The intrinsic factors are worse in older optical fibers because the seriousness of PMD was not recognized in the 1980s. Polarization Mode Dispersion Many of the extrinsic effects (especially those due to temperature, twisting, bending, and localized pressure) vary over time. Nearly all of the effects that are shown are probabilistic. Short and Long Birefringent Fibers A short section of uniformly birefringent optical fiber has a fast and a slow optical axis with different effective refractive indices, Nf and Ns, such that Ns > Nf. There are two corre- sponding propagation constants, Bf and Bs, and the difference between them is given by = = W An/c, in which W is the angular frequency. For the phenomena that cause birefringence in real fibers, An is typically around 10-7 to 10-6, which is about three orders of magnitude less than the core-cladding refractive index difference in a transmission fiber. We can define the "Differential Group Delay" (DGD), designated AT, which is the difference in propagation times over a fiber of length L: (6.33) Equation 6.33 indicates a linear variation of DGD with length. It consists of a term that does not have explicit frequency dependence and a dispersive term that does. If we ignore the second (dispersive) term, we can define a length, LB, called the beat length, with the value An. If L = LB, At=A/c=1/v. In other words, the beat length is the fiber length that causes the fast mode to advance one optical cycle (2radians) with respect to the slow mode. Typically, LB is around 1 to 50 m. A single section of fiber with constant birefringence does not usefully represent the numerous influences that are present in real transmission. This follows from the statistical nature of and the many contributors to the PMD. Instead, we conceptualize and mathemati- cally model PMD in the manner shown in Figure 6.27. The fiber link is assumed to be com- posed of many short birefringent fibers, which have randomly oriented axes (Neslon & Jopson, 2005). The coupling between the short sections is cau