A Comprehensive Approach to Polarization Evolution

We extend earlier work on polarization conventions and provide a comprehensive analysis of the effect of both complex sign convention (CSC) and mapping conventions on the representation of Jones and Stokes polarization transformations. Both CSC forms are applied in parallel throughout the text to show their similar and dissimilar properties. Conditions for consistent translation of basis transformations for both CSCs and both representations are developed, and we show the details of an Euler angle approach that aids in those translations. Connecting to Stokes' original paper, we also reformulate the fundamentals of Stokes vectors, developing consistency constraints on their representations and illustrating violation of these by at least one well-known reference.