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

作者：Sujecki S^*

来源：Opto-Electronics Review, 2011, 19(2): 145-150.

DOI：10.2478/s11772-011-0019-1

• finite differences
• optical waveguides
• guided waves

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(h(2)) truncation error only asymptotically for sufficiently small values of the mesh size.

• 出版日期2011-6