Jones matrix for second-order polarization mode dispersion

A Jones matrix is constructed for a fiber that exhibits first- and second-order polarization mode dispersion (PMD). It permits the modeling of pulse transmission for fibers whose PMD vectors have been measured or whose statistics have been determined by established PMD theory. The central portion of our model is a correction to the Bruyère model.     

Jones matrix of polarization mode dispersion

We describe how to calculate the Jones matrix transfer function of a fiber if its principal states of polarization and its differential group delay as functions of frequency are known. Using two counterexamples related to second-order polarization mode dispersion (PMD), we also show that a previous method used for the same purpose induces overestimation of second-order PMD effects by a factor of 2. Our new method is used to solve the problem for both counterexamples.     

Accurate Jones matrix expansion for all orders of polarization mode dispersion

I present a simple method for extracting the dispersive elements from a general unitary Jones matrix in such a way that the parts comprising the phase delays and higher-order dispersion in the two principal states of polarization are separated from those describing the frequency-dependent coupling between them. I then rigorously expand these two parts into power series in relative optical frequency, wherein the coefficients are explicit functions of the polarization mode dispersion vectors of various orders. This accurate expansion of the Jones matrix reveals in particular the amplitudes and phases of the cross-coupled components of the principal states of polarization, which are incorrectly described in most polarization mode dispersion models.     

Jones precoder for polarization mode dispersion compensation

A new electrical-domain precoder is proposed to mitigate polarization mode dispersion (PMD) in optical communications by modeling a PMD-dominant fiber optical channel using a single input multiple output (SIMO) channel. Employing a bank of finite impulse response filters and a polarization modulator, and using parameters derived from the Jones matrix representation of PMD, the proposed precoder efficiently adapts to the time-varying nature of PMD and simultaneously pre-equalizes both polarization modes at the transmitter. The transmitter-only structure avoids losing phase and polarization information due to the nonlinearity of the commonly used square law direct-detection receiver. Analysis is performed to evaluate the impact of channel mismatch due to feedback delay, channel estimation errors, and the impact of the finite length of the precoder filters. The analytical results are used to guide selection of the appropriate feedback rate for the adaptive system. Extensive simulation results confirm the efficiency of the proposed Jones precoder, and present it as an effective, low-cost replacement to the complicated, expensive optical-domain counter-parts.     

Broadband all-order polarization mode dispersion compensation via wavelength-by-wavelength Jones matrix correction

We demonstrate wideband all-order polarization mode dispersion (PMD) compensation by applying high-speed spectral polarization sensing and ultrafast pulse shaping techniques to characterize and correct the frequency-dependent Jones matrix associated with PMD of optical fibers on a wavelength-by-wavelength basis. We report full compensation of approximately 800 fs pulses distorted to more than 10 ps by a PMD module with approximately 5.5 ps mean differential group delay. The sensing and compensation of Jones matrix take approximately 200 and approximately 500 ms, respectively.     

Statistics of the Jones matrix of fibers affected by polarization mode dispersion

We carry out a statistical characterization of Jones matrix eigenvalues and eigenmodes to gain deeper insight into recently proposed fiber models based on Jones matrix spectral decomposition. A set of linear dynamic equations for the Pauli coordinates of the Jones matrix is established. Using stochastic calculus, we determine the joint distribution of the retardation angle of the eigenmodes and, indirectly, their autocorrelation function. The correlation bandwidth of the eigenmodes is found to be radical2/3 that of the polarization mode dispersion vector. The results agree well with simulations performed with the standard retarded plate model.     

Anomalous pulse-width narrowing with first-order compensation of polarization mode dispersion

We present analytical and experimental results to demonstrate the narrowing of pulses transmitted through optical fibers, with polarization mode dispersion compensated for to first order in frequency. The compensation technique splits the optical signal at the fiber output into polarization components that are aligned with the output principal states of polarization, and only one of the two components is subsequently detected. It is shown that it is possible with this compensation technique to have output pulses that are narrower than the input pulses. Pulse narrowing can also be found when the optical signal is split into orthogonal polarization components that are not principal states of polarization.     

Pulse broadening due to polarization mode dispersion with first-order compensation

We give the exact analytical expression for the autocorrelation function of the polarization mode dispersion (PMD) vector of a fiber link in which first-order PMD is compensated for at the output. We use the result to obtain the mean-square width of a Gaussian pulse in the presence of a first-order PMD compensator.     

能够补偿二阶偏振模色散的三阶段偏振模色散补偿器

简要分析了偏振相关色散对光通信系统性能的影响,提出了一种三阶段高阶偏振模色散补偿方案,从理论上分析了它同时补偿偏振相关色散和偏振主态旋转的可能性,并提出了其可能存在的两种工作方式.通过数值模拟与两阶段补偿方案进行了性能比较,其偏振模色散容限比两阶段补偿提高约17%个比特周期 关键词： 光通信 光偏振 光纤色散     

偏光器件的Jones矩阵研究

利用Jones矩阵分析了双λ/4波片对正入射线偏振光的复合效应,结果表明:当入射线偏振光光矢量与第一只λ/4波片的快(慢)轴方向成π/4角时,出射线偏振光光矢量相对入射光光矢量转过的角度只与第二只λ/4波片的快轴与入射光光矢量方向的夹角有关;分析研究了线偏振元件的Jones矩阵,给出了判断偏振态和获得左、右旋圆(或椭圆)偏振光的方法。     

Solitons and polarization mode dispersion

Analytical expressions are presented for Manakov solitons perturbed by polarization mode dispersion (PMD). Comparison is made with computer simulations. Dispersion-managed solitons are also studied. It is concluded that at high bit rates solitons are superior to linear return-to-zero propagation with regard to PMD.     

A polarization mode dispersion (PMD) emulator with tuneable first-order PMD and constant second-order PMD

We design a polarization mode dispersion (PMD) emulator with fixed second-order polarization mode dispersion (SO-PMD) but varying first-order PMD (FO-PMD). The emulator constitutes of an optical delay line (ODL), a polarization controller (PC) and a fixed number of randomly concatenated polarization maintaining fibre (PMF) segments. An understanding of the SO-PMD equation is the first vital step to consider before designing such an emulator. The control of the differential group delay (DGD) statistics with wavelength proves to be the key measure for this design. Results show that the mean DGD (or the mean magnitude of the FO-PMD vector ()) of the emulator is biased towards the dominant wavelength-independent of the ODL. This is provided the dominant is by far greater than FO-PMD contributions from the other cascaded sections. Experimentally it is shown that when the DGD (Δτ) is wavelength-independent due to the absence of mode coupling, or when the wavelength-dependent DGD spectra do not change with time due to fixed mode coupling, there is negligible influence on the SO-PMD. The PC angle is controlled at an angle θ to ensure that the sub-emulator is always parallel to the ODL . Thus by rotating the mode coupling angle θ, we change the wavelength-dependent DGD spectra thereby ensuring SO-PMD variation.     

Optical all-pass filters for polarization mode dispersion compensation

Polarization mode dispersion (PMD) compensation is addressed by decomposition of a fiber's Jones matrix into amplitude and phase responses, which are then compensated for separately. Cubic and higher-order phase compensation substantially reduce the cumulative probability at a given system penalty over first-order PMD compensation, as demonstrated for a 40-Gbit/s non-return-to-zero signal and a fiber PMD with a differential group delay of 20 ps (rms). Single-stage all-pass filters provide tunable compensation that is comparable to that obtained with a variable-delay line, and multistage all-pass filters are well suited for higher-order phase compensation.     

High-speed polarization mode dispersion measurement using digital polarization-state generators and Mueller matrix method

A polarization-mode dispersion （PMD） measurement system using a pair of polarization-state generators （PSGs） is demonstrated. Based on the saturation characteristics of magneto-optic rotators, the PSG can be digitally controlled, ensuring high-speed and highly repeatable generation of five distinct polarization states. Thus, the PSG can make full use of the advantage of the Mueller matrix method of PMD measurement. The experimental result shows that the system has good measurement repeatability and potential for field testing.     

Manakov solitons and polarization mode dispersion

The effect of polarization mode dispersion (PMD) on Manakov solitons and dispersion managed solitons is treated analytically and by numerical simulation. In the analytic approach the internal motion of the Manakov soliton is represented as a damped harmonic oscillator. The PMD functions as a white noise source driving the oscillations. It is shown that the solitons can withstand PMD up to a certain instability threshold for which an analytic expression is obtained. This threshold is also evaluated for dispersion managed solitons. (c) 2000 American Institute of Physics.     

Statistical properties of polarization mode dispersion

Polarization mode dispersion (PMD) is one of the effects which limit bit rates in optical communications systems. The statistics of PMD is complicated because it is multi-dimensional, however, many useful results have been obtained. Much work has been done, but the subject is not yet closed, as witnessed by the existence of this conference. In this talk I will review the way some statistical equations are treated. I will briefly discuss the methods of Ito and Lax, and their application to the PMD problem.     

Comparison of penalties resulting from first-order and all-order polarization mode dispersion distortions in optical fiber transmission systems

We compare the eye-opening penalty from a first-order polarization mode dispersion (PMD) model with that from an all-order PMD model in optical fiber transmission systems. Evaluating the performance by taking into account only first-order PMD produces a good approximation of the true eye-opening penalty of uncompensated systems when the penalty is low. However, when the penalties are high, this model overestimates the penalty for outage probabilities in the range of interest for systems designers, which is typically approximately 10(-5) to 10(-6).     

Measurement of polarization mode dispersion in single mode fibre

Polarization mode dispersion (PMD) in fibre seriously limits the high-capacity optical fibre communication system. The measurement of PMD was realized by three methods — wavelength scanning method, modified OTDR method and modified York S-38 dispersion meter method. Different types of fibres have been measured using the above three methods and the results have been found to be consistent. Finally, we also found that the measured results of longer non-polarization-maintaining fibre satisfied the Maxwellian probability density function and the results of polarization maintaining fibre were derived. Supported by The National Natural Science Foundations of P. R. China.     

Autocorrelation function for polarization mode dispersion emulators with rotators

We derive a recursion relation for the frequency autocorrelation function of the polarization dispersion vector for polarization mode dispersion emulators with rotators. The autocorrelation function has a nonzero background for an emulator with a fixed number of sections. This background diminishes slowly as the number of sections grows. Randomizing the section lengths removes the autocorrelation periodicity exhibited by an emulator with equal sections, but it does not remove the finite background.     

Solitons in fibers with polarization mode dispersion

Evaluating the relative time displacement of the two orthogonally polarized components of a pulse propagating down a birefringent optical fiber is considered. A method that provides analytical expressions for this time displacement is described and generalizes analytical results already published.