Vibrational polaritons form in a planar Fabry–Pérot microcavity when a vibrational mode of a layer of molecules is near resonant with an infrared cavity mode. Here, dispersion relations of vibrational polaritons are studied when the molecular density distribution breaks the macroscopic translational symmetry along the cavity mirror plane. Both perturbative theory and numerical calculations show that, 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 periodic Gaussian in-plane density distribution, only two, yet significantly broadened polariton branches exist in the spectra. This polariton linewidth broadening is caused by the scattering between cavity modes at neighboring in-plane frequencies due to the symmetry breaking, which is distinguished from known origins of polariton broadening such as the homogeneous broadening of molecules, the cavity loss, or the large energetic disorder of molecules. Associated with the broadened polariton branches, under the periodic Gaussian in-plane inhomogeneity, a significant number of the vibrational strong coupling 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.
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