On the symmetry of scattering matrix in waveguide circuits

The well‐known symmetry property of the scattering matrix relative to propagating modes becomes tricky in the case of arbitrary polarization or arbitrary complex modal functions, as in the case of waveguide polarizers and ortho‐mode transducers. A straightforward transformation between different modal bases for the guided waves leads to a loss of symmetry. Only by gaining a deeper insight on the properties of the scattering matrices and with separate transformations for the incident and reflected waves is symmetry recovered.