The interaction of phononic cavities modes in one-dimensional nanobeam-based structures is investigated theoretically. The overlapping of two closely spaced phononic cavity modes leads to the formation of symmetric and antisymmetric modes, which can be used for the modulation of the frequency and the quality factors of the propagating cavity modes. In addition, the efficient coupling of cavity modes with the modes of a phononic waveguide connecting the two phononic cavities has been demonstrated. We show that such coupling can be used for routing, controlling, and modulating the phononic cavity modes over large distances between cavities. This demonstration paves the way to engineering complex on-chip phonon networks utilizing mechanical waves to connect quantum systems as phononic or optomechanical cavities.
