  The coupling of micro- or nanomechanical resonators via a shared substrate is
intensively exploited to built systems for fundamental studies and practical
applications. So far, the focus has been on devices operating in the kHz regime
with a spring-like coupling. At resonance frequencies above several 10 MHz,
wave propagation in the solid substrate becomes relevant. The resonators act as
sources for surface acoustic waves (SAWs) and it is unknown how this effects
the coupling between them. Here, we present a model for MHz frequency
resonators interacting by SAWs and derive the eigenfrequencies and quality
factors of a pair of resonators for the symmetric and antisymmetric mode. Our
results are in agreement with finite element method (FEM) simulations and show
that in contrast to the well-known strain-induced spring-like coupling, the
coupling via SAWs is not only dispersive but also dissipative. This can be
exploited to realize high quality phonon cavities, an alternative to acoustic
radiation shielding by, e.g. phononic crystals.
