Influence of polarization mode dispersion value in dispersion-compensating fibers on the polarization dependence of Raman gain

Polarization mode dispersion (PMD) of amplifying or transmitting fibers may significantly change the polarization dependence of Raman gain. Experimental results are presented that show low polarization dependence of the Raman gain in dispersion-compensating fibers with high PMD values for both copropagating and counterpropagating pumping configurations. The measured data demonstrate that it is possible to avoid the need for depolarization of a pump source in Raman amplifiers.     

用电功率反馈控制信号实现10Gbit/s系统的PMD补偿实验

光纤通信线路检测到的电功率随差分群延迟变化, 可以作为PMD补偿的反馈控制信号.给出了这一变化关系的理论计算和曲线并通过实验验证这一关系, 确定电压信号与DGD的变化关系.建立了一套完整的实验系统, 并考虑了影响反馈电压信号的多种因素以及减小这些影响的措施.眼图给出的实验结果说明了补偿的效果, 还利用误码测试仪测量了补偿前后的接收灵敏度的改变以定量说明补偿的效果, 最后比较了不同情况下的补偿结果.     

Optical fibers with low nonlinearity and low polarization-mode dispersion for terabit communications

Refractive-index nonlinearities have negligible effect on the performance of short-haul fiber-optic communication links utilizing electronic repeaters. However, in long links, nonlinearities can cause severe signal degradations. To mitigate nonlinear effects, a new generation of fibers, referred to as large effective-area fibers, have been introduced in recent years. This paper reviews the latest research and development work on these fibers conducted by several research groups around the world. Attention is focused on a class of large effective-area fibers that are based on a depressed-core multiple-cladding design. Another important issue in long-haul and high capacity fiber optic systems is the polarization-mode dispersion (PMD) which has been recognized as a serious limiting factor. In this paper, an improved fiber design is proposed which, in addition to providing large effective-area and low bending loss, eliminates PMD due to elliptical deformation in the single-mode wavelength region. Furthermore, this design is allowed to provide a small chromatic dispersion about few ps/nmkm, in order to overcome four-wave mixing effects.     

Dependence of polarization mode dispersion of slotted core NZDF ribbon on cable design and environmental conditions

Non-zero dispersion fiber (NZDF) ribbon cable has recently become a considerable alternative in long-haul high-speed network construction. Since long-distance high-bit rate transmission requires low polarization mode dispersion (PMD), it is very important to know the PMD performance of this type of optical fiber cables. In this paper, we report experimental analysis of effects of the cable design and environmental parameters, in particular ribbon thickness, positions of fibers in the ribbon, flexing and vibration, on PMD performances of several slotted-core fiber ribbon cables. Results show that ribbon thickness and positions of fibers in the ribbon alter the PMD values of NZDF ribbon cables. Also, 23% and 11% PMD variations have been determined in flexing and vibration experiments, respectively. Moreover, it has been observed that vibration amplitude has significant effects and vibration frequency has little effects (14% and 6% variations, respectively) on fiber PMD. Results are important for understanding effects of installation conditions and wind, especially for aerial fibers, on PMD values of cables.     

The PMD of sinusoidally spun fibers in the presence of random birefringence perturbations

Although fiber spinning is known to reduce polarization mode dispersion (PMD) effects in optical fibers, relatively few studies have been performed of the dependence of the reduction factor on the strength of random birefringence fluctuations. In this paper, we apply a general mathematical model of random fiber birefringence to sinusoidally spun fibers. We find that while even in the presence of random birefringence perturbations the maximum reduction of PMD is still obtained when the phase matching condition is satisfied, the degree of PMD reduction and the probability distribution function of the DGD both vary with the random birefringence profiles.     

PMD effect on pulse shapes and power penalty in optical communication systems

We present an analytical expression relating the output state of polarization and the first-order polarization mode dispersion (PMD) vector in terms of the angle of precession of the output state of polarization around the PMD vector. We derive, incorporating for the first time this angle of precession, a general relation to study the effect of first-order PMD on pulses of arbitrary shapes, and expressions for pulse shape, pulse broadening and power penalty taking into account both PMD and chromatic dispersion. Measured experiment results are presented for NRZ, RZ, NRZ-DPSK, and RZ-DPSK modulation formats.     

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.     

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.     

Low-PMD spun fibers

In the last ten years there has been an increasing interest in the design and realization of low PMD fibers. This goal can be achieved by properly spinning a fiber when it is still in the hot zone. In this chapter, analytical and numerical results on the design of low-PMD fibers by means of spinning techniques are presented.     

Investigations on PMD-induced penalties in 40 Gbps optical transmission link

Polarization-mode dispersion (PMD) in optical fibers and components can be a limiting impairment in high-speed, long-haul transmission link. In this paper, we have carried out investigations on PMD-induced penalties in a 40 Gbps optical transmission link and we obtained results for DGD, BER, Q² (dB) for different values of the PMD coefficient and different random seeds using computer simulation.     

PMD emulation

As PMD has become an increasingly significant issue in high-bit-rate fiber optic systems, a need has developed for laboratory instruments and software tools capable of rapidly exploring the effects of PMD on various test items. The random nature of PMD dictates that to characterize its effects on transmitter/receiver pairs and on PMD compensation systems, one must repeatedly measure the system performance over a wide sample space of PMD states. This need has spurred the development of several methods for accurately and rapidly emulating the random variations of PMD in real fibers, as well as techniques for generating specific components and combinations of first- and higher-order PMD in a predictable and repeatable way. This chapter reviews several of these methods for both statistical and deterministic PMD emulation. The underlying concepts and rationales for various design architectures are discussed. A common analytical model for describing multisection all-order emulators is presented and a simple design example is used to further illustrate the concepts.     

用于高阶偏振模色散补偿的高效动态补偿器

基于基本偏振态模型,采用三双折射元补偿结构,提出一种用于补偿高速率光纤通信系统中的偏振模色散的可行方案.此方案在一阶偏振模色散补偿的基础上,仅增加了对两个参量的控制,即可对高阶偏振模色散进行补偿,并且高阶补偿过程的参量控制完全独立于一阶补偿过程,极大的提高了偏振模色散的动态补偿效率.数值模拟结果表明,此方案的补偿效果也是显著的.     

Scaling properties of polarization mode dispersion of spun fibers in the presence of random mode coupling

The scaling properties of polarization mode dispersion (PMD) in spun fibers are studied. Simple equations have been obtained to describe the scaling properties of spun fibers as a function of intrinsic fiber birefringence, spin parameters, and mode-coupling length under both optimal and nonoptimal spin conditions. In particular, a counterintuitive result is found for fibers with perfect spin optimization, in which case the fiber PMD increases as the mode-coupling length is shortened. The results are verified with direct numerical modeling.     

两段PMD补偿中的优化算法比较

研究了两段PMD补偿器和补偿算法.存在二阶效应时,PMD补偿中的反馈信号将是一个多峰多谷的复杂信号.粒子群算法(PSO )作为一种优化算法已在实验中实现.研究了模拟退火算法（SA）作为含二阶PMD补偿的反馈信号的应用.通过仿真计算还比较了采用这两种算法的PMD补偿性能.     

双折射光纤中偏振模色散的抑制

利用双折射光纤中孤子自捕获现象可以抑制偏振模色散,但这种抑制技术对传输参量有严格的限制.本文提出在双折射光纤中周期性地改变快慢轴的方法来抑制偏振模色散. 研究发现,这种方法在一定程度上能有效地抑制偏振模色散,并且光纤间偏振轴的夹角偏差有利于对偏振模色散的进一步抑制.     

Statistical determination of the length dependence of high-order polarization mode dispersion

We describe a method of characterizing high-order polarization mode dispersion (PMD). Using a new expansion to approximate the Jones matrix of a polarization-dispersive medium, we study the length dependence of high-order PMD to the fourth order. A simple rule for the asymptotic behavior of PMD for short and long fibers is found. It is also shown that, in long fibers (~1000 km), at 40 Gbits/s the third- and fourth-order PMD may become comparable to the second-order PMD.     

Effects of lateral load and external twist on polarization-mode dispersion of spun and unspun fibers

Using the coupled-mode theory, we have developed a theoretical model to analyze the effects of lateral load and external twist on polarization-mode dispersion (PMD) of spun and unspun fibers. Modeling results show that spun and unspun fibers have very different PMD responses to lateral load and external twist. Experimental results show good agreement with the theory.     

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.     

Polarization mode dispersion of spun fibers: an analytical solution

A simple analytical solution is derived from coupled-mode theory to describe the evolution of polarization mode dispersion (PMD) in spun fibers. For practical fibers with a beat length greater than a few meters, the solution is valid for a whole category of periodic spin profiles. We find that the PMD change factor is independent of the intrinsic birefringence of the fiber and the fiber PMD scales linearly with the fiber length in the short length regime. This solution allows us to determine phase-matching conditions for spun fibers, in which the PMD evolves periodically along the fiber. An example of determining the phase-matching conditions of sinusoidal-type spin profiles is given.     

Improved models of optical fiber birefringence—Part II

In this paper, we employ several general models (introduced in Part I) for the evolution of optical fiber birefringence with longitudinal distance to analyze, both theoretically and numerically, the behavior of the polarization mode dispersion (PMD) in single mode fibers. We find that while the probability distribution function of the differential group delay varies along the fiber length as in existing models, the dependence of the root mean square differential group delay (DGD) on fiber length differs noticeably from earlier predictions.