  Highly mismatched alloys (HMA's) are a class of semiconductor alloys with
large electronegativity differences between the alloying elements. We predict
the absorption spectrum due to transitions between the split bands of a doped
highly mismatched alloy with a conduction band anticrossing. We analyze the
joint densities of states for both direct and indirect transitions between the
split bands. The resulting spectrum has features that reveal the unusual state
distribution that is characteristic of HMAs, hence providing valuable insight
into their electronic structure. In particular, we predict a peak near the
absorption edge, which arises due to the suppression of direct transitions at
large momenta. We present analytic forms for the near-absorption-edge and
large-energy spectra, showing that they are qualitatively different from those
in standard parabolic semiconductors. In particular, as a result of suppressed
direct transitions, indirect transitions dominate the spectrum away from the
edge of absorption.
