Second-order Polarization Mode Dispersion Research Articles

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

PMD induced performance deterioration in NOLM switch

Performance deterioration induced by the first- and second-order PMD in the basic NOLM switch unit in the digital optical communication system and analog microwave photonic communication system is studied by using the split-step Fourier method that can solve the coupled nonlinear Schrödinger equation, the three-dimensional Poincare sphere theory and the Jones matrix method. The simulation results show that the switch performance is badly deteriorated by PMD and the impact of the second-order PMD is far more than that of the first-order PMD when NOLM is at a high working speed or a large modulation bandwidth. In the digital optical communication system, the optical eye graphs of pulses and the extinction ratio of NOLM are deteriorated by PMD and it can partially reduce the impact of PMD to use the right code pattern, in which the performance of CRZ code with positive chirp is better than that of RZ code and the performance of RZ code is better than that of NRZ code when they have the same average power. In the analog microwave photonic communication system, PMD induces the descent of the SNR and the side lobe leak of the signal.

Experimental Determination of System Outage Probability Due to First-Order and Second-Order PMD

In this paper, a polarization-mode dispersion (PMD) tolerance testing procedure for transponders and transmission systems is described. This method exploits programmable PMD sources for testing the first- and second-order joint probability density function to estimate the total PMD network outage. Experimental data show that first-order-only PMD testing is insufficient to quantify the tolerance of a transponder and may falsely underestimate network outage

System Penalty From Second-Order PMD Approximation: Reference Frame Implication

In this paper, we show that second-order PMD approximations, when derived using the input frame and output frame of an optical link, result in two different PMD systems represented by two distinct Jones matrices. In contrast to an all-order representation of a system, which is independent of reference frame, it is found that a finite second-order approximation cannot be obtained simultaneously in both input and output reference frames, except in some limited special cases. The consequences of this are illustrated by analyzing the difference between these two approximations in pulsewidth distortion. It is shown that the second-order PMD approximation in the input frame corresponds to a truncated second-order expansion of the pulse distortion, whereas the second-order PMD approximation in the output frame leads to an infinite-order pulse distortion

Statistical characteristics and effects of polarization mode dispersion in dispersion managed soliton systems

Firstly, the JME (Jones matrix eigen) method is used to simulate the statistical characteristics of first- and second-order PMD in dispersion management system. Then, with help of the CNLSE (coupled nonlinear Schrodinger equations), the effects of PMD on DMS (dispersion managed soliton) transmission is studied with a variatioal method. The simplified relationships of the statistical parameters of second-order and first-order of PMD in dispersion management system have been gotten, from which the detailed information of second-order can be obtained, if the condition of DGD is given. The results have shown that the first and second-order PMD (polarization mode dispersion) vectors influence the evolution of energy and Mean square of time displacement of DMS in high-speed bit rates systems. WhenDPMD1 st>0.3 ps/km1/2, we must consider some means of control (for example the filter) the restrain the PMD.

PMD Characterization of a Dispersion Managed Link up to the Second-order with High Accuracy

We report an algorithm on the characterization up to second-order polarization mode dispersion (PMD). Our algorithm is able to characterize very short link with low PMD coefficient (less than 0.04 ps/ \(\sqrt{km}\)). The link includes dispersion compensating fiber modules and loss compensating optical amplifiers. The estimation for first- and second-order PMD is successfully performed for dispersion-managed links of 85 and 265 km using the Jones matrix eigen-analysis (JME). The algorithm was developed to detect the evolution of the principal state of polarization (PSP) and subsequent calculation of second-order PMD components such as polarization-dependence, chromatic dispersion (PDCD) and depolarization.

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

Comparison study of the average transfer matrix of first- and second-order PMD

This paper presents numerical simulations of the transfer matrix of polarization-mode dispersion (PMD) in long optical fibers, wherein the average frequency dependence of this matrix is calculated conditioned on various given values of the differential group delay that is introduced between signal components in the two principal states of polarization (PSPs) and the second-order PMD parameter that characterizes frequency-dependent cross coupling between the PSPs. The results are then compared with four popular models of first- and second-order PMDs (F&SO-PMD), and it is found that none of them describes the average Jones matrix of F&SO-PMD with acceptable accuracy over the entire range of PMD parameters and optical bandwidth of interest. The differences between the various models and the simulation results are particularly large when the frequency-dependent cross coupling is large.

Geometrical interpretation of second-order PMD

A geometrical interpretation of second-order polarization mode dispersion (SOPMD) as the curved three-dimensional (3-D) area swept by the PMD vector as it increases with propagation in a birefringent system is introduced. The depolarization and polarization-dependent chromatic dispersion parts of the SOPMD can be viewed as projections of this area in orthogonal directions. This interpretation enables us to translate the problem of maximizing the SOPMD in, e.g., PMD emulators and programmable PMD sources to an isoperimetric problem, i.e., a problem of maximizing the area enclosed by a given perimeter, which has well-known solutions. Both the discrete problems corresponding to a set of birefringent wave plates are discussed, and the continuous problem in which an arbitrary birefringent medium is considered. Analytic formulas are derived for the first time for the maximum SOPMD, depolarization, and polarization-dependent chromatic dispersion that can be realized in PMD emulators.

Broadband all-order polarization mode dispersion compensation using liquid-crystal modulator arrays

Polarization mode dispersion (PMD) is a potential limiting factor in long-haul high-speed optical communications, especially in systems beyond 10 Gb/s. Although considerable effort has been devoted to compensation methods for PMD, most of the research is restricted to a small bandwidth, within the limits of the first- and second-order PMD approximations. For the first-order approximation to be valid, the distortions induced by PMD must remain less than a few tenths of the pulse duration or the bit period for return-to-zero (RZ) or non-return-to-zero (NRZ) systems, respectively. In this work, as far as the authors know, the application of ultrafast optical pulse-shaping techniques for experimental broadband all-order PMD compensation is demonstrated for the first time. PMD is treated as arbitrary variations of state of polarization (SOP) and phase versus wavelength, in an all-order sense. Two fiber-pigtailed pulse shapers are implemented in a serial manner to compensate the polarization and phase spectra independently. The first step corrects the wavelength-dependent polarization states to a fixed wavelength-independent state. This reduces the PMD compensation problem to a generalized chromatic dispersion compensation problem. Consequently, equalization of the spectral phase in the second step restores the clean broadband pulse signal. In the experiments, compensation of subpicosecond pulses (14 nm bandwidth around 1550 nm) that are anomalously spread to more than 2 ps due to PMD is demonstrated. These results are potentially relevant for future ultra-high-speed time-division-multiplexed (TDM) systems. Research challenges that must be addressed to bring this approach to practical application are also briefly enumerated, and the potential for scaling to a range compatible with wavelength-division-multiplexed (WDM) systems is discussed.

Comparison of two biasing Monte Carlo methods for calculating outage probabilities in systems with multisection PMD compensators

We evaluate the performance of single-section and three-section polarization-mode-dispersion (PMD) compensators using the biasing Monte Carlo methods of importance sampling (IS) and multicanonical Monte Carlo (MMC). We show that standard IS that biases only first-order PMD is insufficient to compute penalties in most compensated systems, while multiple IS that biases both first- and second-order PMD and MMC work well with all the compensators that we investigated. We show that multiple IS works well even in a system with a three-section compensator, when both first- and second-order PMD are compensated. The applicability of IS in these systems is consistent with the existence of a large correlation between first- and second-order PMD of the transmission line and higher orders of PMD after compensation, so that the first two orders, even when compensated, remain highly correlated with the residual penalty. We directly demonstrate the existence of this correlation.

The Statistical Analysis of Polarziation Mode Dispersion and Filter Control on Dispersion Managed Soliton Links

In this paper, the statistical distributing and magnitude of the first and the second-order PMD (polarization mode dispersion) vectors are evaluated and the filters control PMD effects also are analyzed on DMS (dispersion-managed soliton) links. Firstly, the so-called coarse-step approach is applied to the DMS links. The PMD statistical characteristics of the first and the second-order are simulated and the evolutions of energy and mean square of time displacement of DMS two polarization modes are gotten. Secondly, The DMS transmission of filter control with the conventional model of PMD is analyzed by Varitional method, from which the evolving rules of characteristically DMS parameters are obtained and the stability of filter control the DMS transmission are investigated. The results are not only very useful to simplify the measurement of the second-order PMD and instructively reveal degree of PMD effects in DMS systems, but also give that condition of stability of filter control PMD in DMS systems.

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 system penalties from first- and multiorder polarization-mode dispersion

We experimentally investigate the polarization-mode dispersion (PMD)-induced system penalty arising from first-order and all-order PMD. We use a measurable quantity, "string" length, to parameterize the penalty, find a deterministic correction to the accepted first-order PMD-induced system penalty approximation, and discuss the implications for system outages. Further, we show that higher orders of PMD introduce an additional penalty scatter that is nearly independent of "string" length, and correlated to the magnitude of the second-order PMD vector.

Analysis of pulse broadening induced by the second-order PMD

We propose a new conception of depolarization vector to describe the effect of depolarization induced by the second-order polarization mode dispersion (PMD). Deriving the formula of pulse broadening induced by the second-order PMD, we find that the polarization-dependent chromatic dispersion (PCD) always enhances the pulse broadening. However the depolarization vector decreases the pulse broadening. The pulse broadening is correlated with the bit-rate of a transmission system. By adjusting the directions of the Stokes vector of initial state of polarization, initial first-order polarization dispersion vector and depolarization vector to be parallel to each other, one can obtain an optimum dispersion compensation. But when the PCD is not equal to zero, the optimum dispersion cannot achieve a complete compensation and the minimum pulse broadening is equal to σ = (21/2/4)(DCF/T0).

Biased multicanonical sampling

A modified multicanonical method is introduced that improves computational accuracy within selected regions of system parameters. The numerical accuracy of the method is established by evaluating the joint distribution function of first- and second-order polarization-mode dispersion in weakly birefringent optical fibers.

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.

Improved optical compensator for first- and second-order polarization-mode dispersion

We present an improved transfer matrix for optical compensation of first- and second-order polarization-mode dispersion (PMD), which efficiently offsets the average third- and higher order PMD in the fiber. Numerical simulations reveal that this compensator performs substantially better than other previously known schemes, at least in digital transmission systems using conventional return-to-zero and nonreturn-to-zero formatted signals. This superior performance is largely achieved by employing an empirically determined average frequency dependence for the cross coupling between signals components in the two principal states of polarization.

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.

First- and second-order polarization mode dispersion generated by a two-stage emulator

A two-stage polarization mode dispersion (PMD) emulator design consisting of two variable delay lines separated by a rotatable half-wave linear retarder is analyzed and shown to generate an adjustable amount of first- and second-order PMD without any higher orders. This two-stage PMD emulator configuration provides a simple easy-to-breadboard solution for second-order PMD emulators. When compared with PMD emulators based on birefringent crystals, this two-stage emulator is simpler to calibrate.