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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 18 — Sep. 1, 2008
  • pp: 14057–14063
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PMD monitoring in traffic-carrying optical systems and its statistical analysis

Junfeng Jiang, Sathyanarayanan Sundhararajan, Doug Richards, Steve Oliva, and Rongqing Hui  »View Author Affiliations


Optics Express, Vol. 16, Issue 18, pp. 14057-14063 (2008)
http://dx.doi.org/10.1364/OE.16.014057


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Abstract

Differential group delay (DGD) experienced by the optical signal in in-service terrestrial optical fiber systems has been monitored for the first time without the requirement of looping-back, in which the live traffic carried in the fiber was used as the probing signal. The relationship between the measured DGD using this technique and the actual fiber PMD parameter is formulated and verified by field experiments.

© 2008 Optical Society of America

1. Introduction

In high speed optical fiber communication systems, polarization mode dispersion (PMD) is one of the most important factors of performance degradation. Traditionally the PMD parameter of a fiber can be measured by a number of techniques, such as Jones Matrix Eigen-analysis, Poincare Sphere Analysis and Mueller Matrix method [1

1. B. L. Heffner, “Automated Measurement of Polarization Mode Dispersion Using Jones Matrix Eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992). [CrossRef]

3

3. P. Williams, “PMD measurement techniques and how to avoid the pitfalls,” J. Opt. Fiber Commun. Rep. 1, 84–105 (2004). [CrossRef]

]. Fig. 1 shows the Poincare sphere representation of signal polarization vector. With the frequency change of the optical signal which propagates through an optical fiber, the output state of polarization (SOP) rotates on the Poincare sphere around the principle state of polarization (PSP) vector Ω⃗. For the polarization states S⃗(ω) and S⃗(ωω) of two the frequency components selected from the optical signal shown in Fig. 1, if the separation between their azimuth angles is Δθ, the DGD of the fiber can be found as τ fθω, where Δω is the frequency difference between these two components. Obviously, Δθ has to be small enough so that this linearization is valid for the measurement of the 1st-order PMD. In practice, in order to measure Δθ, several different SOP settings of the input optical signal have to be used to complete a Jones matrix or a Mueller matrix. In addition, both the Jones matrix and the Mueller matrix techniques require the synchronization between the PSP settings of the input optical signal and the polarimeter measurement at the output side. As the consequence, these traditional PMD measurement techniques require the accesses to both ends of the fiber, which prevents their application from monitoring in-service optical systems since the source and the receiver of live optical networks are at distance and usually are not accessible at the same time. However, there is clearly a need for a more practical approach that supports a network provider’s planning and route design process for possible capacity upgrading and the system characterization has to be done without disrupting customer traffic.

Fig. 1. Poincare sphere representation of polarization vectors and output SOP rotation with optical frequency change

2. Theoretical analysis

sin(Δα2)=sin(Δθ2)sinβ
(1)

where, β represents the angle between point A and the PMD vector Ω⃗. When Δθ is small enough, which can be ensured by choosing appropriate frequency difference Δω, Eq.(1) can be simplified to,

Δα=Δθsinβ
(2)

In Stokes space, the well-known PSP model indicates that a long fiber can be regarded as a wave plate with the time retardation equals to the modulus of the PMD vector in the fiber, while the principle axis of the wave plate is aligned with the slow axis of the PMD vector. Thus, the angle between the input polarization state of the signal in Sin and the fiber PMD-vector is also equal to β and therefore,

cosβ=Ω·SinΩSin
(3)

In a Cartesian coordinator, the PMD vector can be decomposed into three orthogonal components, Ω⃗=axΩ1+ayΩ2+azΩ3, where ax, ay and az are unit vectors, and thus Ω=Ω12+Ω22+Ω32. When each of the three orthogonal components Ω1, Ω2 and Ω3 follows an independent Gaussian distribution with zero mean and the same standard deviation q, the statistics of PMD vector will exhibit a Maxwellian distribution [8

8. M. Karlsson, J. Brentel, and P. A. Andrekson, “Long-Term Measurement of PMD and Polarization Drift in Installed Fibers,” J. Lightwave Technol. 18, 941–951 (2000). [CrossRef]

],

p3(τf)=2πτf2q3eτf22q2
(4)

τf=q8π
(5)

where, the mean DGD 〈τ f〉 is the average value of the Maxwellian distribution shown in Eq. (4). In practice, using the live traffic carried in the fiber as the probing signal is critical for the in-service monitoring of live optical systems. Since the SOP of the input optical signal is determined by the laser in the transmitter, it is relatively stable. Without losing generality, one can arbitrarily assume that the SOP of the input optical signal is in Sin=(1, 0, 0), then

Ωcosβ=Ω1
(6)

The combination of Eqs. (2) and (6) yields,

τp=ΔαΔω=Ωsinβ=Ω22+Ω32
(7)

p2(τp)=τpq2eτp22q2
(8)

The mean value of this distribution is

τp=qπ2
(9)

From Eq. (5) and (9), the relationship between 〈τ f〉 and 〈τ p〉 can be easily found as,

τf=4τpπ
(10)

In practical fiber-optic systems, polarization-depend loss (PDL) may exist in addition to PMD. When PDL is taken into accounted, the output polarization state S⃗ will vary with optical frequency as [12

12. Y. Li and A. Yariv, “Solutions to the dynamical equation of polarization-mode dispersion and polarization-dependent losses,” J. Opt. Soc. Am. B. 17, 1821–1827 (2000). [CrossRef]

],

Sω=Ω×S(Λ×S)×S
(11)

(ΔαΔω)2=Ω×S2+(Λ×S)×S2+2Ω×S(Λ×S)×Scosφ
=(Ω2+Λ3)2+(Ω3-Λ2)2
(12)

Where, φ is the angle between the vectors Ω⃗×S⃗. and (Λ⃗×S⃗)×S⃗. Equation (12) indicates that the distribution of Δαω still follows Rayleigh statistics and its mean value is,

ΔαΔω=π(1+L)2q
(13)

Where,

L=(qq)2
(14)

Under the small PDL assumption, the relationship between PMD, PDL and DAS vectors is,

Λ=π8Ω·Γ
(15)

As an example, with a 2dB PDL, the value of L will be 0.021 and the difference between the mean values of τ p with and without PDL is only 1.03%. Therefore one can generally conclude that the impact of PDL on PMD measurement is negligible when system PDL is less than 2 dB.

Fig. 2. Block diagram of the coherent PMD monitor

3. Experimental setup and results

In the current measurement apparatus, since polarization scrambling is used for LO, the variation of signal SOP at the fiber output cannot be monitored. If the signal SOP needs to be measured, one can programmatically switch the SOP of the LO between three orthogonal polarization states on the Poincare sphere and performing Stokes parameter analysis of the detected IF signal.

Fig. 3. (a) Normalized partial DGD versus time measured over a 900km link; (b) normalized statistic distribution of (a). Solid lines in (b): Rayleigh distribution, dotted lines: Maxwellian distribution with the same mean value. Inset in (b) is the autocorrelation function.

4. Conclusion

In conclusion, PMD monitoring in traffic-carrying DWDM optical fiber systems is reported for the first time without the requirement of looping-back. The simple relationship between the partial DGD measured with the coherent detection technique and the actual PMD parameter of the fiber is theoretically derived and verified, which allows the accurate evaluation of the PMD parameter in installed fiber systems without disturbing the commercial traffic. The measured partial DGD statistics fits well with a Rayleigh distribution as predicted by the theory.

Acknowledgments

This work was supported by Sprint-Nextel, Nortel-Networks and National Science Foundation CNS0435381. The authors would like to thank Drs. M. O’Sullivan and C. Allen for many helpful discussions.

References and links

1.

B. L. Heffner, “Automated Measurement of Polarization Mode Dispersion Using Jones Matrix Eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992). [CrossRef]

2.

R. M. Jopson, L. E. Nelson, and H. Kogelnik, “Measurement of Second-Order Polarization-Mode Dispersion Vectors in Optical Fibers,” IEEE Photon. Technol. Lett. 11, 1153–1155 (1999). [CrossRef]

3.

P. Williams, “PMD measurement techniques and how to avoid the pitfalls,” J. Opt. Fiber Commun. Rep. 1, 84–105 (2004). [CrossRef]

4.

M. Boroditsky, M. Brodsky, N. J. Frigo, P. Magill, and J. Evankow, “Estimation of eye penalty and PMD from frequency-resolved in-situ SOP measurements,” Proc. 17th Annual Meeting of the IEEE Lasers and Electro-Optics Society, (Piscataway, 2004), pp.88–89.

5.

S. X. Wang, A. M. Weiner, M. Boroditsky, and M. Brodsky, “Monitoring PMD-induced penalty and other system performance metrics via a high-speed spectral polarimeter,” IEEE Photon. Technol. Lett. 18, 1753–1755 (2006). [CrossRef]

6.

B. Fu and R. Hui, “Fiber chromatic dispersion and polarization-mode dispersion monitoring using coherent detection,” IEEE Photon. Technol. Lett. 17, 1561–1563 (2005). [CrossRef]

7.

R. Hui, R. Saunders, B. Heffner, D. Richards, B. Fu, and P. Adany, “Non-blocking PMD monitoring in live optical systems,” Electron. Lett. 43, 53–54 (2007). [CrossRef]

8.

M. Karlsson, J. Brentel, and P. A. Andrekson, “Long-Term Measurement of PMD and Polarization Drift in Installed Fibers,” J. Lightwave Technol. 18, 941–951 (2000). [CrossRef]

9.

H. Kogelnik, L. E. Nelson, and R. M. Jopson, “Polarization-mode dispersion,” in Optical Fiber Telecommunications IVB, I. P. Kaminov and T. Li, Eds. (Academic, New York, 2002).

10.

G. Bosco, B. E. Olsson, and D. J. Blumenthal, “Pulsewidth distortion monitoring in a 40-Gb/s optical system affected by PMD,” IEEE Photon. Technol. Lett. 14, 307–309 (2002). [CrossRef]

11.

M. Karlsson and H. Sunnerud, “PMD impact on optical systems: Single- and multichannel effects,” J. Opt. Fiber Commun. Rep. 1, 123–140 (2004). [CrossRef]

12.

Y. Li and A. Yariv, “Solutions to the dynamical equation of polarization-mode dispersion and polarization-dependent losses,” J. Opt. Soc. Am. B. 17, 1821–1827 (2000). [CrossRef]

13.

J. P. Elbers, C. Glingener, M. Duser, and E. Voges, “Modelling of polarisation mode dispersion in singlemode fibres,” Electron. Lett. 33, 1894–1894 (1997). [CrossRef]

14.

C. Antonelli, A. Mecozzi, K. Cornick, M. Boroditsky, and M. Brodsky, “PMD-induced penalty statistics in fiber links,” IEEE Photon. Technol. Lett. 17, 1013–1015 (2005). [CrossRef]

15.

C. Antonelli, A. Mecozzi, M. Brodsky, and M. Boroditsky, “A Simple Analytical Model for PMD Temporal Evolution,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2006), paper OWJ4.

OCIS Codes
(060.2330) Fiber optics and optical communications : Fiber optics communications
(260.5430) Physical optics : Polarization

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: April 21, 2008
Revised Manuscript: August 7, 2008
Manuscript Accepted: August 22, 2008
Published: August 26, 2008

Citation
Junfeng Jiang, Sathyanarayanan Sundhararajan, Doug Richards, Steve Oliva, and Rongqing Hui, "PMD monitoring in traffic-carrying optical systems and its statistical analysis," Opt. Express 16, 14057-14063 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-18-14057


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References

  1. B. L. Heffner, "Automated Measurement of Polarization Mode Dispersion Using Jones Matrix Eigenanalysis," IEEE Photon. Technol. Lett. 4, 1066-1069 (1992). [CrossRef]
  2. R. M. Jopson, L. E. Nelson, and H. Kogelnik, "Measurement of Second-Order Polarization-Mode Dispersion Vectors in Optical Fibers," IEEE Photon. Technol. Lett. 11, 1153-1155 (1999). [CrossRef]
  3. P. Williams, "PMD measurement techniques and how to avoid the pitfalls," J. Opt. Fiber Commun. Rep. 1, 84-105 (2004). [CrossRef]
  4. M. Boroditsky, M. Brodsky, N. J. Frigo, P. Magill, and J. Evankow, "Estimation of eye penalty and PMD from frequency-resolved in-situ SOP measurements," Proc. 17th Annual Meeting of the IEEE Lasers and Electro-Optics Society, (Piscataway, 2004), pp. 88- 89.
  5. S. X. Wang, A. M. Weiner, M. Boroditsky, and M. Brodsky, "Monitoring PMD-induced penalty and other system performance metrics via a high-speed spectral polarimeter," IEEE Photon. Technol. Lett. 18, 1753-1755 (2006). [CrossRef]
  6. B. Fu and R. Hui, "Fiber chromatic dispersion and polarization-mode dispersion monitoring using coherent detection," IEEE Photon. Technol. Lett. 17, 1561-1563 (2005). [CrossRef]
  7. R. Hui, R. Saunders, B. Heffner, D. Richards, B. Fu, and P. Adany, "Non-blocking PMD monitoring in live optical systems," Electron. Lett. 43, 53-54 (2007). [CrossRef]
  8. M. Karlsson, J. Brentel, and P. A. Andrekson, "Long-Term Measurement of PMD and Polarization Drift in Installed Fibers," J. Lightwave Technol. 18, 941-951 (2000). [CrossRef]
  9. H. Kogelnik, L. E. Nelson, and R. M. Jopson, "Polarization-mode dispersion," in Optical Fiber Telecommunications IVB, I. P. Kaminov and T. Li, Eds. (Academic, New York, 2002).
  10. G. Bosco, B. E. Olsson, and D. J. Blumenthal, "Pulsewidth distortion monitoring in a 40-Gb/s optical system affected by PMD," IEEE Photon. Technol. Lett. 14, 307-309 (2002). [CrossRef]
  11. M. Karlsson and H. Sunnerud, "PMD impact on optical systems: Single- and multichannel effects," J. Opt. Fiber Commun. Rep. 1, 123-140 (2004). [CrossRef]
  12. Y. Li and A. Yariv, "Solutions to the dynamical equation of polarization-mode dispersion and polarization-dependent losses," J. Opt. Soc. Am. B. 17, 1821-1827 (2000). [CrossRef]
  13. J. P. Elbers, C. Glingener, M. Duser, and E. Voges, "Modelling of polarisation mode dispersion in singlemode fibres," Electron. Lett. 33, 1894-1894 (1997). [CrossRef]
  14. C. Antonelli, A. Mecozzi, K. Cornick, M. Boroditsky, and M. Brodsky, "PMD-induced penalty statistics in fiber links," IEEE Photon. Technol. Lett. 17, 1013-1015 (2005). [CrossRef]
  15. C. Antonelli, A. Mecozzi, M. Brodsky, and M. Boroditsky, "A Simple Analytical Model for PMD Temporal Evolution," in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2006), paper OWJ4.

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