Dimensional crossover of excitons in one- and two-photon absorption processes

We develop a theory of one- and two-photon absorptions (OPA and TPA) of Wannier excitons in the intermediate regime, where the dimensionality of the excitons is intermediate between one and two. We find that the TPA spectrum changes drastically with variations in the dimensionality, whereas the OPA spectrum keeps its qualitative nature. The theory explains the puzzling results of a recent experiment on the TPA spectrum of a quantum wire [R. Cingolani et al., Phys. Rev. Lett. 69, 1276 (1992)].