  The optomechanical coupling of quantum dots and flexural mechanical modes is
studied in suspended nanophononic strings. The investigated devices are
designed and monolithically fabricated on an (Al)GaAs heterostructure. Radio
frequency elastic waves with frequencies ranging between $f$=250 MHz to 400 MHz
are generated as Rayleigh surface acoustic waves on the unpatterned substrate
and injected as Lamb waves in the nanophononic string. Quantum dots inside the
nanophononic string exhibit a 15-fold enhanced optomechanical modulation
compared to those dynamically strained by the Rayleigh surface acoustic wave.
Detailed finite element simulations of the phononic mode spectrum of the
nanophononic string confirm, that the observed modulation arises from valence
band deformation potential coupling via shear strain. The corresponding
optomechanical coupling parameter is quantified to $0.15 \mathrm{meV nm^{-1}}$.
This value exceeds that reported for vibrating nanorods by approximately one
order of magnitude at 100 times higher frequencies. Using this value, a derive
vertical displacements in the range of 10 nm is deduced from the experimentally
observed modulation. The results represent an important step towards the
creation of large scale optomechanical circuits interfacing single optically
active quantum dots with optical and mechanical waves.
