Analysis of solving multimode-coupled equations and its improvement for modulated fiber Bragg gratings.

An efficient numerical method to solve multimode-coupled equations with two point boundary conditions is improved. Our method [Abrishamian et al., Opt. Fiber Technol.13, 32-38 (2007)] based on theoretical matrix integration of coupled differential equations and then solving the system of equations by use of initial or final conditions would be straightforward and thus beneficial in comparison with previously used fundamental matrix methods that depend strongly on the initial guess. However, we found that the new analysis depends on how accurately the integrals of the matrix element are calculated. For accuracy in the matrix integration it is required to divide the system of equations into a large number of subsections. Then, the reflectivity calculated is found to be comparable to experimental data reported so far. The present method is highly applicable for simulation of any type of fiber Bragg gratings modulated by long period gratings.