Surface Plasmons (SP) are elementary excitations mixing electrons and photons at metal surfaces,which can be seen in a classical electrodynamics framework as electromagnetic surface eigenmodesof a metal-dielectric system. The present work bases on the ability of mapping SP eigenmodes withnanometric spatial resolution over a broad spectral range using spatially resolved fast electron basedspectroscopies in a Scanning Transmission Electron Microscope (STEM). Such an ability has beenseparately demonstrated during the last few years by many spatially resolved experiments of ElectronEnergy Loss Spectroscopy (EELS), which measures the energy lost by fast electrons interactingwith the sample, and CathodoLuminescence (CL), which measures the energy released by subsequentlyemitted photons. In the case of EELS, the experimental results are today well accountedfor by strong theory elements which tend to show that the quantity measured in an experiment canbe safely interpreted in terms of the surface eigenmodes of the sample. In order to broaden thisinterpretation to fast electron based spectroscopies in general, I have performed combined spatiallyresolved EELS and CL experiments on a simple single nanoparticle (a gold nanoprism). I have shownthat EELS and CL results bear strong similarities but also slight differences, which is confirmed bynumerical simulations. I have extended the theoretical analysis of EELS to CL to show that CLmaps equally well than EELS the radiative surface eigenmodes, yet with slightly different spectralfeatures. This work is a proof of principle clarifiying the quantities measured in EELS and CL,which are shown to be respectively some nanometric equivalent of extinction and scattering spectroscopieswhen applied to metal-dielectric systems. Based on this interpretation, I have applied EELSto reveal the SP eigenmodes of random metallic media (in our case, semicontinuous metal films beforethe percolation threshold). These SP eigenmodes constitute a long standing issue in nanooptics.I have directly identified the eigenmodes from measurements and data processing. I havefully characterized these eigenmodes experimentally through an electric field intensity pattern, aneigenenergy and a relaxation rate. Doing so, I have shown that the fractal geometry of the medium,which grows towards the percolation, induces random-like eigenmodes in the system at low energies.Keywords: Surface plasmons, fast electron based spectroscopies, scanning transmission electronmicroscopy, disordered media
