Statistical Engineering Division, ITL
Paul A. Williams
Optoelectronics Division, EEEL
Polarization dispersion arises in single-mode fibers when there is imperfect circular symmetry in the fiber core. An optical pulse input to a fiber is split into two orthogonally polarized pulses. Distortion arises as a result of a differential group-delay (DGD) time between these two pulses at the output. Since DGD can have a limiting effect on the speed of digital communication systems and therefore is a good indicator of the performance of a lightwave system, it is routinely measured both at the manufacturing stage and in installed systems.
In long-fiber spans, DGD is a random effect, since it depends on the details of the birefringence along the entire fiber length. It is also sensitive to temperature and mechanical perturbations of the fiber. For this reason, a useful way to characterize DGD in long fibers is in terms of its expected value, or polarization mode dispersion (PMD).
Among the methods of PMD measurement, the fixed analyzer technique
is perhaps the simplest to use.
Light is polarized with an input polarizer and then launched into the
The transmission, through an output analyzer, is measured as a function
of frequency (or wavelength).
Based on the normalized transmission spectrum, ,
estimated by either
where is the width of the frequency window over which the measurement is taken, Nm is the number of mean-value (0.5) crossings, and Ne is the number of extrema in the frequency window . The factor 4 was obtained analytically, while the factor 0.824 was obtained through simulation, in the literature. Under regular conditions, Nm and Ne depend on and only through their product. That is, the smaller the PMD, the bigger the window size required in order to estimate the PMD with the same precision. Since is everywhere differentiable and continuous in , the number of discrete frequency measurements made will affect the outcome of Nm and Ne.
Simulation was used to study the effects of sampling density on the estimation of PMD. Fibers were simulated as a stack of 2700 waveplates with their optic axes randomly oriented. A new value for the polarization mode coupling factor of 0.805 (a 2% discrepancy with the old value of 0.824) was found. Systematic biases due to sampling density were quantified, and a simple correction algorithm was proposed. This and related work will appear in the Journal of Lightwave Technology.
Figure 11: Calculated mode coupling constants versus sampling density. The horizontal axis is the value of where nf is the number of points used to sample . The right and left vertical axes are, respectively, the mode coupling constants (k1and k2) associated with Nm and Ne. As becomes large, and .
Date created: 7/20/2001