Ray-Wave Duality of Electromagnetic Fields: A Feynman Path integral Approach to Classical Vectorial Imaging

TL;DR

This paper introduces a novel Feynman path integral framework for classical vectorial imaging that incorporates polarization by generalizing the optical path length to a matrix form, enabling covariant descriptions of light propagation.

Contribution

It presents a new matrix-based path integral approach to model polarization effects in classical optics, extending the scalar methods to include vectorial properties.

Findings

Provides a covariant formulation of light propagation with polarization.

Demonstrates the approach using a gradient index background.

Enables analysis of rapidly varying polarization in imaging systems.

Abstract

We consider how vectorial aspects (polarization) of light propagation can be implemented, and its origin, within a Feynman path integral approach. 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 the rays allows a covariant formulation where propagation can take place along a general curve. A general gradient index background is used to demonstrate the scheme. This affords a description of classical imaging optics when the polarization aspects may be varying rapidly and cannot be neglected.