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 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.