A resonant monochromatic pump laser generates coherent excitons in an
n-type-doped semiconductor. Both exciton-exciton and exciton-donor int
eractions come into play. The former interaction can give rise to the
appearance of optical bistability. which is heavily influenced by the
latter one. When optical bistability occurs at a fixed laser frequency
both its holding intensity and hysteresis-loop size are shown to decr
ease with increasing donor concentration. Two possibilities are sugges
ted for experimentally determinng one of the two parameters of the sys
tem. the exciton-donor coupling constant or the donor concentration if
the other is known.