  The exciton absorption coefficient is determined analytically for a
semiconductor superlattice in crossed electric and magnetic fields, for the
magnetic field being parallel and the electric field being perpendicular to the
superlattice axis. Our investigation applies to the case where the magnetic
length, while being much smaller than the exiton Bohr radius, considerably
exceeds the superlattice period. The optical absorption in superlattices
displays a spectral fine structure related to the sequences of exciton states
bound whose energies are adjacent to the Landau energies of the charge carriers
in the magnetic field. We study effects of external fields and of the
centre-of-mass exciton motion on the fine structure peak positions and
oscillator strengths. In particular, we find that the inversion of the
orientation of the external fields and of the in-plane total exciton momentum
notably affects the absorption spectrum. Conditions for the experimental
observation of the exciton absorption are discussed.
