experiment, the sample was excited using a pulsed Nd:YAG laser with a pulse duration of $500~{\mathrm{ps}}$. This is three orders of magnitude larger than the polariton relaxation time (0.4 ${\mathrm{ps}}$) which is determined from the spectral linewidth of the condensate emission. Thus, we can assume a quasi–continuous-wave excitation, which justifies the comparison with numerical simulations based on a steady state theory as will be discussed in Sec. \[sec:fit\_of\_exp\_data\]. Further details about the experimental setup can be found in Appendix \[sec:sample\_setup\]. The MC consists of a half wavelength ZnO cavity, which simultaneously acts as active medium, showing a quality factor of about 1000 and a maximum coupling strength of about 45 meV ($\Omega_{{\mathrm{Rabi}}} \approx 90~{{\mathrm{m}} {\mathrm{e}} {\mathrm{V}}}$) at $T = 10~{\mathrm{K}}$. By using a wedge-shaped cavity, the detuning between the cavity mode energy and the excitonic transition energy strongly varies with the lateral sample position. Structural investigations (atomic force microscopy, X-ray diffraction, cross-sectional transmission electron microscopy) yield a smooth but polycrystalline cavity layer, exhibiting a low interface roughness of $R_{{\mathrm{rms}}}$ = 1.9 nm. Furthermore, the cavity layer is preferentially $c$-plane oriented and laterally textured, containing large grains aligned in the growth direction reaching from the bottom to the top (grain sizes 