Local optical spectroscopy of semiconductor nanostructures in the linear regime

We present a theoretical approach to calculate the local absorption spectru m of excitons confined in a semiconductor nanostructure. Using the density- matrix formalism, we derive a microscopic expression for the nonlocal susce ptibility, both in the linear and nonlinear regimes, which includes a three -dimensional description of electronic quantum states and their Coulomb int eraction. The knowledge of the nonlocal susceptibility allows us to calcula te a properly defined local absorbed power, which depends on the electromag netic field distribution. We report on explicit calculations of the local l inear response of excitons confined in single and coupled T-shaped quantum wires with realistic geometry and composition. We show that significant int erference effects in the interacting electron-hole wave function induce new features in the space-resolved optical spectra, particularly in coupled na nostructures. When the spatial extension of the electromagnetic held is com parable to the exciton Bohr radius, Coulomb effects on the local spectra mu st be taken into account for a correct assignment of the observed features.