Reciprocity in the wave reflection and transmission problem: Part 1. Symmetry of the matrices of reflection coefficients

The reciprocity theorem in Lyamshev’s formulation is used to derive a general symmetry relationship for the matrices of reflection coefficients in homogeneous media and one-dimensional waveguides. This relationship is shown to be equivalent to the normalization of the amplitudes by the cross power flux of the forward and backward waves. The relationship is valid for both propagating and evanescent waves, and all the symmetry relationships known from the literature represent its particular cases.