Transient evolution of the polarization-dispersion vector's probability distribution

Abstract

We determine the transient evolution of the probability distribution of the polarization dispersion vector both analytically and numerically, using a physically reasonable model of the fiber birefringence. We show that, for all practical birefringence parameters, the distribution of the differential group delay (DGD), which is the magnitude of the polarization dispersion vector, becomes Maxwellian in just a few kilometers, except in the tail region, where the DGD is large. In this limit, the approach to a Maxwellian distribution takes much longer, of the order of tens of kilometers. In addition, we show that in the transient regime the DGD distribution is very different from Maxwellian. We also find that the probability-distribution function for the polarizationdispersion vector at the output of the fiber depends upon the angle between it and the local birefringence vector on the Poincaré sphere, showing that the DGD remains correlated with the orientation of the local birefringence axes over arbitrarily long distances.

Analytical treatment of randomly birefringent periodically spun fibers

“…We implement the RMM and the FMM and perform Monte Carlo simulations solving (1) for a set of 15 000 fibers and for both birefringence models and different values of and . For each value of , we consider a fiber of length so that the transient behavior has completely died out [18]. We then estimate the mean DGD, first for the unspun fiber and then for a fiber with the same birefringence parameters, which is spun using the sinusoidal function There are four quantities that influence the mean DGD of a sinusoidally spun fiber-, , , and .…”

Joint-characteristic Function of the First- and Second-order Polarization-mode-dispersion Vectors in Linearly Birefringent Optical Fibers

“…It implies that, in the asymptotic region, we have P(τ, L)=A 0 (, L) ultimately. This can be verified also using a multiple-scale method [15].…”

“…We will solve the Fokker-Planck equation in the Fourier domain by introducing a joint characteristic function, (15) where k=(k1, k2, k3) and kω=(kω1, kω2, kω3). Our definition of the join]t characteristic function is the complex conjugate of the conventional one.…”

Low-PMD spun fibers

“…In order to investigate the system's behavior in that case, we performed numerical simulations for both the RMM and the FMM fiber models, and calculated the SIRF as the ratio betwen the average DGD of the spun and corresponding unspun fiber. We estimated the average DGD over an ensemble of 15,000 fibers, considering a fiber of length z 100LF , so that the transient behavior has completely died out [41].…”