On the problem of normal modes of a waveguide

Various approaches to calculating normal modes of a closed waveguide are considered. A review of the literature was given, a comparison of the two formulations of this problem was made. It is shown that using a self-adjoint formulation of the problem of normal waveguide modes eliminates the occurrence of artifacts associated with the appearance of a small imaginary additive to the eigenvalues. The implementation of this approach for a rectangular waveguide with rectangular inserts in the Sage computer algebra system is presented and tested on hybrid modes of layered waveguides. The tests showed that our program copes well with calculating the points of the dispersion curve corresponding to the hybrid modes of the waveguide.