Figure 3: Plasmon modes of straight edges and their dispersion relation.

(a) TEM image (scale bar, 500 nm) of a laterally structured 30-nm-thick silver film with a 0.95-μm-long lower edge superimposed with EEL maps acquired in the indicated energy ranges. The maps show standing wave patterns corresponding to antisymmetric plasmons of linear mode order m, denoted by . (b) EEL spectrum (red line) integrated along the lower film edge shown in a. The energy windows of the EEL maps in a are marked by the dashed boxes, the Gaussian curves (black lines) are fits to the experimental EEL peaks. (c) Intensity cross-cuts taken from a, the dashed lines mark the lateral film extension. The parts plotted in black (experimental data) are fit by a sinusoidal describing a standing wave (red lines). (d) Dispersion relation of edge plasmons (blue symbols), the grey line is a guide to the eye. The error bar size is discussed in detail in Supplementary Figs 3–5 and Supplementary Note 2. The red curve plots the calculated F_A dispersion relation for an extended 30-nm-thick silver film on a 15-nm-thick Si₃N₄ membrane.