Ray-wave duality of electromagnetic fields: a Feynman path integral approach to classical vectorial imaging

We consider how vectorial aspects (polarization) of light propagation can be implemented and their origin within a Feynman path integral approach. A key part this scheme is in generalizing the standard optical length from scalar to matrix quantity. Reparametrization invariance along rays allows covariant formulation where take place general curve. gradient index background used demonstrate scheme. This affords description classical imaging optics when polarization may varying rapidly cannot neglected.