Vibrational lifetimes of strongly coupled nanostructures

Nanostructures have low frequency vibrational modes corresponding to changes in size and shape. When two structures are brought together, these modes can couple to each other, producing mixed states that have shifted vibrational frequencies. The frequency shifts in different systems have been analyzed using the coupled harmonic oscillator model, as well as by analytical and numerical continuum mechanics calculations. However, the way the lifetimes change with coupling has not been investigated in detail to date. Here, the coupling between the breathing modes of two nanoplates separated by a layer of a different material is investigated by analytical continuum mechanics calculations. The model developed includes damping via the radiation of sound waves and, thus, provides predictions for both the vibrational frequencies and the damping constants of the coupled system. The results show that the damping constants for the coupled states are an average of the damping constants of the uncoupled nanostructures, weighted by the mixing coefficients.