On the Choice of Conventions in Polarization Evolution Calculations and Representations

Calculations involving polarization propagation in dielectric media require the adoption of various, often unstated, conventions, an important one of which is the sign of the complex argument
$\mathbf {\pm {i}(\boldsymbol{\omega } {t} - \boldsymbol{\beta } {z})}$
. In this paper we show that the form of the dielectric tensor and, hence, the forms of both the Jones and Stokes representations of states, operators, and transformations depend on that sign choice. We show that, while physical observables cannot depend on the choice of convention, errors and ambiguities can occur if adherence to the various conventions is not followed consistently. By methodically developing polarization propagation in both sign conventions we provide a means for unambiguous comparison of results from analyses that employ different, sometimes mixed, conventions. We also include conventions such as assignment of Pauli matrices to Stokes axes and choice of chirality for circular polarizations.