“…To elucidate the underlying physics of observed OSHE under electron stimulation, scattering intensity of different multipole moments was investigated with the multipolar decomposition, where the calculated scattered field was decomposed into vector spherical harmonics according to the general multipole scattering theory ( 48 – 50 ) where P , M , T , Q αβ , and M αβ correspond to the electrical dipole, magnetic dipole, toroidal dipole, electrical quadrupole, and magnetic quadrupole; c is the speed of light in vacuum; α, β = x , y , z. Relevant components for edge excitation are P y , P z , M y , and Q αα , which are calculated with asymptotic far-field approximations for dipoles and quadrupoles in the presence of a substrate.…”