Effects of Broken In-Plane Translational Symmetry on Vibrational Polaritons

Vibrational polaritons have been experimentally demonstrated in planar Fabry-Pérot cavities. In most studies, the molecular layer confined within the cavity is assumed to be homogeneous. Here, we theoretically investigate the formation of vibrational polaritons when the molecular density distribution inside the planar cavity breaks the macroscopic translational symmetry along the cavity mirror plane. Using both perturbative theory and numerical calculations, we show how the molecular density distribution pattern alters the polariton dispersion relation. Notably, when the molecular density obeys a periodic Gaussian distribution along the mirror plane, both the upper and lower polariton branches become significantly broadened. This polariton linewidth broadening arises from scattering between cavity modes at neighboring in-plane wavevectors due to symmetry breaking, which differs from established origins of polariton broadening, such as molecular homogeneous broadening, cavity losses, or large energetic disorder of molecules. Additionally, the broadened polariton branches are associated with a significant number of light-matter eigenstates which exhibit non-zero contributions from the cavity photon mode at zero in-plane wavevector. This photonic distribution blurs the distinction between the bright and dark modes. Looking forward, our theoretical investigation may facilitate the experimental exploration of vibrational polaritons with patterned in-plane molecular density distributions.