Direct space-time modeling of mechanically dressed dipole-dipole interactions with electromagnetically coupled oscillating dipoles

We study the radiative dynamics of coupled electric dipoles, modelled as Lorentz oscillators, in the presence of real-time mechanical oscillations. The dipoles are treated in a self-consistent way through a direct electromagnetic simulation approach that fully includes the dynamical movement of the charges, accounting for radiation reaction, emission and absorption. This allows for a powerful numerical solution of optomechanical resonances without any perturbative approximations for the mechanical motion. The scaled population (excitation) dynamics of the Lorentz oscillators are investigated as well as the emitted radiation and electromagnetic spectra, which demonstrates how the usual dipole-dipole resonances couple to the underlying Floquet states, yielding multiple spectral peaks that are separated from the superradiant and subradiant states by an integer number of the mechanical oscillation frequency. Moreover, we observe that when the mechanical amplitude and frequency are sufficiently large, these additional spectral peaks undergo further modification, including spectral splitting, spectral squeezing, or shifting. These observations are fully corroborated by a theoretical Floquet analysis conducted on two coupled harmonic oscillators.