Exploiting spatial transformations of the light state for precise ellipsometry

Two techniques are described for measuring polarization precisely: (1) Total internal reflection produces retardance that is an exact function of the incident angle, and can be the basis for an achromatic ellipsometer without wave plates useful within a limited angular field of view. (2) Rotation of a single linear polarizer always can be used to calibrate ellipsometers that are based upon insertable or rotating unknown Jones optical elements. Both techniques are based upon reversible processes in which the light-matter interaction does not change with the light path through the material. For all such processes there is a correspondence between transformations of the light state in physical space and transformations of the Stokes parameters on the Poincare sphere. This correspondence is important because it can be shown that the 3D transformation group for the Stokes parameters arises as a consequence of the definition of the Stokes parameters as quantum observables without referring to spatial characteristics for the light-state dual-element wave function. The correspondence is discussed.