Stereographic coordinates for simpler far-field radiation analysis

TL;DR

This paper introduces a stereographic coordinate system for analyzing far-field radiation that avoids singularities and naturally incorporates Ludwig polarization, simplifying automated radiation pattern analysis.

Contribution

The paper proposes a novel stereographic coordinate system for far-field radiation analysis that eliminates singularities and integrates Ludwig polarization naturally.

Findings

Coordinates have no singularities over the far-field hemi-sphere.

Ludwig polarization basis arises naturally from the stereographic coordinates.

Simplifies automated analysis of radiation patterns.

Abstract

A coordinate system is proposed for the purposes of analysis of far-field radiation from a localized source at the origin. The proposed coordinates exhibit no singularities over the far-field hemi-sphere, making them a good choice for automated radiation pattern analysis. Finally, it is shown that Ludwig polarization basis, commonly used to represent polarization of the far-field radiation, arises naturally, as a coordinate basis, when one uses stereographic coordinates.