On the second-order approximation of PMD

A second-order polarization mode dispersion (PMD) approximation based upon the pulse-width distortion has been studied. It shows that a complete second-order approximation should include the second derivative of the PR-ID vector as well as the first derivative of the PMD vector. Second-order pulse distortions are explicitly expressed including a `first-order' term involving principal states of polarization (PSP) of the pulse and a second-order term involving the beating between fiber chromatic dispersion and effective PMD chromatic dispersion. An analytical result is derived for the probability of second-order PR-ID power penalty. It shows that the mean PMD of the fiber should be restricted to 26 ps and 18 ps, respectively for an optical link with zero and 850 ps/nm chromatic dispersion, in order to maintain a one dB second-order PMD power penalty with a probability below 10^-6 at a data rate of 10 Gb/s. The analysis also indicates that a second-order PMD compensator can be used as a dynamic chromatic dispersion compensator     

Optimal choice of compensation PMD vector in feedforward-type second-order PMD compensation

In this paper, the formula of an optimal compensation vector, which is defined as an input polarization-mode dispersion (PMD) vector of the compensator, for second-order PMD compensation has been derived from the minimization of the root-mean-square (rms) pulse-broadening factor. The derived optimal compensation vector is a linear combination of frequency-averaged PMD vectors and output states of polarization, which shows a similar trend to the previously reported optimal first-order PMD compensation. The rms pulse-broadening factor after optimal second-order PMD compensation has been semianalytically calculated and compared with the previously reported simulation result. They are in good agreement. The formula of the optimal second-order compensation vector derived in this paper provides indispensable information for feedforward second-order PMD compensation.     

Distortion related to polarization-mode dispersion in analoglightwave systems

Analog transmission in single-mode fiber using chirped sources gives rise to nonlinear distortion when polarization-mode dispersion (PMD) is present. We investigate experimentally and theoretically two mechanisms for this distortion: for chirped sources, PMD in the presence of polarization-mode coupling results in second-order distortion that is proportional to the square of the modulation frequency; when polarization-dependent loss is present, an additional second-order distortion term occurs that is independent of modulation frequency. Both mechanisms give rise to distortion that is time varying due to the sensitivity of PMD to ambient temperature changes. Numerical examples indicate that these effects can limit the capacity of analog systems that use directly modulated semiconductor lasers     

Pulsewidth compression in optical components with polarization modedispersion using polarization controls

An algorithm capable of finding the input and output states of polarization for pulsewidth narrowing at the output of an optical fiber with polarization mode dispersion (PMD) is analytically presented and numerically solved. It has been demonstrated theoretically and experimentally that the output pulses can he narrower than the input pulses when PMD is compensated by controlling both the input polarization and the receiver polarization states. The cost of this improvement is a reduction of the optical power in the output pulse     

DOP ellipsoids for systems with frequency-dependent principalstates

The effects of polarization mode dispersion (PMD) in optical communication systems limit the practical length of fiber optic links. Characterization of the PMD of an optical system can be performed by observing the surface obtained from the vector whose length is the degree of polarization and direction is defined by the output state of polarization for a randomly varying input polarization. An analytical solution to the ellipsoid is derived for a simple higher order PMD system that is composed of two polarization-maintaining fibers. An approximate inverse relationship between the ellipsoid radii and the first- and second-order components of the PMD vector is also derived     

微环谐振器中各参数对光速控制输出脉冲畸变的影响仿真分析

利用微环谐振器进行光速控制时,各参数对光脉冲传输的影响是不可忽略的,它除了导致光脉冲展宽,还引起脉冲的畸变。基于微环谐振器的传输特性,推导了单环谐振器的二阶色散和三阶色散表达式,针对无损耗/增益情形,分析了利用微环谐振器进行光速控制时,高阶色散和输入脉冲中心波长对输出脉冲畸变的影响,分析了损耗/增益对单环谐振器输出脉冲畸变的影响。结果表明,二阶色散导致脉冲展宽,三阶色散导致脉冲畸变,输入脉冲中心波长位置影响脉冲分裂谷底的深浅,而损耗和增益影响脉冲畸变情况。为利用微环谐振器实现光速控制的应用提供了设计优化依据。     

The Second Order PMD in Optic Fiber and Compensation Experiment

1　Introduction　Inhigh speed /long distanceopticalfibertransmissionsystem ,PMDisoneofthemainfactorslimitingthebitrateandthetransmissiondistance ,becomingespeciallyimportantasthebitrateincreaseshigherthan 2 5Gb/s .TheinstantaneousPMDoftransmissionlineischangingfromtimetotimeandfromfrequencytofre quencyrandomly .InfrequencydomainPMDcanbeex pressedbytheTaylorexpansionatcenterfrequencyanddividedintofirstorder ,secondorder ,…ofwhichhigh erthansecondareallcalledhighorderPMD[1] .Fromfrequenc…     

二阶偏振模色散高速光纤通信的影响及补偿

讨论了二阶偏振模色散对光脉冲的影响,模拟结果表明,二阶偏振模色散对信号影响起主要作用的是去偏振项,使得信号波形边缘出现能量过冲;同时也讨论了二阶偏振模色散补偿的方法,利用二段偏振模色散补偿器对二阶偏振模色散进行了有效的补偿,并给出了补偿的实验结果.     

Second-order distortion generated by amplification ofintensity-modulated signals with chirping in erbium-doped fiber

A rate equation analysis for second-order distortion generated in an erbium-doped fiber amplifier is reported. It is shown that the relevant mechanism of distortion is the interaction between the frequency chirping of input light and the local gain tilt in the erbium-doped fiber. It is found that the output light distortion is highly affected by the phase difference between the input light distortion and the chirping-induced distortion. This indicates that second-order distortion is not always degraded by erbium-doped fiber amplifiers     

Real-time first- and second-order PMD characterization using averaged state-of-polarization of filtered signal and polarization scrambling

A real-time estimation technique for first- and second-order polarization-mode dispersion (PMD) is presented. It makes use of the spectrum of telecommunication signals. At the output of the transmission fiber, the signal is tapped and filtered. Three filters are used: a high-pass filter, a low-pass filter, and a narrow-band filter. The averaged states of polarization (SOPs) of the filtered signals are then measured using a polarimeter. We repeat the measurement for several different input SOPs using a polarization scrambler at the input of the fiber. From these measurements, we deduce the first-order PMD and, subsequently, the second-order PMD.     

The effect of the frequency dependence of PMD on the performance of optical communications systems

The authors study numerically the importance of the frequency dependence of the polarization-mode dispersion (PMD) vector to the operation of optical systems and evaluate the validity of the second-order PMD approximation. They show that there is no relevant range of parameters in which the second-order PMD approximation is useful and question the validity of considering discrete high-orders of PMD.     

The accuracy assessment of different polarization mode dispersion models

Several polarization mode dispersion (PMD) models were developed to help understanding PMD effects and simplify the analysis regarding their impact on the system performance. Whether or not a PMD model can be used to accurately predict the system impairments depends on how well it approximates fiber PMD. In this paper, we assess the accuracy of six commonly used first- and second-order PMD models by comparing them with an all-order PMD model. Both PMD induced pulse broadening and optical-signal-to-noise-ratio (OSNR) penalties are determined, analyzed, and compared for each PMD model. To separate first- and higher-order PMD effects, we investigate the system performance with and without PMD compensation. We find that, compared with the all-order PMD model, all the known first- and second-order PMD models overestimate the PMD distortions, and the PMD models that do not contain higher than second-order PMD generate the largest deviation. Our results show that the first-order PMD model can be used to approximate the all-order PMD model when no PMD compensation is used, but none of the known PMD models can generate results close enough to those of the all-order PMD model for a PMD compensated system. This indicates that to accurately evaluate the performance of PMD mitigation techniques, the all-order PMD model has to be used.     

Distortion properties of the interval spectrum of IPFM generatedheartbeats for heart rate variability analysis

The integral pulse frequency modulation (IPFM) model converts a continuous-time signal into a modulated series of event times, often represented as a pulse train. The IPFM process is important to the field of heart rate variability (HRV) as a simple model of the sinus modulation of heart rate. In this paper, we discuss the distortion properties associated with employing the interval spectrum for the recovery of the input signal from an IPFM process's output pulse train. The results state, in particular for HRV, how precisely the interval spectrum can be used to infer the modulation signal responsible for a series of heartbeats. We have developed a detailed analytical approximation of the interval spectrum of an IPFM process with multiple sinusoids as the input signal. Employing this result, we describe the structure and the distortion of the interval spectrum. The distortion properties of the interval spectrum are investigated systematically for a pair of frequency components. The effects of linear and nonlinear distortion of the fundamentals, the overall contribution of harmonic components to the total power, the relative contribution of "folded back" power due to aliasing and the total distortion of the input spectrum are investigated. We also provide detailed comparisons between the interval spectrum and the spectrum of counts (SOC). The spectral distortion is significant enough that caution should be taken when interpreting the interval spectrum, especially for high frequencies or large modulation amplitudes. Nevertheless, the distortion levels are not significantly larger than those of the SOC. Therefore, the spectrum of intervals may be considered a viable technique that suffers more distortion than the SOC.     

On the robustness of the finite-length MMSE-DFE with respect to channel and second-order statistics estimation errors

The finite-length minimum mean square error decision-feedback equalizer (MMSE-DFE) is an efficient structure mitigating intersymbol interference (ISI) introduced by practically all communication channels at high-enough symbol rates. The filters constituting the MMSE-DFE, as well as related performance measures, can be computed by assuming perfect knowledge of the channel impulse response and the input and noise second-order statistics (SOS). In practice, we estimate the unknown quantities, and thus, inevitable estimation errors arise. We model the estimation errors as small perturbations, and we derive a second-order approximation to the excess MSE. Furthermore, we derive second-order approximations to the mean excess MSE in terms of the parameter estimation error covariance matrices and simple and informative bounds, revealing the factors that govern the behavior of MMSE-DFE under mismatch. Simulations confirm that the derived second-order approximations provide accurate estimates of the MMSE-DFE performance degradation due to mismatch.     

System outage probability due to first- and second-order PMD

A theoretical approach is proposed that allows one to quantify the impact of fiber polarization mode dispersion (PMD) on optical binary transmission taking into account not only first-order polarization mode dispersion, but also signal distortion induced by second-order PMD. Using this approach the impact of the spectral signal width on PMD-induced system outage probability could be studied for the first time. An analysis of 10-Gb/s transmission exhibits that, as long as the mean PMD remains below the commonly accepted limit (about 10 ps) for negligible outage, a linear chirp of up to 30 GHz does not lead to an additional increase of the system outage. This result confirms that low bandwidth modulation schemes (external modulator, low chirp laser) do not suffer from additional outage degradation due to second-order PMD     

Automatic compensation of polarization-mode dispersion for 40 Gb/s transmission systems

We present an automatic compensator that effectively mitigates signal distortion due to polarization-mode dispersion (PMD). Accurate compensation is achieved by utilizing a degree of polarization (DOP) monitor with a measurement uncertainty of better than 1% achieved by applying a self-dependent precalibration procedure. The compensation performance at 43 Gb/s was evaluated systematically with respect to both first- and second-order PMD by using a crystal-optical PMD emulator. The compensator extended the tolerable differential group-delay (DGD) limit from 8 to 28 ps, while maintaining the Q penalty below 1 dB. In terms of the average of a Maxwellian-distributed DGD, the PMD compensator enabled transmission for up to 8 ps, or about three times higher than the level tolerated in the uncompensated case. In addition to the compensation performance, we demonstrate successful operation, even for distorted signals with high chromatic dispersion. We believe this capability will be a key enabler for a combined operation with adaptive chromatic dispersion compensators.     

Comparison of system penalties from first- and multiorder polarization-mode dispersion

We experimentally investigate the polarization-mode dispersion (PMD)-induced system penalty arising from first-order and all-order PMD. We use a measurable quantity, "string" length, to parameterize the penalty, find a deterministic correction to the accepted first-order PMD-induced system penalty approximation, and discuss the implications for system outages. Further, we show that higher orders of PMD introduce an additional penalty scatter that is nearly independent of "string" length, and correlated to the magnitude of the second-order PMD vector.     

光纤传输系统偏振模色散对输出信号偏振度的影响

光纤通信系统的偏振模色散(PMD)是限制系统传输容量和距离的关键因素。系统输出信号的偏振度(DOP)反映了系统的偏振模色散。利用光纤通信系统的Jones矩阵模型，在理论上得到了系统的输出光脉冲Stokes矢量的表达式。在此基础上分析和计算了系统的输出脉冲的偏振度特性。结果表明，系统的输出信号的偏振度随入射脉冲偏振态的变化而变化，当入射脉冲偏振态与系统的主偏振态一致时，系统的输出信号的偏振度达到极大；同时，随着系统的偏振模色散幅度的增大而变小。系统的输出信号的偏振度还随着信号原始啁啾系数绝对值的增大而减小，但与啁啾系数的符号无关。     

Isolation Rating of Ferrite Components at High Pulse Powers (Correspondence)

Any method used to measure the isolation provided by a ferrite component at high pulse powers must also consider the effect of possible distortion to the pulse shape owing to the nonlinear phenomena in ferrites. When such pulse shape distortion occurs, measurement methods based on average crystal current measurement or temperature rise in a calorimeter yield erroneous results. It is necessary that the method of measurement of isolation must be one which finds the difference between the maximum heights of the input and output pulses to the component irrespective of the pulse shape at the two ports.     

Transient Electromagnetic Guided Wave Propagation in Moving Media

An analytical study of the influence of moving media on the propagation of transient electromagnetic modal waves in dispersive waveguides is presented. The response to impulsive excitation is determined in exact closed form and used to demonstrate that the nature of the pulse distortion differs in each of the three cases, 1) 0 < u < c /spl equiv/ (/spl epsi//spl mu/)/sup -1/2/, 2) v = c, and 3) c < v < c/sub 0/ /spl equiv/ (/spl epsi//sub 0//spl mu//sub 0/)/sup -1/2/ (v = speed of the medium). An expression is derived from which the pulse waveform generated by an input of arbitrary form can be readily determined when 0 < v < c if the transient response to a similar input is known for v = 0. An untabulated Laplace transform pair is derived and used to determine the unusual pulse distortion in case 3) which shows a markedIy discontinuous change from the pulse distortion in case 2). The theory illuminates a singular circumstance in which the Lorentz transformation is consistent with the "speed of light" differing from one inertial reference frame to another.