Effects of residual stress on polarization mode dispersion of fibers made with different types of spinning

We analyze the effects of residual stress on the polarization mode dispersion (PMD) of fibers made with different types of spinning. A theoretical scheme is developed from a previous model by the incorporation of a circular birefringence term contributed by residual torsional stress. It is found that the residual stress can significantly affect the PMD of unidirectionally spun fibers when the fiber birefringence is low, but it has little effect on the PMD of bidirectionally spun fibers.     

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.     

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.     

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.     

Statistics of polarization mode dispersion-induced gain fluctuations in Raman amplified optical transmissions

A systematic experimental evaluation of polarization mode dispersion (PMD) -induced polarization-dependent gain (PDG) in forward pumped Raman amplification in dispersion-shifted and in dispersion-compensating fiber was performed. Good agreement was obtained between the measured statistical parameters and the current analytical model for PDG fluctuation statistics. The probability distribution of the PDG was approximately Maxwellian within the range PMD >0.05 ps/km(1/2). The interplay between PMD and gain fluctuations is discussed; random birefringence strongly reduces PDG fluctuations. However, the trade-off between reduction of the power penalties for PDG and increase of the penalties for PMD distortion precludes the use of PMD instead of source depolarization techniques for reduction of PDG.     

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.     

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.     

偏振模色散矢量的研究

研究了无损光纤的密勒矩阵,进而得出了偏振模色散矢量的解析表达式、主偏振态对应的斯托克斯矢量的解析表达式,以及高阶偏振模色散矢量的解析表达式.这些解析表达式是由光纤参数决定的.讨论了局部偏振模色散矢量与整体偏振模色散矢量的关系,讨论了利用偏振模色散矢量进行偏振模色散补偿的原理.引入了偏振模色散补偿元件的偏振模色散补偿矢量C,具体计算了正规的非圆光波导类的补偿元件的C.从理论上证明了仅仅利用一个正规的非圆光波导类的补偿元件,例如一根保偏光纤或是一个双折射晶体,是不能实现偏振模色散补偿 关键词： 偏振模色散 密勒矩阵 色散补偿 主偏振态斯托克斯矢量     

Polarization mode dispersion in long single-mode-fiber links: A review

Polarization mode dispersion (PMD) is the interplay of birefringence (both systematic and random) and coupling between orthogonal polarizations, in a single-mode fiber. PMD will set the ultimate limit to the fiber length × capacity product, when all the deterministic causes of dispersion are under control. We review the state of the art in this field, with emphasis on experiments, which demonstrate that the behavior of long links can be predicted with full confidence, in a statistical sense, from factory-based tests on individual cables. Successful application of the same experimental technique to detecting fiber stresses is also demonstrated.     

Soliton Propagation in Birefringent Fibers

In this article, the propagation of solitons in a single mode fiber with polarization mode dispersion (PMD) is analyzed. In optical fibers, the randomly varying birefringence degrades soliton transmission system in two aspects. First, the dispersive waves cause pulse broadening. Second, the dispersive waves interact with other soliton pulses. Here we studied the effects of PMD on a single pulse and the variation of pulse broadening, energy decay, and degree of polarization on a single soliton pulse propagating over a very long distance.     

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.     

Soliton stability against polarization-mode-dispersion in dispersion-managed systems

We study the dynamics of two-component solitons in a dispersion-managed (DM) system, built as a periodic concatenation of segments of optical fibers with anomalous and normal group-velocity dispersion (GVD). The model includes, in addition to the usual GVD and nonlinear terms, birefringence and polarization-mode-dispersion (PMD), in the form of the polarization scrambling (random rotation of the polarization) taking place at randomly distributed defects. We propose a numerical algorithm for finding optimized DM solitons in such a system, which secure stable transmission over a large distance. The analysis includes effects of the PMD-induced noise, together with the noise due to the spontaneous amplifier emission, and the input-source noise. It is concluded that, if the group-velocity birefringence is not excessively large, the use of the optimized solitons makes it possible to tolerate the PMD effects in the long-haul DM link.     

Polarization effects and performance of fiber optic recirculating loops

Polarization effects such as PMD and PDL in a straight-line optical fiber communication system are random due to the random birefringence of optical fiber. However, since there is periodicity in a fiber recirculating loop, the polarization effects are quite different than in a straight line. Theoretically and experimentally we analyze the polarization effects in a loop and their effect on performance and the evolution of the state of polarization of a channel. Using this analysis, we are able to better understand the physical impact of the evolution of the state of polarization of a channel on performance. We show that loop-synchronous polarization scrambling is an effective way of breaking this periodicity in an attempt to make the recirculating loop perform more like a straight-line system.     

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.     

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.     

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.     

Effects of polarization-mode dispersion on fiber-based parametric amplification and wavelength conversion

We present a vector theory of four-wave mixing in optical fibers and use it to discuss the effect of polarization-mode dispersion (PMD) on the performance of parametric amplifiers and wavelength converters. We show that PMD distorts the gain spectrum and makes it less uniform than that expected in the absence of residual birefringence. PMD also induces large fluctuations in the amplified or wavelength-converted signal.     

Origin and System Effects of Polarization Mode Dispersion in Chirped Bragg Gratings

Polarization mode dispersion of chirped Bragg gratings is analyzed in terms of key birefringence phenomena and impact on telecommunication systems performance. The influence on polarization mode dispersion (PMD) of fiber birefringence, grating chromatic dispersion, and ripples of the group delay curve is pointed out. Polarization mode dispersion influence on systems performance is investigated by numerical simulations and transmission experiments at 10 Gbit/s. The deterministic nature of Bragg gratings PMD determines a moderate, upper-limited system penalty for a transmission line employing a single compensating device. However, in the case of broadband components, a non-negligible PMD penalty may be observed due to the difficulty of controlling accurately the group delay linearity.     

Origin and System Effects of Polarization Mode Dispersion in Chirped Bragg Gratings

Polarization mode dispersion of chirped Bragg gratings is analyzed in terms of key birefringence phenomena and impact on telecommunication systems performance. The influence on polarization mode dispersion (PMD) of fiber birefringence, grating chromatic dispersion, and ripples of the group delay curve is pointed out. Polarization mode dispersion influence on systems performance is investigated by numerical simulations and transmission experiments at 10 Gbit/s. The deterministic nature of Bragg gratings PMD determines a moderate, upper-limited system penalty for a transmission line employing a single compensating device. However, in the case of broadband components, a non-negligible PMD penalty may be observed due to the difficulty of controlling accurately the group delay linearity.     

Field Measurements of Polarization Mode Dispersion

Polarization mode dispersion (PMD) measurements are presented for a sample of installed optical fibers. High PMD values are fairly common, with 9 of the 71 fibers having PMD coefficients above 0.3 ps km1 2. The results are analyzed in terms of the age of the fibers and the type of cabling. Measurements are presented for a number of concatenated fiber links, and the results show that the PMD value of the link is approximately equal to the square root of the sum of the squares of the PMD values of the individual fibers.