Beyond spatial averaging: Simulations of near-field scanning spectroscopy of quantum structures with interfacial roughness

A theoretical approach for the simulation of scanning local optical spectroscopy in disordered quantum structures is proposed. The local optical spectra at subwavelength resolution show the spectral lines from the lowest states of the exciton center-of-mass motion located at the individual potential minima as well as from the excited states that merge into quasicontinua near the potential barriers in agreement with the experimental findings. The simulations show the crucial impact that spatial resolution may have on the local spectra. When the spatial resolution is lowered many lines disappear owing to destructive spatial interference of quantum states.