Helmholtz decomposition analysis of electron energy loss: differentiating resonances on polarization and radiation eigenmodes

Abstract

Helmholtz decomposition is a powerful mathematical tool for investigation and analysis of vector fields, particularly in electrodynamic systems. In this paper, we apply it to electron energy loss spectroscopy of magnetically inactive structures to get insight into field composition of energy losses. The obtained results show that losses are incurred through two pathways—excitation of transverse/longitudinal fields by solenoidal/conservative currents. Separation of these processes gives us important information about the fields and the type of eigenmodes (polarization or radiation) being in resonance with the electron beam. Capabilities of such analysis are demonstrated in the study case of metal nanofilms and nanodiscs, where we perform differentiation of the resonances that have occurred on plasmons (polarization eigenmodes) and plasmon polaritons (radiation eigenmodes).