Numerical solution of Brillouin and Raman fiber amplifiers using bvp6c
Purpose - The purpose of this paper is to demonstrate an effective and faster numerical solution for nonlinear-coupled differential equations describing fiber amplifiers which have no explicit solution. MATLAB boundary value problem (BVP) solver of bvp6c function is addressed for the solution. Design/methodology/approach - Coding method with the bvp6c is introduced, signal evolution, threshold calculation method is introduced, gain and noise figure are plotted and superiority of the bvp6c solver is compared with the Newton-Raphson method. Findings - bvp6c function appears to be an effective tool for the solution fiber amplifier equations and can be used for different pump configurations of BFAs and RFAs. The excellent agreement between the proposed and reported results shows the reliability of the proposed threshold power calculation method. Research limitations/implications - The paper eases the work of the fiber optic research community, who suffer from two point BVPs. 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 the future studies. Practical implications - The main outcome of this paper is the numerically calculation of the threshold values of fiber amplifiers without the necessity of the experiment. The robustness improvement of the solution is that the solver is able to solve the equations even with the poor guess values and the solution can be obtained without the necessity of analytical Jacobian matrix. Originality/value - MATLAB bvp6c solver has proven to be effective for the numerical solution of nonlinear-coupled intensity differential equations describing fiber amplifiers with two-point boundary. values. Beside the signal evolution, thresholds of Brillouin and Raman fiber amplifiers can also be calculated by using the proposed solver. This is a notable and promising improvement of the paper, at least from a fiber optic amplifier designer point of view.
fiber amplifiers boundary value problems bvp6c function threshold nonlinear differential equations