PMD monitoring in traffic-carrying optical systems and its statistical analysis

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1 PMD monitoring in traic-carrying otical systems and its statistical analysis Juneng Jiang 1,, Sathyanarayanan Sundhararajan 1, Doug Richards, Steve Oliva and Rongqing Hui 1,* 1 Electrical Engineering & Comuter Science, University o Kansas, Lawrence, KS 66045, USA Srint-Nextel, Overland Park, KS 6651, USA On leave rom College o Precision Instrument & Otoelectronics Engineering, Key Lab o Otoelectronics Inormation Technology & Science, MEC, Tianjin University, Tianjin 0007 China A * Corresonding author: rhui@ku.edu Abstract: Dierential grou delay (DGD) exerienced by the otical signal in in-service terrestrial otical iber systems has been monitored or the irst time without the requirement o looing-back, in which the live traic carried in the iber was used as the robing signal. The relationshi between the measured DGD using this technique and the actual iber PMD arameter is ormulated and veriied by ield exeriments. 008 Otical Society o America OCIS codes: (060. 0) Fiber otics communications; (60.540) Polarization. Reerences and links 1. B. L. Hener, Automated Measurement o Polarization Mode Disersion Using Jones Matrix Eigenanalysis, IEEE Photon. Technol. Lett. 4, (199).. R. M. Joson, L. E. Nelson, and H. Kogelnik, Measurement o Second-Order Polarization-Mode Disersion Vectors in Otical Fibers, IEEE Photon. Technol. Lett. 11, (1999).. P. Williams, PMD measurement techniques and how to avoid the italls, J. Ot. Fiber Commun. Re. 1, (004). 4. M. Boroditsky, M. Brodsky, N. J. Frigo, P. Magill, and J. Evankow, Estimation o eye enalty and PMD rom requency-resolved in-situ SOP measurements, Proc. 17th Annual Meeting o the IEEE Lasers and Electro-Otics Society, (Piscataway, 004), S. X. Wang, A. M. Weiner, M. Boroditsky, and M. Brodsky, Monitoring PMD-induced enalty and other system erormance metrics via a high-seed sectral olarimeter, IEEE Photon. Technol. Lett. 18, (006). 6. B. Fu and R. Hui, Fiber chromatic disersion and olarization-mode disersion monitoring using coherent detection, IEEE Photon. Technol. Lett. 17, (005). 7. R. Hui, R. Saunders, B. Hener, D. Richards, B. Fu, and P. Adany, Non-blocking PMD monitoring in live otical systems, Electron. Lett. 4, 5 54 (007). 8. M. Karlsson, J. Brentel, and P. A. Andrekson, Long-Term Measurement o PMD and Polarization Drit in Installed Fibers, J. Lightwave Technol. 18, (000). 9. H. Kogelnik, L. E. Nelson, and R. M. Joson, Polarization-mode disersion, in Otical Fiber Telecommunications IVB, I. P. Kaminov and T. Li, Eds. (Academic, New York, 00). 10. G. Bosco, B. E. Olsson, and D. J. Blumenthal, Pulsewidth distortion monitoring in a 40-Gb/s otical system aected by PMD, IEEE Photon. Technol. Lett. 14, (00). 11. M. Karlsson and H. Sunnerud, PMD imact on otical systems: Single- and multichannel eects, J. Ot. Fiber Commun. Re. 1, (004). 1. Y. Li and A. Yariv, Solutions to the dynamical equation o olarization-mode disersion and olarizationdeendent losses, J. Ot. Soc. Am. B. 17, ( 000). 1. J. P. Elbers, C. Glingener, M. Duser, and E.Voges, Modelling o olarisation mode disersion in singlemode ibres, Electron. Lett., (1997). 14. C. Antonelli, A. Mecozzi, K. Cornick, M. Boroditsky, and M. Brodsky, PMD-induced enalty statistics in iber links, IEEE Photon. Technol. Lett. 17, (005). 15. C. Antonelli, A. Mecozzi, M. Brodsky, and M. Boroditsky, A Simle Analytical Model or PMD Temoral Evolution, in Otical Fiber Communication Conerence and Exosition and The National Fiber Otic Engineers Conerence, Technical Digest (CD) (Otical Society o America, 006), aer OWJ4. # $15.00 USD Received 1 Ar 008; revised 7 Aug 008; acceted Aug 008; ublished 6 Aug 008 (C) 008 OSA 1 Setember 008 / Vol. 16, No. 18 / OPTICS EXPRESS 14057

2 1. Introduction In high seed otical iber communication systems, olarization mode disersion (PMD) is one o the most imortant actors o erormance degradation. Traditionally the PMD arameter o a iber can be measured by a number o techniques, such as Jones Matrix Eigenanalysis, Poincare Shere Analysis and Mueller Matrix method [1-]. Fig. 1 shows the Poincare shere reresentation o signal olarization vector. With the requency change o the otical signal which roagates through an otical iber, the outut state o olarization (SOP) S(ω) β O Δθ S ( ω + ) O Fig. 1. Poincare shere reresentation o olarization vectors and outut SOP rotation with otical requency change rotates on the Poincare shere around the rincile state o olarization (PSP) vector. For the olarization states S (ω) and S( ω + ) o two the requency comonents selected rom the otical signal shown in Fig. 1, i the searation between their azimuth angles is Δθ, the DGD o the iber can be ound as = Δθ, where Δ ω is the requency dierence between these two comonents. Obviously, Δθ has to be small enough so that this linearization is valid or the measurement o the 1 st -order PMD. In ractice, in order to measure Δθ, several dierent SOP settings o the inut otical signal have to be used to comlete 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 o the inut otical signal and the olarimeter measurement at the outut side. As the consequence, these traditional PMD measurement techniques require the accesses to both ends o the iber, which revents their alication rom monitoring in-service otical systems since the source and the receiver o live otical networks are at distance and usually are not accessible at the same time. However, there is clearly a need or a more ractical aroach that suorts a network rovider s lanning and route design rocess or ossible caacity ugrading and the system characterization has to be done without disruting customer traic. Recently, several techniques were roosed or in-situ evaluation o PMD utilizing the otical signal carried in the iber as the robe signal. A heterodyne olarimeter with an RF sectrum analyzer was used to estimate the PMD-induced system enalty by measuring the state o olarization string length in a nonintrusive way [4]. A similar technique with a higher measurement seed was roosed in [5], which uses direct detection with a high resolution otical sectrum analyzer consisting o an InGaAs line-scan camera and a virtually imaged hase array. We have roosed a simliied method to directly measure the DGD in traic-carrying otical links using coherent detection and RF signal rocessing [6]. For all these non-intrusive PMD monitoring techniques, the SOP o the inut otical signal is not adjustable and the measurement o Δθ in Fig. 1 is thereore not easible. In act, the core angle shown in Fig. 1 is usually measured in these in-service monitoring techniques, because it only deends on the relative olarization walk-o between two requency # $15.00 USD Received 1 Ar 008; revised 7 Aug 008; acceted Aug 008; ublished 6 Aug 008 (C) 008 OSA 1 Setember 008 / Vol. 16, No. 18 / OPTICS EXPRESS 14058

3 comonents within the otical sectrum o the robe. However, since it is Δθ instead o which reresents the DGD between the ast and the slow axis o the iber, it is imortant to ind the relationshi between them. is generally smaller than Δθ and = reresents the actual DGD seen by the robing signal. In order to correctly interret the results obtained by the in-service PMD monitoring technique, it is imortant to rigorously examine the relationshi between the PMD arameter o the iber and the DGD measured by the technique demonstrated in reerences [6] and [7].. Theoretical analysis Figure 1 indicates that is related to Δθ by, Δθ sin( ) = sin( )sin β (1) where, β reresents the angle between oint A and the PMD vector. When Δθ is small enough, which can be ensured by choosing aroriate requency dierence Δ ω, Eq.(1) can be simliied to, α = Δθ sin β Δ () In Stokes sace, the well-known PSP model indicates that a long iber can be regarded as a wave late with the time retardation equals to the modulus o the PMD vector in the iber, while the rincile axis o the wave late is aligned with the slow axis o the PMD vector. and the iber PMD- Thus, the angle between the inut olarization state o the signal S in vector is also equal to β and thereore, S in cos β = () Sin In a Cartesian coordinator, the PMD vector can be decomosed into three orthogonal comonents, = ax1 + a y + az, where a x, a and y a are unit vectors, and thus z = When each o the three orthogonal comonents, 1 and ollows an indeendent Gaussian distribution with zero mean and the same standard deviation q, the statistics o PMD vector will exhibit a Maxwellian distribution [8], q ( ) = e (4) π q In general, the iber PMD arameter is regarded as its mean DGD which is related to the arameter q by, = q 8/π (5) where, the mean DGD is the average value o the Maxwellian distribution shown in Eq. (4). In ractice, using the live traic carried in the iber as the robing signal is critical or the in-service monitoring o live otical systems. Since the SOP o the inut otical signal is determined by the laser in the transmitter, it is relatively stable. Without losing generality, one can arbitrarily assume that the SOP o the inut otical signal is cos β = 1 The combination o Eqs. () and (6) yields, S in = (1, 0, 0), then (6) # $15.00 USD Received 1 Ar 008; revised 7 Aug 008; acceted Aug 008; ublished 6 Aug 008 (C) 008 OSA 1 Setember 008 / Vol. 16, No. 18 / OPTICS EXPRESS 14059

4 = = sin β = + (7) Note that, a Maxwellian distribution is reerred to as a Chi distribution with degrees o reedom because it is related to three indeendent comonents, 1 and. In our case, Eq. (7) indicates that is only related to two o the three indeendent orthogonal comonents, and thereore, it should ollow a Chi distribution with degrees o reedom, which is also known as Rayleigh distribution and its robability density unction can be exressed as [9], q ( ) = e q (8) The mean value o this distribution is = q π / (9) From Eq. (5) and (9), the relationshi between and can be easily ound as, = π (10) 4 It is worth noting that quantity in eq.(7) is a artial DGD, which is in act the rojection o the iber PMD vector erendicular to the signal SOP direction. However, the mean and the statistic distribution o the actual iber DGD can be derived rom the measured, and it is suicient or most o the ractical alications since it is directly related to system eyeclosure enalty [10, 11]. In ractical iber-otic systems, olarization-deend loss (PDL) may exist in addition to PMD. When PDL is taken into accounted, the outut olarization state S will vary with otical requency as [1], S = S ( Λ S) S (11) ω where, Λ is the dierential attenuation sloe (DAS) vector which is related to PDL vector Γ. Λ can be decomosed into three orthogonal and indeendent random Gaussian comonents with the same standard deviation q when PDL is small enough: Λ = axλ1 + a yλ + azλ. Again, let S = (1,0,0), = = S ( + Λ ) + ( Λ ) + ( Λ S) S + S ( Λ S) S cosϕ Where, ϕ is the angle between the vectors S and ( Λ S) S. Equation (1) indicates that the distribution o Δ α still ollows Rayleigh statistics and its mean value is, Where, = π ( 1+ L) q ( q / q) (1) (1) L = (14) Under the small PDL assumtion, the relationshi between PMD, PDL and DAS vectors is, # $15.00 USD Received 1 Ar 008; revised 7 Aug 008; acceted Aug 008; ublished 6 Aug 008 (C) 008 OSA 1 Setember 008 / Vol. 16, No. 18 / OPTICS EXPRESS 14060

5 π Λ = Γ (15) 8 As an examle, with a db PDL, the value o L will be 0.01 and the dierence between the mean values o with and without PDL is only 1.0%. Thereore one can generally conclude that the imact o PDL on PMD measurement is negligible when system PDL is less than db. From system monitoring ort db PD RF Am. Polarization controller 1 RF ower meter RF ower meter Tunable laser Normalization and calculation Fig.. Block diagram o the coherent PMD monitor. Exerimental setu and results We have assembled an exerimental setu or in-service PMD monitoring using coherent detection [6] as schematically shown in Fig., where a small ortion o the otical signal is taed rom the transmission link or the measurement. A tunable laser is used as a local oscillator (LO) or coherent heterodyne detection and transmission channel selection. A olarization controller is laced at the outut o the local oscillator to randomly scramble the SOP o the local oscillator. When the SOP o the LO is aligned with the received otical signal at the requency comonent ω, the relative angular walk-o between S (ω) and S( ω + ) will be equal to the angle between S( ω + ) and the SOP o LO. Under this condition the angle can obtained through the measured IF intensity I ( ω + ), which is roortional to P LP s cos( ), where P L and P s are the otical owers o the signal and the LO [7]. Ater the heterodyne IF sectrum is amliied, two RF ilters with 1GHz bandwidth are used to select two dierent requency comonents o the signal and their central requency dierence is 10 GHz. The measurement is relatively indeendent o modulation ormat o the otical signal since the signal average ower is used or measurement. The two requency comonents selected by the RF bandass ilters can be any art within the modulated signal sectrum. By measuring the dierential olarization walk-o between the two requency comonents, the irst-order DGD exerienced by the otical signal can be evaluated. The accuracy o the PMD measurement in the laboratory environment was veriied by using a PMD emulator and setting β = 90 [6]. The smallest DGD that can be measured by the current setu is about 0. s which was veriied in a system without DGD. This measurement error is believed to be mainly caused by electrical circuit noise. In a revious ield trial, we have also demonstrated that the system Q margin was inversely roortional to the instantaneous DGD measured by this technique [7]. In the current measurement aaratus, since olarization scrambling is used or LO, the variation o signal SOP at the iber outut cannot be monitored. I the signal SOP needs to be measured, one can rogrammatically switch the SOP o the LO between three orthogonal olarization states on the Poincare shere and erorming Stokes arameter analysis o the detected IF signal. In order to veriy the statistical distribution redicted by our analysis, we have recently carried out a number o ield trials in various long-distance terrestrial iber-otic systems # $15.00 USD Received 1 Ar 008; revised 7 Aug 008; acceted Aug 008; ublished 6 Aug 008 (C) 008 OSA 1 Setember 008 / Vol. 16, No. 18 / OPTICS EXPRESS 14061

6 carrying DWDM traics at 10Gb/s data rate with non-return-to-zero (NRZ) modulation. Fig. shows the results o DGD measurements at Srint s Kansas City switch site and -0dBm o signal otical ower was taed to erorm the measurement. Figure (a) shows the result o 68-hour continuous measurement o artial DGD, as the unction o time or a iber link between Kansas City and Chicago which is aroximately 900 km, while Fig.(b) shows the statistical distribution o which is comosed o aroximately 480,000 data oints. The correlation time o this link is about 0.5 h as shown in the inset o Fig. (b). Our 68 hours o monitoring is equivalent to 56 uncorrelated samles, which is reasonably suicient to reconstruct a statistic distribution. The solid line in Fig. (b) is a Rayleigh distribution which its well to the measured artial DGD, while as a comarison the dotted line in the same igure shows a Maxwellian distribution which is obviously not a good it. It is noticed that Fig. (b) looks very similar to Fig. 1 in [1] where the statistics o PMD-induced system imairments was numerically simulated. Since the eye-closure enalty in the receiver deends on the alignment between the SOP o the otical signal and the PSP o the otical iber [14, 15], a Rayleigh distribution was exected. From in-service system monitoring oint o view, our coherent detection technique evaluates which has a mean value o. Eq.(10) can be used to convert this result to the more traditionally deined mean DGD o the iber,. The PDL o this system was estimated to be aroximately 0.997dB through another measurement, thereore the imact o PDL in the PMD measurement is only about 0.6% and is negligible. To the best o our knowledge, this is the irst PMD measurement reorted in commercial DWDM systems carrying live traic and without the requirement o looingback. / mean (a) Probability Density (b) Autocorrelation Time (h) Time (h) / mean Fig.. (a) Normalized artial DGD versus time measured over a 900km link; (b) normalized statistic distribution o (a). Solid lines in (b): Rayleigh distribution, dotted lines: Maxwellian distribution with the same mean value. Inset in (b) is the autocorrelation unction. 4. Conclusion In conclusion, PMD monitoring in traic-carrying DWDM otical iber systems is reorted or the irst time without the requirement o looing-back. The simle relationshi between the artial DGD measured with the coherent detection technique and the actual PMD arameter o the iber is theoretically derived and veriied, which allows the accurate evaluation o the PMD arameter in installed iber systems without disturbing the commercial traic. The measured artial DGD statistics its well with a Rayleigh distribution as redicted by the theory. # $15.00 USD Received 1 Ar 008; revised 7 Aug 008; acceted Aug 008; ublished 6 Aug 008 (C) 008 OSA 1 Setember 008 / Vol. 16, No. 18 / OPTICS EXPRESS 1406

7 Acknowledgments This work was suorted by Srint-Nextel, Nortel-Networks and National Science Foundation CNS The authors would like to thank Drs. M. O Sullivan and C. Allen or many helul discussions. # $15.00 USD Received 1 Ar 008; revised 7 Aug 008; acceted Aug 008; ublished 6 Aug 008 (C) 008 OSA 1 Setember 008 / Vol. 16, No. 18 / OPTICS EXPRESS 1406

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