Elliptic polarization represented by the Carter and Smith charts

The graphical method using the Poincaré sphere for representing elliptically polarized light is based on the fact that the latitude and longitude of a point on the unit-radius sphere represent the ellipticity and the azimuth of the corresponding light ellipse. Stereographic projections of the unit-diameter Poincaré sphere either on a western plane tangent at the equator of the sphere or on an equatorial plane tangent to either of the poles lead to a representation of any elliptical polarization state on the so-called Carter charts, while charts derived from orthographic projections in the Poincaré sphere and consisting again of families of orthogonal circles traced inside either the equator or the principal meridian of the unit-radius Poincaré sphere yielding either ellipticity-azimuth or amplitude ratio-phase angle niveau lines constitute the Smith charts. Both types of charts consist of families of orthogonal circles. These families of circles, traced on either chart and corresponding to parametric families with different properties for the corresponding elliptically polarized light, yield an easy and accurate solution to the problem of graphical evaluation of the optical properties of the resulting polarization state when an elliptically polarized plane wave is passing through different optically active elements.