An analytical characterization of polarization dispersion measurements is presented. The authors report the solution of Poole's stochastic dynamical equation for the evolution of the polarization dispersion vector with fiber length. The authors extend this to a more complete description by considering small, second-order dispersion effects through the frequency derivative of the dispersion vector. The complete analytical solution is seen to accord with what were originally empirically derived features of the joint probability distribution of the polarization dispersion vector and its frequency derivatives. Among the analytically determined properties are the Gaussian probability densities of the three components of the dispersion vector, and the hyperbolic secant (soliton shaped) probability densities of the components of the derivative of the dispersion vector. >

Statistical theory of polarization dispersion in single mode fibers

Polarization mode dispersion and the polarization decorrelation and diffusion lengths are calculated in fibers with randomly varying birefringence. Two different physical models in which the birefringence orientation varies arbitrarily are studied and are shown to yield nearly identical results. These models are appropriate for communication fibers. We show that both the length scales for polarization mode dispersion and polarization decorrelation measured with respect to the local axes of birefringence are equal to the fiber autocorrelation length. We also show that the coupled nonlinear Schrodinger equation which describes wave evolution over long length along a communication fiber can be reduced to the Manakov equation. The appropriate averaging length for the linear polarization mode dispersion is just the fiber autocorrelation length but the appropriate averaging length for the nonlinear terms is the diffusion length in the azimuthal direction along the Poincare sphere which can be different, The implications for the nonlinear evolution are discussed.

Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence

Polarization mode dispersion (PMD), which can limit the bandwidth of optical transmission links, has been difficult to measure in a manner independent of human judgment, leading to difficulties in automating the measurement. It is shown that PMD in any linear, time-invariant network can be completely characterized by eigenanalysis of Jones matrices measured at a series of discrete wavelengths, even for networks exhibiting polarization-dependent loss. A fast, automated system using a tunable laser and an accurate, real-time polarimeter affords the temporal accuracy of approximately 2% down to a limit of several femtoseconds, as demonstrated by comparison with other techniques and comparison with known samples. Both the principal states of polarization and the group delay difference were measured as a function of optical frequency. >

http://www.hpl.hp.com/techreports/92/HPL-92-63.pdf

Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis

Publisher Summary Polarization mode dispersion (PMD) is a linear effect that can be compensated in principle. In an ideal circularly symmetric fiber, the two orthogonally polarized modes have the same group delay. However, in reality, fibers exhibit a certain amount of birefringence because of imperfections in the manufacturing process or mechanical stress on the fiber after manufacture. It is noted that fluctuations in the polarization mode and fiber birefringence produced by the environment lead to dispersion that varies statistically with time and frequency. PMD causes different delays for different polarizations and when the difference in the delays approaches a significant fraction of the bit period, it leads to pulse distortion and system penalties. Environmental changes— including temperature and stress—cause the fiber PMD to vary stochastically in time. PMD, illustrating the basic concepts, the measurement techniques, the PMD measurement, the PMD statistics for first- and higher orders, the PMD simulation and emulation, the system impairments, and the mitigation methods has been summarized in the chapter. Both the optical and the electrical PMD compensations are considered.

Polarization-Mode Dispersion

Routine characterization of polarization-mode dispersion (PMD) in single-mode fiber, both at the manufacturing stage and in installed systems, requires an easy-to-implement measurement technique. One method that is particularly simple to implement involves counting the number of extrema (i.e., maxima and minima) per unit wavelength interval in the transmission spectrum measured through a polarizer (analyzer) placed at the output of a test fiber. In this paper, we establish accurate equations relating both the extrema density and mean-level crossing densities in such spectra to the expected value of PMD. These equations are used to measure several fiber samples, and are compared to measured values obtained with a commercially available test set. It is shown that measuring both mean-level crossings and extrema densities provides a simple means for establishing whether a fiber is scaling as /spl radic/L (long-length regime) or L (short-length regime). Using Monte Carlo simulations, the accuracy of the fixed-analyzer measurements is examined as a function of the width of the wavelength interval over which measurements are made. In addition, the simulations indicate that fixed-analyzer measurements are quite robust with respect to the presence of polarization-dependent loss (PDL) in the span, an important consideration for measurements in amplified systems. >

Polarization-mode dispersion measurements based on transmission spectra through a polarizer

We report some results of measurements of the frequency dependence of the state of polarization at the end of a low-birefringence long-cabled (50-km) optical fiber. The principal states of polarization and their group-delay difference were determined by making use of the Poincare sphere representation.

D. Andresciani

Papers

Measurement of the group-delay difference between the principal states of polarization on a low-birefringence terrestrial fiber cable.