  The vector cross product and pseudoscalar dot products of electric (E) and
magnetic (H) fields are separately finite in vacuum transverse electric and
magnetic (TEM) plane waves, and angular momentum structured light. Current
theories of interactions beyond the standard model of particle physics invoke
non-zero dot(E,H) as the source term in the axion law that describes
interactions with the cosmological dark matter axion particles outside of the
quartet of Maxwells equations. The non-zero dot(E,H) also drives relativistic
spin-charge magnetoelectric excitations of axion quasiparticles at a
distinctively higher condensed matter scale in magnetic and topological
materials. Yet, how to drive coherent dot(E,H) responses is unknown, and
provides motivation to examine the field polarizations in structured light on a
deep sub-diffraction limited spatial scale and sub-optical cycle temporal scale
by ultrafast nonlinear photoemission electron microscopy. By analytical theory
and ultrafast coherent photoemission electron microscopy, we image dot(E,H)
fields in surface plasmon polariton vortex cores at subwavelength scales, where
we find that the magnetoelectric relative to the dipole density is intensified
on a ~10 nm diameter scale as a universal property of plasmonic vortex fields.
The generation and nanoscale localization of dot(E,H) fields introduces the
magnetoelectric symmetry class, having the parity and time reversal broken, but
the joint parity-time reversal symmetry preserved. The ability to image the
optical fields of plasmonic vortex cores opens the research of ultrafast
microscopy of magnetoelectric responses and interactions with axion
quasiparticles in solid state materials.
