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

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    A general theory of the parametric gain of amplified spontaneous emission (ASE) noise in periodic dispersionmanaged (DM) optical links is presented, based on a linearization of the nonlinear Schrödinger 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

    Jones Transfer Matrix for Polarization Mode Dispersion Fibers

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    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 effect

    A Simple and Useful Model for Jones Matrix to Evaluate Higher Order Polarization Mode Dispersion Effects

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    Starting from the differential equation that relatesthe Jones matrix of a polarization-mode dipersion (PMD) fiber toits output dispersion vector, the analytical expressions of the matrixcoefficients are determined in the case of a dispersion vectorrotating on a circonference in the Stokes space. This model, thatneeds only few parameters with known statistics, is applied to evaluatethe performance of an optical system. The results obtainedwith it and with other models proposed in literature are comparedto those evaluated by numerical simulations with all-order PMDeffects, showing that our model gives an accurate representation ofreal system performances

    Analytical evaluation of optical system impairments caused by high-order polarization-mode dispersion effects

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    The differential equation that relates the Jones matrix of a polarization-mode dispersion fiber to its output dispersion vector is solved for a dispersion vector that moves on a circumference in the Stokes space, It yields a new simple model that can be usefully exploited to calculate the pulse-broadening analytical expression and to evaluate the system performance in terms of outage probability. A comparison among the results obtained with it, with other models proposed in literature, and with the numerical DRW model show its best accuracy
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