Polarization Mode Dispersion In Optical Fibers Research Articles

A Geometrical Perspective on the Coherent Multimode Optical Field and Mode Coupling Equations

The generalization of the Poincare sphere to $N \ge 2$ modes is the ( $N-1$ )-dimensional complex projective space CP( $N-1$ ). There is a minimal set of $2N-2$ Stokes vector components that determine the coherent multimode optical field. These are obtained from the inverse stereographic projection of coordinate hyperplanes in CP( $N-1$ ) into a $2N-2$ sphere, just as in the $N=2$ case. We derive $N$ -mode analogs of Poole’s optical fiber polarization-mode dispersion (PMD) equations that involve only $2N-2$ independent variables. This is achieved by means of an explicit generalized coherent state representation of the optical field, which enables the components of the PMD vector to be expressed in terms of the optical state and its frequency derivatives. Poole’s equations describe mode coupling as a flow on CP( $N-1$ ). We give general constraints on the mode-coupling matrix and Stokes vector components. The group delay operator is shown to be a rank-2 perturbation of a diagonal matrix.

光纤偏振模色散的缓解与补偿技术研究与进展

光纤偏振模色散的缓解与补偿技术研究与进展

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.

Broadband all-order polarization mode dispersion compensation via wavelength-by-wavelength Jones matrix correction

We demonstrate wideband all-order polarization mode dispersion (PMD) compensation by applying high-speed spectral polarization sensing and ultrafast pulse shaping techniques to characterize and correct the frequency-dependent Jones matrix associated with PMD of optical fibers on a wavelength-by-wavelength basis. We report full compensation of approximately 800 fs pulses distorted to more than 10 ps by a PMD module with approximately 5.5 ps mean differential group delay. The sensing and compensation of Jones matrix take approximately 200 and approximately 500 ms, respectively.

Local Birefringence in Unidirectionally Spun Fibers

The application of a spinning step in the drawing process is known to improve optical-fiber polarization mode dispersion. For a more comprehensive understanding of the mechanism through which spinning modifies fiber performances, in this paper, the authors investigate the effect of unidirectional spinning on local fiber birefringence in terms of the effectiveness of spin-function transfer and reduction of the local intrinsic birefringence under different drawing conditions. The actual frozen-in spin is experimentally recovered by means of a cut-back procedure. Different from the case of a periodic spinning, a unidirectional spinning correctly reproduces the nominally imparted spin rate in agreement with theoretical modelizations of the transfer effectiveness of the spinning process. A theoretical explanation for the experimental evidence, recently proved by tomographic stress measurements, of spinning affecting fiber linear intrinsic birefringence is provided. In particular, the interaction of drawing parameters and spinning process in defining stress development into fibers is considered. To validate the proposed model, further tomographic reconstructions of stress profiles in fiber spun at different rates and drawing speed were carried out. Besides, corresponding stress-induced birefringence values were estimated and compared with those recovered by the cut-back technique. Variations of spun fiber beatlength values with respect to the unspun case, as obtained from both measurement techniques, are in good agreement, providing a further reliable confirmation that an improvement of the beatlength may proceed as a consequence of the applied spin

Genealogical particle analysis of rare events

In this paper an original interacting particle system approach is developed for studying Markov chains in rare event regimes. The proposed particle system is theoretically studied through a genealogical tree interpretation of Feynman–Kac path measures. The algorithmic implementation of the particle system is presented. An estimator for the probability of occurrence of a rare event is proposed and its variance is computed, which allows to compare and to optimize different versions of the algorithm. Applications and numerical implementations are discussed. First, we apply the particle system technique to a toy model (a Gaussian random walk), which permits to illustrate the theoretical predictions. Second, we address a physically relevant problem consisting in the estimation of the outage probability due to polarization-mode dispersion in optical fibers.

Analysis of Signal Degree of Polarization Degradation Induced by Polarization-Mode Dispersion in Optical Fibers

We study analytically and numerically optical signal degree of polarization (DOP) degradation induced by polarization-mode dispersion (PMD) in optical fiber transmissions, using the Eyal-Marshall-Tur-Yariv (EMTY) model and Monte Carlo simulations. The results show the inaccuracy of second-order PMD approximation in the EMTY model and the inapplicability of employing DOP as feedback signal for high-order PMD compensation.

A Random Walk Procedure for Evaluating Probability Distribution Functions in Communication Systems

We demonstrate that probability distribution functions (pdfs) such as those of interest in communication theory can be efficiently calculated through a random walk algorithm. To illustrate the procedure, we determine the pdf of polarization-mode dispersion in optical fibers. We find that the technique efficiently samples configurations with extremely low probability for which it converges far more rapidly than the multicanonical procedure.

Compensation of Polarization Mode Dispersion with Electrical Nonlinear Transmission Lines

A new compensation scheme for signal distortion caused by optical fiber polarization mode dispersion (PMD) is proposed. Because of the time-varying nature of PMD, any scheme that is to compensate for PMD must be adaptive. Moreover, the PMD fluctuation has the time scale of a few milliseconds. The proposed scheme utilizes nonlinear transmission lines (NLTLs) as the key device. The NLTLs can produce equalized output even if the input pulses have a wide range of PMD distortion, thus making adaptive control simpler than is possible with conventional schemes. This paper describes the configuration, the operating principle, and the design criteria of the proposed PMD compensation scheme.

Robustness of dispersion-managed solitons to the polarization-mode dispersion in optical fibers

The robustness of dispersion-managed (DM) solitons to polarization-mode dispersion (PMD) is studied by numerical simulations. It is shown clearly that DM solitons are robust to PMD, and generally, DM solitons are more robust to PMD than conventional solitons. The robustness of DM solitons depends on both map strength and average group velocity dispersion (GVD). We show that the larger the map strength and average GVD, the more robust are the DM solitons to PMD, which is due to the increased power of DM solitons with the large map strength and average GVD.

Nonlinear polarization-mode dispersion in optical fibers with randomly varying birefringence

Randomly varying birefringence leads to nonlinear polarization-mode dispersion (PMD) in addition to the well-known linear PMD. Here we calculate the variance of the field fluctuations produced by this nonlinear PMD. Knowing the size of these fluctuations is useful for assessing when nonlinear PMD is important and for its proper incorporation in fast numerical algorithms. We also derive the equilibrium probability distributions for the PMD coefficients, and we track the evolution of the polarization state's probability distribution from its initial delta-function distribution to its steady-state uniform distribution on the Poincaré sphere.