Q. Yu, R. Khosravani, D. Gurkan, D. W. Kim, D. W. Lee, A. E. Willner, “Statistics of polarization dependent gain in Raman fiber amplifiers due to PMD,” in Postconference Digest of Conference on Lasers and Electro-optics (CLEO) (Optical Society of America, Washington, D.C., 2001), paper CTuJ.

J. Zhang, V. Dominic, M. Misey, S. Sanders, D. Mehuys, “Dependence of Raman polarization dependent gain on pump degree of polarization at high gain levels,” in Optical Amplifiers and Their Applications, A. Mecozzi, M. Shimizu, J. Zyskind, eds., Vol. 44 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper OMB4.

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Figures (3)

Fig. 1
Fig. 1

Calculated normalized Raman gain coefficient profile of the tested DCF.

Fig. 2
Fig. 2

Raman gain profiles of the DCF with PMD of 0.22 ps for (a) copropagating and (b) counterpropagating pumping. The pump wavelength is 1452 nm. Circles, experimental data; triangles, simulation results. Solid curves, gain profile with depolarized pumping; dashed curves and dotted curves, maximum and minimum gain profile, respectively with polarized pumping.

Fig. 3
Fig. 3

Raman gain profiles for copropagating pumping configuration. The pump wavelength is 1466 nm. The average PMD of the tested DCF is (a) 0.22 ps and (b) 0.72 ps. Curves are as in Fig. 2.

Equations (15)

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

Ep=[xAx exp(ikpxz)+yAy exp(ikpyz)]ψ8πnc1/2exp(-iωpt),
Es=expγz2[xBx exp(iksxz)+yBy exp(iksyz)]ψ8πnc1/2exp(-iωst),
γBx=β|Ax|2Bx+βAxAy*ByK,
γBy=β|Ay|2By+βAyAx*BxK,
K=0Lexp(iΔkz)Ldz=expiΔkL2sin[(ΔkL)/2](ΔkL)/2,
Δk=(kpx-kpy)-(ksx-ksy)=2πcδnδν,
γ=(1±K)2βP,
lp=cδnδν.
Re(K)=cosΔkL2sin[(ΔkL)/2](ΔkL)/2=sin[2π(L/lp)]2π(L/lp).
±dPkdz=-αkPk+j=1k-1gνj(νj-νk)KeffAeffPjPk-j=k+1m+nνkνjgνk(νk-νj)KeffAeffPjPk.
Keff*=[(1±K)/2]-1.
lp0=cδnδν0.
Keff*=21±sin[2π(Lk/lp)]2π(Lk/lp),k=1, 2,, N,
δn=LfiberΔτc,
lp0=LfiberΔτδν0.

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