A General Model for Linearly Polarized Optical Vector Beams

TL;DR

This paper introduces a comprehensive model for inhomogeneously polarized vector beams using a complex scalar potential and Lagrangian energy density, unifying phase and polarization considerations.

Contribution

It presents a novel formulation that incorporates polarization inhomogeneities via a simple addition to the complex potential phase, linking polarization and phase energetically.

Findings

Polarization inhomogeneities can be modeled by adding a spatially dependent angle.

The complex scalar potential naturally arises from polarization symmetry considerations.

A new definition of linear momentum density offers advantages for inhomogeneous beams.

Abstract

We propose an approach for deriving a broad class of propagation models for inhomogeneously, linearly polarized ``vector'' beams. Our formulation leverages a complex scalar potential along with an appropriately constructed Lagrangian energy density. Importantly, we show that polarization inhomogeneities can be included by simple addition of a spatially dependent polarization angle to the complex potential phase. Thus, phase and polarization are seen to be equivalent from an energy perspective. As part of our development, we also show how the complex scalar potential arises naturally when considering polarization angle as a field symmetry during construction of the Lagrangian. We further show that the definition of linear momentum density in terms of the complex potential holds a distinct advantage over the conventional definition for inhomogeneously polarized beams.