An appropriate Way to display the state of polarization is the representation via the Poincaré sphere.
The center of the Poincaré sphere is located in the origin of a Cartesian coordinate system. The three normalized Stokes Parameter S1, S2 and S3 may be regarded as the Cartesian coordinates of a point P on a sphere of radius S0. The azimuth and ellipticity angles of the polarization ellipse can be mapped uniquely onto spherical angular coordinates with 2X to the latitude and 2(Psi) to the altitude position.
Each point P on the Poincaré sphere describes a defined state of polarization of a plane monochromatic wave of a given constant intensity S0.
Since X is positive or negative the polarization is right-handed or left-handed. The points lying above the equatorial plane represent right-handed states of polarization and respectively points lying below the equatorial plane represent left-handed states. The equatorial plane itself represents all linear states of polarization. Right-handed circular polarization is represented by the North Pole (S1=S2=0, S3=S0) and left-handed circular polarization by the South Pole (S1=S2=0, S3=-S0).
All other points on the upper (lower) half sphere correspond to elliptical states of polarization with right (left) handed rotation. Poincaré’s representation is very useful in crystal optics for determining the effect of crystalline media on the state of polarization of light traversing it.