We study a doped transition metal dichalcogenide 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 the exciton-polaritons and trion-polaritons, we report additional polaritonic modes that become bright due to the interaction of excitons with free carriers. At large doping, we reveal strongly coupled modes reminiscent of higher-order trion modes that hybridize with a cavity mode. We also demonstrate that rising the carrier concentration enables to change the nature of the systems 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.
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