Poincar\'e sphere representation for spatially varying birefringence

TL;DR

This paper introduces a four-dimensional Poincaré hypersphere to represent spatially varying birefringence, providing an intuitive geometric framework to analyze polarization transformations and their impact on optical image quality.

Contribution

It extends the Poincaré sphere concept to a hypersphere for spatially varying birefringence, enabling better visualization and understanding of polarization effects in optical systems.

Findings

Provides a geometric description of birefringence effects

Quantifies impact on optical image quality

Offers a new visualization tool for polarization transformations

Abstract

The Poincar\'e sphere is a graphical representation in a three-dimensional space for the polarization of light. Similarly, an optical element with spatially varying birefringence can be represented by a surface on a four-dimensional "Poincar\'e hypersphere". A projection of this surface onto the traditional Poincar\'e sphere provides an intuitive geometric description of the polarization transformation performed by the element, as well as the induced geometric phase. We apply this formalism to quantify the effects of birefringence on the image quality of an optical system.