to characterize the electrodynamic environment.

An important special case is that of transverse, propagating fields, where$$\mathbf{E}^{2}-\mathbf{B}^{2}=0,\quad\mathbf{E\cdot B}=0. \label{aj6}$$ The properties (\[aj6\]) lead to radiation fields as sometimes being called null fields. (The terms radiation field, propagating field, transverse field, plane-wave field, are here used interchangeably.) Radiation fields propagate at the speed of light in vacuum, and they have the unique character that, after initial formation, they propagate indefinitely in vacuum without the presence of sources.

However, the invariants (\[aj6\]) are not unique to radiation fields; they apply also to constant crossed fields. That is, it is always possible to generate static electric and magnetic fields of equal magnitude that are perpendicular to each other, and will thus possess zero values for both of the Lorentz invariants of the electromagnetic field. Constant crossed fields do not propagate, and they cannot exist without the presence of sources. They are unrelated to radiation fields despite sharing the same values of the Lorentz invariants. Most importantly, constant crossed fields cannot be considered as the zero-frequency limit of radiation fields, as they are sometimes described [@nikrit66; @ritus85]. All radiation fields propagate at the speed of light for all frequencies, no matter how low. There is 