Soliton interaction in birefringent optical fibers: Effects of nonlinear gain devices

This paper presents the influences of polarization mode dispersion (PMD) on the performance of soliton transmission system in birefringent fibers. Dispersive waves generated in single mode fibers due to PMD degrade the soliton transmission system in two aspects. First, solitons continuously lose their energy, thus cause enhancement in pulse width. Second, the dispersive waves interact with neighboring pulses and cause distortion in a sequence of pulses. Both these effects reduce the effective bit-rate and degrade the performance of high-speed optical transmission systems. Optical fibers with large group velocity dispersion (GVD) have less dispersive waves and are relatively robust to pulse broadening, but it enhances the interaction between the adjacent pulses. In this paper, we analyzed these effects of PMD on soliton propagation in birefringent fibers and introduced nonlinear gain devices with perturbation terms proportional to second and fourth power of amplitudes to reduce these effects. We proposed Symmetric Split-Step Fourier Method to solve the coupled nonlinear Schrödinger equations (CNLSE); which yields better results over the existing Split-Step Fourier Method.     

二阶偏振模色散对高速高斯光脉冲在单模光纤中传输的影响

研究二阶偏振模色散（PMD）对高斯光脉冲在单模光纤中传输产生的影响，给出输出光脉冲的时域表达式。分析表明，输出光脉冲在每个基本偏振态上仍保持高斯形状，但其频率啁啾及脉宽等特性都已改变，文中对这些变化与二阶偏振模色散之间的关系进行了讨论。通过比较10Gb/s和40Gb/s的光传输系统中二阶偏振模色散的影响，可以发现，若规定脉冲展宽不能超过脉宽的十分之一，40Gb/s系统所能容忍的二阶偏振模色散极限值比10Gb/s系统小一个数量级。     

二阶偏振模色散矢量致脉冲展宽的理论分析

我们首次提出了消偏矢量的概念，并用它来描述二阶偏振模色散中偏振模色散矢量方向的变化。本文导出了由于二阶偏振模色散所引起的脉冲展宽的解析表达式，结论指出，偏振相关的本征色散总是使脉冲展宽加剧；而偏振模色散矢量方向的变化（消偏矢量），却是使脉冲展宽减弱。二阶偏振模色散对脉冲的展宽，不仅与偏振相关的本征色散和消偏矢量有关，而且还与信号的传输速率以及初始一阶偏振模色散的大小有关。信号速率的提高，将明显的使二阶偏振模色散的影响增强。在偏振相关的本征色散不为零的情况下，通过调整初始偏振态矢量、初始一阶偏振模色散矢量以及消偏矢量三者的方向，使它们互相平行，可以获得最佳的色散补偿。但是却不能获得完全的色散补偿。在最佳色散补偿时的最小脉冲展宽为σ= (2^1/2/4)( DCF/T₀).     

光纤偏振效应导致脉冲展宽的解析模型

在10Gb／s,尤其是40Gb／s以上高速光纤通信系统中,光纤的偏振特性已成为限制系统传输距离的主要因素之一。光纤的偏振效应主要包括偏振模色散和偏振依赖损耗。而脉冲均方根展宽是判断信号传输性能的一个主要物理量。本文讨论了光纤线路偏振模色散与偏振相关损耗的相互作用及对信号脉宽的影响。给出了线路偏振模色散矢量和偏振相关损耗矢量之间的关系式,并基于严格的数学方法,导出了在光纤偏振模色散和偏振相关损耗共同作用下的信号均方根脉宽变化的解析形式,同时考虑了光纤色散,啁啾等。该模型可用于分析高阶偏振模色散和偏振相关损耗,任意线性光纤通信系统脉冲展宽分析。     

Impacts of polarization mode dispersion on the pulse-width with considering initial pulse chirp and fiber GVD

The impacts of polarization mode dispersion (PMD) on the pulse-width in linear systems have been investigated. The analytical solutions, including the effects of initial frequency chirp and group velocity dispersion (GVD), are derived. Analyses show that the pulse broadening effects induced by the second-order PMD depend on GVD and chirp parameter, which are different from those induced by the first-order PMD. An initially chirped Gaussian pulse is taken as an example, upon which analytical solutions of rms pulse-width are derived before and after the first-order PMD compensation. The first-order PMD compensator is also evaluated based on these solutions. The results show that the pulse broadening effects will be resisted efficiently by choosing appropriate GVD and chirp parameter; in general, the post-transmission compensation method will be less efficient than the PSP-transmission method.     

高速光纤通信系统中高阶PMD的优化建模

为了评估随机变化的偏振模色散(PMD)(包括一阶和二阶PMD)使系统信号裂化的程度,降低其对高速光纤通信系统传输速率和传输容量的不利影响,在斯托克斯空间中推导了偏振模色散(PMD)矢量的数学表达式。对PMD效应所导致的脉冲展宽进行了数学分析,给出了差分群时延(DGD)的变化、一阶PMD矢量和二阶PMD矢量方向的变化对脉冲展宽的影响。通过数学推导得出,在大多数情况下,二阶PMD无法完全补偿,需通过控制单元的调整使其对系统的影响达到极小值。通过实验分析,得到了和数学推导中同样的结果,从而证明了模型的正确性。     

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.     

Analytical theory for pulse broadening induced by all-order polarization mode dispersion combined with frequency chirp and group-velocity dispersion

We derive an analytical expression for the expected root-mean-square (rms) pulse broadening with considering the combined effects of all-order polarization mode dispersion (PMD), group velocity dispersion (GVD) and frequency chirp. It is shown that two commonly used first-order PMD compensators lose their efficiency quickly with chirp parameter increasing if GVD is ignored. When GVD is added, prechirp technique is helpful for the enhancement of PMD tolerance for both uncompensated case and first-order compensators when GVD and PMD coefficient satisfy some special relationship.     

偏振模色散影响色散控制孤子传输的理论研究

采用变分法分析高速色散控制孤子在双折射光纤中的传输规律。首先建立了色散控制孤子在双折射光纤中的扰动传输模型 ,然后解析了偏振模色散影响下色散控制孤子各参量的传输演化规律 ,最后对解析结果进行了计算。研究结果表明 ,偏振模色散参量对色散控制孤子能量、脉宽的演化影响很大 ,当偏振模色散很大时 ,如Dp>0 .3ps/km1/ 2 时 ,必须考虑采用某些在线控制手段来有效抑制偏振模色散对传输系统的影响 ,然而 ,当Dp≤ 0 .1ps/km1/ 2 时 ,系统几乎不受影响 ,同时本文还证明了色散控制孤子抗偏振模色散扰动的能力强的这一特点。为研究偏振模色散对高速非线性传输系统、特别是色散控制孤子传输系统的影响提供了理论依据和研究方法。     

高速传输系统中高阶PMD的影响

研究由于偏振模色散(PMD)引起的时域脉冲响应从传输矩阵的角度分析了包含各阶与频率相关的差分相时延(DPD)、主偏振态(PSP)对脉冲波形的影响,并通过仿真结果验证理论的有效性同时,也分析了PMD对系统带来的眼图代价,对40Gb/s系统做出了预测.     

偏振模色散影响下飞秒孤子的传输特性研究

以Maxwell电磁场理论为基础，在综合考虑了高阶色散、高阶非线性、自相位调制、交叉相位调制、自变陡、脉冲内喇曼散射及偏振模色散等因素的基础上，推导了飞秒孤子脉冲在双折射光纤中传输的耦合非线性薛定谔方程，并利用分步傅里叶方法对该方程进行了数值计算，研究分析了偏振模色散对飞秒孤子传输的影响。结果发现：当Dp≤0.1ps/km1/2时，偏振模色散对系统的影响很小，随着偏振模色散值的增大，系统的传输性能迅速恶化，当偏振模色散值达到0.3ps/km1/2时，系统的传输距离已经不到无偏振模色散时的1/3；若同时考虑光纤的高阶效应，以飞秒孤子作为载体的系统已经不能实现高速长距离的传输。     

Asymmetric W-shaped and M-shaped soliton pulse generated from a weak modulation in an exponential dispersion decreasing fiber

We study localized waves on continuous wave background in an exponential dispersion decreasing fiber with two orthogonal polarization states. We demonstrate that asymmetric W-shaped and M-shaped soliton pulse can be generated from a weak modulation on continuous wave background. The numerical simulation results indicate that the generated asymmetric soliton pulses are robust against small noise or perturbation. In particular, the asymmetric degree of the asymmetric soliton pulse can be effectively controlled by changing the relative frequency of the two components. This character can be used to generate other nonlinear localized waves, such as dark–antidark and antidark–dark soliton pulse pair, symmetric W-shaped and M-shaped soliton pulse. Furthermore, we find that the asymmetric soliton pulse possesses an asymmetric discontinuous spectrum.     

高速光纤通信系统中抑制偏振模色散的新机制

重点研究了偏振模色散、群速度色散、自相位调制三者之间在高速光纤通信系统中的相互作用，从时域角度分析脉冲的演变，从频域角度分析频谱的变化，提出一定条件下，啁啾、色散、自相位调制可以部分补偿偏振模色散的思想。通过对40Gbit／s系统进行偏振模色散、群速度色散和自相位调制共同作用的仿真，从统计意义上验证了它们之间的相互影响，并找到最佳传输方案，对系统设计提供了参考。     

偏振模色散引起的脉冲展宽对接收灵敏度及频谱的影响

在10Gbit/s以上的光纤通信系统中，偏振模色散的影响已不可忽略，它可以引起信号脉冲的展宽，使接收系统的误码率上升，分析了偏振模色散引起的脉冲展宽对接收灵敏度及接收信号频谱的影响，并进行了实验验证，对进行偏振模色散的自动补偿具有重要意义。     

Soliton Transmission in Fibers with Polarization-Mode Dispersion

Abstract

The polarization-mode dispersion (PMD) is a dominant statistical effect in ultra-high bit rate transmission systems. In this article, soliton transmission in constant and randomly varying birefringent fibers is reviewed. In particular, soliton robustness to PMD is analyzed and compared with that of linear pulses. It is found that solitons broaden in proportion to the square root of distance, like in the case of linear pulses, but with a reduced coefficient.     

Pulse Self-trapping Robustness to Polarization Mode Dispersion in Optical Fiber

In this paper, pulse self-trapping robustness to polarization mode dispersion in optical fibers is studied. Nonlinear pulse can be used to suppress PMD despite the input pulse shapes is found. When the nonlinear effect is stronger (initial pulse amplitude is larger), the suppression degree to PMD is better. As the initial chirp is considered, we find that the chirp is harmful to suppress PMD. The more is initial chirp, the more is the PMD value.     

The Statistical Analysis of Polarziation Mode Dispersion and Filter Control on Dispersion Managed Soliton Links

In this paper, the statistical distributing and magnitude of the first and the second-order PMD (polarization mode dispersion) vectors are evaluated and the filters control PMD effects also are analyzed on DMS (dispersion-managed soliton) links. Firstly, the so-called coarse-step approach is applied to the DMS links. The PMD statistical characteristics of the first and the second-order are simulated and the evolutions of energy and mean square of time displacement of DMS two polarization modes are gotten. Secondly, The DMS transmission of filter control with the conventional model of PMD is analyzed by Varitional method, from which the evolving rules of characteristically DMS parameters are obtained and the stability of filter control the DMS transmission are investigated. The results are not only very useful to simplify the measurement of the second-order PMD and instructively reveal degree of PMD effects in DMS systems, but also give that condition of stability of filter control PMD in DMS systems.     

Pulse Self-trapping Robustness to Polarization Mode Dispersion in Optical Fiber

In this paper, pulse self-trapping robustness to polarization mode dispersion in optical fibers is studied. Nonlinear pulse can be used to suppress PMD despite the input pulse shapes is found. When the nonlinear effect is stronger (initial pulse amplitude is larger), the suppression degree to PMD is better. As the initial chirp is considered, we find that the chirp is harmful to suppress PMD. The more is initial chirp, the more is the PMD value.     

PMD impact on optical systems: Single- and multichannel effects

We discuss the influence of polarization mode dispersion (PMD) on optical communication channels by putting special emphasis on PMD-induced pulse broadening. We present the analytical theory for PMD-induced pulse broadening, first in the deterministic and then for the random case. We then apply this theory to a comparison between a few different simple PMD-compensators. We also discuss the systems implications and outage probabilities that arise for different compensating techniques, including active optical compensation, alternative modulation formats and error correcting codes. Then we consider wavelength division multiplexing (WDM) systems, and present the unique aspects of PMD and PMD compensation that distinguish WDM transmission from the single-channel case. Finally the temporal drift is discussed, and the associated autocorrelation function is presented.     

A model to characterize the effect of cross phase modulation on polarization in an optical fiber transmission system

This paper presents a model that described the process of inter-influence between cross phase modulation (XPM) and polarization effects such as polarization mode dispersion (PMD) and polarization dependant loss (PDL) in an optical fiber communication system. Previous papers have discussed PMD-PDL and PMD-XPM effects in separate models, but in this work we developed a model that is capable of characterizing and evaluating PMD, PDL and XPM simultaneously. From the model, we found that PMD and PDL can be affected by XPM. The presence of XPM changed the vector directions of PMD and PDL in Stokes space.