  The optical properties of two-dimensional materials can be effectively tuned
by strain induced from a deformable substrate. In the present work we combine
first-principles calculations based on density functional theory and the
effective Bethe-Salpeter equation with high-pressure optical measurements in
order to thoroughly describe the effect of strain and dielectric environment
onto the electronic band structure and optical properties of a few-layered
transition metal dichalcogenide. Our results show that WS2 remains fully
adhered to the substrate at least up to a -0.6% in-plane compressive strain for
a wide range of substrate materials. We provide a useful model to describe
effect of strain on the optical gap energy. The corresponding
experimentally-determined out-of-plane and in-plane stress gauge factors for
WS2 monolayers are -8 and 24 meV/GPa, respectively. The exceptionally large
in-plane gauge factor confirm transition metal dichalcogenides as very
promising candidates for flexible functionalities. Finally, we discuss the
pressure evolution of an optical transition closely-lying to the A exciton for
bulk WS2 as well as the direct-to-indirect transition of the monolayer upon
compression.
