Plasmonic vortices host magnetoelectric interactions

The vector <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi mathvariant="bold">E</a:mi><a:mo>×</a:mo><a:mi mathvariant="bold">H</a:mi></a:mrow></a:math> and pseudoscalar <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi mathvariant="bold-italic">E</d:mi><d:mo>·</d:mo><d:mi mathvariant="bold-italic">H</d:mi></d:mrow></d:math> products of electric and magnetic 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 <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi mathvariant="bold-italic">E</g:mi><g:mo>·</g:mo><g:mi mathvariant="bold-italic">H</g:mi><g:mo>≠</g:mo><g:mspace width="0.16em"/><g:mn>0</g:mn></g:mrow></g:math> as the source term in the axion law that describes interactions with the cosmological dark matter axion particles outside of the quartet of Maxwell's equations. <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:mi mathvariant="bold-italic">E</k:mi><k:mo>·</k:mo><k:mi mathvariant="bold-italic">H</k:mi><k:mo>≠</k:mo><k:mspace width="0.16em"/><k:mn>0</k:mn></k:mrow></k:math> 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 <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"><o:mrow><o:mi mathvariant="bold-italic">E</o:mi><o:mo>·</o:mo><o:mi mathvariant="bold-italic">H</o:mi></o:mrow></o:math> response is unknown, and provides motivation to examine the field polarizations in structured light on a deep subdiffraction limited spatial scale and suboptical cycle temporal scale by ultrafast nonlinear photoemission electron microscopy. By analytical theory and ultrafast coherent photoemission electron microscopy, we image <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"><r:mrow><r:mi mathvariant="bold-italic">E</r:mi><r:mo>·</r:mo><r:mi mathvariant="bold-italic">H</r:mi></r:mrow></r:math> fields in surface plasmon polariton vortex cores at subwavelength scales, where we find that the magnetoelectric relative to the dipole density is intensified on an ∼10-nm-diameter scale as a universal property of plasmonic vortex fields. The generation and nanoscale localization of <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"><u:mrow><u:mi mathvariant="bold-italic">E</u:mi><u:mo>·</u:mo><u:mi mathvariant="bold-italic">H</u:mi></u:mrow></u:math> fields introduces the magnetoelectric symmetry class, having the parity <x:math xmlns:x="http://www.w3.org/1998/Math/MathML"><x:mi mathvariant="script">P</x:mi></x:math> and time reversal <z:math xmlns:z="http://www.w3.org/1998/Math/MathML"><z:mi mathvariant="script">T</z:mi></z:math> broken, but the joint <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML"><bb:mrow><bb:mi mathvariant="script">P</bb:mi><bb:mi mathvariant="script">T</bb:mi></bb:mrow></bb:math> 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.