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We present a unified theory for two-photon absorption (TPA) spectra of Wannier excitons in a low-dimensional semiconductor of an arbitrary dimension d=0, 1, 2, and 3. It is found that the spectra strongly reflect the anisotropies of both the band structure and the quasi-d-dimensional exciton envelope functions. Therefore the low dimensionality can be sensitively detected by the TPA spectroscopy. This is in striking contrast to the one-photon absorption spectra, anisotropies of which cannot be taken as evidence of quantum confinements.
Shimizu et al. (1992) studied this question.