Abstract
A modification of the finite difference scheme for thin dielectric layers is presented and implemented into the method of lines. The thin layers may be placed between two consecutive discretisation lines, i.e. no line is inside the layer. The analysis is based on the treatment of dielectric boundaries. So, formulas for the finite difference scheme at interfaces are given, too. The expressions are tested by determining the effective index of a slab waveguide with a very thin film-layer. A comparison with the analytical solution proves the accuracy of the derived formulas. Another test was the analysis of a Bragg-grating, here only the treatment of interfaces was checked. The modified difference scheme works very well in the TE-case whereas there remain problems for the TM-polarisation.
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Helfert, S.F., Pregla, R. Analysis of thin layers and discontinuities. Optical and Quantum Electronics 31, 721–732 (1999). https://doi.org/10.1023/A:1006929303579
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DOI: https://doi.org/10.1023/A:1006929303579