Solution of Raman fiber amplifier equations using MATLAB BVP solvers

Abstract

Purpose - The purpose of this paper is to demonstrate an effective and robust numerical solution for Raman fiber amplifier (RFA) equations which have no explicit solution. MATLAB BVP solvers are addressed for the solution.

Design/methodology/approach - The continuation method proposed for the solution of RFA equations using MATLAB BVP solvers is explained. Scripts for improving the power values at the boundaries with continuation, extending fiber length with continuation and calculation of the analytical partial derivatives using the MATLAB Symbolic toolbox are introduced. Comparisons among the different MATLAB BVP solvers have been made. Using the continuation method, signal evolutions for different kinds of RFA amplifier configurations are plotted.

Findings - The paper finds that MATLAB BVP solver with the continuation method can be used in the design of various kinds of RFAs for high powers/long gain fiber spans.

Research limitations/implications - The paper will assist the fiber optic research community who suffer from two or more point boundary-value problems. Moreover, the stiffness of the signal evolution which is faced with high pump powers and/or long fiber lengths can be solved with continuation. This superiority of the solver can be used to overcome any stiff changes of the signals for future studies.

Practical implications - The increased research interests and practical demands for RFAs have been calling for reasonable and efficient means for the performance evaluation of RFAs before the real amplifiers are fabricated. The solution method presented in this paper will be an efficient means for the solution of this issue.

Originality/value - MATLAB BVP solvers have been proven to be effective for the numerical solution of RFAs with multiple pumps and signal waves. Using the continuation method, in a distributed RFA with ten pump sources, 2,400 mW total input pump power is achieved. The improvement of the total power is about 1.4 times compared with those of the previously reported methods. Using the MATLAB BVP solvers, total power/fiber span can be improved further using the continuation process with the cost of computational time. This is a notable and promising improvement from a RFA designer's point of view.