Following the recent observation of localised phonon polaritons in user-defined silicon carbide
nano-resonators, here we demonstrate strong and coherent coupling between those localised modes
and propagating phonon polaritons bound to the surface of the nano-resonator’s substrate. In order
to obtain phase-matching, the nano-resonators have been fabricated to serve the double function of
hosting the localised modes, while also acting as grating for the propagating ones. The coherent
coupling between long lived, optically accessible localised modes, and low-loss propagative ones,
opens the way to the design and realisation of phonon-polariton based coherent circuits.