field measurement of polarization mode dispersion of ...

Journal of the Technical University Sofia, branch Plovdiv “Fundamental Sciences and Applications”, Vol. 19, 2013

FIELD MEASUREMENT OF POLARIZATION MODE DISPERSION OF COMMUNICATION FIBERS USING THE FIXED ANALYZER METHOD WITH POLARIZATION AVERAGING VANYA PLACHKOVA and TINKO EFTIMOV Faculty of Physics and Engineering Technologies, PU “P. Hilendarski”, Plovdiv

Abstract: Averaging over a sequence of random input polarization states, we have determined the polarization mode dispersion (PMD) in an optical cable line made of 144 stacked fiber pieces. The fixed analyzer method in a transmission mode has been used. Due to the insufficient dynamic range of the optical spectrum analyzer the measurements could not be performed in reflection mode because of the accumulated losses. The field tests performed at a fiber cable installation company show that the empiric distribution of experimental results can be fitted by a Maxwell distribution with 95% confidence level. Reference to the international communication standards shows that the fibers under test are convenient for building 40 Gb/s high bit-rate systems.

1. Introduction: High-speed high-capacity communications are the basis of contemporary global communication networks using single mode optical fibers. In these fibers pulse broadening is caused by chromatic and polarization mode dispersion. When the former can be compensated and is nullified the only limitation to high bit-rate communication is the polarization mode dispersion. While modern fibers are manufactured with more stringent control on fiber quality, older brands already installed and in use feature more imperfections and exhibit higher PMD. For the present day communications

systems the PMD is the key limiting factor for achieving 10Gb/s and 40 Gb/s The accurate determination of the PMD is of paramount importance for the characterization of the transmission properties of high-speed (above 2.5 Gb/s) long-haul (above 100 km) optical communication lines. A number of methods have been developed to measure PMD and the group-delay statistics and several types of PMD meters are commercially available. In the present paper we apply the well known fixed analyzer method in combination with input polarization changes to generate a large number of independent measurements

which enable statistical treatment of the effect of random perturbations on the PMD.. 2. Pulse broadening in single mode optical fibers In optical fibers the differential group delay  between the fastest and the slowest components of a light pulse is given by 2 2  2   chr   PMD

(1)

where  chr is the broadening due to the chromatic dispersion, while  PMD is the broadening caused by the different delays of the X and Y polarizations of the fundamental mode. The corresponding dispersion is physically the intermodal dispersion between two orthogonal polarization modes known as polarization mode dispersion (PMD). Since chromatic dispersion can be nullified or compensated, i.e.  chr  0 , the only limitation to bit-rate is the PMD. 3. Birefringence in optical fibers and PMD State of polarization in optical fibers

The state of polarization in optical fibres is determined by the input polarization state and by

Copyright  2013 by Technical University Sofia, branch Plovdiv, Plovdiv, BULGARIA. ISSN 1310 - 8271

the existence of birefringence in the fibre. Birefringence can be either linear, circular or, generally, elliptical. Core/cladding ellipticity, lateral stress and bending cause linear birefringence and the fibre preserves linear polarization launched along the X or Y axis. Twists, helical winding and Faraday effect cause circular birefringence so the fibre preserves circular polarizations. Combining linear and circular birefringence produces elliptical birefringence. Birefingence can be unform and random. Uniform birefringence is caused by a constant and uniformly distributed perturbations imposed upon the fibre. When the strength and the position of the perturbations vary randomly so is the birefringence.

The PMD thus is the DGD per unit length. If we measure the average group delay  g , then the average PMD will be:

 g 

 g L

ps / km

Random birefringence and PMD coefficient With random birefringence fast and slow axes interchange so the slow and the fast modes interchange optical power. This causes slow modes to move faster and fast modes more slowly on the average, so DGD does not grow linearly with fiber length bus is proportional to

 g   g Lc .L .   g ,coeff L

Uniform birefringence and PMD

(5)

(6)

In (6) We consider uniform linear birefringence along a fibre caused, for example, by an elliptical core. The propagation constants for the X- and Y-polarized fundamental modes LP01x and LP01y . x and y are

different and the propagation constant difference  at a central frequency 0  n  n  n (1)  0    x 0    y 0   0 s  0 f  0 c

c

c

is nonzero. In (1) n  ns  n f  n x  n y is the fiber modal birefringence where n s and n f are the effective refractive indices along the slow and the fast axes, denoted as X and Y, and the refractive indices become n x and n y which are different. This causes the different polarizations to delay differently and hence a differential group delay (DGD) g. We now expand (1) in series and restrict to the first order term    0   g   0  (2) where  0 is the propagation constant difference at 0. Multiplying (2) on both sides by the fiber length L yields the total phase difference accumulated between the two polarization modes.   L   0 L   g    0 L (3) In (3)

 g   g L

(4)

is the DGD, while  g (in ps/km) is the polarization mode dispersion (PMD).

 g ,coeff   g Lc

(7)

is the PMD coefficient measured in ps/km, and Lc is a critical fiber length over which polarization mode mixing is complete. So the PMD coefficient which describes polarization mode dispersion in randomly perturbed fibres is calculated as

 g ,coeff 

 g L

ps / km

(8)

So (5) is the PMD for distances L Lc. 4. The fixed analyzer method

Basic scheme The fixed analyzer method is one of the standardized methods for the measurement of PMD and the PMD coefficient. The method is based on the classical polarimetric scheme in which the birefringent medium is placed between crossed polarizers with X-axis oriented at 45º with respect to the polarizer transmission axis. It can easily be shown that in the case of a non-polarized source, the response of the fixed analyzer scheme is 1 1 (9) S 0  1  cos    1  cos(L) 4 4 Or also, after reworking (3) the spectral dependence of (8) can be written as

1    1  cos  0  2c g 2 z  (10)  4    where  is the mean wavelength and  0   0 L S0 

For a 2 phase shift of the above cos response the spectral period  is found as:

 

  g L.c

Broadband source JW3107 ASE

2

(11)

FO polarizer Spool with 144 optical fibers

From (10) we can calculate the DGD and the PMD

 g   g z 

2  c

Optical Spectrum Analyzer AQ6331

(12)

FO analyzer

Polarization averaging For randomly birefringent long-haul fiber lines (L>Lc) the response (9) does not have a constant period . Instead we observe a response with randomly varying periodicity. The particular pattern depends on the input polarization. By varying the polarization prior to the test fiber we can achieve a variety of random period patterns and accumulate statistics on the distribution of the DGD. To vary input polarization we use the scheme in Fig. 1.

Fig.2. Schematic representation of the experimental set-up for the field measurement of the PMD in transmission mode. Fig. 3 presents a spectral dependence of the polarimetric response. lmax2

lmax1

-10

lmax3

-12 -14

A (-45º)

Polarization controller

Fiber under test

Загуби , (dB)

-16

P (45º)

-18 -20

lmin3

lmin2

lmin1

-22 -24 -26 -28 -30 1530

1540

1550

1560

1570

1580

1590

1600

1610

Fig. 1 Schematic representation of the fixed analyzer method with input polarization controller.

Fig. 3. Spectral response in transmission mode.

In Fig.1 the polarization controller is represented as a phase plate with a phase difference , rotated trough an angle  Using Mueller matrices the response in this case is

Fig. 4 shows the statistical distributuon of the measured DGD a Maxwellian fit for  = 3 degrees of freedom and for a 95% confidence level the 2 test yields

S0 

 





1 1  2 cos  sin 2 2  cos 2 2 cos   4

 sin  cos 2 sin 

 2  3.157  23  7.82

(14)

(13)

If we vary  and  the amplitude and the phase of the spectral response change.

  0.188 ps

   0.148 ps

5. Field measurement of PMD in transmission mode Field measurements of the PMD were realized with the DC Corporation using a multi-fiber cable. The individual fibers were spliced in series and a total length of 57,752 km, measured with a OTDR (Optical Time Domain Reflectometer). The experimental set up is shown in Fig. 2. By varying the orientation of the polarization controller’s coils placed after the polarizer we create different input polarizations and generate responses with randomly varying spectral periods .

Fig. 4. Statistics of the field measurement of DGD by the fixed analyzer method in transmission mode. The average DGD was measured to be   0.188 ps and the average PMD was found as

Copyright  2013 by Technical University Sofia, branch Plovdiv, Plovdiv, BULGARIA. ISSN 1310 - 8271

 g  0.0034 ps / km while the PMD coefficient is :  g ,coeff  0.025 ps / km

(15)

3. Measurement in reflection mode demands either more optical power from the ASE or greater dynamic range of the OSA.

(16)

From (7) we find the critical length Lc as

R EF ER E NC E S

2

  g ,coeff   Lc      g  and the value obtained is Lc  54 km.

(17)

In reflection mode the total losses in one direction measured by an OTDR were of the order of 22.95 dB. With a double pass losses

become approximately 46 dB which surpasses the dynamic range of the OSA so measurements become impossible.

1. Brandon Collings, Fred Heismann, Gregory Lietaert, “Advanced Fiber Optic Testing High-Speed Fiber Link and Network Characterization”, Reference Guide to Fiber Optic Testing, JDSU, 2010 . 2. Fedor Mitchke, „Fiber Optics Physics and Technology”, Heidelberg, Springer, 2010. 3. Paul Hernday, ”Dispersion Measurements in Fiber-optic Test and measurements”, Dennis Derickson, ed. Prentice Hall, 1998. 4. Gregory Lietaert, Product Manager “Testing Polarization Mode Dispersion (PMD) in the Field”, JDSU , 2006.

Fig.5. OTDR trace to measure the losses obtained for a fiber length of 57.752 km. The results obtained for the PMD and PMD coefficient show that the fibers can be used for building 40 Gb/s communication systems for the international standards shown Table 1 below. Bit-rate

SDH format

SONET format

40 Gb/s

STM-256

OC-768

Equivalent time slot

DGD limit

PMD coefficient for 400 km

25.12 ps

2.5 ps

≤ 0.125 ps/√km

6. Conclusions 1. The tested schemes of the method used here are mobile, easy to apply for long-haul communication lines in field conditions 2. The use of polarization averaging by changing the input polarization provides responses with varying spectral periodicities and helps generate statistical data.

5. Sergey Ten, Merrion Edwards, „An Introduction to the Fundamentals of PMD in fibers,White Paper WP5051, Corning, 2006 6. Poh-Boon Phua, “Deterministic Approach to Polarization Mode Dispersion”, PhD Dissertation, MIT, USA, 2004

7. Daniel A. Nolan, Member, Xin Chen, Member, and Ming-Jun Li, “Fibers With Low Polarization-Mode Dispersion”, Journal of Lightwave Technology, Vol. 22, Issue 4, pp. 1066 (2004)