Coarse-grid computation of the one-way propagation of coupled modes in a varying cross-section waveguide

A one-way approximation is investigated for the computation of wave propagation in varying cross-section waveguides. The proposed method derives as a basic approximation of the extensively studied multimodal admittance method. When integrated with a Magnus scheme, this matrix one-way equation exhibits an unexpected behavior, as the deviation from the exact solution is minimum when only two discretization points per wavelength are taken. This peculiar property makes this method efficient to compute the wave propagation for a large variety of geometries, beyond the initially stated framework of weakly non-uniform waveguides.