Polarization Mode Dispersion Models Research Articles

Narrow- or wide-band channel for a high baud rate fiber communication system: a judgment based on a temporal and spectral evolution PMD model.

In optical fiber communication systems, the tendency to prefer increasingly higher baud rates, up to 100 or 200 Gbaud, compels us to deal with wideband fiber channels in which polarization effects must be treated in a more complicated manner. In contrast to the conventional 50 GHz bandwidth wavelength division multiplexing channel, polarization mode dispersion (PMD) is observed in an all-order manner in a wideband fiber channel beyond 100 GHz, rather than only first- and second-order. In this study, certain principles that should be followed in establishing a PMD emulation model in a wideband fiber channel were put forward. Then, a temporal and spectral evolution PMD model that can reflect and emulate the evolution features of the polarization effects in a real fiber channel was proposed and demonstrated. The analyses show the PMD model satisfies all the principles for the wideband channels. Finally, we suggested some approaches to define a narrowband or wideband channel only considering the polarization effects to deal with PMD in a high baud rate optical fiber communication system.

PMD Effects in Fiber Optic Transmission Systems

Polarization mode dispersion (PMD) remains the most important limiting impairment for high bit rate transmission over optical fibers. In this article, after a brief description of PMD model and the associated statistic, we study the pulse distortion due to PMD using a powerful time-frequency diagram. This approach allows a very simple illustration of the second and high order PMD effects through effective pulse broadening. Finally, the PMD emulation issue and both electronic and optical compensation techniques are presented, that is a current field of cooperation between ENST-Bretagne and France Telecom R&D.

Emulation and Inversion of Polarization Mode Dispersion: A Lumped System and Pade Approximation Perspective

Polarization mode dispersion (PMD) has been a major impediment in achieving higher speeds in optical fiber communication systems. Various approaches and techniques for the basic theoretical analysis, modeling, simulation, and compensation of PMD have been proposed in the literature. In this paper, we present a novel and fresh approach to the modeling, emulation and inversion of PMD in optical fibers. In our approach, we first build a full PMD model based on coupled mode theory as a continuous-time, lumped and lossless system. We then develop systematic model dimension reduction techniques, adapted from Krylov-subspace based methods for large electronic systems, in order to obtain compact and low complexity PMD models. The reduced complexity models produced by our technique match the full PMD model over a specifiable frequency range of interest, have the same structure as the full model, and are amenable to efficient software and low complexity hardware implementations for emulation and inversion. Furthermore, the reduced compexity PMD modeling framework we develop in this paper can serve as a general formalism for studying the compressibility of PMD models and emulators.

Optical Equalization: System Modeling and Performance Evaluation

Optical equalization in fiber-optic systems is theoretically investigated. First, a wide variety of optical equalizers is presented by giving their equivalent models, by describing the basic principles of operation, and by showing analogies and differences among different structures and configurations. Then, evaluation of the bit error rate and outage probability, in the presence of optical noise, chromatic dispersion (CD), and polarization mode dispersion (PMD), is discussed by comparing different methods based either on the PMD vector and its related statistics or on Markov chain Monte Carlo (MCMC) simulations applied to a random waveplate model. As the first relevant result, the accuracy and complexity of different PMD models in compensated systems are tested and compared, and a novel reduced Bruyegravere-Kogelnik (BK) model, which is more accurate and simple than the complete BK model or other second-order models, is proposed. As an additional result, the ultimate theoretical performance for different configurations and numbers of stages of the equalizers is given, and it is shown that when a single equalizer is used for a pair of polarization-multiplexed channels, the system tolerance to PMD is highly increased

Effective pulse dynamics in optical fibers with polarization mode dispersion

This paper investigates pulse propagation in randomly birefringent optical fibers. We consider two polarization-mode dispersion models. Using a separation of scales technique we derive an effective stochastic partial differential equation for the envelope of the field. This equation is driven by three independent Brownian motions, and it depends on the polarization-mode dispersion model through a single effective parameter. This shows that pulse dynamics in randomly birefringent fibers does not depend on the microscopic model. Numerical simulations are in excellent agreement with the theoretical predictions.

The accuracy assessment of different polarization mode dispersion models

Several polarization mode dispersion (PMD) models were developed to help understanding PMD effects and simplify the analysis regarding their impact on the system performance. Whether or not a PMD model can be used to accurately predict the system impairments depends on how well it approximates fiber PMD. In this paper, we assess the accuracy of six commonly used first- and second-order PMD models by comparing them with an all-order PMD model. Both PMD induced pulse broadening and optical-signal-to-noise-ratio (OSNR) penalties are determined, analyzed, and compared for each PMD model. To separate first- and higher-order PMD effects, we investigate the system performance with and without PMD compensation. We find that, compared with the all-order PMD model, all the known first- and second-order PMD models overestimate the PMD distortions, and the PMD models that do not contain higher than second-order PMD generate the largest deviation. Our results show that the first-order PMD model can be used to approximate the all-order PMD model when no PMD compensation is used, but none of the known PMD models can generate results close enough to those of the all-order PMD model for a PMD compensated system. This indicates that to accurately evaluate the performance of PMD mitigation techniques, the all-order PMD model has to be used.

Extended Jones matrix for first-order polarization mode dispersion

I present numerical simulations of the average transfer function of polarization mode dispersion (PMD) in optical fibers conditioned on various given values of the differential group delay (DGD). I find that even fibers with relatively small mean DGD can exhibit significant coupling between the two principal states of polarization. The average frequency dependence of this coupling can be approximated by a generic analytic function that deviates substantially from the quadratic frequency dependence that is often assumed in second-order PMD models. Finally, I define an extended transfer matrix for first-order PMD that describes the average frequency dependence of all PMD-induced distortions as a function of the DGD and show that this matrix is much better suited for optical PMD compensation than that of a conventional first- and second-order PMD model.

Accurate Jones matrix expansion for all orders of polarization mode dispersion

I present a simple method for extracting the dispersive elements from a general unitary Jones matrix in such a way that the parts comprising the phase delays and higher-order dispersion in the two principal states of polarization are separated from those describing the frequency-dependent coupling between them. I then rigorously expand these two parts into power series in relative optical frequency, wherein the coefficients are explicit functions of the polarization mode dispersion vectors of various orders. This accurate expansion of the Jones matrix reveals in particular the amplitudes and phases of the cross-coupled components of the principal states of polarization, which are incorrectly described in most polarization mode dispersion models.

Comparison of penalties resulting from first-order and all-order polarization mode dispersion distortions in optical fiber transmission systems.

We compare the eye-opening penalty from a first-order polarization mode dispersion (PMD) model with that from an all-order PMD model in optical fiber transmission systems. Evaluating the performance by taking into account only first-order PMD produces a good approximation of the true eye-opening penalty of uncompensated systems when the penalty is low. However, when the penalties are high, this model overestimates the penalty for outage probabilities in the range of interest for systems designers, which is typically approximately 10(-5) to 10(-6).