Statistical correlation between first and second-order PMD

We investigate the statistical correlation between first- and second-order polarization mode dispersion (PMD) effects, which is important for PMD mitigation. The theoretical results are compared to numerical simulations and experimental data from a real high-PMD fiber. A new dependence between first- and second-order PMD is found. We show that the root mean square (RMS) value of the second-order PMD component, perpendicular to the PMD vector, increases with the length of the PMD vector     

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     

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.     

Variable second-order PMD module without first-order PMD

We propose a module that generates variable second-order polarization mode dispersion (PMD) without producing any first-order PMD. It is based on four identical fixed differential group delay segments arranged in a symmetrical manner. Only one control parameter varies the magnitude of second-order PMD.     

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     

Statistical characteristics and effects of polarization mode dispersion in dispersion managed soliton systems

Recently,the dispersion-managed solitons(DMS) areof great interest in soliton communication systems .Be-cause of some prior advantages compared with conven-tional solitons ,such as higher pulse energy and signalnoise ratio,lower averaged dispersionline an…     

Statistical PMD emulator using variable DGD elements

We report on a novel polarization-mode dispersion (PMD) emulator with exact Maxwellian statistics. The proposed PMD emulator was implemented by using variable differential group-delay elements and polarization controllers. Unlike the previous PMD emulators, the proposed PMD emulator could generate not only the first-order PMD with exact Maxwellian distribution, but also the second-order 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.     

Probability densities of second-order polarization mode dispersionincluding polarization dependent chromatic fiber dispersion

We describe experiments and simulation of second-order polarization mode dispersion (PMD) components in optical fibers with emphasis on polarization-dependent chromatic dispersion (PCD). Excellent agreement is found in comparisons of experimental, simulated, and theoretical probability densities. To our knowledge, these are the first such comparisons for the second-order PMD magnitude and the PCD     

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     

Analysis of signal degree of polarization degradation induced by polarization-mode dispersion in optical fibers

We study analytically and numerically optical signal degree of polarization (DOP) degradation induced by polarization-mode dispersion (PMD) in optical fiber transmissions, using the Eyal-Marshall-Tur-Yariv (EMTY) model and Monte Carlo simulations. The results show the inaccuracy of second-order PMD approximation in the EMTY model and the inapplicability of employing DOP as feedback signal for high-order PMD compensation.     

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.     

A deterministically controlled four-segment polarization-mode dispersion emulator

In this paper, we propose a novel design of a first- and second-order polarization-mode dispersion (PMD) emulator based on four concatenated first-order PMD segments. Instead of polarization scrambling at each junction, we set these polarization rotators according to a statistical schedule, so as to produce a realistic probability density function of the first- and second-order PMD presented in long-haul transmission fiber.     

Protection interoperability for WDM optical networks

The failure of a single optical link or node in a wavelength division multiplexing (WDM) network may cause the simultaneous failure of several optical channels. In some cases, this simultaneity may make it impossible for the higher level (SONET or IP) to restore service. This occurs when the higher level is not aware of the internal details of network design at the WDM level. We call this phenomenon “failure propagation.” We analyze three types of failure propagation, called “bottleneck,” “connectivity,” and “multiple groups.” Then we present a solution based on the definition of appropriate requirements at network design and a WDM channel placement algorithm, protection interoperability for WDM (PIW). Our method does not require the higher level to be aware of WDM internals, but still avoids the three types of failure propagation mentioned above. We finally show the result on various network examples     

Polarization mode dispersion compensation at 10, 20, and 40 Gb/swith various optical equalizers

Polarization mode dispersion (PMD), especially in “old” fibers, is considered harmful for installation and upgrading of trunk lines. An optical PMD equalizer should have several or many differential group delay (DGD) sections with polarization transformers in between which can endlessly transform any input polarization into a principal state of the following DGD section. The sections must practically have fixed DGDs unless there is only one section. The small-signal baseband transfer function for PMD, higher order PMD, and the necessary number of sections as well as their control by the output signals of an electrical filter bank in the receiver are also discussed in this context. Several PMD equalizers have been realized and successfully tested in transmission systems with bit rates of 10, 20, and 40 Gb/s. The systems operated stably with well-opened eye diagrams for DGDs ranging between 0 and 1.7 bit durations. Best performance is obtained from a distributed PMD equalizer with one piece of polarization-maintaining fiber twisted by 64 stepper motors. The principle can also be realized in LiNbO₃     

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.     

Reducing the number of polarization controllers in all-fiber polarization-mode-dispersion emulators using polarization maintaining fiber sub-sections with unequal lengths

Using polarization-maintaining fiber (PMF) sub-sections with unequal lengths, an all-fiber polarization mode dispersion (PMD) emulator with reduced number of polarization controllers is proposed and demonstrated. With six polarization controllers and seven PMF sections, each consists of four sub-sections with unequal lengths and spliced at 45° relative to each other, the generated PMD first- and second-order statistical distributions are close to those of the real fiber link with negligible deviations, therefore, the cost of all-fiber PMD emulators, mainly from the electrically driven polarization controllers, is significantly reduced.     

Variable differential-group-delay module without second-order PMD

We propose a design for a variable differential-group-delay (DGD), formed by concatenation of four identical fixed DGD segments. Due to the symmetry involved, it produces zero second-order polarization mode dispersion (PMD). The generated third-order PMD is half the value of the conventional two-segment concatenation for variable DGD.     

Deterministic approach to first- and second-order PMD compensation

The authors show that three concatenated first-order polarization mode dispersion (PMD) segments are sufficient to compensate any first- and second-order PMD present in a transmission fiber. They determine analytically the required individual rotation matrix of the polarization rotators and the required differential group delay for the variable delay line in the compensator.