Vibrational Polaritons with Broken In-Plane Translational Symmetry

For the calculation of polariton dispersion relations in planar Fabry-P\'erot microcavities, the single-mode approximation is usually applied. This approximation becomes invalid when the molecular distribution along the cavity mirror plane breaks the in-plane translational symmetry. Herein, both perturbative theory and numerical calculations have been performed to study polariton dispersion relations with various in-plane molecular distribution patterns under vibrational strong coupling conditions. If a homogeneous in-plane molecular distribution is modulated by sinusoidal fluctuations, in addition to a pair of upper and lower polariton branches, a discrete number of side polariton branches may emerge in the polariton dispersion relation. Moreover, for a Gaussian molecular density distribution, only two, yet significantly broadened polariton branches exist in the spectra. This polariton linewidth broadening is due to the breakdown of the single-mode approximation and the scattering between cavity modes at different in-plane frequencies, which is distinguished from known causes of polariton broadening such as the homogeneous broadening of molecules and the cavity loss. Associated with the broadened polariton branches, under the Gaussian in-plane inhomogeneity, a significant amount of the VSC eigenstates contain a non-zero contribution from the cavity photon mode at zero in-plane frequency, blurring the distinction between the bright and the dark modes. Looking forward, our theoretical investigation should facilitate the experimental exploration of vibrational polaritons with patterned in-plane molecular density distributions.