Emulation and inversion of polarization-mode dispersion

When a fiber is characterized by measured polarization mode dispersion (PMD) vector data, inversion of these data is required to determine the frequency dependence of the fiber's Jones matrix and, thereby, its pulse response. This tutorial reviews the principal concepts and theory employed in approaches to PMD inversion and in the closely related emulation of PMD. We discuss three second-order emulator models and the distinction between the PMD vectors and the eigenvectors of the fiber's Jones matrix. We extend emulation and inversion to fourth-order and sixth-order PMD using higher order concatenation rules, rotations of higher power designating higher rates of acceleration with frequency, and representation of these rotations by Stokes' vectors.     

Importance sampling for polarization-mode dispersion

We describe the application of importance sampling to Monte-Carlo simulations of polarization-mode dispersion (PMD) in optical fibers. The method allows rare differential group delay (DGD) events to be simulated much more efficiently than with standard Monte-Carlo methods and, thus, it can be used to assess PMD-induced system outage probabilities at realistic bit-error rates. We demonstrate the technique by accurately calculating the tails of the DGD probability distribution with a relatively small number of Monte-Carlo trials     

Full characterization of polarization-mode dispersion withrandom-mode coupling in single-mode optical fibers

Theoretical expression has been derived for polarization-mode dispersion with random-mode coupling in optical fiber by simple means. The square-root dependence of polarization-mode dispersion not only on a fiber length but on a mean-coupling length has been experimentally verified for the first time. This characterization became possible only by the use of highly birefringent polarization-maintaining fiber and introduction of fusion splices with desired coupling lengths     

Fibers with low polarization-mode dispersion

Fibers with low polarization-mode dispersion (PMD) enable high-bit-rate time-division-multiplexed optical communication systems. These fibers are becoming increasingly important with the growing implementation of wavelength-division-multiplexing (WDM) transmission with channel bit rates of 40 Gb/s. Important to the realization of low PMD fibers are the fiber's index and stress profiles, polarization-mode coupling, and the evolution of the polarization state with length. This paper reviews recent progress in the understanding of the fabrication and characteristics of these fibers. The paper also discusses the important fiber physical parameters, including the fiber index profile and fiber spinning parameters and their impacts on the realization of low PMD performance.     

Emulator of first- and second-order polarization-mode dispersion

Contrary to approaches which try to mimic a standard fiber as closely as possible, the emulator presented here gives constant (but user adjustable) values for differential group delay (DGD) and ratio of first- to second-order polarization-mode dispersion (PMD). Once it is set, the ratio is conserved while the DGD can be easily varied within a range of 0-300 ps. This allows to investigate the low-probability events of large DGD and second-order PMD important for system outage     

Interferometer measurement of polarization-mode dispersion statistics

A new relationship between polarimeter and interferometer measurements of polarization mode dispersion is proposed. This model bridges the gap between interferometer patterns and probability density function of the principal states of polarization group delay. Experimental results supporting the theory are presented.     

Average frequency dependence of polarization-mode dispersion

We present a numerical analysis of the average frequency dependence of a Jones matrix describing polarization-mode dispersion (PMD) with arbitrarily large differential group delay (DGD). Using a properly oriented autocorrelation matrix, we calculate the relative frequency dependence of the phase delays in the principal states of polarization (PSP) and of the cross coupling between the PSPs. Our results show that the averaged frequency dependence of these components scales with the product of the relative optical frequency times the average DGD. We also find a previously unknown correlation between the third-order PMD vector and the cross product of the first- and second-order PMD vector.     

Planar lightwave circuit polarization-mode dispersion compensator

In this letter, we fabricated an integrated polarization-mode dispersion compensator on a silica-based planar lightwave circuit that incorporated an endless polarization controller and a fixed polarization dependent delay line. The compensator consisted of polarization beam splitters, thermooptic phase shifters, tunable couplers, and polarization converters. We experimentally confirmed its operation at a data rate of 43 Gb/s     

Distributed polarization-mode dispersion compensation using polarizers

We numerically evaluate the performance of two kinds of distributed polarization-mode dispersion compensation techniques using either linear or elliptic variable polarizers. Each in-line compensator is characterized by only one or two degrees of freedom and the average power is used as a monitor signal, which simplifies the control algorithm. The use of polarizers causes inevitable attenuation of the optical signal, which induces additional noise in amplified systems. Nevertheless, the noise enhancement due to the distributed polarizer-induced loss is shown to be limited in systems operated with erbium-doped fiber amplifiers in gain saturation and the tolerable differential group delay can be improved if the frequency of insertions is increased.     

偏振模色散补偿方案研究

阐述了偏振模色散的产生原因及其特性,介绍了几种高速光通信系统中基于电域和光域的偏振模色散补偿方案,对其性能和实现方式作了分析.波分复用技术是当前光通信网中常用的技术,为此,介绍了几种基于波分复用系统的PMD补偿方案,指出了各方案的优势以及不足之处.     

Principles for electronic equalization of polarization-mode dispersion

System performance of optical fiber transmission in the presence of polarization-mode dispersion (PMD) can be improved by various types of electronic equalizers, which will be discussed in this paper. After a brief review of equalization and detection theory, equalizer concepts are adapted to the nonlinear optical channel and the architecture is optimized for high bit rate applications. Simulation results accounting for implementation losses in state-of-the-art technologies and realistic transmission conditions indicate that these concepts provide adequate solutions for equalization in lightwave transmission systems.     

Pulse propagation in fibers with polarization-mode dispersion

The propagation of pulses in optical fibers with polarization mode dispersion (PMD) is considered. The approach taken differs from those previously used, adapting Marcuse's perturbation method to analyze pulse dispersion rather than using Jones matrices or Stokes parameters. This allows the complex stochastic partial differential equations to be reduced to a simple propagation equation for the pulse power. This may be solved to obtain the transfer function of the fiber. The impact of PMD on optical fiber communications systems is considered, with the effect on pulsewidth and eye closure calculated. Finally, the statistical behavior of the phenomenon is considered to calculate the system outage probability due to PMD     

Independently tunable first- and second-order polarization-mode dispersion emulator

By solving the equation set for the first- and second-order polarization-mode dispersion (PMD) in retro-verse manner, we show that the independent control of first- and second-order PMD is possible, with only two control parameters. The analysis on the emulation algorithm as well as the operation range/resolution shows excellent agreement with the experimental demonstration operated with a sample emulator constructed of a fixed differential group delay (DGD), a polarization rotator, and a variable-DGD element.     

Coherent frequency-selective polarimeter for polarization-mode dispersion monitoring

Frequency-selective polarimeters measure the state of polarization of the individual spectral components of a modulated optical signal. They can be used either as stand-alone measuring devices or as parts of adaptive polarization-mode dispersion (PMD) compensators. This paper presents a novel frequency-selective polarimeter based on coherent detection, which has superior accuracy compared to previously proposed direct detection-based counterparts. This is due to the high-frequency resolution and power sensitivity of coherent detection, features that minimize the systematic and random error, respectively, in the measurement of the state of polarization of the individual spectral components of the received optical signal. The accuracy of the measurement is independent of the received signal bit rate and modulation format. The proposed frequency-selective polarimeter is studied both theoretically and experimentally. The primary theoretical contribution of this paper is a unified formalism, which allows the modeling of both direct and coherent detection-based frequency-selective polarimeters. Analytical expressions for the output signal of both types of frequency-selective polarimeters are derived. Based on these expressions, a common algorithm is proposed for the evaluation of the Stokes parameters. In addition, an example error signal is used as a metric in order to test the agreement of the theoretical model with the experimental measurements. The successful operation of the coherent frequency-selective polarimeter is demonstrated experimentally for a 10-Gb/s intensity-modulated nonreturn-to-zero (NRZ) optical signal in the presence of first-order polarization-mode dispersion. There is an excellent agreement between theory and experiment.     

A deterministically controlled four-segment polarization-mode dispersion emulator

In this paper, we propose a novel design of a first- and second-order polarization-mode dispersion (PMD) emulator based on four concatenated first-order PMD segments. Instead of polarization scrambling at each junction, we set these polarization rotators according to a statistical schedule, so as to produce a realistic probability density function of the first- and second-order PMD presented in long-haul transmission fiber.     

Practical considerations for optical polarization-mode dispersion compensators

For transmission systems at 10 Gb/s and beyond, polarization-mode dispersion (PMD) is one of the limiting factors. Optical PMD compensators aim at increasing the PMD value tolerated by the system; however, they do not cancel out its effects. Therefore, the performance of a PMD compensator is assessed statistically. Requirements for optical PMD compensators include a response time in the range of 1 ms in order to follow polarization fluctuations over the line. The system design should account for the interaction of other transmission impairments with the PMD compensator operation. For instance, transmitter chirp and residual chromatic dispersion have a deleterious impact on the compensator performance. While self-phase modulation is harmless, cross-phase modulation greatly reduces the compensator efficiency. System design rules have been applied to a one-year field trial, showing the compensator's efficiency and reliability. However, reducing their cost is the next challenge that will bring optical PMD compensators to be used in installed systems.     

Mitigation of polarization-mode dispersion in optical multichannel systems

Simulations of first-order polarization-mode dispersion (PMD) mitigation, based on the electrical power spectrum has been performed. We show that, although first-order compensation significantly improves the signal quality for PMD values of a few tenths of the bit-slot, the improvement still is deficient for telecom purposes when the PMD value neighbors a third of the bit-slot. We, therefore, propose and analyze a novel concept for PMD mitigation in optical multichannel systems, which increases the systems reliability at the expense of the total capacity for the same system. With the proposed method, which uses switching to redundant channels based on measurements of signal quality of all channels in the actual system, the PMD value can be increased to a half of the bit-slot while still keeping the probability for signal outage at acceptable low levels. In the appendixes we simulate the statistical impact of different PMD-emulator models and we show that static bit sequences may induce notches in the electrical power spectrum. These notches may obstruct the extraction of feedback signals for PMD-mitigator schemes based on electrical power spectrum.     

Distortion related to polarization-mode dispersion in analoglightwave systems

Analog transmission in single-mode fiber using chirped sources gives rise to nonlinear distortion when polarization-mode dispersion (PMD) is present. We investigate experimentally and theoretically two mechanisms for this distortion: for chirped sources, PMD in the presence of polarization-mode coupling results in second-order distortion that is proportional to the square of the modulation frequency; when polarization-dependent loss is present, an additional second-order distortion term occurs that is independent of modulation frequency. Both mechanisms give rise to distortion that is time varying due to the sensitivity of PMD to ambient temperature changes. Numerical examples indicate that these effects can limit the capacity of analog systems that use directly modulated semiconductor lasers     

Measurement of second-order polarization-mode dispersion vectors inoptical fibers

A polarization-mode dispersion (PMD) measurement technique is described that allows the determination of second- and higher order PMD vectors in optical fibers. The algorithm, based on Muller matrices, requires the launch of only two polarizations per wavelength and uses large rotation angles as well as interleaving to attain low-noise high-resolution PMD data. It has been applied to fibers ranging from 2 to 40 ps in mean PMD     

Impact of chirping on polarization-mode dispersion compensated systems

Investigates the effect of chirp, resulting from either the transmitter, chromatic dispersion, or Kerr effect in the fiber, on polarization-mode dispersion (PMD) compensated systems. We demonstrate both experimentally and numerically the deleterious impact of chirping on systems with first-order PMD compensation. We present a way to optimize the PMD compensator performance by minimizing the total chirp of the signal at the receiver side.