  We study a doped transition metal dichalcogenide (TMDC) monolayer in an
optical microcavity. Using the microscopic theory, we simulate spectra of
quasiparticles emerging due to the interaction of material excitations and a
high-finesse optical mode, providing a comprehensive analysis of optical
spectra as a function of Fermi energy and predicting several modes in the
strong light-matter coupling regime. In addition to exciton-polaritons and
trion-polaritons, we report polaritonic modes that become bright due to the
interaction of excitons with free carriers. At large doping, we reveal strongly
coupled modes corresponding to excited trions that hybridize with a cavity
mode. We also demonstrate that rising the carrier concentration enables to
change the nature of the system's ground state from the dark to the bright one.
Our results offer a unified description of polaritonic modes in a wide range of
free electron densities.
