The RP method: a new tool for the iterative solution of the nonlinear Schrodinger equation

Abstract

An original approach to the solution of the nonlinear Schrodinger equation (NLSE) is pursued in this paper, following the regular perturbation (RP) method. Such an iterative method provides a closed-form approximation of the received field and is thus appealing for devising nonlinear equalization/compensation techniques for optical transmission systems operating in the nonlinear regime. It is shown that, when the nonlinearity is due to the Kerr effect alone, the order n RP solution coincides with the order 2n + 1 Volterra series solution proposed by Brandt-Pearce and co-workers. The RP method thus provides a computationally efficient way of evaluating the Volterra kernels, with a complexity comparable to that of the split-step Fourier method (SSFM). Numerical results on 10 Gb/s single-channel terrestrial transmission systems employing common dispersion maps show that the simplest third-order Volterra series solution is applicable only in the weakly nonlinear propagation regime, for peak transmitted power well below 5 dBm. However, the insight in the nonlinear propagation phenomenon provided by the RP method suggests an enhanced regular perturbation (ERP) method, which allows the first order ERP solution to be fairly accurate for terrestrial dispersion mapped systems up to launched peak powers of 10 dBm.