  The large coupling rate between the acoustic and optical fields confined in
GaAs/AlAs superlattice cavities makes them appealing systems for cavity
optomechanics. We have developed a mathematical model based on the scattering
matrix that allows the acoustic guided modes to be predicted in nano and
micropillar superlattice cavities. We demonstrate here that the reflection at
the surface boundary considerably modifies the acoustic quality factor and
leads to significant confinement at the micropillar center. Our mathematical
model also predicts unprecedented acoustic Fano resonances on nanopillars
featuring small mode volumes and very high mechanical quality factors, making
them attractive systems for optomechanical applications.
