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 Schrödinger 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 RP solution coincides with the order 2 + 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 firstorder ERP solution to be fairly accurate for terrestrial dispersionmapped systems up to launched peak powers of 10 dBm.

On the Accuracy of the Gaussian Nonlinear Model for Dispersion-unmanaged Coherent Links

“…Each channel had 4096 random symbols and random carrier state of polarization (SOP). Fiber propagation was modeled using either the enhanced first order regular perturbation (eRP) 9 or the logarithmic perturbation (LP) 10 , and solved using the algorithm in 9 . Polarization mode dispersion (PMD) was neglected.…”

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

“…Thus, in order to gain physical insight about the effect of pre-and postcompensation on the DM-NLSE (3), we search for an enhanced regular perturbation solution in 1 [27], [30]. The initial condition is , with being the unchirped field transmitted by the laser source and the precompensation.…”

“…We start with a change of variable that removes the average nonlinear cumulated phase and the inline cumulated GVD (11) and then expand the new field in series of 1 . Using such an expansion in (11), and the result into (3), it is possible to solve iteratively (3) by equating equal powers in 1 [30]. If we stop the series to first power in 1…”

Statistical evaluation of transmission performance degradation originating with cross‐phase modulation

“…The RP method uses the expansion in terms of γ n [5], in which the order n of γ corresponds to the order of the higher-order effect.…”

“…Other methods of deriving approximate solutions are the Volterra method [4] and the regular perturbation (RP) method [5]. In these methods, the solution of the nonlinear Schrödinger equation is represented by a series expansion using the nonlinear coefficient γ, where the first-order term of the expansion corresponds to the transfer function in the filtering method.…”