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

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.

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

“…Firstly, let us recap 7,8 the path integral form that we will apply to a general refractive index media of the gradient index (GRIN) type. We choose a GRIN media because it brings out general features that may be overlooked in a piecewise constant refractive index background.…”

“…To start with, we will just write down the final form the path integral takes in either phase space or configuration space (for details see 8 )…”

“…An important aspect of this approach is the removal of gauge degrees of freedom to obtain physical results. Subsequently in, 8 this was further extended by firstly elucidating more on gauge invariance and fixing in path integrals, and secondly, moving to a full vector description (thereby including polarization). Details are presented on gauge invariance and gauge fixing in the path integral in terms of the Faddeev-Popov determinant.…”

“…In this current work we firstly review the path integral formalism as described in. 8 Then we turn to examples based on the quadratic GRIN media. It is also a topic of current practical value and research.…”

Rays, waves, SU(2) symmetry and geometry: toolkits for structured light

“…The preponderance of wave-like or ray-like property can be actually controlled by the parameters in SU(2) wave-packet. It is also worth to note that the ray-wave duality effect discussed above originates from laser cavity optomechanism, it is also available to study the ray-wave duality in general freespace electromagnetic fields [50,58,59], which should have more flexible applicability beyond the limit of laser cavity condition.…”