Discontinuous behaviour of polarization angular parameters at the poles of Poincare sphere

The behavior of four angular parameters describing polarization ellipse is analyzed in the vicinity of Poincare sphere poles. It is shown that the phenomenon of step-wise change of azimuthal angle of polarization ellipse at π/2 near poles s3 = ±1 is not accompanied by discontinuities in other parameters of polarization ellipse. In particular the dual system of angular parameters “amplitude-ratio angle and phase difference” do not experience any discontinuities near the poles s3 = ±1. The same is true for the area of polarization ellipse, which is shown to be continuous on the whole Poincare sphere. Analogously, step-wise change of phase difference at π near poles s1 = ±1 is not accompanied by any discontinuities in basic system of angular parameters “azimuth-ellipticity”. General features of angular parameters behavior are illustrated by the results of numerical modelling.