  A splitting of the fundamental optical modes in micro/nano-cavities
comprising semiconductor heterostructures is commonly observed. Given that this
splitting plays an important role for the light-matter interaction and hence
quantum technology applications, a method for controlling the mode-splitting is
important. In this work we use an open microcavity composed of a "bottom"
semiconductor distributed Bragg reflector (DBR) incorporating an n-i-p
heterostructure, paired with a "top" curved dielectric DBR. We measure the
mode-splitting as a function of wavelength across the stopband. We demonstrate
a reversible in-situ technique to tune the mode-splitting by applying uniaxial
stress to the semiconductor DBR. The method exploits the photoelastic effect of
the semiconductor materials. We achieve a maximum tuning of $\sim$11 GHz. The
stress applied to the heterostructure is determined by observing the
photoluminescence of quantum dots embedded in the sample, converting a spectral
shift to a stress via deformation potentials. A thorough study of the
mode-splitting and its tuning across the stop-band leads to a quantitative
understanding of the mechanism behind the results.
