Vibrations of Dimers of Mechanically Coupled Nanostructures: Analytical and Numerical Modeling

The coupling effects affecting the vibrations of two close nanostructures (e.g., two metal nanoplates or nanospheres separated by a thin dielectric layer) may considerably alter their vibrational eigenfrequencies, as demonstrated by several recent experimental studies. In this work, we present theoretical investigations of these coupling processes based on a continuum mechanics approach, considering various systems composed by two identical nanostructures mechanically coupled by a spacer made of a different material and computing their eigenfrequencies as a function of the spacer thickness. We first discuss the vibrations of stacked slabs, a one-dimensional problem which can be treated analytically. The more complex configurations of dimers of rods or spheres coupled by a finite cylindrical spacer are then treated numerically. In all cases, the frequency shifts occurring for thin spacers can be simply interpreted as a modification of the boundary conditions of the problem as compared to the single nanostructure case, while those predicted near specific spacer thicknesses are ascribed to an avoided crossing effect, happening when the individual building blocks of the dimers (nanostructures and spacer) present common eigenfrequencies.