Accuracy of three-point finite difference approximations for optical waveguides with step-wise refractive index discontinuities

Abstract

A rigorous truncation error analysis of three-point finite difference approximations for optical waveguides with step-wise refractive index discontinuities is given. As the basis for the analysis we use the exact coefficients of the series that expresses the field value at a given finite difference node in terms of the field value and its derivatives at a neighbouring node. This series is applied to develop a rigorous formalism for the truncation error analysis of the three-point finite difference approximations used in the numerical modelling of light propagation in optical waveguides with step-wise discontinuities of the refractive index profile. The results show that the approximations reach O(h2) truncation error only asymptotically for sufficiently small values of the mesh size.

Simple and efficient method of lines based algorithm for modeling of erbium doped Q-switched fluoride fiber lasers

“…A standard first order accurate algorithm is presented that was adapted from the field of semiconductor laser modelling [17]. Then the concept of the Extended Taylor Series (ETS) [18][19][20][21] is applied to derive second order finite difference (FD) approximations and develop a FD-MOL algorithm for modelling Q-switched erbium doped fluoride glass fiber lasers. It is shown that the FD-MOL using second order finite difference approximations is significantly more efficient than the one using the first order approximations.…”