Probing the Photonic Local Density of States with Electron Energy Loss Spectroscopy

Electron energy loss spectroscopy performed in transmission electron microscopes is shown to directly render the photonic local density of states with unprecedented spatial resolution, currently below the nanometer. Two special cases are discussed in detail: (i) 2D photonic structures with the electrons moving along the translational axis of symmetry and (ii) quasiplanar plasmonic structures under normal incidence. Nanophotonics in general and plasmonics, in particular, should benefit from these results connecting the unmatched spatial resolution of electron energy loss spectroscopy with its ability to probe basic optical properties such as the photonic local density of states.

Figure 1

EELS probability for 200-keV electrons moving parallel to an array of 13 Si nanowires of 300 nm in diameter (solid curve), as compared to an isolated nanowire (broken curve). The nanowires are arranged in a hexagonal lattice with a period of 350 nm. The contour-plot insets show the impact-parameter dependence of the EELS probability for selected energy losses (labeled A–G), with the position of the electron beam considered in the curves indicated by an open symbol and the cylinder contours shown by dashed curves.

Figure 2

Relation between EELS and LDOS in planar geometries. (a) We consider an Ag disk of height 10 nm and radius 30 nm. The electrons move along $z$, perpendicular to the disk. The EELS probability for 200-keV (d) and 100-keV (e) electrons mimics closely the $z$-projected LDOS in a plane 10 nm above the disk (b), and less closely the unprojected LDOS $\rho ={\rho }_x+{\rho }_y+{\rho }_z$) (c). The CL emission only picks up part of the inelastic signal (f).