Atomically thin two-dimensional semiconducting transition metal
dichalcogenides (TMDs) can withstand large levels of strain before their
irreversible damage occurs. This unique property offers a promising route for
control of the optical and electronic properties of TMDs, for instance by
depositing them on nano-structured surfaces, where position-dependent strain
can be produced on the nano-scale. Here, we demonstrate strain-induced
modifications of the optical properties of mono- and bilayer TMD WSe$_2 $
placed on photonic nano-antennas made from gallium phosphide (GaP).
Photoluminescence (PL) from the strained areas of the TMD layer is enhanced
owing to the efficient coupling with the confined optical mode of the
nano-antenna. Thus, by following the shift of the PL peak, we deduce the
changes in the strain in WSe$_2$ deposited on the nano-antennas of different
radii. In agreement with the presented theory, strain up to $\approx 1.4 \%$ is
observed for WSe$_2$ monolayers. We also estimate that $>3\%$ strain is
achieved in bilayers, accompanied with the emergence of a direct bandgap in
this normally indirect-bandgap semiconductor. At cryogenic temperatures, we
find evidence of the exciton confinement in the most strained nano-scale parts
of the WSe$_2$ layers, as also predicted by our theoretical model. Our results,
of direct relevance for both dielectric and plasmonic nano-antennas, show that
strain in atomically thin semiconductors can be used as an additional parameter
for engineering light-matter interaction in nano-photonic devices.