The dispersion of excitons,polaritons and biexcitons in direct-gap semiconductors

Excitons are the energetically lowest excitations of the electronic system in an ideal semiconductor at zero temperature. If the excitons couple to the electromagnetic field, a mixed state is formed, the quanta of which are called excitonic polaritons. Associates of two excitons, so-called biexcitons, have been observed in many semiconductors. Excitons are known for about forty years. During the first three decades, they have been investigated mainly by the classical spectroscopic methods, i.e., reflection, transmission and luminescence spectroscopy. In the last decade, several new techniques have been developed, which allow for a direct spectroscopy in momentum space. In this contribution, we review these novel techniques, both linear and nonlinear ones, and present results obtained for excitons, polaritons and biexcitons. The review is restricted to semiconductors which have their conduction band minimum and their valence band maximum at the same point of the Brillouin zone (direct-gap materials) and which have a band to band transition which is dipole allowed.