单模光纤中偏振效应的理论研究及分析
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摘要
偏振模色散是高速通信系统的限制因素之一,其起因来自于光纤内部分布的不均匀性以及外部环境的干扰。对于偏振模色散的研究,分段模型是较优的选择。原级联模型经过数学推导,可转化为迭代模型。转化后的模型物理意义明晰,在直观上便于看出偏振模色散随光纤分段增加的累积过程,具有较强的移植性。理论分析中指明了数值方法产生误差的缘由,我们将由级联模型得出的迭代模型,应用于一阶偏振模色散的研究,指出了一阶模拟计算中必需注意的问题。在一阶分析的基础上进行二阶偏振模色散的研究,数值模拟表明,该方法简洁明了,对于二阶偏振模色散的两个正交分量的研究,提供了非常直观的方法,统计结果与理论相符。
在偏振模色散数值模型处理中,光纤分段数N和分段长度L是两个基本的参数,直接影响偏振模色散的随机特性,其选择是比较复杂的问题。在基本级联模型的基础上,对偏振模色散的随机特性进行了分析,指出N和L的处理直接关系到级联模型的分析结果。对N和L的选择进行的分析和探讨中可以发现,分段数N的合适选取以及L的合理分布对建立模型至关重要,直接决定一阶偏振模色散的分布特征。数值模拟表明,参数特性在级联模型中起到决定性的作用。另一方面,级联模型本身含有随机特性,这是在讨论偏振模色散随机分布特性时应该考虑的因素。数值模拟给出了一阶偏振模色散矢量的随机性特征,其特征通过三个分量表现出来。在一阶的基础上,进行了二阶偏振模色散矢量的模拟计算,计算结果与理论曲线吻合较好。二阶偏振模色散可以分解为平行分量与垂直分量,模拟结果给出了这两个矢量的随机分布特性,对二阶偏振模色散的随机性分析提供了比较全面的指导作用。
偏振相关损耗是光通信系统中另一限制因素,偏振模色散和偏振相关损耗共同的作用,影响了系统的传输性能,在偏振模色散和偏振相关损耗特征矩阵的基础上,对偏振模色散和偏振相关损耗之间的相互影响进行了分析和模拟。结果表明,偏振相关损耗的增加单向改变偏振模色散的值,可能增大也可能减少。而偏振模色散的改变对偏振相关损耗的影响表现为复杂的关系:在偏振模色散增加的情况下,偏振相关损耗的大小的改变起伏不定。
偏振模色散的测量是目前研究的一个热点问题,在庞加莱球的基础上,对原来偏振模色散的测量方法给出理论分析,研究表明,一阶偏振模色散测量的误差影响二阶偏振模色散的测量。在偏振相关损耗很微弱可以忽略的情况下,我们提出一种全新的方法来测量二阶偏振模色散。通过新方法,二阶偏振模色可以直接测量,不需要通过一阶偏振模色散对频率求导。另一方面我们推导了偏振相关损耗的测量方程,得到了简易的偏振相关损耗的测量方法,测量速度较快。
前面的内容主要在频域里面进行研究,在时域范围里面,偏振模色散和偏振相关损耗会导致脉冲的展宽,这就要求提出一个更完善的方案,以分析存在偏振相关损耗条件下,脉冲的传输情况。我们给出新的数学描述方法,将偏振模色散,偏振相关损耗,以及啁啾都包含在内。研究表明,啁啾高斯脉冲传输的时延不仅受到偏振相关损耗的影响,还与自身的啁啾有关。在某种程度上,系统的偏振模色散可以通过改变偏振相关损耗和啁啾以得到控制。
最后,我们讨论了偏振态的演变规律和偏正效应的补偿方法。在无解偏的光纤通信系统中,弥勒矩阵可以用来描述输入输出偏振态之间的关系,而对于光源为准单色光的高速通信系统,严格来讲解偏效应是不能忽略的,弥勒矩阵必须加以修正以将解偏效应引入进来,通过理论推导,我们得到了严格考虑解偏效应条件下,任意输入偏振态都满足的通用方程。
One of the most serious limits to high bit-rate optical transmission systems is polarization-mode dispersion (PMD). PMD arises from the perturbations that are unavoidably induced in a real fiber by the production process and the external environment. Segment-dividing model is appropriate for research on PMD. Mathematical deduction is made to change it into iterative model. It is easy to find the new model gives clear meaning in physics and reveals the process of PMD accumulation in fiber. It is applicable for being transplanted to analysis on PMD. Theoretic analysis gives the reason for error in Numerical calculation.
Iterative model can be attained by concatenated model and is applied to analysis on first order PMD. It is pointed out that some problems should be paid attention to in the simulation. Second order analysis on PMD is made on the basis of first order. Numerical simulation shows the method is clear and brief. It provides direct technique for research on the two orthogonal parts of second order PMD. Statistical calculation accords with theoretical result.
In numerical model for PMD research, the number of the whole segments N and the length of each segment L are basic parameters, which affect the randomicity of PMD. The choice on them is complex. Analysis is given on randomicity of PMD on the basis of the basic concatenated model in this paper, and it is pointed out that treatment for N and L determines the analytic result. By analysis and exploration on the choice of these two parameters, it is found that appropriate N and logical L are very important in PMD modeling and determines the distributing character of first-order PMD. Numerical simulation shows the character of parameters is the decisive element in concatenated model. On the other hand, the concatenated model shows character of randomicity and this element should be taken into account for analysis on character of probability for PMD. Simulation results show randomicity of first-order PMD, which is laid out by the three orthogonal parts. On the basis of first order, calculation for second-order PMD is put in practice. Simulation results tally well with theoretic curve. It is known second-order can be decomprised of two orthogonal parts: parallel part and vertical part. Simulation for the two vectors is given, which guides analysis on the character of probability for second-order PMD comprehensively.
Polarization dependent loss (PDL) is the other limit to optical communication system. Interaction between PMD and PDL affects performance of communication system. On basis of characteristic transfer matrix of PMD and PDL, analysis and simulation is executed on the interaction between PMD and PDL. Results show that increase of PDL can change the value of PMD in single direction. The value of PMD may increase or decrease. But affected PDL shows complex relationship with PMD according to variational value of PMD: while PMD increase, the value of PDL fluctuates.
Measurement of polarization mode dispersion is one of the most popular topics. On the basis of Poincarésphere, theoretical analysis is given on the measurement of second order PMD. Research shows that error in measurement of first order PMD influence second order. While the effect of PDL is weak and can be neglected, a new polarization-mode dispersion measurement technique is described that allows the determination of second order PMD (SOPMD) vectors in optical fibers. SOPMD can be directly measured, not derived from first order PMD. If the effect of PDL should be taken into account, a generalized method is provided to measure the DGD. The algorithm requires the launch of three polarizations per wavelength and uses large rotation angles as well as interleaving to attain low-noise high-resolution PMD data. On the other hand, we derived the equation for measurement of PDL and obtained an easy method to measure PDL. The measurement process is fast.
Questions discussed above are focused on the domain of frequency. However on the domain of time, a combination of PMD and PDL in optical fiber may lead to anomalous pulse broadening. It raises the issue for more complete assessments when studying the pulse propagation in the presence of polarization-dependent loss. A mathematical description is put forward to including the effect of PMD, PDL and chirp. Simulation shows the delay of a chirped Gaussian pulse depends not only on PDL, but also on the chirp of the pulse itself. To some degree, effective PMD can be controlled by PDL and chirp.
At last, we discuss the conception of DOP and method of depolarization. In a non-depolarizing optical system, Mueller-Jones matrix can be used to describe the relation between input Stokes vector and output Stokes vector. However, even if the input light is quasi-monochromatic, effect of depolarization can not be neglected in practical optical fiber system. Mueller-Jones matrix should be modified to have the depolarizing effect included. The newly formulated equations are generalized for input light with arbitrary degree of polarization in optical fiber system where effect of depolarization is seriously considered.
在偏振模色散数值模型处理中,光纤分段数N和分段长度L是两个基本的参数,直接影响偏振模色散的随机特性,其选择是比较复杂的问题。在基本级联模型的基础上,对偏振模色散的随机特性进行了分析,指出N和L的处理直接关系到级联模型的分析结果。对N和L的选择进行的分析和探讨中可以发现,分段数N的合适选取以及L的合理分布对建立模型至关重要,直接决定一阶偏振模色散的分布特征。数值模拟表明,参数特性在级联模型中起到决定性的作用。另一方面,级联模型本身含有随机特性,这是在讨论偏振模色散随机分布特性时应该考虑的因素。数值模拟给出了一阶偏振模色散矢量的随机性特征,其特征通过三个分量表现出来。在一阶的基础上,进行了二阶偏振模色散矢量的模拟计算,计算结果与理论曲线吻合较好。二阶偏振模色散可以分解为平行分量与垂直分量,模拟结果给出了这两个矢量的随机分布特性,对二阶偏振模色散的随机性分析提供了比较全面的指导作用。
偏振相关损耗是光通信系统中另一限制因素,偏振模色散和偏振相关损耗共同的作用,影响了系统的传输性能,在偏振模色散和偏振相关损耗特征矩阵的基础上,对偏振模色散和偏振相关损耗之间的相互影响进行了分析和模拟。结果表明,偏振相关损耗的增加单向改变偏振模色散的值,可能增大也可能减少。而偏振模色散的改变对偏振相关损耗的影响表现为复杂的关系:在偏振模色散增加的情况下,偏振相关损耗的大小的改变起伏不定。
偏振模色散的测量是目前研究的一个热点问题,在庞加莱球的基础上,对原来偏振模色散的测量方法给出理论分析,研究表明,一阶偏振模色散测量的误差影响二阶偏振模色散的测量。在偏振相关损耗很微弱可以忽略的情况下,我们提出一种全新的方法来测量二阶偏振模色散。通过新方法,二阶偏振模色可以直接测量,不需要通过一阶偏振模色散对频率求导。另一方面我们推导了偏振相关损耗的测量方程,得到了简易的偏振相关损耗的测量方法,测量速度较快。
前面的内容主要在频域里面进行研究,在时域范围里面,偏振模色散和偏振相关损耗会导致脉冲的展宽,这就要求提出一个更完善的方案,以分析存在偏振相关损耗条件下,脉冲的传输情况。我们给出新的数学描述方法,将偏振模色散,偏振相关损耗,以及啁啾都包含在内。研究表明,啁啾高斯脉冲传输的时延不仅受到偏振相关损耗的影响,还与自身的啁啾有关。在某种程度上,系统的偏振模色散可以通过改变偏振相关损耗和啁啾以得到控制。
最后,我们讨论了偏振态的演变规律和偏正效应的补偿方法。在无解偏的光纤通信系统中,弥勒矩阵可以用来描述输入输出偏振态之间的关系,而对于光源为准单色光的高速通信系统,严格来讲解偏效应是不能忽略的,弥勒矩阵必须加以修正以将解偏效应引入进来,通过理论推导,我们得到了严格考虑解偏效应条件下,任意输入偏振态都满足的通用方程。
One of the most serious limits to high bit-rate optical transmission systems is polarization-mode dispersion (PMD). PMD arises from the perturbations that are unavoidably induced in a real fiber by the production process and the external environment. Segment-dividing model is appropriate for research on PMD. Mathematical deduction is made to change it into iterative model. It is easy to find the new model gives clear meaning in physics and reveals the process of PMD accumulation in fiber. It is applicable for being transplanted to analysis on PMD. Theoretic analysis gives the reason for error in Numerical calculation.
Iterative model can be attained by concatenated model and is applied to analysis on first order PMD. It is pointed out that some problems should be paid attention to in the simulation. Second order analysis on PMD is made on the basis of first order. Numerical simulation shows the method is clear and brief. It provides direct technique for research on the two orthogonal parts of second order PMD. Statistical calculation accords with theoretical result.
In numerical model for PMD research, the number of the whole segments N and the length of each segment L are basic parameters, which affect the randomicity of PMD. The choice on them is complex. Analysis is given on randomicity of PMD on the basis of the basic concatenated model in this paper, and it is pointed out that treatment for N and L determines the analytic result. By analysis and exploration on the choice of these two parameters, it is found that appropriate N and logical L are very important in PMD modeling and determines the distributing character of first-order PMD. Numerical simulation shows the character of parameters is the decisive element in concatenated model. On the other hand, the concatenated model shows character of randomicity and this element should be taken into account for analysis on character of probability for PMD. Simulation results show randomicity of first-order PMD, which is laid out by the three orthogonal parts. On the basis of first order, calculation for second-order PMD is put in practice. Simulation results tally well with theoretic curve. It is known second-order can be decomprised of two orthogonal parts: parallel part and vertical part. Simulation for the two vectors is given, which guides analysis on the character of probability for second-order PMD comprehensively.
Polarization dependent loss (PDL) is the other limit to optical communication system. Interaction between PMD and PDL affects performance of communication system. On basis of characteristic transfer matrix of PMD and PDL, analysis and simulation is executed on the interaction between PMD and PDL. Results show that increase of PDL can change the value of PMD in single direction. The value of PMD may increase or decrease. But affected PDL shows complex relationship with PMD according to variational value of PMD: while PMD increase, the value of PDL fluctuates.
Measurement of polarization mode dispersion is one of the most popular topics. On the basis of Poincarésphere, theoretical analysis is given on the measurement of second order PMD. Research shows that error in measurement of first order PMD influence second order. While the effect of PDL is weak and can be neglected, a new polarization-mode dispersion measurement technique is described that allows the determination of second order PMD (SOPMD) vectors in optical fibers. SOPMD can be directly measured, not derived from first order PMD. If the effect of PDL should be taken into account, a generalized method is provided to measure the DGD. The algorithm requires the launch of three polarizations per wavelength and uses large rotation angles as well as interleaving to attain low-noise high-resolution PMD data. On the other hand, we derived the equation for measurement of PDL and obtained an easy method to measure PDL. The measurement process is fast.
Questions discussed above are focused on the domain of frequency. However on the domain of time, a combination of PMD and PDL in optical fiber may lead to anomalous pulse broadening. It raises the issue for more complete assessments when studying the pulse propagation in the presence of polarization-dependent loss. A mathematical description is put forward to including the effect of PMD, PDL and chirp. Simulation shows the delay of a chirped Gaussian pulse depends not only on PDL, but also on the chirp of the pulse itself. To some degree, effective PMD can be controlled by PDL and chirp.
At last, we discuss the conception of DOP and method of depolarization. In a non-depolarizing optical system, Mueller-Jones matrix can be used to describe the relation between input Stokes vector and output Stokes vector. However, even if the input light is quasi-monochromatic, effect of depolarization can not be neglected in practical optical fiber system. Mueller-Jones matrix should be modified to have the depolarizing effect included. The newly formulated equations are generalized for input light with arbitrary degree of polarization in optical fiber system where effect of depolarization is seriously considered.
引文
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