The electromagnetic symmetry sphere: a framework for energy, momentum, spin and other electromagnetic quantities

TL;DR

This paper introduces the electromagnetic symmetry sphere framework, unifying various electromagnetic quantities and revealing underlying symmetries and mathematical structures through different basis projections of electromagnetic fields.

Contribution

It proposes a novel framework that unifies electromagnetic quantities using multiple bases, highlighting symmetry structures and their implications for light-matter interactions.

Findings

Reveals a Bloch sphere structure for electromagnetic energy asymmetries

Unifies electromagnetic quantities through basis projections

Derives symmetry-driven equations in light-matter interaction

Abstract

Electromagnetic quantities such as energy density, momentum, spin, and helicity bring meaning and intuition to electromagnetism and possess intricate interrelations, particularly prominent in complex non-paraxial near-fields. These quantities are conventionally expressed using electric and magnetic field vectors, yet the electric-magnetic basis is one among other often overlooked alternatives, including parallel-antiparallel and right-left-handed helicity bases, related to the parity and duality symmetries of electromagnetism. Projecting time-harmonic electromagnetic fields into a variety of bases allows re-interpreting established quantities and reveals underlying mathematical structures: a Bloch sphere which describes asymmetries in electromagnetic energy, a systematic path to unify and uncover relations between electromagnetic quantities, and the unlocking of symmetry-driven equations in light-matter interaction.