First-principle variational formulation of polarization effects in geometrical optics

TL;DR

This paper develops a classical variational framework to describe polarization effects, including ray bending and spin precession, in electromagnetic wave propagation through isotropic dielectric media with local dispersion.

Contribution

It introduces a novel Lagrangian formulation that captures polarization-driven effects in geometrical optics, extending beyond traditional Berry connection approaches.

Findings

Derivation of Lagrangians for polarization effects from first principles

The theory applies to eigenrays, continuous waves, and entangled polarization states

Framework accommodates generalizations to various media

Abstract

The propagation of electromagnetic waves in isotropic dielectric media with local dispersion is studied under the assumption of small but nonvanishing $\lambda/l$, where $\lambda$ is the wavelength, and $l$ is the characteristic inhomogeneity scale. It is commonly known that, due to nonzero $\lambda/l$, such waves can experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the wave "spin". The present work reports how Lagrangians describing these effects can be deduced, rather than guessed, within a strictly classical theory. In addition to the commonly known ray Lagrangian featuring the Berry connection, a simple alternative Lagrangian is proposed that naturally has a canonical form. The presented theory captures not only eigenray dynamics but also the dynamics of continuous wave fields and rays with mixed polarization, or "entangled" waves. The calculation assumes stationary lossless media with isotropic local dispersion, but generalizations to other media are straightforward to do.