Ray-wave dual descriptions of classical light and birefringence: a path integral story

Abstract

I discuss how light propagation, both wave and ray dual aspects, can be implemented and its origin within a Feynman path integral approach. This can be done for both scalar fields and the full vectorial field descriptions of classical electromagnetism as applied to imaging problems. A key part of this scheme is in generalising the standard optical path length integral from a scalar to a matrix quantity. Reparametrization invariance along rays allows a covariant formulation where propagation can take place along a general curve. The current programme then gives a practical realisation of both gauge invariance and differential geometry concepts. As a specific example, a general gradient index (GRIN) rod fiber background is used to demonstrate the scheme. Calculations such as the evaluation of the Gouy phase, and parallel transport of states of polarisation provide examples of applicability of the scheme. As a particular noteworthy example and application, I show how the current approach allows for the evaluation of observable effects in GRIN lens cascades where additionally there is a spatially varying birefringence. This is a prime candidate for a perturbative Feynman diagram evaluation since the birefringence is much smaller than the bulk refractive index.