Abstract

The time-averaged Stokes vectors obtained after polarization-scrambled light containing multiple, independently polarized frequency components traverses an optical fiber collectively form a surface in Stokes space. The geometry of this surface can be directly related to the polarization mode dispersion of the fiber. This paper examines both numerically and experimentally an improved method for performing such measurements. Additionally, it quantifies the surfaces associated with input pulses containing an arbitrary set of equally spaced frequencies.

© 2014 Optical Society of America

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References

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  1. A. E. Willner, S. M. R. M. Nezam, L. Yan, and M. C. Hauer, “Monitoring and control of polarization-related impairments in optical fiber systems,” J. Lightwave Technol. 22, 106–125 (2004).
    [CrossRef]
  2. P. C. Chou, J. M. Fini, and H. A. Haus, “Real-time principal state characterization for use in PMD compensators,” IEEE Photon. Technol. Lett. 13, 568–570 (2001).
    [CrossRef]
  3. C. D. Poole and J. Nagel, “Polarization effects in lightwave systems,” in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, 1997), pp. 114–161.
  4. J. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000).
    [CrossRef]
  5. M. Reimer, “Modeling and simulation of polarization mode dispersion and polarization dependent loss,” M.Sc. thesis (University of Waterloo, 2007).
  6. M. Reimer, “Simulation methods for the temporal and frequency dynamics of optical communication systems,” Ph.D. thesis (University of Waterloo, 2012).
  7. J. Damask, Polarization Optics in Telecommunications (Springer, 2005).
  8. R. Noe, D. Sandel, M. Yoshida-Dierolf, S. Hinz, V. Mirvoda, A. Schopflin, C. Gungener, E. Gottwald, C. Scheerer, G. Fischer, T. Weyrauch, and W. Haase, “Polarization mode dispersion compensation at 10, 20, and 40  Gb/s with various optical equalizers,” J. Lightwave Technol. 17, 1602–1616 (1999).
    [CrossRef]
  9. T. Merker, N. Hahnenkamp, and P. Meissner, “Comparison of PMD-compensation techniques at 10  Gbit/s using an optical first-order compensator and electrical transversal filter,” Opt. Commun. 182, 135–141 (2000).
    [CrossRef]
  10. F. Buchali and H. Bulow, “Adaptive PMD compensation by electrical and optical techniques,” J. Lightwave Technol. 22, 1116–1126 (2004).
    [CrossRef]
  11. P. Krummrich and K. Kotton, “Extremely fast (microsecond timescale) polarization changes in high-speed long haul WDM transmission systems,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2004), paper FI3.
  12. G. Soliman, M. Reimer, and D. Yevick, “Measurement and simulation of polarization transients in dispersion compensation modules,” J. Opt. Soc. Am. A 27, 2532–2541 (2010).
    [CrossRef]
  13. S. M. R. M. Nezam, J. E. McGeehan, and A. E. Willner, “Degree-of-polarization-based PMD monitoring for subcarrier-multiplexed signals via equalized carrier/sideband filtering,” J. Lightwave Technol. 22, 1078–1085 (2004).
    [CrossRef]
  14. S. M. R. M. Nezam and A. E. Willner, “Measuring fiber and component DGD using polarized limited-bandwidth optical sources and monitoring the DOP,” IEEE Photon. Technol. Lett. 16, 1694–1696 (2004).
    [CrossRef]
  15. P. B. Phua, J. M. Fini, and H. A. Haus, “Real-time first- and second-order PMD characterization using averaged state-of-polarization of filtered signal and polarization scrambling,” J. Lightwave Technol. 21, 982–989 (2003).
    [CrossRef]
  16. C. Francia, F. Bruyere, J.-P. Thiery, and D. Penninckx, “Simple dynamic polarisation mode dispersion compensator,” Electron. Lett. 35, 414–415 (1999).
    [CrossRef]
  17. H. Bulow, W. Baumert, H. Schmuck, F. Mohr, T. Schulz, F. Kuppers, and W. Weiershausen, “Measurement of the maximum speed of PMD fluctuations in installed field fiber,” in Optical Fiber Communication Conference and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, 1999), Vol. 2, pp. 83–85.

2010 (1)

2004 (4)

2003 (1)

2001 (1)

P. C. Chou, J. M. Fini, and H. A. Haus, “Real-time principal state characterization for use in PMD compensators,” IEEE Photon. Technol. Lett. 13, 568–570 (2001).
[CrossRef]

2000 (2)

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

T. Merker, N. Hahnenkamp, and P. Meissner, “Comparison of PMD-compensation techniques at 10  Gbit/s using an optical first-order compensator and electrical transversal filter,” Opt. Commun. 182, 135–141 (2000).
[CrossRef]

1999 (2)

Baumert, W.

H. Bulow, W. Baumert, H. Schmuck, F. Mohr, T. Schulz, F. Kuppers, and W. Weiershausen, “Measurement of the maximum speed of PMD fluctuations in installed field fiber,” in Optical Fiber Communication Conference and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, 1999), Vol. 2, pp. 83–85.

Bruyere, F.

C. Francia, F. Bruyere, J.-P. Thiery, and D. Penninckx, “Simple dynamic polarisation mode dispersion compensator,” Electron. Lett. 35, 414–415 (1999).
[CrossRef]

Buchali, F.

Bulow, H.

F. Buchali and H. Bulow, “Adaptive PMD compensation by electrical and optical techniques,” J. Lightwave Technol. 22, 1116–1126 (2004).
[CrossRef]

H. Bulow, W. Baumert, H. Schmuck, F. Mohr, T. Schulz, F. Kuppers, and W. Weiershausen, “Measurement of the maximum speed of PMD fluctuations in installed field fiber,” in Optical Fiber Communication Conference and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, 1999), Vol. 2, pp. 83–85.

Chou, P. C.

P. C. Chou, J. M. Fini, and H. A. Haus, “Real-time principal state characterization for use in PMD compensators,” IEEE Photon. Technol. Lett. 13, 568–570 (2001).
[CrossRef]

Damask, J.

J. Damask, Polarization Optics in Telecommunications (Springer, 2005).

Fini, J. M.

P. B. Phua, J. M. Fini, and H. A. Haus, “Real-time first- and second-order PMD characterization using averaged state-of-polarization of filtered signal and polarization scrambling,” J. Lightwave Technol. 21, 982–989 (2003).
[CrossRef]

P. C. Chou, J. M. Fini, and H. A. Haus, “Real-time principal state characterization for use in PMD compensators,” IEEE Photon. Technol. Lett. 13, 568–570 (2001).
[CrossRef]

Fischer, G.

Francia, C.

C. Francia, F. Bruyere, J.-P. Thiery, and D. Penninckx, “Simple dynamic polarisation mode dispersion compensator,” Electron. Lett. 35, 414–415 (1999).
[CrossRef]

Gordon, J.

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

Gottwald, E.

Gungener, C.

Haase, W.

Hahnenkamp, N.

T. Merker, N. Hahnenkamp, and P. Meissner, “Comparison of PMD-compensation techniques at 10  Gbit/s using an optical first-order compensator and electrical transversal filter,” Opt. Commun. 182, 135–141 (2000).
[CrossRef]

Hauer, M. C.

Haus, H. A.

P. B. Phua, J. M. Fini, and H. A. Haus, “Real-time first- and second-order PMD characterization using averaged state-of-polarization of filtered signal and polarization scrambling,” J. Lightwave Technol. 21, 982–989 (2003).
[CrossRef]

P. C. Chou, J. M. Fini, and H. A. Haus, “Real-time principal state characterization for use in PMD compensators,” IEEE Photon. Technol. Lett. 13, 568–570 (2001).
[CrossRef]

Hinz, S.

Kogelnik, H.

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

Kotton, K.

P. Krummrich and K. Kotton, “Extremely fast (microsecond timescale) polarization changes in high-speed long haul WDM transmission systems,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2004), paper FI3.

Krummrich, P.

P. Krummrich and K. Kotton, “Extremely fast (microsecond timescale) polarization changes in high-speed long haul WDM transmission systems,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2004), paper FI3.

Kuppers, F.

H. Bulow, W. Baumert, H. Schmuck, F. Mohr, T. Schulz, F. Kuppers, and W. Weiershausen, “Measurement of the maximum speed of PMD fluctuations in installed field fiber,” in Optical Fiber Communication Conference and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, 1999), Vol. 2, pp. 83–85.

McGeehan, J. E.

Meissner, P.

T. Merker, N. Hahnenkamp, and P. Meissner, “Comparison of PMD-compensation techniques at 10  Gbit/s using an optical first-order compensator and electrical transversal filter,” Opt. Commun. 182, 135–141 (2000).
[CrossRef]

Merker, T.

T. Merker, N. Hahnenkamp, and P. Meissner, “Comparison of PMD-compensation techniques at 10  Gbit/s using an optical first-order compensator and electrical transversal filter,” Opt. Commun. 182, 135–141 (2000).
[CrossRef]

Mirvoda, V.

Mohr, F.

H. Bulow, W. Baumert, H. Schmuck, F. Mohr, T. Schulz, F. Kuppers, and W. Weiershausen, “Measurement of the maximum speed of PMD fluctuations in installed field fiber,” in Optical Fiber Communication Conference and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, 1999), Vol. 2, pp. 83–85.

Nagel, J.

C. D. Poole and J. Nagel, “Polarization effects in lightwave systems,” in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, 1997), pp. 114–161.

Nezam, S. M. R. M.

Noe, R.

Penninckx, D.

C. Francia, F. Bruyere, J.-P. Thiery, and D. Penninckx, “Simple dynamic polarisation mode dispersion compensator,” Electron. Lett. 35, 414–415 (1999).
[CrossRef]

Phua, P. B.

Poole, C. D.

C. D. Poole and J. Nagel, “Polarization effects in lightwave systems,” in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, 1997), pp. 114–161.

Reimer, M.

G. Soliman, M. Reimer, and D. Yevick, “Measurement and simulation of polarization transients in dispersion compensation modules,” J. Opt. Soc. Am. A 27, 2532–2541 (2010).
[CrossRef]

M. Reimer, “Modeling and simulation of polarization mode dispersion and polarization dependent loss,” M.Sc. thesis (University of Waterloo, 2007).

M. Reimer, “Simulation methods for the temporal and frequency dynamics of optical communication systems,” Ph.D. thesis (University of Waterloo, 2012).

Sandel, D.

Scheerer, C.

Schmuck, H.

H. Bulow, W. Baumert, H. Schmuck, F. Mohr, T. Schulz, F. Kuppers, and W. Weiershausen, “Measurement of the maximum speed of PMD fluctuations in installed field fiber,” in Optical Fiber Communication Conference and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, 1999), Vol. 2, pp. 83–85.

Schopflin, A.

Schulz, T.

H. Bulow, W. Baumert, H. Schmuck, F. Mohr, T. Schulz, F. Kuppers, and W. Weiershausen, “Measurement of the maximum speed of PMD fluctuations in installed field fiber,” in Optical Fiber Communication Conference and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, 1999), Vol. 2, pp. 83–85.

Soliman, G.

Thiery, J.-P.

C. Francia, F. Bruyere, J.-P. Thiery, and D. Penninckx, “Simple dynamic polarisation mode dispersion compensator,” Electron. Lett. 35, 414–415 (1999).
[CrossRef]

Weiershausen, W.

H. Bulow, W. Baumert, H. Schmuck, F. Mohr, T. Schulz, F. Kuppers, and W. Weiershausen, “Measurement of the maximum speed of PMD fluctuations in installed field fiber,” in Optical Fiber Communication Conference and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, 1999), Vol. 2, pp. 83–85.

Weyrauch, T.

Willner, A. E.

Yan, L.

Yevick, D.

Yoshida-Dierolf, M.

Electron. Lett. (1)

C. Francia, F. Bruyere, J.-P. Thiery, and D. Penninckx, “Simple dynamic polarisation mode dispersion compensator,” Electron. Lett. 35, 414–415 (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

S. M. R. M. Nezam and A. E. Willner, “Measuring fiber and component DGD using polarized limited-bandwidth optical sources and monitoring the DOP,” IEEE Photon. Technol. Lett. 16, 1694–1696 (2004).
[CrossRef]

P. C. Chou, J. M. Fini, and H. A. Haus, “Real-time principal state characterization for use in PMD compensators,” IEEE Photon. Technol. Lett. 13, 568–570 (2001).
[CrossRef]

J. Lightwave Technol. (5)

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

Opt. Commun. (1)

T. Merker, N. Hahnenkamp, and P. Meissner, “Comparison of PMD-compensation techniques at 10  Gbit/s using an optical first-order compensator and electrical transversal filter,” Opt. Commun. 182, 135–141 (2000).
[CrossRef]

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

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

Other (6)

M. Reimer, “Modeling and simulation of polarization mode dispersion and polarization dependent loss,” M.Sc. thesis (University of Waterloo, 2007).

M. Reimer, “Simulation methods for the temporal and frequency dynamics of optical communication systems,” Ph.D. thesis (University of Waterloo, 2012).

J. Damask, Polarization Optics in Telecommunications (Springer, 2005).

C. D. Poole and J. Nagel, “Polarization effects in lightwave systems,” in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, 1997), pp. 114–161.

P. Krummrich and K. Kotton, “Extremely fast (microsecond timescale) polarization changes in high-speed long haul WDM transmission systems,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2004), paper FI3.

H. Bulow, W. Baumert, H. Schmuck, F. Mohr, T. Schulz, F. Kuppers, and W. Weiershausen, “Measurement of the maximum speed of PMD fluctuations in installed field fiber,” in Optical Fiber Communication Conference and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, 1999), Vol. 2, pp. 83–85.

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Figures (1)

Fig. 1.
Fig. 1.

Error for 2% additive noise of simulated measurements of a single-section DGD emulator with 1τ25ps. The planar methods are far more accurate than the ellipsoidal methods for 1τ5ps but are inferior for 15τ25ps.

Tables (1)

Tables Icon

Table 1. MSE of Eqs. (7) and (8) in the Presence of 2% Additive Noise Together with the MSE of the Two-Frequency Ellipsoidal and Planar Methods

Equations (16)

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

R=cos(τΔω)1+(1cos(τΔω))p^p^T+sin(τΔω)p^×ΦτΔω+ΛτΔω,
χo¯=ΛτΔωs^¯=π4sin(τΔω).
χo2¯=1313(23cos(τΔω)+13)2.
ϵτ2=1Si=1S(τest,iτactual)2,
ϵp^2=1Si=1Smink{±1}(p^est,i+k·p^actual2),
t^=(Nmod2/N)A0Φ0s^+(2/N)m>0cos(mα)AmΦmτΔωs^+(2/N)m>0sin(mα)AmΛmτΔωs^,
cos2(τΔω2)=3χo2¯32+12cos(α)2cos(α),
pi2=3(t^·x^i)2¯+12cos(α)(12cos2(τΔω2))12cos(α)(1cos2(τΔω2)).
Φa=cos(a)1+(1cos(a))p^p^T,Λa=sin(a)p^×,
ΦaΦb=12(Φa+b+Φab),
ΛaΛb=12(Φa+bΦab),
ΛaΦb=12(Λa+b+Λab).
tr(ΦakΦb)=1+2cosk(a)cos(b),
tr(ΛakΛb)={2(1)k+2sink(a)sin(b),if(k+)even,0,if(k+)odd,
tr(ΦaPiΦb)=cos(a)cos(b)+(1cos(a)cos(b))pi2,
tr(ΛaPiΛb)=sin(a)sin(b)(1pi2),

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