I have recently realized that in my paper “Wavelength-flattened directional couplers: a geometrical approach” [1], I made a wrong statement about reciprocity of some of the transformations. On page 7142, the claim “It can be shown [2] that the time reversal combined to the unitarity condition implies ${{\textbf{U}}^\dagger} = {{\textbf{U}}^*}$” or, in other words, that the matrix ${\textbf{U}}$ must be symmetric, is incorrect. The demonstration in the cited reference [2] deals with the scattering matrix of reciprocal systems with uniform scalar permittivity and permeability, which indeed must be symmetric, and therefore of the form

Nevertheless, the matrices ${\textbf{U}}$ studied in the paper were not scattering matrices but transfer matrices instead. The transfer matrix ${\textbf{T}}$ associated to a scattering matrix ${\textbf{S}}$ can be easily derived as