Bremmer series for the multimodal sound propagation in inhomogeneous waveguides

The method of Bremmer series is presented and implemented for the multimodal sound propagation in a waveguide with varying cross-section. The solution is constructed iteratively by summing terms of increasing order, with each order representing the number of scattering events. This formulation generalizes to higher dimensions the series decomposition proposed by Bremmer in one-dimensional inhomogeneous media, and it also gives an insight on the complex wave scattering of the coupled guided modes. The accuracy and convergence of the solution are inspected and a comparison is made with the one-way coupled mode equation derived assuming no reflected waves. It is notably shown that the first-order Bremmer series, simply obtained by quadrature, is a relevant alternative to classical WKB or one-way approximations.