Non-reflecting boundary conditions for solving Maxwell’s equations in waveguides

Abstract

We present here a method for solving the electromagnetic wave–matter interaction, on the one hand in closed waveguides, single or multi-port, and on the other hand with infinite materials periodic in two directions. In this presentation, the guides are coaxial or rectangular, but extension to any regular guide section is straightforward. This paper presents a method for solving Maxwell’s equations in real or virtual waveguides, using a decomposition of the DtN operator, and also introduces an adapted basis of the solution space based on a variational formulation. Finally, 2D axisymmetric and 3D finite elements are used. The text presents a number of resolutions of guided plane-wave scattering problems in a material, confirming the validity of the method and its generality.