In the experimental part, I studied four split-ring resonators (SRRs) with sizes and shapes slightly different lithographed by a technique compatible with an EELS study. The EELS experiments allowed me to detect the first surface plasmon eigenmodes (SPs) of these SRRs in the vis-NIR spectral range. The numerical calculations also showed that the spatial distribution of SPs in the SRRs is similar to that of a plasmonic standing wave of a nanoantenna with same cross section and same length, while it is not the case for the electric field. More, compared to a nanoantenna, the coupling between the two legs of the SRR introduced a different energy spacing between the different modes taken successively, while the energy spacing between the symmetric modes in charge on the one hand and the antisymmetric modes on the other hand can still be maintained in a SRR. In the theoretical part, I introduced a new type of quasistatic eigenmodes, called geometrical eigenmodes which are independent of the energy and the nature of the underlying media, but which depend only on the geometry of the particle studied. These modes allowed me to obtain, for the first time, an universal expression of the electromagnetic local density of states (EMLDOS) for a plasmonic system and to clarify the quantities which are measured in EELS and SNOM experiments. Finally, a density of states for the geometrical eigenmodes depending only on the shape of the particle has been introduced, by analogy with the "standard" EMLDOS for the photonic eigenmodes.
