Composition law for polarizers

TL;DR

This paper explores the polarization process through polarizers, providing explicit polarization trajectories, a composition law akin to relativistic velocity addition, and a new measure for polarizer quality.

Contribution

It introduces a composition law for polarizers based on a relativistic analogy and defines a Wigner-like angle to quantify polarizer combinations.

Findings

Polarization trajectories are not always geodesics on the Poincaré sphere.

A composition law for polarizers similar to relativistic velocity addition is derived.

A Wigner-like angle quantifies the combined effect of successive polarizers.

Abstract

The polarization process when polarizers act on an optical field is studied. We give examples for two kinds of polarizers. The first kind presents an anisotropic absorption - as in a polaroid film - and the second one is based on total reflection at the interface with a birefringent medium. Using the Stokes vector representation, we determine explicitly the trajectories of the wave light polarization during the polarization process. We find that such trajectories are not always geodesics of the Poincar\'e sphere as it is usually thought. Using the analogy between light polarization and special relativity, we find that the action of successive polarizers on the light wave polarization is equivalent to the action of a single resulting polarizer followed by a rotation achieved for example by a device with optical activity. We find a composition law for polarizers similar to the composition law for noncollinear velocities in special relativity. We define an angle equivalent to the relativistic Wigner angle which can be used to quantify the quality of two composed polarizers.