  We present a theoretical study on polaritons in highly doped semiconductor
microcavities. In particular, we focus on a cavity mode that is resonant with
the absorption threshold (`Fermi edge'). In agreement with experimental
results, the strong light-matter coupling is maintained under very high doping
within our ladder diagram approximation. While the lower polariton is
qualitatively unaltered, it acquires a finite lifetime due to relaxation of the
valence band hole if the electron density exceeds a certain critical value. On
the other hand the upper polariton has a finite lifetime for all densities,
because it lies in the electron-hole continuum where no bound state exists. Our
calculations show that a narrow upper polariton quasiparticle still exists as a
result from the interplay between light-matter coupling and final state Coulomb
interaction.
