Standard form of the scattering matrix for time reversal symmetric system

In this paper, we present the standard form of the scattering matrix of mesocopic system with spin-orbital coupling which preserves time reversal symmetry. We found some analytical structure of the scattering matrix related to the sub-matrices between arbitrary two channels. In particular, we proved that in the two-terminal mono-channel scattering problem, the transmission matrix is proportional to a SU(2) matrix. We obtained these properties through direct and elementary way and found it in agreement with polar decomposition known before.