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).     

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.     

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.     

Schemes for complete compensation for polarization mode dispersion up to second order

The required structure and elements of polarization mode dispersion (PMD) compensators for complete second-order compensation are investigated by use of a general PMD vector formalism of concatenated PMD elements based on Mueller matrices and Stokes vectors. The investigation shows that two- and three-stage compensators with five independent parameters can compensate for polarization-dependent chromatic dispersion as well as the depolarization component of second-order PMD.     

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.     

A deeper analysis of the second order polarization mode dispersion in optical communications systems

This article presents a new approach to the combined analysis of the first and second-order polarization mode dispersion (SOPMD) and shows their importance in optical communication systems performance. How it affects the relation between second-order polarization mode dispersion (PMD) and the differential group delay (DGD) in a single mode fiber is discussed. The analysis is based on time or wavelength and temperature variations changing/impacting PMD and DGD measured values. We present long term statistical characteristics of second-order PMD over a PMD emulator, and investigate the correlation between SOPMD, depolarization (DEP) and polarization dependent chromatic dispersion (PCD). Some authors calculate these modes from measurements obtained from the first order polarization mode dispersion, assuming a positive correlation between these effects, but this not the real relationship between them. A new interpretation of SOPMD was used to analyze the problem of the spectral stability in terms of the temperature. Actual techniques for determination SOPMD, consequently DEP and PCD, use the variation in time and/or wavelength. In some studies the results obtained for SOPMD are correlated to first-order PMD (FOPMD). This paper shows, based on measurements, that the correlation between first and second order Polarization Mode Dispersion (PMD) in the case where the last one is a function of the temperature can assume positive or negative values.     

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。     

Simultaneously compensating tunable CD and adaptive PMD using two different nonlinearly chirped fiber Bragg gratings

Experimental research of simultaneous tunable chromatic dispersion(CD)and adaptive polarization mode dispersion(PMD)compensations in optical fiber communication system was reported.Two different nonlinearly chirped fiber Bragg gratings fabricated through the equivalent chirp technology were adopted in the experiment.One of the gratings was used as CD compensator,with a tunable dispersion range from 300 to 600 ps/nm.The other made of photosensitive polarization maintaining fiber was used as a tunable delay line of PMD compensator,which provided a varying amount of differential group delay(DGD)from 40 to 110 ps.Our experiment was operated at 10-Gb/s non-return-to-zero(NRZ)system and the results showed that the eye pattern recovery is excellent after both PMD and CD are compensated.Especially,the power penalty at a bit error rate(BER)of 10-9 is about 1 dB.     

偏振效应损伤的光通信系统失效概率估算

采用多重重要抽样方法,研究了受偏振模式色散和偏振相关损耗损伤的10 Gbit/s光通信系统的功率代价和失效概率.仿真结果表明,光滤波器对功率代价有重要影响.采用法布里-珀罗滤波器的系统比采用四阶高斯型滤波器的系统有更好的性能表现;发现功率代价通常随着啁啾因子的增大而增大,但当啁啾因子为0.5左右时,系统性能达到最好.仿真结果也表明,即使偏振模式色散和偏振相关损耗同时存在,DPSK系统比OOK系统有更强的PMD和PDL耐受性.     

All optical microwave photonic filters with a round-trip configuration

We propose novel photonic microwave multi-tap filters using a section of Hi-Bi fiber in a round-trip configuration, together with their application in a 20 km single mode fiber (SMF) radio-over-fiber (RoF) link. We demonstrate for the first time that the effect of chromatic dispersion in these multi-tap filters can be reduced in an RoF link when a linearly chirped fiber Bragg grating (FBG) is adopted. This result can be used to combat radio frequency power fading in an RoF link. The configurations are free from optical coherent interference and phase noise. Measured results show 3-tap filters with notch rejections greater than 35 dB and suppression of the level of secondary sidelobes by adjusting a polarization controller. PACS 42.81.-I; 42.81.Gs; 07.50.Qx     

Polarization mode dispersion and vectorial modulational instability in air-silica microstructure fiber

The birefringence of an air-silica microstructure fiber has been studied by measurement of the fiber polarization mode dispersion (PMD) over the wavelength range 545-640 nm. The experimental results are shown to be in good agreement with vectorial numerical calculations, assuming an elliptical core with an eccentricity of 7%. We also report controlled experiments studying nonlinear vectorial modulation instability in the fiber, yielding 3.9-THz modulational instability sideband shifts that are in good agreement with theoretical predictions based on the calculated fiber dispersion and PMD characteristics.     

Assessment of Fiber Chromatic Dispersion Based on Elimination of Second-Order Harmonics in Optical OFDM Single Sideband Modulation Using Mach Zehnder Modulator

This work addresses the analytical and numerical investigations of the transmission performance of an optical Single Sideband (SSB) modulation technique generated by a Mach Zehnder Modulator (MZM) with a 90° and 120° hybrid coupler. It takes into account the problem of chromatic dispersion in single mode fibers in Passive Optical Networks (PON), which severely degrades the performance of the system. Considering the transmission length of the fiber, the SSB modulation generated by maintaining a phase shift of π/2 between the two electrodes of the MZM provides better receiver sensitivity. However, the power of higher-order harmonics generated due to the nonlinearity of the MZM is directly proportional to the modulation index, making the SSB look like a quasi-double sideband (DSB) and causing power fading due to chromatic dispersion. To eliminate one of the second-order harmonics, the SSB signal based on an MZM with a 120° hybrid coupler is simulated. An analytical model of conventional SSB using 90° and 120° hybrid couplers is established. The latter suppresses unwanted (upper/lower) first-order and second-order (lower/upper) sidebands. For the analysis, a varying quadrature amplitude modulation (QAM) Orthogonal Frequency Division Multiplexing (OFDM) signal with a data rate of 5 Gb/s is upconverted using both of the SSB techniques and is transmitted over a distance of 75 km in Single Mode Fiber (SMF). The simulation results show that the SSB with 120° hybrid coupler proves to be more immune to chromatic dispersion as compared to the conventional SSB technique. This is in tandem with the theoretical analysis presented in the article.     

Electronic compensator for 100-Gb/s PDM-CO-OFDM long-haul transmission systems

We study an electronic compensator (EC) as a receiver for a 100-Gb/s polarization division multiplexing coherent optical orthogonal frequency division multiplexing (PDM-CO-OFDM) system without optical dispersion compensation.EC,including electrical dispersion compensation (EDC),least squares channel estimation and compensation (LSCEC),and phase compensation (PC),is used to compensate for chromatic dispersion (CD),phase noise,polarization mode dispersion (PMD),and channel impairments,respectively.Simulations show that EC is highly effective in compensating for those impairments and that the performance is close to the theoretical limitation of optical signal-to-noise rate (OSNR),CD,and PMD.Its robustness against those transmission impairments and fiber nonlinearity are also systematically studied.     

Improved chromatic dispersion monitoring technique

We consider and investigate an improved chromatic dispersion monitoring method using two RF tones with an inserted dispersion offset. This improved technique can be used to monitor both the positive and negative accumulated dispersion caused by optical fibers as well as other optical components in optical networks. We experimentally demonstrate that the monitoring range of the improved technique can be greater than 1150 ps/nm and the monitoring sensitivity better than 0.064 dB/ps/nm by selecting appropriate RF frequencies and dispersion offsets. Our investigations reveal that the RF modulation index should be greater than 10% but less than 20% so as to acquire a large monitoring range with a small power penalty. We also examine the CD monitoring errors caused by polarization mode dispersion (PMD) and self-phase modulation, and show that the use of a dispersion offset can effectively reduce the PMD-induced monitoring errors.     

单模光纤偏振模色散统计特性的分析

用琼斯矩阵本征分析法对偏振模色散各参量的统计特性进行了分析 ,得到了一阶和二阶偏振模色散的统计规律 ,并给出了二阶偏振模色散各参量与一阶偏振模色散各参量之间的比例关系 ,对二阶偏振模色散的获取、补偿和系统设计均有指导意义。     

基于偏振度的偏振模色散补偿中检测信号对不同归零码型的响应研究

从理论上数值分析和比较了一阶和二阶偏振模色散对各种光调制码型（RZ、CSRZ、RZ-DPSK、CSRZ-DPSK）的偏振模色散的影响,结果表明:不同码型的偏振度大不相同,RZ码受偏振度影响最大,CSRZ-DPSK码受二阶偏振模色散的影响最小,在补偿系统中更适合缓解偏振模色散.     

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.     

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.     

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 transmission performance degradation of the optical millimeter-wave signals by fiber chromatic dispersion

The influence of the fiber chromatic dispersion on double sideband (DSB), optical carrier suppression (OCS), and single sideband (SSB) optical mm-wave signals is investigated based on the Taylor expansion of the propagation constant and is verified by simulation. According to our theoretical results, the fading effect suppresses the signal power of the DSB optical mm-wave periodically in a cosine-like pattern, and it can be described by the zero-order Taylor expansion of the propagation constant. For the optical mm-wave with the signal modulated on two or more tones, the bit pulses of the mm-wave signal are distorted by the dispersion-inducing bit walk-off effect between tones, which is expressed by the first-order Taylor expansion of the propagation constant. Moreover, as the signal rate and the transmission distance are increased further, higher-order Taylor expansion of the propagation constant still degrades the optical mm-wave signal even if both the fading effect and the bit walk-off effect are eliminated completely. The distortion of the signal pulses of SSB optical mm-wave is derived based on the second-order Taylor expansion of the propagation constant. This degradation is verified by the simulation with the eye diagram evolution of the SSB optical mm-wave signal.