Near-field optical spectroscopy of an extended interacting electron system

We investigate theoretically the local optical properties of electrons and holes interacting via the Coulomb potential in a discrete lattice. This prototype example shows what happens when a homogeneous extended system is locally probed and gives indications on the interpretation of high resolution near field spectra. We find a noticeable deformation and a blueshift of the local absorption spectra at nanometric spatial resolutions.