  A fully planar two-dimensional optomechanical crystal formed in a silicon
microchip is used to create a structure devoid of phonons in the GHz frequency
range. A nanoscale photonic crystal cavity is placed inside the phononic
bandgap crystal in order to probe the properties of the localized acoustic
modes. By studying the trends in mechanical damping, mode density, and
optomechanical coupling strength of the acoustic resonances over an array of
structures with varying geometric properties, clear evidence of a complete
phononic bandgap is shown.
