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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Four-wave mixing of picosecond pulses in hollow fibers: Phase matching and the influence of high-order waveguide modes

The processes of third-harmonic and difference-frequency generation through the four-wave mixing of picosecond pulses in gas-filled hollow fibers are experimentally studied. Due to the improvement of phase-matching conditions with an appropriate choice of the gas pressure and optimal parameters of the hollow fiber, we were able to use hollow fibers with a large length (up to 30 cm) for difference-frequency generation, which resulted in a considerable increase in the power of the difference-frequency signal at the output of the fiber. Our experimental data reveal a considerable influence of high-order waveguide modes on four-wave mixing processes in a hollow fiber. It is shown that the waveguide regime of nonlinear optical interactions implemented in hollow fibers removes the limitations on the efficiency of third-harmonic and sum-frequency generation, which are characteristic of the tight-focusing regime in media with normal dispersion and which are due to the geometric phase shift arising in tightly focused light beams.     

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.     

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.     

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.     

多叶应力区扭转光纤的耦合模理论

从线性极化模的耦合模理论出发,分析了双叶应力区扭转光纤,即扭转保偏光纤,和四叶应力区扭转光纤.推导应力引起的在光纤芯区各向异性的介质张量表达式;利用该表达式得到线性极化模在有转角时的多叶应力区光纤中传输的耦合模方程;从而推得多叶应力区扭转光纤中的超本地模,由超本地模的相位常数来确定该光纤的双折射.在双叶、四叶应力区理想对称的条件下,前者可以得到较高的椭圆双折射,而后者则无任何双折射.同样的结论可推广到8叶或16叶的扭转光纤,都无任何双折射.     

Phase-matched four-photon mixing processes in birefringent fibers

We describe several new phase-matching processes for four-photon mixing in polarization-preserving birefringent fibers. The frequency shifts and polarization conditions of the waves involved in this nonlinear interaction are specified for a single-mode fused silica birefringent fiber. Our calculations include the effect of dispersion in the birefringence of the fibers.     

光子晶体光纤四波混频光谱中相位匹配特性的研究

与传统光纤不同,光子晶体光纤可以具有多个零色散波长,在四波混频光谱中,具有更丰富的相位匹配特性。目前很多文献报道了光子晶体光纤非线性光学特性的实验结果,但对其产生机理及光谱的变化规律缺乏详细的理论分析。为此对光纤中四波混频原理进行了分析,给出了高增益的相位匹配条件。利用多极法计算了光子晶体光纤的非线性系数及色散特性。对具有多个零色散波长光子晶体光纤的相位失配特性进行了分析,得到了相位匹配波长随泵浦波长及泵浦功率的变化规律。给出了相位匹配曲线,分析了不同色散曲线的相位匹配波长特点,两个零色散波长光子晶体光纤,在四波混频光谱中将激发出四个新的波长。实验得到了两个零色散波长光子晶体光纤的四波混频光谱,与理论分析一致,验证了相位匹配理论的可靠性。多个零色散波长光纤,能产生丰富的相位匹配曲线,会出现更多的四波混频波长,可以有效的控制光孤子及超短脉冲的四波混频及共振散射产生的光谱特性。为光子晶体光纤中基于四波混频的波长变换及超连续谱的研究提供了理论指导。     

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.     

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.