Low energy exciton states in a nanoscopic semiconducting ring

We consider an effective mass model for an electron-hole pair in a simplified confinement potential, which is applicable to both a nanoscopic self-assembled semiconducting InAs ring and a quantum dot. The linear optical susceptibility, proportional to the absorption intensity of near-infrared transmission, is calculated as a function of the ring radius $% R_0$. Compared with the properties of the quantum dot corresponding to the model with a very small radius $R_0$, our results are in qualitative agreement with the recent experimental measurements by Pettersson {\it et al}.