Mesoscale Molecular Simulations of Fabry-P\'erot Vibrational Strong Coupling

Developing theoretical frameworks for vibrational strong coupling (VSC) beyond the single-mode approximation is crucial for a comprehensive understanding of experiments with planar Fabry-P\'erot cavities. Herein, a generalized cavity molecular dynamics (CavMD) scheme is developed to simulate VSC of a large ensemble of realistic molecules coupled to an arbitrary 1D or 2D photonic environment. This approach is built upon the Power-Zienau-Woolley Hamiltonian in the normal mode basis and uses a grid representation of the molecular ensembles to reduce the computational cost. When simulating the polariton dispersion relation for a homogeneous distribution of molecules in planar Fabry-P\'erot cavities, our data highlight the importance of preserving the in-plane translational symmetry of the molecular distribution. In this homogeneous limit, CavMD yields the consistent polariton dispersion relation as analytic theory, i. e. , incorporating many cavity modes with varying in-plane wave vectors (k_) produces the same spectrum as the system with a single cavity mode. Furthermore, CavMD reveals that the validity of the single mode approximation is challenged when nonequilibrium polariton dynamics are considered, as polariton-polariton scattering occurs between modes with nearest neighbor k_. Looking forward, our generalized CavMD approach may facilitate understanding vibrational polariton transport and condensation.