There is an emerging (non-fringe) field called “toroidal electrodynamics” that seems to enjoy the most purchase in condensed matter theory but is increasingly making headway in the vacuum:
Observation of Toroidal Pulses of Light
Abstract: The transverse electromagnetic waves are major information and energy carriers. In 1996, Hellwarth and Nouchi theoretically identified a radically different, non-transverse type of electromagnetic pulses of toroidal topology. These pulses, which are propagating counterparts of localized toroidal dipole excitations in matter and exhibit unique electromagnetic wave properties, have never been observed before. Here, we report the generation and characterization of such optical and terahertz Toroidal Light Pulses (TLPs), launched from tailored nanostructured metasurfaces comprising toroidal emitters. This achievement paves the way for experimental studies of energy and information transfer with TLPs, their space-time “entanglement”, and their light-matter interactions involving anapoles, localized space-time entangled excitations, skyrmions, and toroidal qubits that are of growing interest for the fundamental science of light and applications.
This field intersects with fringe physics involving the magnetic vector potential in that the primary toroid usually studied is a poloidal charge current configuration sporting an external curl free vector potential.
This is sometimes called a “longitudinal” vector potential*, which relates directly to the Aharonov Bohm effect on the phase of matter waves such as the electron as is typically affected in the Aharonov Bohm effect.
This, in turn, brings us back to the study of condensed matter.
*I won’t here take us further into the fringes involving “longitudinal scalar waves” that base their theories on longitudinal vector potential.