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The coupling effects affecting the vibrations of two close nanostructures(e.g., two metal nanoplates or nanospheres separated by a thin dielectriclayer) may considerably alter their vibrational eigenfrequencies, asdemonstrated by several recent experimental studies. In this work, we presenttheoretical investigations of these coupling processes based on a continuummechanics approach, considering various systems composed by two identicalnanostructures mechanically coupled by a spacer made of a different materialand computing their eigenfrequencies as a function of the spacer thickness. Wefirst discuss the vibrations of stacked slabs, a one-dimensional problem whichcan be treated analytically. The more complex configurations of dimers of rodsor spheres coupled by a finite cylindrical spacer are then treated numerically.In all cases, the frequency shifts occurring for thin spacers can be simplyinterpreted as a modification of the boundary conditions of the problem ascompared to the single nanostructure case, while those predicted near specificspacer thicknesses are ascribed to an avoided crossing effect, happening whenthe individual building blocks of the dimers (nanostructures and spacer)present common eigenfrequencies.

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