An improved algorithm for simulation of backward multipumped Raman amplifier

Abstract

ABSTRACT An adaptive step-size method for the coupled equations of multi-pumped broadband Raman amplifiers is proposed based on Runge-Kutta-Fehlberg methods. This algorithm adjusts the step-size appropriately according to the presupposed precision and the local truncation error of each step. Simulation results indicate that our adaptive step-size method improves the accuracy and the simulating speed efficiently compared with other traditional algorithms and suits the numerical simulation for fiber Raman amplifier. Keyword: multi-pumped fiber Raman amplifier; stimulated Raman scattering; Raman gain; local truncation error 1. INTRODUCTION Fiber Raman amplifier (FRA) has flexible gain range and low noise level. The use of distributed fiber Raman amplifier can lower amplified spontaneous emission noise power, allow for closer channel spacing and higher bit rates in wavelength division multiplexing (WDM) systems, and extend transmission distances [1]. For these advantages, FRA becomes a core component in dense wavelength division multiplexing (DWDM) systems. In practice, to avoid the crosstalk caused by pumps, FRA always uses backward pumps to decrease power fluctuation. The analysis of FRA with backward pumps is based on a set of Raman power coupled equations. It is a two-point boundary problem. It takes exhaustive computing time to achieve well-behaved results by using direct integration approach. Fortunately, some practical methods are proposed, such as average power analysis [2], multi-steps methods [3][4], which improve computing speed remarkably. But their main drawback is that the large number of manipulations is needed each time the step-size changes [5]. We expect a solution in which step-size follows the change of power. Smaller step-size is taken where power changes fast, and larger step-size with slow change of power. Methods for automatic step-size adjustment are often based on an estimate of the local truncation error. Runge-Kutta-Fehlberg (RKF45) methods can estimate the local truncation error of each step and be used to implement the variable step-size problem. In this paper, we propose an adaptive step-size method (ASM) based on RKF45. The proposed method can deal with adaptive step-size adjustment expediently and solve a two-point boundary value problem for the Raman amplifier propagation equations appropriately. * binwu@sdu.edu.cn ; phone 86-531-8361608