Multiple vibro-polaritons formation from a thin polyethylene film embedded in a resonant mid-infrared cavity

We experimentally resolve the dispersion of multiple vibro-polariton modes issued from the strong coupling of different vibrational bands of the methylene group (CH2) in a 2.56$mu$m thick polyethylene film with the confined modes of a mid-infrared Fabry-Perot micro-cavity. We measure a Rabi frequency of 111 cm$^{-1}$ for the stretching doublet around 2950 cm$^{-1}$ and a Rabi frequency of 29 cm$^{-1}$ for the scissoring doublet around 1460 cm$^{-1}$. This simple experimental approach offers the possibility to accurately fit the measured molecular film dielectric function. We show that the polariton dispersion and Rabi splitting can be precisely predicted from numerical simulations, offering a valuable tool for the design of strongly coupled system and the development of novel molecular films with crystalline organization.