Alessandra Orlandini

Parametric-gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise

This paper presents a novel method based on a parametric gain (PG) approach to study the impact of nonlinear phase noise in single-channel dispersion-managed differentially phase-modulated systems. This paper first shows through Monte Carlo simulations that the received amplified spontaneous emission (ASE) noise statistics, before photodetection, can be reasonably assumed to be Gaussian, provided a sufficiently large chromatic dispersion is present in the transmission fiber. This paper then evaluates in a closed form the ASE power spectral density by linearizing the interaction between a signal and a noise in the limit of a distributed system. Even if the received ASE is nonstationary in time due to pulse shape and modulation, this paper shows that it can be approximated by an equivalent stationary process, as if the signal were continuous wave (CW). This paper then applies the CW-equivalent ASE model to bit-error-rate evaluation by using an extension of a known Karhunen-Loe/spl acute/ve method for quadratic detectors in colored Gaussian noise. Such a method avoids calculation of the nonlinear phase statistics and accounts for intersymbol interference due to a nonlinear waveform distortion and optical and electrical postdetection filtering. This paper compares binary and quaternary schemes with both nonreturn- and return-to-zero (RZ) pulses for various values of nonlinear phases and bit rates. The results confirm that PG deeply affects the system performance, especially with RZ pulses and with quaternary schemes. This paper also compares ON-OFF keying (OOK) differential phase-shifted keying (DPSK) systems, showing that the initial 3-dB advantage of DPSK is lost for increasing nonlinear phases because DPSK is less robust to PG than OOK.

A simple and useful model for Jones matrix to evaluate higher order polarization-mode dispersion effects

Starting from the differential equation that relates the Jones matrix of a polarization-mode dispersion (PMD) fiber to its output dispersion vector, the analytical expressions of the matrix coefficients are determined in the case of a dispersion vector rotating on a circumference in the Stokes space. This model, that needs only few parameters with known statistics, is applied to evaluate the performance of an optical system. The results obtained with it and with other models proposed in literature are compared to those evaluated by numerical simulations with all-order PMD effects, showing that our model gives an accurate representation of real system performances.

A Unified Design Framework for Single-Channel Dispersion-Managed Terrestrial Systems

This paper provides a unified framework to the design, performance optimization, and accurate numerical simulation of periodic, dispersion-managed (DM) single-channel long-haul optical transmission systems for nonsoliton on-off keying (OOK) modulation. The focus is on DM terrestrial systems, with identical spans composed of a long transmission fiber compensated at the span end by a linear dispersion compensating module, with pre- and postcompensation fibers at the beginning and end of the link. The framework is based on the dispersion-managed nonlinear Schrodinger equation (DM-NLSE). First, expressions of the DM-NLSE kernel are provided both in the frequency and the time domain, and a novel map strength parameter, appropriate for terrestrial systems, is introduced. It is then shown that the DM-NLSE contains all the basic information needed for system design, as summarized by three parameters: i) nonlinear phase, ii) in-line dispersion, and iii) map strength. Through a large-signal perturbative analysis of the DM-NLSE, the well-known linear relationship between the in-line dispersion and the optimal precompensation is derived, along with the large-signal step response of the DM link, from which the ghost pulses energy growth and a first estimation of the link memory are derived. The DM-NLSE is then linearized around the average signal field to get the amplitude/phase small-signal system matrix of the overall DM link, including pre- and postcompensation. By a singular-value decomposition of the small-signal DM link matrix, a novel expression of the memory of the optimized DM link is finally provided. Knowledge of such a memory is mandatory to run accurate numerical simulations and laboratory measurements with a sufficiently long pseudorandom bit sequence to avoid patterning effects.

A simple formula for the degree of polarization degraded by XPM and its experimental validation

We derive a closed-form expression for the DOP of polarized signals affected by XPM, in a modulated pump-probe scheme. Results are checked against simulations and experiments on a dispersion managed 3 /spl times/100 km link.

Comparison of the Jones matrix analytical models applied to optical system affected by high-order PMD

The analytical models for the Jones matrix of an optical fiber affected by high-order polarization-mode dispersion (PMD) are studied in an original comparative analysis with the purpose of finding a useful, precise, and stable tool for the system performance evaluation. First, a preliminary deterministic study is done to explain how the conceptual difference among the models reflects onto their representation of the fiber PMD effects in terms of Jones matrix coefficients and dispersion vector. Then, the analytical models with PMD up to third order are exploited for the calculation of the outage probability on the sensitivity penalty at the receiver, and the results obtained are compared with those of the discrete random wave-plate numerical model, assumed as a faithful description of the real fiber. Two different approaches are used for the outage probability evaluation: an analytical method, which is precise and faster but can only be used with PMD parameters up to second order, and a semi-analytical method that allows a comparison of the numerical and analytical results with homogeneity, when the statistics of high-order PMD are not known. The analytical model, which describes the dispersion vector as rotating on a circumference in the Stokes space, is found to be the most accurate in the system performance computation.

Fundamental laws of parametric gain in periodic dispersion-managed optical links

A general theory of the parametric gain of amplified spontaneous emission (ASE) noise in periodic dispersion-managed (DM) optical links is presented, based on a linearization of the nonlinear Schrodinger equation around a constant-wave input signal. Closed-form expressions are presented of the in-phase and quadrature ASE power spectral densities (PSDs), valid in the limit of infinitely many spans, for a limited total cumulated nonlinear phase and in-line dispersion, a typical case for nonsoliton systems. PSDs are shown to solely depend on the in-line cumulated dispersion and on the so-called DM kernel. Kernel expressions for both typical terrestrial and submarine DM links are provided. By Taylor expanding the kernel in frequency, we introduce a definition of DM map strength that is more appropriate for limited nonlinear phase DM systems with lossy transmission fibers than the standard definition for soliton systems. Various important special cases of PSDs are discussed in detail. Novel insights, to our knowledge, into the effect of a postdispersion-compensating fiber on such PSDs are included. Finally, examples of application of the PSD formulas to the performance evaluation of both on-off keying and differential phase keying modulated systems are provided.

An Alternative Analysis of Nonlinear Phase Noise Impact on DPSK Systems

We propose an alternative analysis of the impact of nonlinear phase noise in DPSK systems with realistic receivers, showing that ASE noise is Gaussian after practical optical filtering, which allows using known exact BER formulae.

A deterministic emulator for the statistical reproduction of a real fiber with accurate PMD statistics up to the third order

A novel deterministic polarization-mode dispersion (PMD) emulator, consisting of delay-sections coupled by rotators is proposed. By opportunely choosing the rotation angles, this device is shown to correctly reproduce the higher order PMD statistics with a reduced number of sections.

Jones transfer matrix for polarization mode dispersion fibers

With the advent of long distance high bit rate optical systems, polarization mode dispersion (PMD) has become an important source of limitation for the system performance. In a first order approximation, PMD, that is described by a differential group delay (DGD) between two orthogonal states of polarization (PSPs), causes an undesired output pulse broadening; the frequency dependence of DGD and PSPs produces other distorting effects, considered as higher order PMD effects. A useful theoretical means of predicting the overall distortion of the transmitted signal is the evaluation of the Jones transfer matrix of the fiber but, unfortunately, the statistics of its coefficients are not available up to now. On the other hand, the statistical behavior of the three-dimensional dispersion vector, that characterizes the PMD of the fiber in the Stokes space and can be measured, is known up to a second order PMD approximation. Consequently, finding the analytical relationship between the PMD vector and the coefficients of the Jones matrix is mandatory. In the work, the tight methodology of calculating the Jones matrix, starting from the knowledge of the PMD vector, is shown. This new method is used to determine the output temporal pulse expression in a second order PMD approximation and it is applied to evaluate the performance of a system affected by PMD. The results obtained with the present model are compared to the performance evaluated by numerical simulations, where all order PMD effects are taken into account; our model gives a performance curve that is more accurate in the approximation of all order PMD effects.

Scaling Laws for Weakly-nonlinear WDM Dispersion Managed OOK Systems

We show that kerr-induced nonlinear effects in long-haul dispersion mapped WDM systems follow general scaling laws that quickly allow both a nding the best dispersion map and setting up accurate numerical simulations.