OThD3.pdf' A novel perturbat'ion method for silgnal-noilse i'nteractilon i*n nonlinear dispersive fibers M. Secondini and E. Forestieri Scuola Superiore Sant Anna and Photonics Network National Laboratory, CNIT, Via G. Moruzzi 1, I-56124 Pisa, Italy marco.secondinioa cnit. it C. R. Menyuk University of Maryland Baltimiore County, CSEE Dept., 1000 Hilltop Circle, Baltimore, MD, USA 21250 Abstract: A novel perturbation method for signal-noise interaction in nonlinear dispersive fibers is presented. It is simple and, more accurate than the regular perturbation method, and is suitable for system performance analysis. ( 2006 Optical Society of America OCIS codes: (060.2330) Fiber optics communications; (060.2360) Fiber optics links and subsystems 1 Introduction The propagation of light in optical fibers is governed by the nonlinear Schrodinger equation (NLSE) and its modifica- tions. In systems operating in the linear regime, the ASE noise introduced by amplifiers is not affected by propagation through the fiber, and can be modeled as additive white Gaussian noise (AWGN) at the end of the link. On the other hand, when nonlinear effects are not negligible, signal and. noise interact during propagation, and the noise may become colored or even non-Gaussian. In some previous work [1L-3], this problem has been tackled by a regular perturbation (RP) expansion of the NLSE. For a small perturbation, only the first order term of the RP can be retained, and, the NLSE can be linearized. More recently, other works have shown that a simple linearization does not hold in many cases [4], and second-order terms may not be simply neglected, since they can produce a strong degradation of the system performance [51. In this paper, we introduce a novel perturbation approach to the NLSE, derived by a com- bination of the RP and the logarithmic perturbation (LP) described in [6,7]. The intuitive idea behind this approach, like in [4], is that the nonlinearity produces phase rotations and so at high powers one wishes to perturb the phase and amplitude, rather than the two quadratures of the signal as is done in the R-P approach. The difficulty when perturbing the amplitude and phase is to avoid singularities at low power, and our approach does that. We derive a set of differen- tial equations for the propagation of the perturbed solution of the NLSE. As in the R-P approach, the equations can be linearized. The resulting linear model is very simple, but much more robust than the linearized, RP model, and, can be used for the evaluation of system performance. Some examples are considered that show excellent agreement of the approach with simulations even in regimes where the RP approach fails. 2 The combined regular-logarithmic perturbation (CRLP) As done in [1-3], we make the hypothesis that, for the purpose of investigating the interaction between signal and noise, the signal can be considered as a continuous wave (CW), and, the noise can be treated as a perturbation of the CW solution of the NLSE au P2 a2U 2 j 2 az =jat2-Y 2-2:(1 where u is the normalized electrical field, 12 is the chromatic dispersion coefficient, y is the nonlinear coefficient, and oc is the attenuation. We note however that this approach can be extended to fully modulated. signals. Combining the R lP with the logarithmic perturbation (LP) described in [6,7], we write the perturbed solution of the NLSE as u (z, t) Po[+a(zt) jb(z, t)]exp(-ocz/2)exp{-i[L +L (z, t)] (2) Equation (2) is inspired by the evidence that the LP approach to the solLution of the NLSE can be rmore accurate than the introduced in [4]. The termrs P0L exp(-ocz/2), and exp(-j NT ) take into account power, attenuation, and nonlLinear p:hase rotation of the noise-free solution, respective:ly, w:hereas az (z, t) and. b (z, t) are the RltP terms, and (z, t) is the LP term. Su.bstituting (2) in (1), after some algebraic manlipu.lation, equ.ation (11) can be split inlto a system of three