Local optical spectroscopy of semiconductor nanostructures in the linear regime

We present a theoretical approach to calculate the {\it local} absorption spectrum of excitons confined in a semiconductor nanostructure. Using the density-matrix formalism, we derive a microscopic expression for the non-local susceptibility, both in the linear and non-linear regimes, which includes a three-dimensional description of electronic quantum states and their Coulomb interaction. The knowledge of the non-local susceptibility allows us to calculate a properly defined local absorbed power, that depends on the electro-magnetic field distribution. We report on explicit calculations of the local linear response of excitons confined in single and coupled T-shaped quantum wires with realistic geometry and composition. We show that significant interference effects in the interacting electron-hole wavefunction induce new features in the space-resolved optical spectra, particularly in coupled nanostructures. When the spatial extension of the electromagnetic field is comparable to the exciton Bohr radius, Coulomb effects on the local spectra must be taken into account for a correct assignment of the observed features.