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

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 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.