We review the effects of Coulomb correlation on the linear and non-linear
optical properties of semiconductor quantum wires, with emphasis on recent
results for the bound excitonic states. Our theoretical approach is based on
generalized semiconductor Bloch equations, and allows full three-dimensional
multisubband description of electron-hole correlation for arbitrary confinement
profiles. In particular, we consider V- and T-shaped structures for which
significant experimental advances were obtained recently. Above band gap, a
very general result obtained by this approach is that electron-hole Coulomb
correlation removes the inverse-square-root single-particle singularity in the
optical spectra at band edge, in agreement with previous reports from purely
one-dimensional models. Strong correlation effects on transitions in the
continuum are found to persist also at high densities of photoexcited carriers.
Below bandgap, we find that the same potential- (Coulomb) to kinetic-energy
ratio holds for quite different wire cross sections and compositions. As a
consequence, we identify a shape- and barrier-independent parameter that
governs a universal scaling law for exciton binding energy with size. Previous
indications that the shape of the wire cross-section may have important effects
on exciton binding are discussed in the light of the present results.Comment: Proc. OECS-5 Conference, G\"ottingen, 1997 (To appear in Phys. Stat.
Sol. (b)