A deeper analysis of the second order polarization mode dispersion in optical communications systems

This article presents a new approach to the combined analysis of the first and second-order polarization mode dispersion (SOPMD) and shows their importance in optical communication systems performance. How it affects the relation between second-order polarization mode dispersion (PMD) and the differential group delay (DGD) in a single mode fiber is discussed. The analysis is based on time or wavelength and temperature variations changing/impacting PMD and DGD measured values. We present long term statistical characteristics of second-order PMD over a PMD emulator, and investigate the correlation between SOPMD, depolarization (DEP) and polarization dependent chromatic dispersion (PCD). Some authors calculate these modes from measurements obtained from the first order polarization mode dispersion, assuming a positive correlation between these effects, but this not the real relationship between them. A new interpretation of SOPMD was used to analyze the problem of the spectral stability in terms of the temperature. Actual techniques for determination SOPMD, consequently DEP and PCD, use the variation in time and/or wavelength. In some studies the results obtained for SOPMD are correlated to first-order PMD (FOPMD). This paper shows, based on measurements, that the correlation between first and second order Polarization Mode Dispersion (PMD) in the case where the last one is a function of the temperature can assume positive or negative values.     

Introduction to polarization mode dispersion in optical systems

This introduction covers concepts important to the understanding of polarization mode dispersion (PMD), including optical birefringence, mode coupling in long optical fibers, the Principal States Model, and the time and frequency domain behavior of PMD. Other topics addressed include the concatenation rules, bandwidth of the Principal States, PMD statistics and scaling, PMD system impairments, and PMD outage probability calculations.     

Effect of cross-phase-modulation-induced polarization scattering on optical polarization mode dispersion compensation in wavelength-division-multiplexed systems

Interchannel cross-phase-modulation-induced polarization scattering (XPMIPS) and its effect on the performance of optical polarization mode dispersion (PMD) compensation in wavelength-division-multiplexed (WDM) systems are studied. The level of XPMIPS in long-haul WDM transmission systems is theoretically quantified, and its effect on optical PMD compensation is evaluated with numerical simulations. We show that in 10-Gbit/s ultra-long-haul dense WDM systems XPMIPS could reduce the PMD compensation efficiency by 50%, whereas for 40-Gbit/s systems the effect of XPMIPS is smaller.     

Filter control polarization mode dispersion in dispersion managed soliton systems

In this paper, the dispersion managed soliton (DMS) transmission equation is built on considering the effects of polarization mode dispersion (PMD) and filter control. The DMS transmission of filtering control in constant birefringence fibers is firstly analyzed by varitional method, from which the evolving rules of characteristical DMS parameters are obtained. Secondly, the stability of DMS transmission and its timing jitter are investigated in the random varying birefringence fibers with the conventional model of PMD. The results reveal that filter control DMS system has powerful robustness to PMD effects and DMS's timing jitter can be decreased considerably with the help of filters.     

Spectral-resolved backreflection measurement of polarization mode dispersion in optical fibers

An improved backreflection technique is proposed to perform the spectral-resolved measurement of polarization mode dispersion (PMD) in optical fibers. This technique is based on the PMD dynamical equation and realized by measuring the polarization state evolutions of the reflected signal in both frequency and time domains. Two experimental setups, employing the far-end Fresnel reflection, are constructed to verify this technique. The agreement between the results of the proposed backreflection technique and the conventional forward technique is observed.     

能够补偿二阶偏振模色散的三阶段偏振模色散补偿器

简要分析了偏振相关色散对光通信系统性能的影响,提出了一种三阶段高阶偏振模色散补偿方案,从理论上分析了它同时补偿偏振相关色散和偏振主态旋转的可能性,并提出了其可能存在的两种工作方式.通过数值模拟与两阶段补偿方案进行了性能比较,其偏振模色散容限比两阶段补偿提高约17%个比特周期 关键词： 光通信 光偏振 光纤色散     

光纤偏振模色散对信号偏振度的影响

采用一种简化的线路传输模型，详细讨论了在高速光纤通信系统中，线路偏振模色散（PMD ），尤其是二阶PMD、输入信号偏振态等对信号偏振度（DOP）的影响，并指出以信号DOP做 反馈控制信号适合于一阶PMD优化补偿系统，但在较大二阶PMD的影响下，将增加控制算法的 复杂性，使系统可能陷入局部最优解. 关键词： 信号偏振度 偏振模色散 信号偏振态     

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).     

Loss of polarization entanglement in a fiber-optic system with polarization mode dispersion in one optical path

We characterize theoretically and experimentally the degradation of polarization entanglement in a fiber-optic entanglement distribution system where one of the optical fibers is exposed to the effects of polarization mode dispersion (PMD). We show gradual reduction of entanglement with increasing PMD and find that the highest PMD tolerance is achieved when the bandwidth of the pump used to generate the entangled photons in a χ((3)) process is approximately half the bandwidth of the quantum channels.     

Solitons and polarization mode dispersion

Analytical expressions are presented for Manakov solitons perturbed by polarization mode dispersion (PMD). Comparison is made with computer simulations. Dispersion-managed solitons are also studied. It is concluded that at high bit rates solitons are superior to linear return-to-zero propagation with regard to PMD.     

General demonstration of principal states of polarization and real-time monitoring of polarization mode dispersion in optical fibres

We investigated the general properties of polarization effects in optical fibres and demonstrated the existence of socalled principal states of polarization (PSP), which mean the fixed points in mathematics, in different polarization effects,such as birefringence and polarization mode dispersion, by using fixed point theory. Furthermore, a time evolution vector is defined to describe the time evolution of polarization state in optical fibres, which is used to investigate the time evolution of polarization mode dispersion vector (PDV), including differential group delay and PSP. The experimental results of real-time monitoring of PDV by using this method are reported. To our knowledge, this is the first report on monitoring PSP evolution in optical fibres.     

Measurement of polarization mode dispersion in single mode fibre

Polarization mode dispersion (PMD) in fibre seriously limits the high-capacity optical fibre communication system. The measurement of PMD was realized by three methods — wavelength scanning method, modified OTDR method and modified York S-38 dispersion meter method. Different types of fibres have been measured using the above three methods and the results have been found to be consistent. Finally, we also found that the measured results of longer non-polarization-maintaining fibre satisfied the Maxwellian probability density function and the results of polarization maintaining fibre were derived. Supported by The National Natural Science Foundations of P. R. China.     

Jones matrix of polarization mode dispersion

We describe how to calculate the Jones matrix transfer function of a fiber if its principal states of polarization and its differential group delay as functions of frequency are known. Using two counterexamples related to second-order polarization mode dispersion (PMD), we also show that a previous method used for the same purpose induces overestimation of second-order PMD effects by a factor of 2. Our new method is used to solve the problem for both counterexamples.     

Statistical properties of polarization mode dispersion

Polarization mode dispersion (PMD) is one of the effects which limit bit rates in optical communications systems. The statistics of PMD is complicated because it is multi-dimensional, however, many useful results have been obtained. Much work has been done, but the subject is not yet closed, as witnessed by the existence of this conference. In this talk I will review the way some statistical equations are treated. I will briefly discuss the methods of Ito and Lax, and their application to the PMD problem.     

Impact of polarization mode dispersion on the performance of optical CDMA transmission system

The impact of fiber polarization mode dispersion (PMD) on the bit error rate (BER) performance of a direct sequence optical code-division multiple-access system is analyzed by the split-step Fourier method based on the coupled nonlinear Schrödinger equation, the three-dimensional Poincare sphere theory and the Jones matrix method. When the incident pulse's width is bigness than the chip duration, which causes spreading and overlapping of chips and degrades system performance due to increased interchip interference and reduced received optical power conduce cannot decoding or error decoding. When the incident pulse's width is less than the chip duration, good encoding/decoding performance can be achieved.     

Effects of polarization mode dispersion on cross-phase modulation in a WDM optical transmission system

The cross-phase modulation (XPM) changes the state-of-polarization (SOP) of various channels and leads to amplitude modulation of the propagating waves in a WDM system. Due to the presence of polarization mode dispersion (PMD), the angles between the SOP of the channels change randomly and cause the modulation amplitude fluctuation random in the perturbed channel. We analytically derive the dynamic equation of the perturbed channel, determine the combined probability density function of the random angle between the SOP of pumps and probe channel and evaluate the effects of PMD on XPM for a 4-channel IM-DD WDM system in terms of BER at bit rate of 10 Gb/s per channel. We also simulate the impact PMD on XPM for a 4-channel WDM system in terms of eye diagram and found that eye opening penalty is 1.85 dB higher when the fiber PMD coefficient increases from 0.5 to 1.5 ps/√km.     

Solitons in fibers with polarization mode dispersion

Evaluating the relative time displacement of the two orthogonally polarized components of a pulse propagating down a birefringent optical fiber is considered. A method that provides analytical expressions for this time displacement is described and generalizes analytical results already published.     

Manakov solitons and polarization mode dispersion

The effect of polarization mode dispersion (PMD) on Manakov solitons and dispersion managed solitons is treated analytically and by numerical simulation. In the analytic approach the internal motion of the Manakov soliton is represented as a damped harmonic oscillator. The PMD functions as a white noise source driving the oscillations. It is shown that the solitons can withstand PMD up to a certain instability threshold for which an analytic expression is obtained. This threshold is also evaluated for dispersion managed solitons. (c) 2000 American Institute of Physics.     

A modified split—step fourier method for optical pulse propagation with polarization mode dispersion

A modified split-step Fourier method (SSFM) is presented to solve the coupled nonlinear Schroedinger equation (CNLS) that can be used to model high-speed pulse propagation in optical fibres with polarization mode dispersion (PMD). We compare our approach with the SSFM and demonstrate that our approach is much faster with no loss of pre-chirped RZ(CRZ) formats in the presence of high PMD through this approach. The simulation results show that CRZ pulses are the most tolerant to high PMD values and the extinct ratio has a great impact on the transmission performance.     

Interaction of nonlinearity and polarization mode dispersion

The derivation of the coupled nonlinear Schrödinger equation and the Manakov-PMD equation is reviewed. It is shown that the usual scalar nonlinear Schrödinger equation can be derived from the Manakov-PMD equation when polarization mode dispersion is negligible and the signal is initially in a single polarization state as a function of time. Applications of the Manakov-PMD equation to studies of the interaction of the Kerr nonlinearity with polarization mode dispersion are then discussed.