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.     

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 properties of constantly spun randomly birefringent fibers

We calculate the asymptotic first-order polarization mode dispersion statistics of constantly spun fibers. We show that in the long length regime the mean differential group delay of constantly spun fibers grows linearly with distance at the same rate as for unspun fibers. Conversely, the short length regime of constantly spun fibers may be much longer, even for limited spin rates.     

Properties of polarization evolution in spun fibers

We study the properties of polarization evolution in sinusoidally spun fibers. It is found that, similar to linear birefringent fibers, the evolution of the state of polarization exhibits periodicity, which can be measured by distributed measurement, such as those made with a polarization optical time domain reflectometer. The spatial period is linked with the spin parameters and fiber beat length in a simple equation. In combination with a previous finding, it is shown that the spatial period is uniquely related to spun-fiber polarization mode dispersion. This suggests that distributed fiber polarization mode dispersion can be determined throughthe measurement of the spatial period obtained in a distributed measurement.     

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.     

Polarization mode dispersion in single mode optical fibers due to core-ellipticity

The variation of polarization mode dispersion (PMD) with V-parameter in single mode optical fibers due to core-ellipticity is studied by performing numerical simulations taking into account both geometrical and thermal-stress-induced birefringences as well as the variation of fiber refractive indices with wavelength. Simple empirical relations are given for calculating the mean PMD for any value of core-ellipticity and V-parameter of a standard single mode fiber. It is observed that the mean PMD saturates for V ? 1.8 leading to very small second order PMD.     

Study of the frequency autocorrelation of the differential group delay in fibers with polarization mode dispersion

We study the frequency autocorrelation of the differential group delay (DGD) in fibers with polarization mode dispersion (PMD). We show that the correlation bandwidth of the DGD is comparable with that of the orientation of the PMD vector. Furthermore, we show that all the most general statistical properties of polarization mode dispersion in long fibers are uniquely determined by the mean DGD. An estimate of the accuracy of measurements in which the mean DGD is extracted by frequency averaging in a single fiber is obtained as a function of the measured bandwidth.     

Effect of fiber-spinning profile on plug-and-play quantum-key distribution systems

The spin profile of a fiber is usually optimized to reduce transmission impairments caused by polarization-mode dispersion (PMD). In this paper, we show that fiber-optic-based plug-and-play quantum-key distribution systems using polarization modulation and fibers with a spin profile optimal for PMD may suffer from a large Faraday rotation induced by the geomagnetic field. We show that, for periodic spin patterns of small periods, the Faraday rotation is minimum when no spin is applied to the fiber.     

Calculation of the mean differential group delay of periodically spun, randomly birefringent fibers

Spinning is one of the most effective and well-known ways to reduce polarization mode dispersion of optical fibers. In spite of the popularity of spinning, a detailed theory of spin effects is still lacking. We report an analytical expression for the mean differential group delay of a randomly birefringent spun fiber. The result holds for any periodic spin function with a period shorter than the fiber's beat length.     

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.     

Fiber spin-profile designs for producing fibers with low polarization mode dispersion

Using coupled-mode theory, we develop a theoretical model to analyze the effects of fiber spin profiles on polarization mode dispersion (PMD). Constant, sinusoidal, and frequency-modulated spin profiles are examined, and phase-matching conditions are analyzed. Our analysis shows that PMD can be reduced effectively by use of frequency-modulated spin profiles.     

旋转光纤圆起偏器的特性分析

基于旋转光纤耦合模理论,对窄带和宽带旋转光纤圆起偏器的特性进行了计算分析.研究了注入光的偏振态、光纤固有线双折射和旋转速率对窄带圆起偏器最小工作长度的影响,并借助多包层光纤的分析方法,分析了旋转光纤各参量变化对宽带圆起偏器工作带宽的影响.结果表明:窄带圆起偏器的最小工作长度与光纤固有线双折射和光纤旋转速率有关,而与注入光的偏振态无关|改变光纤旋转速率可调节宽带圆起偏器的工作带宽,改变应力区到纤芯的距离可改变宽带圆起偏器的中心波长.     

Discontinuous basalt and glass fiber reinforced PP composites from textile prefabricates: effects of interfacial modification on the mechanical performance

Spun and blown basalt fibers and their PP matrix composites were investigated. The composites were manufactured by hot pressing technology from carded and needle punched prefabricate using PP fiber as matrix material. Glass and blown basalt fibers were treated with reaction product of maleic acid-anhydride and sunflower oil while spun basalt fibers had a surface coating of silane coupling agent. Fibers were investigated with tensile tests while composites were subjected to static and dynamic mechanical tests. The results show that blown basalt fibers have relatively poor mechanical properties, while spun basalt fibers are comparable with glass fibers regarding geometry and mechanical performance. The static and dynamic mechanical properties of glass and spun basalt fiber reinforced composites are similar and are higher than blown basalt fiber reinforced composites. Results were supported with SEM micrographs.     

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.     

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.     

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.     

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.     

High-speed transmission limitations due to Polarization Mode Dispersion

In this paper, the impacts of Polarization Mode Dispersion (PMD) on the performance of high-speed optical communication system have been reported at different bit rates. The two systems are modeled using older fibers with same PMD coefficient at different bit rates and third is with the new fiber with less PMD coefficient than that of the previous two. The attenuation, chromatic dispersion and non-linear effects have been disabled, so that all the variation of the results is due to PMD. The bit rate is varied from 2.5 to 40 Gbps and the length is varied from 1000 to 20,000 km. It is shown that the impact of PMD increases with the bit rate of system. It is also reported that the impact of PMD becomes intolerable at the bit rates of more than 40 Gbps. And also the PMD produces very minute impact on the system performance for same bit rate with the variation in the fiber length.     

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.