Order dependence and independence of weak polarization elements

The order dependence of weak polarization elements is investigated and it is shown that weak polarization elements are very weakly order dependent; if the diattenuation or retardance is a small term, the order dependence is a higher order term. This has particular application to the polarization properties of an arbitrary ray path through a sequence of antireflection coatings. The polarization properties are explored through expansion of Jones matrices into sums of Pauli spin matrices. It is shown that the polarization properties of a meridional ray path are independent of the order in which the interfaces are encountered, and that the ray path will act as a linear diattenuator aligned or perpendicular to the meridional plane and/or as a linear retarder aligned or perpendicular to the meridional plane. A skew ray does have order dependence in its polarization properties. Due to these order dependent terms, the ray path in general acts as an elliptical diattenuator and/or retarder, despite the fact that all individual interfaces act only as linear polarization elements.