A Property of Symmetric Hybrid Waveguide Junctions (Correspondence)

It is well known that in symmetric hybrid junctions such as the short-slot, branched-guide, and transvar types, the signals in the main and auxiliary guides are in phase quadrature. Another property of fully symmetric lossless hybrids is that if all the arms are matched, the amplitudes of the waves traveling in the reverse direction in the main and auxiliary guides are equal. A proof is given below.