Study of the stability of polarization mode dispersion in fibre

Polarization mode dispersion (PMD) is the ultimate limitation to high bit-rate fibre communication system. The stability of PMD is very important to its measurement and compensation. This paper puts forward a method to measure the stability of PMD by measuring the stability of the state of polarization (SOP) and introduces the conception of time evolution vector (TEV) of SOP. We observe the fact that the regularity of the principal state of polarization changing with time is the same as other SOPs‘‘, if we neglect the dependence of TEV on wavelength. We also measure the SOP‘‘s stability of some fibres with different lengths, and obtain results of PMD changing with time.     

光纤偏振模色散测试模拟实验

以光纤偏振模色散测试为核心设计了模拟教学实验，该实验可综合展示偏振光的特点，揭示波片、偏振片、偏振棱镜、干涉仪的性质。     

Tuneable polarization mode dispersion emulator: Fixed polarization maintaining fibre sections and rotatable polarization orientations

We design a polarization mode dispersion (PMD) emulator capable of adjusting first-order (FO-) and second-order (SO-) PMD statistics, making it capable to mimick differerent fibre links or fibre plants. The emulator can adjust PMD statistics by controlling mode coupling angles between polarization maintaining fibres (PMFs) of fixed length using its seven rotatable electro-optic polarization rotators which act as half waveplates (HWPs). The stability and repeatability of the emulator under a stable laboratory environment makes PMD statistics reproducible. The control mechanism of the emulator is in real-time.     

Design of single polarization single mode dispersion compensating photonic crystal fiber

In this paper, we present a photonic crystal fiber based on hexagonal structure for improved negative dispersion as well as high birefringence in the telecom wavelength bands. It is demonstrated that it is possible to obtain negative dispersion coefficient of −712 ps/(nm km) and relative dispersion slope (RDS) perfectly match to that of single mode fiber (SMF) of about 0.0036 nm⁻¹ at the operating wavelength 1550 nm. The proposed fiber exhibits high birefringence of the order 2.11 × 10⁻² with nonlinear coefficient about 57.57 W⁻¹ km⁻¹ at 1550 nm. Moreover, it is confirmed that the designed fiber successfully operates as a single mode in the entire band of interest.     

Analysis of polarization mode dispersion fluctuations in single mode fibres due to temperature

We have studied the effect of temperature on the birefringence and polarization mode dispersion PMD in standard single mode fibre (SSMF) with elliptical core cross section by using numerical computations. On the basis of simulation we have concluded that PMD fluctuates more rapidly than the stress-induced birefringence. In addition, DGD is inversely proportional to temperature.     

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     

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.     

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.     

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.     

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.     

偏振模色散模拟器的特性

通过对微分群时延差(DGD)统计特性和偏振模色散(PMD)矢量自相关函数的数值模拟，分析比较了目前常用的三种PMD模拟器的性能. 结果表明：在DGD分布方面，由DGD发生器构成的模拟器，一个DGD发生器就可与实际光纤PMD的统计特性相符合，而由保偏光纤和可旋转的连接器构成的模拟器则至少需要15段. 在自相关函数方面，基于保偏光纤的模拟器取决于各段光纤的延时量，而基于DGD发生器的模拟器在中心频带外的自相关值很平稳，可视为常数. 关键词： 光纤通信 偏振模色散 偏振模色散模拟器 自相关函数     

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.     

Statistics of the polarization mode dispersion dynamics

We characterize the joint two-time statistics of the polarization-mode dispersion (PMD) vector. Good agreement with experimental PMD measurements taken on an installed system is achieved. The results can be used to obtain the temporal evolution of the average penalty of a system close to an outage condition.     

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.     

Extreme outages caused by polarization mode dispersion

We study the dependence on fiber birefringence of the bit-error rate (BER) caused by amplifier noise in a linear optical fiber telecommunication system. We show that the probability-distribution function of the BER obtained by averaging over many realizations of birefringent disorder has an extended tail that corresponds to anomalously large values of BER. We specifically discuss the dependence of the tail on such details of pulse detection at the fiber output as setting the clock and filtering procedures.     

Jones matrix for second-order polarization mode dispersion

A Jones matrix is constructed for a fiber that exhibits first- and second-order polarization mode dispersion (PMD). It permits the modeling of pulse transmission for fibers whose PMD vectors have been measured or whose statistics have been determined by established PMD theory. The central portion of our model is a correction to the Bruyère model.     

Jones precoder for polarization mode dispersion compensation

A new electrical-domain precoder is proposed to mitigate polarization mode dispersion (PMD) in optical communications by modeling a PMD-dominant fiber optical channel using a single input multiple output (SIMO) channel. Employing a bank of finite impulse response filters and a polarization modulator, and using parameters derived from the Jones matrix representation of PMD, the proposed precoder efficiently adapts to the time-varying nature of PMD and simultaneously pre-equalizes both polarization modes at the transmitter. The transmitter-only structure avoids losing phase and polarization information due to the nonlinearity of the commonly used square law direct-detection receiver. Analysis is performed to evaluate the impact of channel mismatch due to feedback delay, channel estimation errors, and the impact of the finite length of the precoder filters. The analytical results are used to guide selection of the appropriate feedback rate for the adaptive system. Extensive simulation results confirm the efficiency of the proposed Jones precoder, and present it as an effective, low-cost replacement to the complicated, expensive optical-domain counter-parts.     

Modelling of polarization mode dispersion in optical communications systems

With the rapid increase in the data rates transmitted over optical systems, as well as with the recent extension of terrestrial systems to ultra-long haul reach, polarization mode dispersion (PMD) has become one of the most important and interesting limitations to system performance. This phenomenon originates from mechanical and geometrical distortions that break the cylindrical symmetry of optical fibers and create birefringence. It is the random variations of the local birefringence along the propagation axis of the optical fiber that create the rich and complicated bulk of phenomena that is attributed to PMD. The detailed statistical properties of the local birefringence and its dependence on position are only important as long as the overall system length is comparable with the correlation length of the birefringence in the fiber. In typical systems, however, the latter is smaller by more than three orders of magnitude so that the specific properties of the local birefringence become irrelevant. Instead, the fiber can be viewed as a concatenation of a large number of statistically independent birefringent sections characterized only by the mean square value of their birefringence. This model has been used extensively in the study of PMD and its predictions have been demonstrated to be in excellent agreement with experimental results. This approach opens the door to the world of stochastic calculus, which offers many convenient tools for studying the PMD problem. In this article we review the modelling of PMD and discuss the properties of this phenomenon as a stochastic process. We explain the use of stochastic calculus for the analysis of PMD and describe the derivation of the frequency autocorrelation functions of the PMD vector, its modulus and the principal states. Those quantities are then related to commonly used parameters such as the bandwidth of the first order PMD approximation, the bandwidth of the principal states and to the accuracy of PMD measurements.