Higher Order Polarization Mode Dispersion Research Articles

Study on High-order Polarization Mode Dispersion and its Compensation Method in High-speed Optical Communication Systems

With the development of high-speed, long-distance optical fiber communication systems, single-mode fiber polarization mode dispersion (PMD: Polarization mode dispersion) becomes one of the important factor limiting high-speed, long-distance optical fiber transmission. Polarization mode dispersion can cause pulse broadening in thedigital transmission system, result inter-symbol interference in digital communications, has seriously affected the quality of signal transmission. Because PMD has statistical properties under external influences during transmission, polarization mode dispersion compensation technology is much more complex than chromatic dispersion compensation techniques. This paper mainly discusses PMD and high-order PMD compensation method, simulate the first order PMD statistical properties, second order PMD statistical properties, and the broaden factor under un-compensation, the first-order compensation, the second-order compensation and the third-order compensation. the simulations have obtained that the compensation method based on center frequency Taylor series expansion does not apply to large PMD pulse-width ratio, but the high-order PMD compensation method based on the average frequency can reduce the broadening factor.

A DOP feedback controlling multi-stage electrical PMD compensator in digital coherent receiver

We proposed a degree of polarization (DOP) controlling multi-stage electrical polarization mode dispersion (PMD) compensator in digital coherent receiver. The compensator is modulation format independent and can mitigate both first order and higher order PMD. We evaluated this PMD compensator in both 100-Gb/s 16-QAM and QPSK signal transmission systems with 15ps and 20ps average differential group delay (DGD) respectively. The results show that, for both two cases, less than 0.2dB optical signal to noise ratio (OSNR) penalty at 1e−3 symbol error rate (SER) can be achieved after 4-stage PMD compensation.

Effect of Polarization Mode Dispersion on the BER Performance of Optical CDMA

In this paper, impact of polarization mode dispersion (PMD) on the bit error rate (BER) performance of direct sequence optical code division multiple access with in-line optical amplifiers is analytically investigated. Intensity modulation direct detection technique is employed in optical correlator receiver. Optical orthogonal codes are used as address sequence. The system BER performance is determined in presence of PMD and different noises induced from receiver, optical amplifiers, and multiple access interference. The power penalty suffered by the system is evaluated at BER of 10 -9 . It is found that the BER performance of the proposed system degraded more at high chip rate, chirp parameter and long fiber length due to the effect of PMD. Further, the BER performance of the proposed system is studied in presence of PMD compensation with frequency advanced higher order PMD vectors. The results demonstrate that the system BER performance is improved significantly for a particular fiber length and third-order PMD compensation technique shows better performance compared to first-, and second-order compensations.

640-Gb/s/Channel Single-Polarization DPSK Transmission Over 525 km With Ultrafast Time-Domain Optical Fourier Transformation

A single-channel 640-Gb/s differential phase-shift-keying transmission over 525 km was successfully demonstrated in a single polarization. A new ultrafast time-domain optical Fourier transformation (OFT) circuit was developed, in which the strong chirp required for the OFT of a subpicosecond optical pulse was realized with a phase modulator operated in a round-trip configuration. By applying this technique to a 640-Gb/s transmission, the tolerance to higher order polarization-mode dispersion was greatly improved and error-free transmission was achieved.

Elementary Matrix Method for Dispersion Analysis in Optical Systems

In this paper, dispersion analysis of optical components and systems is presented using a formalism based on the elementary matrices and the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> -matrix, first described by Jones. This approach readily incorporates both phase and amplitude dispersion in a generalized dispersion framework. The method simplifies the analysis of the combined effects of group delay, differential group delay, amplitude slope, and differential amplitude slope as compared to traditional Jones matrix methods. Higher order polarization-mode dispersion and the effects of concatenation are presented along with a discussion of measurement principles. The application of the elementary matrix concept to Mueller matrix methods in Stokes space is also discussed.

Higher-Order Modal Dispersion in Graded-Index Multimode Fiber

Previously, we proposed a field-coupling model for propagation in graded-index multimode fiber (MMF), analogous to the principal states model for polarization-mode dispersion (PMD) in single-mode fiber. That model was based on the concept of first-order principal modes, which have well-defined group delays that depend on the strength of the mode coupling. That first-order model predicts a linear relationship between the intensity waveforms at the MMF input and output. Here, we extend that model to account for higher order modal dispersion. The higher-order model predicts several effects analogous to higher-order PMD: pulse broadening, filling-in between peaks of the pulse response, depolarization and pattern blurring at the MMF output, and a nonlinear relationship between input and output intensity waveforms.

PMD compensation via real-time phase retrieval from spectral interference

We present a technique for pulse recovery based on real-time measurement of the differential optical phase spectrum from spectral interference patterns. Using a phase retrieval algorithm we can obtain accurate all order polarization mode dispersion (PMD) information for the optical signal and correspondingly compensate the impairment in optical transmission lines. Linear PMD is accurately extracted from measurements, and analytical simulations show recovery of pulses distorted by higher order PMD.

Performance of a 46-Gbps Dual-Polarization QPSK Transceiver With Real-Time Coherent Equalization Over High PMD Fiber

We report experimental results on the transmission performance of a coherent dual-polarization quadrature phase-shift-keyed (DP-QPSK) transceiver with real-time electronic equalization over fiber having 50-ps mean polarization mode dispersion (PMD). Both single-channel, single-span and multi-channel, multi-span measurements were performed over the high PMD fiber, which has near Maxwellian statistics for the differential group delay (DGD) as well as higher order PMD as expected for a long, mode-coupled fiber. Transmission of eighty channels was achieved over 8 times100 km of TrueWave Reduced Slope fiber plus distributed high PMD fiber, where individual channels had instantaneous DGD as high as 127 ps. The dependence of the OSNR penalty on the launch state of polarization was evaluated and found to be minimal, and the contribution of fiber nonlinearities to the transmission penalty was evaluated for two different per-channel launch powers. Finally, using a transceiver equipped with forward-error-correction, error-free transmission over the 800-km link was demonstrated over a 10-day period; during this time the DGD of the measured channel varied from 13 to 116 ps.

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.

320-Gb/s Single-Polarization DPSK Transmission Over 525 km Using Time-Domain Optical Fourier Transformation

A 320-Gb/s single-polarization differential phase-shift keying transmission is successfully demonstrated over a 525-km straight transmission line using time-domain optical Fourier transformation (OFT). The tolerance to higher order polarization-mode dispersion is greatly improved and long-term stable transmission performance is achieved with OFT.

On the Decision-Feedback Equalizer in Optically Amplified Direct-Detection Systems

This paper investigates the combined feed-forward and decision-feedback equalizer (DFE) in a lightwave system with optical amplifiers and a direct-detection receiver. Based on a nonlinear channel model, the paper provides a modification of the classical minimum mean square error theory of the DFE. Furthermore, an analytical method that is capable of accurate bit error rate (BER) evaluation is used to optimize the DFE for minimum BER. The paper evaluates the DFE performance for both optical ON-OFF keying and duobinary modulation formats in the presence of chromatic dispersion as well as the DFE performance for the mitigation of higher order polarization mode dispersion in first-order compensated systems. The paper shows that the DFE can compensate for the BER degradation due to narrow-band receiver-side optical filtering and can significantly improve the spectral efficiency of dense wavelength-division multiplexed systems.

Frequency Interpolation of Jones Matrices

We estimate the frequency-dependence of the Jones matrix of an optical fiber from its values at several discrete optical frequencies and illustrate our procedures through calculations of higher order polarization-mode dispersion effects in optical fibers

MLSE receiver tolerance to all-order polarization mode dispersion

We experimentally characterize a maximum likelihood sequence estimation (MSLE) based receiver's tolerance to first- and all-order polarization mode dispersion (PMD). We show that the response of the MLSE receiver to first-order PMD can be characterized in two ways depending on the differential group delay (DGD). In addition we show that first-order PMD-induced system penalties dominate those from high-order PMD. High-order PMD induces a large system penalty only when the first-order penalty is small, or the DGD exceeds a bit period.

Higher Order Polarization-Mode Dispersion in the Presence of Polarization-Dependent Loss in Optical Fiber Systems

The statistics of first- and second-order polarization-mode dispersion and statistical dependencies between corresponding quantities are investigated with regard to fiber-optic links with polarization-dependent loss (PDL). We show the occurrence of an infinite depolarization rate of the principal states of polarization (PSPs) caused by an abrupt interchange of the two PSPs with a probability that grows with the global PDL. We finally discuss the influence of the frequency resolution of measurement and simulation methods on the depolarization results

Higher-order optical polarization mode dispersion compensator evaluation using Markov chain Monte Carlo simulation

We describe how to use Markov chain Monte Carlo simulation (MCMC) to accurately estimate the outage probability of the optical communication system compensated by higher-order optical polarization mode dispersion (PMD) compensators. Markov chain fiber channel samples can drastically reduce the number of simulations required to estimate the outage probability of the compensated systems to 10 –6 or less. Using MCMC, the efficiency of our proposed higher-order optical PMD compensator is proved further, and the accuracy of MCMC is affirmed.

Degree-of-polarization and eye-closure penalty associated with optical signals with orthogonal polarizations

We perform a systematic measurement of the degree-of-polarization (DOP) and eye-closure penalty for optical signals with orthogonal polarizations. We find that the symmetry of DOP is maintained for the orthogonal polarizations under both first and higher order polarization-mode dispersion (PMD), whereas the symmetry of eye-closure penalty is broken under second-order PMD. An orthogonal polarization pair can have large disparity of eye-closure penalty despite an identical DOP. We also demonstrate a novel approach to estimate the maximum eye-closure penalty asymmetry with three orthogonal polarizations on the Poincareacute sphere

New optical compensator for higher-order polarization mode dispersion in optical fiber channels

We propose a new optical compensator for both first-order and higher-order polarization mode dispersion (PMD) effects in an optical fiber channel. The compensation scheme needs just one more polarization controller and one more variable differential group delay (DGD) element than first-order optical compensators with adjustable DGD elements. And the control algorithm for this compensator is easier and more stable than that for the typical higher-order optical polarization mode dispersion compensators. By an advised control method, the proposed compensator can always have better performance than first-order optical compensators. Numerical results are given to prove the efficiency of the proposed compensation scheme.

The effect of variable PSP angles in a PMD compensator

A polarization mode dispersion compensator (PMDC) composed of two polarization mode dispersion (PMD) elements and one polarization dependent loss (PDL) element is proposed. Simulation shows that, due to the variable angle between the two principal states of polarization (PSPs) of the compensator, the proposed compensator can improve the PMD compensation efficiency for systems with both PMD and PDL, especially when higher order PMD is compensated.

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.

Comparison of polarization-mode dispersion tolerances in polarization-multiplexing systems with different modulation formats

The polarization-mode dispersion (PMD) tolerance of 10Gb/s polarization-multiplexing (PM) system is investigated. Using the importance sampling (IS) method, the outage probabilities of the PM systems with three modulation formats, including on-off keying (OOK), differential phase-shift keying (DPSK) and differential quadrature phase-shift keying (DQPSK), are quantified. When the amplified spontaneous emission (ASE) noise is assumed to be dominant, we evaluate the optical power penalties caused by the PMD effect at bit error rate (BER) of 10−12. The performance of compensated PM systems with variable optical delay line is also described. The simulation results indicate that the OOK signal with higher duty cycle (DC) performs better in the PM systems with PMD compensation. It is found that the higher-order PMD impairs seriously the performance of the PM system, and phase-keying formats are more sensitive to the PMD than the OOK.